By Randley Morales
Problem Statement¶
Business Context¶
Renewable energy sources play an increasingly important role in the global energy mix, as the effort to reduce the environmental impact of energy production increases.
Out of all the renewable energy alternatives, wind energy is one of the most developed technologies worldwide. The U.S Department of Energy has put together a guide to achieving operational efficiency using predictive maintenance practices.
Predictive maintenance uses sensor information and analysis methods to measure and predict degradation and future component capability. The idea behind predictive maintenance is that failure patterns are predictable and if component failure can be predicted accurately and the component is replaced before it fails, the costs of operation and maintenance will be much lower.
The sensors fitted across different machines involved in the process of energy generation collect data related to various environmental factors (temperature, humidity, wind speed, etc.) and additional features related to various parts of the wind turbine (gearbox, tower, blades, break, etc.).
Objective¶
“ReneWind” is a company working on improving the machinery/processes involved in the production of wind energy using machine learning and has collected data of generator failure of wind turbines using sensors. They have shared a ciphered version of the data, as the data collected through sensors is confidential (the type of data collected varies with companies). Data has 40 predictors, 20000 observations in the training set and 5000 in the test set.
The objective is to build various classification models, tune them, and find the best one that will help identify failures so that the generators could be repaired before failing/breaking to reduce the overall maintenance cost. The nature of predictions made by the classification model will translate as follows:
- True positives (TP) are failures correctly predicted by the model. These will result in repairing costs.
- False negatives (FN) are real failures where there is no detection by the model. These will result in replacement costs.
- False positives (FP) are detections where there is no failure. These will result in inspection costs.
It is given that the cost of repairing a generator is much less than the cost of replacing it, and the cost of inspection is less than the cost of repair.
“1” in the target variables should be considered as “failure” and “0” represents “No failure”.
Data Description¶
The data provided is a transformed version of the original data which was collected using sensors.
- Train.csv - To be used for training and tuning of models.
- Test.csv - To be used only for testing the performance of the final best model.
Both the datasets consist of 40 predictor variables and 1 target variable.
Installing and Importing the necessary libraries¶
# Installing the libraries with the specified version
!pip install --no-deps tensorflow==2.18.0 scikit-learn==1.3.2 matplotlib===3.8.3 seaborn==0.13.2 numpy==1.26.4 pandas==2.2.2 -q --user --no-warn-script-location
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 61.0/61.0 kB 1.4 MB/s eta 0:00:00 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 615.5/615.5 MB 852.3 kB/s eta 0:00:00 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 10.8/10.8 MB 89.7 MB/s eta 0:00:00 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 11.6/11.6 MB 83.3 MB/s eta 0:00:00 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 18.0/18.0 MB 70.4 MB/s eta 0:00:00
Note:
- After running the above cell, kindly restart the runtime (for Google Colab) or notebook kernel (for Jupyter Notebook), and run all cells sequentially from the next cell.
- On executing the above line of code, you might see a warning regarding package dependencies. This error message can be ignored as the above code ensures that all necessary libraries and their dependencies are maintained to successfully execute the code in *this notebook*.
# Import libraries for data manipulation
import numpy as np
import pandas as pd
# Import libraries for data visualization
import matplotlib.pyplot as plt
import seaborn as sns
import plotly.express as px
# Set default Seaborn theme for plots
sns.set()
# Suppress warnings to prevent them from being displayed during code execution
import warnings
warnings.filterwarnings('ignore')
# Enable the inline plotting of matplotlib figures directly within the notebook
%matplotlib inline
# Set the display format for float values to three decimal places
pd.set_option('display.float_format', lambda x: '%.4f' % x)
# Removes the limit for the number of displayed columns
pd.set_option("display.max_columns", None)
# Sets the limit for the number of displayed rows
pd.set_option("display.max_rows", 100)
# Distribution Libraries for statistical tests
import scipy.stats as stats
from scipy.stats import norm, uniform, binom, expon, t
from scipy.stats import ttest_1samp, ttest_ind
# Libraries for model building and evaluation
import statsmodels.api as sm
from sklearn.model_selection import train_test_split, GridSearchCV, RandomizedSearchCV, StratifiedKFold, cross_val_score
# Libraries to get different metric scores
from sklearn import metrics
from sklearn.metrics import (
confusion_matrix,
accuracy_score,
precision_score,
recall_score,
f1_score,
roc_auc_score,
ConfusionMatrixDisplay,
classification_report
)
# Libraries for model building (Logistic Regression, Decision Tree, etc.)
from sklearn.linear_model import LogisticRegression, LinearRegression
from sklearn.tree import DecisionTreeClassifier, DecisionTreeRegressor
# Libraries for ensemble methods and boosting
from sklearn.ensemble import (
BaggingClassifier,
RandomForestClassifier,
AdaBoostClassifier,
GradientBoostingClassifier,
StackingClassifier,
)
# Libraries for working with XGBoost
from xgboost import XGBClassifier
# Libraries for oversampling and undersampling (imbalanced data handling)
from imblearn.over_sampling import SMOTE
from imblearn.under_sampling import RandomUnderSampler
# Libraries for scaling and transforming data
from sklearn.preprocessing import LabelEncoder, StandardScaler, MinMaxScaler, OneHotEncoder
# Libraries for missing value imputation
from sklearn.impute import SimpleImputer
# Libraries for creating and managing pipelines
from sklearn.pipeline import Pipeline
from sklearn.compose import ColumnTransformer
# Libraries to help with model tuning and hyperparameter optimization
from sklearn.model_selection import GridSearchCV, RandomizedSearchCV
# Time related functions.
import time
#Imports the tensorflow,keras and layers.
import tensorflow
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense
from tensorflow.keras.layers import Dense, Input, Dropout,BatchNormalization
from tensorflow.keras import backend
Loading the Data¶
# Google Colab
from google.colab import drive
drive.mount('/content/drive')
Mounted at /content/drive
# Load the Train and Test dataset
train_data = pd.read_csv("/content/drive/MyDrive/Introduction to Neural Networks/ReneWind/Train.csv")
test_data = pd.read_csv("/content/drive/MyDrive/Introduction to Neural Networks/ReneWind/Test.csv")
# Copying Train and Test data to another variable to avoid any changes to original data
df = train_data.copy()
df_test = test_data.copy()
Data Overview¶
# Display the first few rows of the dataset
print("First few rows of train dataset")
df.head()
First few rows of train dataset
| V1 | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 | V10 | V11 | V12 | V13 | V14 | V15 | V16 | V17 | V18 | V19 | V20 | V21 | V22 | V23 | V24 | V25 | V26 | V27 | V28 | V29 | V30 | V31 | V32 | V33 | V34 | V35 | V36 | V37 | V38 | V39 | V40 | Target | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | -4.4646 | -4.6791 | 3.1015 | 0.5061 | -0.2211 | -2.0325 | -2.9109 | 0.0507 | -1.5224 | 3.7619 | -5.7147 | 0.7359 | 0.9813 | 1.4179 | -3.3758 | -3.0473 | 0.3062 | 2.9141 | 2.2700 | 4.3949 | -2.3883 | 0.6464 | -1.1905 | 3.1330 | 0.6653 | -2.5108 | -0.0367 | 0.7262 | -3.9822 | -1.0726 | 1.6671 | 3.0597 | -1.6904 | 2.8463 | 2.2352 | 6.6675 | 0.4438 | -2.3692 | 2.9506 | -3.4803 | 0 |
| 1 | 3.3659 | 3.6534 | 0.9097 | -1.3675 | 0.3320 | 2.3589 | 0.7326 | -4.3321 | 0.5657 | -0.1011 | 1.9145 | -0.9515 | -1.2553 | -2.7065 | 0.1932 | -4.7694 | -2.2053 | 0.9077 | 0.7569 | -5.8337 | -3.0651 | 1.5966 | -1.7573 | 1.7664 | -0.2671 | 3.6250 | 1.5003 | -0.5857 | 0.7830 | -0.2012 | 0.0249 | -1.7955 | 3.0328 | -2.4675 | 1.8946 | -2.2978 | -1.7310 | 5.9088 | -0.3863 | 0.6162 | 0 |
| 2 | -3.8318 | -5.8244 | 0.6340 | -2.4188 | -1.7738 | 1.0168 | -2.0989 | -3.1732 | -2.0819 | 5.3926 | -0.7707 | 1.1067 | 1.1443 | 0.9433 | -3.1638 | -4.2478 | -4.0389 | 3.6885 | 3.3112 | 1.0590 | -2.1430 | 1.6501 | -1.6606 | 1.6799 | -0.4508 | -4.5507 | 3.7388 | 1.1344 | -2.0335 | 0.8408 | -1.6004 | -0.2571 | 0.8035 | 4.0862 | 2.2921 | 5.3608 | 0.3520 | 2.9400 | 3.8392 | -4.3094 | 0 |
| 3 | 1.6181 | 1.8883 | 7.0461 | -1.1473 | 0.0831 | -1.5298 | 0.2073 | -2.4936 | 0.3449 | 2.1186 | -3.0530 | 0.4597 | 2.7045 | -0.6361 | -0.4537 | -3.1740 | -3.4043 | -1.2815 | 1.5821 | -1.9518 | -3.5166 | -1.2060 | -5.6279 | -1.8177 | 2.1241 | 5.2946 | 4.7481 | -2.3085 | -3.9630 | -6.0287 | 4.9488 | -3.5844 | -2.5775 | 1.3638 | 0.6227 | 5.5501 | -1.5268 | 0.1389 | 3.1014 | -1.2774 | 0 |
| 4 | -0.1114 | 3.8725 | -3.7584 | -2.9829 | 3.7927 | 0.5450 | 0.2054 | 4.8490 | -1.8549 | -6.2200 | 1.9983 | 4.7238 | 0.7091 | -1.9894 | -2.6327 | 4.1844 | 2.2454 | 3.7345 | -6.3128 | -5.3799 | -0.8867 | 2.0617 | 9.4456 | 4.4900 | -3.9451 | 4.5821 | -8.7804 | -3.3830 | 5.1065 | 6.7875 | 2.0442 | 8.2659 | 6.6292 | -10.0687 | 1.2230 | -3.2298 | 1.6869 | -2.1639 | -3.6446 | 6.5103 | 0 |
# Display the last few rows of the dataset
print("Last few rows of train dataset")
df.tail()
Last few rows of train dataset
| V1 | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 | V10 | V11 | V12 | V13 | V14 | V15 | V16 | V17 | V18 | V19 | V20 | V21 | V22 | V23 | V24 | V25 | V26 | V27 | V28 | V29 | V30 | V31 | V32 | V33 | V34 | V35 | V36 | V37 | V38 | V39 | V40 | Target | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 19995 | -2.0713 | -1.0883 | -0.7962 | -3.0117 | -2.2875 | 2.8073 | 0.4814 | 0.1052 | -0.5866 | -2.8994 | 8.8684 | 1.7172 | 1.3578 | -1.7771 | 0.7098 | 4.9449 | -3.1005 | -1.1992 | -1.0846 | -0.3650 | 3.1312 | -3.9481 | -3.5785 | -8.1391 | -1.9369 | -1.3277 | -0.4027 | -1.7348 | 9.9965 | 6.9554 | -3.9385 | -8.2740 | 5.7450 | 0.5890 | -0.6500 | -3.0432 | 2.2165 | 0.6087 | 0.1782 | 2.9278 | 1 |
| 19996 | 2.8903 | 2.4831 | 5.6439 | 0.9371 | -1.3809 | 0.4121 | -1.5934 | -5.7625 | 2.1501 | 0.2723 | -2.0948 | -1.5258 | 0.0716 | -3.5401 | -2.7620 | -10.6322 | -0.4952 | 1.7201 | 3.8716 | -1.2096 | -8.2221 | 2.1209 | -5.4918 | 1.4523 | 1.4500 | 3.6847 | 1.0768 | -0.3842 | -0.8386 | -0.7483 | -1.0886 | -4.1591 | 1.1815 | -0.7424 | 5.3690 | -0.6930 | -1.6690 | 3.6600 | 0.8199 | -1.9873 | 0 |
| 19997 | -3.8970 | -3.9424 | -0.3514 | -2.4175 | 1.1075 | -1.5276 | -3.5199 | 2.0548 | -0.2340 | -0.3577 | -3.7820 | 2.1800 | 6.1118 | 1.9847 | -8.3300 | -1.6392 | -0.9150 | 5.6723 | -3.9242 | 2.1332 | -4.5020 | 2.7772 | 5.7279 | 1.6198 | -1.6997 | -0.0419 | -2.9231 | -2.7602 | -2.2538 | 2.5520 | 0.9819 | 7.1122 | 1.4761 | -3.9537 | 1.8556 | 5.0292 | 2.0826 | -6.4093 | 1.4771 | -0.8741 | 0 |
| 19998 | -3.1873 | -10.0517 | 5.6960 | -4.3701 | -5.3548 | -1.8730 | -3.9472 | 0.6794 | -2.3893 | 5.4568 | 1.5830 | 3.5715 | 9.2266 | 2.5536 | -7.0391 | -0.9936 | -9.6649 | 1.1552 | 3.8769 | 3.5236 | -7.0153 | -0.1320 | -3.4462 | -4.8014 | -0.8757 | -3.8119 | 5.4221 | -3.7323 | 0.6088 | 5.2565 | 1.9148 | 0.4028 | 3.1637 | 3.7521 | 8.5299 | 8.4506 | 0.2040 | -7.1299 | 4.2494 | -6.1123 | 0 |
| 19999 | -2.6869 | 1.9612 | 6.1371 | 2.6001 | 2.6572 | -4.2909 | -2.3443 | 0.9740 | -1.0275 | 0.4974 | -9.5891 | 3.1766 | 1.0545 | -1.4159 | -4.6686 | -5.4054 | 3.7198 | 2.8929 | 2.3286 | 1.4577 | -6.4285 | 1.8182 | 0.8059 | 7.7860 | 0.3309 | 5.2574 | -4.8674 | -0.8189 | -5.6674 | -2.8610 | 4.6743 | 6.6208 | -1.9888 | -1.3489 | 3.9518 | 5.4497 | -0.4554 | -2.2021 | 1.6782 | -1.9744 | 0 |
# Display the first few rows of the test dataset
print("First few rows of test dataset")
df_test.head()
First few rows of test dataset
| V1 | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 | V10 | V11 | V12 | V13 | V14 | V15 | V16 | V17 | V18 | V19 | V20 | V21 | V22 | V23 | V24 | V25 | V26 | V27 | V28 | V29 | V30 | V31 | V32 | V33 | V34 | V35 | V36 | V37 | V38 | V39 | V40 | Target | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | -0.6135 | -3.8196 | 2.2023 | 1.3004 | -1.1849 | -4.4960 | -1.8358 | 4.7230 | 1.2061 | -0.3419 | -5.1229 | 1.0170 | 4.8185 | 3.2690 | -2.9843 | 1.3874 | 2.0320 | -0.5116 | -1.0231 | 7.3387 | -2.2422 | 0.1555 | 2.0538 | -2.7723 | 1.8514 | -1.7887 | -0.2773 | -1.2551 | -3.8329 | -1.5045 | 1.5868 | 2.2912 | -5.4114 | 0.8701 | 0.5745 | 4.1572 | 1.4281 | -10.5113 | 0.4547 | -1.4484 | 0 |
| 1 | 0.3896 | -0.5123 | 0.5271 | -2.5768 | -1.0168 | 2.2351 | -0.4413 | -4.4057 | -0.3329 | 1.9668 | 1.7965 | 0.4105 | 0.6383 | -1.3896 | -1.8834 | -5.0179 | -3.8272 | 2.4181 | 1.7623 | -3.2423 | -3.1930 | 1.8575 | -1.7080 | 0.6334 | -0.5879 | 0.0837 | 3.0139 | -0.1823 | 0.2239 | 0.8652 | -1.7822 | -2.4749 | 2.4936 | 0.3152 | 2.0593 | 0.6839 | -0.4855 | 5.1284 | 1.7207 | -1.4882 | 0 |
| 2 | -0.8749 | -0.6406 | 4.0842 | -1.5905 | 0.5259 | -1.9576 | -0.6954 | 1.3473 | -1.7323 | 0.4665 | -4.9282 | 3.5651 | -0.4493 | -0.6562 | -0.1665 | -1.6302 | 2.2919 | 2.3965 | 0.6013 | 1.7935 | -2.1202 | 0.4820 | -0.8407 | 1.7902 | 1.8744 | 0.3639 | -0.1691 | -0.4838 | -2.1190 | -2.1566 | 2.9073 | -1.3189 | -2.9975 | 0.4597 | 0.6198 | 5.6315 | 1.3235 | -1.7522 | 1.8083 | 1.6757 | 0 |
| 3 | 0.2384 | 1.4586 | 4.0145 | 2.5345 | 1.1970 | -3.1173 | -0.9240 | 0.2695 | 1.3224 | 0.7023 | -5.5783 | -0.8507 | 2.5905 | 0.7674 | -2.3908 | -2.3420 | 0.5719 | -0.9338 | 0.5087 | 1.2107 | -3.2595 | 0.1046 | -0.6589 | 1.4981 | 1.1003 | 4.1430 | -0.2484 | -1.1365 | -5.3558 | -4.5459 | 3.8087 | 3.5179 | -3.0741 | -0.2842 | 0.9546 | 3.0293 | -1.3672 | -3.4121 | 0.9060 | -2.4509 | 0 |
| 4 | 5.8282 | 2.7683 | -1.2345 | 2.8093 | -1.6416 | -1.4067 | 0.5686 | 0.9650 | 1.9184 | -2.7749 | -0.5300 | 1.3745 | -0.6509 | -1.6795 | -0.3792 | -4.4431 | 3.8939 | -0.6076 | 2.9449 | 0.3672 | -5.7891 | 4.5975 | 4.4503 | 3.2249 | 0.3967 | 0.2478 | -2.3620 | 1.0794 | -0.4731 | 2.2428 | -3.5914 | 1.7738 | -1.5016 | -2.2267 | 4.7768 | -6.5597 | -0.8056 | -0.2760 | -3.8582 | -0.5377 | 0 |
# Display the last few rows of the test dataset
print("Last few rows of test dataset")
df_test.tail()
Last few rows of test dataset
| V1 | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 | V10 | V11 | V12 | V13 | V14 | V15 | V16 | V17 | V18 | V19 | V20 | V21 | V22 | V23 | V24 | V25 | V26 | V27 | V28 | V29 | V30 | V31 | V32 | V33 | V34 | V35 | V36 | V37 | V38 | V39 | V40 | Target | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 4995 | -5.1205 | 1.6348 | 1.2513 | 4.0359 | 3.2912 | -2.9322 | -1.3287 | 1.7541 | -2.9846 | 1.2486 | -6.8777 | 3.7152 | -2.5118 | -1.3950 | -2.5541 | -2.1974 | 4.7717 | 2.4029 | 3.7918 | 0.4868 | -2.0281 | 1.7779 | 3.6680 | 11.3749 | -1.9771 | 2.2516 | -7.3185 | 1.9070 | -3.7337 | -0.0125 | 2.1205 | 9.9791 | 0.0634 | 0.2173 | 3.0364 | 2.1093 | -0.5574 | 1.9387 | 0.5127 | -2.6942 | 0 |
| 4996 | -5.1725 | 1.1717 | 1.5791 | 1.2199 | 2.5296 | -0.6686 | -2.6183 | -2.0005 | 0.6338 | -0.5789 | -3.6712 | 0.4602 | 3.3206 | -1.0750 | -7.1125 | -4.3559 | -0.0011 | 3.6984 | -0.8464 | -0.2223 | -3.6450 | 0.7360 | 0.9257 | 3.2777 | -2.2768 | 4.4576 | -4.5429 | -1.3480 | -1.7794 | 0.3522 | -0.2143 | 4.4239 | 2.6038 | -2.1522 | 0.9174 | 2.1566 | 0.4670 | 0.4701 | 2.1968 | -2.3765 | 0 |
| 4997 | -1.1141 | -0.4036 | -1.7649 | -5.8795 | 3.5716 | 3.7108 | -2.4830 | -0.3076 | -0.9219 | -2.9991 | -0.1117 | -1.9769 | -1.6230 | -0.9455 | -2.7351 | -0.8130 | 0.6098 | 8.1488 | -9.1992 | -3.8725 | -0.2957 | 1.4684 | 2.8843 | 2.7921 | -1.1357 | 1.1979 | -4.3417 | -2.8694 | 4.1241 | 4.1967 | 3.4707 | 3.7918 | 7.4815 | -10.0614 | -0.3872 | 1.8485 | 1.8182 | -1.2456 | -1.2609 | 7.4747 | 0 |
| 4998 | -1.7032 | 0.6146 | 6.2205 | -0.1041 | 0.9559 | -3.2787 | -1.6339 | -0.1039 | 1.3882 | -1.0656 | -7.9698 | 2.2621 | 3.1340 | -0.4858 | -3.4983 | -4.5617 | 3.1358 | 2.5364 | -0.7922 | 4.3984 | -4.0730 | -0.0376 | -2.3713 | -1.5420 | 2.9079 | 3.2145 | -0.1687 | -1.5413 | -4.7244 | -5.5250 | 1.6680 | -4.1004 | -5.9493 | 0.5504 | -1.5736 | 6.8239 | 2.1393 | -4.0362 | 3.4361 | 0.5792 | 0 |
| 4999 | -0.6037 | 0.9595 | -0.7210 | 8.2296 | -1.8156 | -2.2755 | -2.5745 | -1.0415 | 4.1296 | -2.7313 | -3.2924 | -1.6738 | 0.4645 | -1.6459 | -5.2634 | -7.9876 | 6.4805 | 0.2263 | 4.9633 | 6.7520 | -6.3058 | 3.2705 | 1.8972 | 3.2708 | -0.6371 | -0.9250 | -6.7589 | 2.9902 | -0.8138 | 3.4990 | -8.4347 | 2.3698 | -1.0624 | 0.7908 | 4.9520 | -7.4408 | -0.0695 | -0.9181 | -2.2912 | -5.3629 | 0 |
# Display the shape of the train dataset
df.shape
print("There are", df.shape[0], "rows and", df.shape[1], "columns. In the train dataset")
There are 20000 rows and 41 columns. In the train dataset
# Display the data types of the columns in the train dataset
df.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 20000 entries, 0 to 19999 Data columns (total 41 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 V1 19982 non-null float64 1 V2 19982 non-null float64 2 V3 20000 non-null float64 3 V4 20000 non-null float64 4 V5 20000 non-null float64 5 V6 20000 non-null float64 6 V7 20000 non-null float64 7 V8 20000 non-null float64 8 V9 20000 non-null float64 9 V10 20000 non-null float64 10 V11 20000 non-null float64 11 V12 20000 non-null float64 12 V13 20000 non-null float64 13 V14 20000 non-null float64 14 V15 20000 non-null float64 15 V16 20000 non-null float64 16 V17 20000 non-null float64 17 V18 20000 non-null float64 18 V19 20000 non-null float64 19 V20 20000 non-null float64 20 V21 20000 non-null float64 21 V22 20000 non-null float64 22 V23 20000 non-null float64 23 V24 20000 non-null float64 24 V25 20000 non-null float64 25 V26 20000 non-null float64 26 V27 20000 non-null float64 27 V28 20000 non-null float64 28 V29 20000 non-null float64 29 V30 20000 non-null float64 30 V31 20000 non-null float64 31 V32 20000 non-null float64 32 V33 20000 non-null float64 33 V34 20000 non-null float64 34 V35 20000 non-null float64 35 V36 20000 non-null float64 36 V37 20000 non-null float64 37 V38 20000 non-null float64 38 V39 20000 non-null float64 39 V40 20000 non-null float64 40 Target 20000 non-null int64 dtypes: float64(40), int64(1) memory usage: 6.3 MB
# Display the shape of the test dataset
df_test.shape
print("There are", df_test.shape[0], "rows and", df_test.shape[1], "columns. In the test dataset")
There are 5000 rows and 41 columns. In the test dataset
# Display the data types of the columns in the test dataset
df_test.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 5000 entries, 0 to 4999 Data columns (total 41 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 V1 4995 non-null float64 1 V2 4994 non-null float64 2 V3 5000 non-null float64 3 V4 5000 non-null float64 4 V5 5000 non-null float64 5 V6 5000 non-null float64 6 V7 5000 non-null float64 7 V8 5000 non-null float64 8 V9 5000 non-null float64 9 V10 5000 non-null float64 10 V11 5000 non-null float64 11 V12 5000 non-null float64 12 V13 5000 non-null float64 13 V14 5000 non-null float64 14 V15 5000 non-null float64 15 V16 5000 non-null float64 16 V17 5000 non-null float64 17 V18 5000 non-null float64 18 V19 5000 non-null float64 19 V20 5000 non-null float64 20 V21 5000 non-null float64 21 V22 5000 non-null float64 22 V23 5000 non-null float64 23 V24 5000 non-null float64 24 V25 5000 non-null float64 25 V26 5000 non-null float64 26 V27 5000 non-null float64 27 V28 5000 non-null float64 28 V29 5000 non-null float64 29 V30 5000 non-null float64 30 V31 5000 non-null float64 31 V32 5000 non-null float64 32 V33 5000 non-null float64 33 V34 5000 non-null float64 34 V35 5000 non-null float64 35 V36 5000 non-null float64 36 V37 5000 non-null float64 37 V38 5000 non-null float64 38 V39 5000 non-null float64 39 V40 5000 non-null float64 40 Target 5000 non-null int64 dtypes: float64(40), int64(1) memory usage: 1.6 MB
# Checking missing values across each column of train Data Set
missing_values = df.isnull().sum()
print("The number of missing values on each column of the train data set is:")
missing_values
The number of missing values on each column of the train data set is:
| 0 | |
|---|---|
| V1 | 18 |
| V2 | 18 |
| V3 | 0 |
| V4 | 0 |
| V5 | 0 |
| V6 | 0 |
| V7 | 0 |
| V8 | 0 |
| V9 | 0 |
| V10 | 0 |
| V11 | 0 |
| V12 | 0 |
| V13 | 0 |
| V14 | 0 |
| V15 | 0 |
| V16 | 0 |
| V17 | 0 |
| V18 | 0 |
| V19 | 0 |
| V20 | 0 |
| V21 | 0 |
| V22 | 0 |
| V23 | 0 |
| V24 | 0 |
| V25 | 0 |
| V26 | 0 |
| V27 | 0 |
| V28 | 0 |
| V29 | 0 |
| V30 | 0 |
| V31 | 0 |
| V32 | 0 |
| V33 | 0 |
| V34 | 0 |
| V35 | 0 |
| V36 | 0 |
| V37 | 0 |
| V38 | 0 |
| V39 | 0 |
| V40 | 0 |
| Target | 0 |
# Checking missing values across each column of test Data Set
missing_values = df_test.isnull().sum()
print("The number of missing values on each column of the test data set is:")
missing_values
The number of missing values on each column of the test data set is:
| 0 | |
|---|---|
| V1 | 5 |
| V2 | 6 |
| V3 | 0 |
| V4 | 0 |
| V5 | 0 |
| V6 | 0 |
| V7 | 0 |
| V8 | 0 |
| V9 | 0 |
| V10 | 0 |
| V11 | 0 |
| V12 | 0 |
| V13 | 0 |
| V14 | 0 |
| V15 | 0 |
| V16 | 0 |
| V17 | 0 |
| V18 | 0 |
| V19 | 0 |
| V20 | 0 |
| V21 | 0 |
| V22 | 0 |
| V23 | 0 |
| V24 | 0 |
| V25 | 0 |
| V26 | 0 |
| V27 | 0 |
| V28 | 0 |
| V29 | 0 |
| V30 | 0 |
| V31 | 0 |
| V32 | 0 |
| V33 | 0 |
| V34 | 0 |
| V35 | 0 |
| V36 | 0 |
| V37 | 0 |
| V38 | 0 |
| V39 | 0 |
| V40 | 0 |
| Target | 0 |
Observations:¶
Dataset Shapes:
- Training set: 20,000 rows × 41 columns (40 predictors + 1 target variable)
- Test set: 5,000 rows × 41 columns
Missing Values:
- Train: 36 missing values across the dataset
- Test: 11 missing values
# Check for complete duplicate records of the train
duplicate_records = df.duplicated().sum()
print("The number of duplicate values on the train data set is:", duplicate_records)
The number of duplicate values on the train data set is: 0
# Check for complete duplicate records of the test
duplicate_records = df_test.duplicated().sum()
print("The number of duplicate values on the test data set is:", duplicate_records)
The number of duplicate values on the test data set is: 0
print("Target Value Counts for train dataset:")
print(df['Target'].value_counts())
print("\nTarget Distribution (%):")
print(df['Target'].value_counts(normalize=True) * 100)
Target Value Counts for train dataset: Target 0 18890 1 1110 Name: count, dtype: int64 Target Distribution (%): Target 0 94.4500 1 5.5500 Name: proportion, dtype: float64
print("Target Value Counts for test dataset:")
print(df_test['Target'].value_counts())
print("\nTarget Distribution (%):")
print(df_test['Target'].value_counts(normalize=True) * 100)
Target Value Counts for test dataset: Target 0 4718 1 282 Name: count, dtype: int64 Target Distribution (%): Target 0 94.3600 1 5.6400 Name: proportion, dtype: float64
Observations on Target Distribution:¶
Training Dataset
- Class 0 (No Failure): 18,890 samples (~94.45%)
- Class 1 (Failure): 1,110 samples (~5.55%)
Test Dataset
Class 0 (No Failure): 4,718 samples (~94.36%)
Class 1 (Failure): 282 samples (~5.64%)
Highly Imbalanced Classes
- Both train and test datasets show a similar imbalance (~94% non-failures vs ~6% failures).
- This imbalance is expected in predictive maintenance (failures are rare events).
Consistency Across Train & Test
- The failure rate in train (5.55%) and test (5.64%) are almost identical.
- This suggests the datasets are well-sampled and representative of real-world conditions.
Business Implication of Imbalance
Since failures are rare but costly (replacement > repair > inspection), the model should prioritize recall (catching failures) over plain accuracy.
A naïve model predicting all 0s (no failures) would already achieve ~94% accuracy, but it would miss all failures → disastrous in terms of business costs.
# Display the complete statistical summary for the train dataset
print("Complete Statistical Summary for train dataset")
df.describe(include="all").T
Complete Statistical Summary for train dataset
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| V1 | 19982.0000 | -0.2720 | 3.4416 | -11.8765 | -2.7371 | -0.7479 | 1.8401 | 15.4930 |
| V2 | 19982.0000 | 0.4404 | 3.1508 | -12.3200 | -1.6407 | 0.4715 | 2.5440 | 13.0893 |
| V3 | 20000.0000 | 2.4847 | 3.3890 | -10.7081 | 0.2069 | 2.2558 | 4.5662 | 17.0909 |
| V4 | 20000.0000 | -0.0832 | 3.4316 | -15.0821 | -2.3477 | -0.1352 | 2.1306 | 13.2364 |
| V5 | 20000.0000 | -0.0538 | 2.1048 | -8.6034 | -1.5356 | -0.1020 | 1.3405 | 8.1338 |
| V6 | 20000.0000 | -0.9954 | 2.0410 | -10.2271 | -2.3472 | -1.0005 | 0.3803 | 6.9758 |
| V7 | 20000.0000 | -0.8793 | 1.7616 | -7.9497 | -2.0309 | -0.9172 | 0.2237 | 8.0061 |
| V8 | 20000.0000 | -0.5482 | 3.2958 | -15.6576 | -2.6427 | -0.3891 | 1.7230 | 11.6795 |
| V9 | 20000.0000 | -0.0168 | 2.1606 | -8.5963 | -1.4950 | -0.0676 | 1.4092 | 8.1376 |
| V10 | 20000.0000 | -0.0130 | 2.1932 | -9.8540 | -1.4112 | 0.1010 | 1.4770 | 8.1085 |
| V11 | 20000.0000 | -1.8954 | 3.1243 | -14.8321 | -3.9224 | -1.9212 | 0.1189 | 11.8264 |
| V12 | 20000.0000 | 1.6048 | 2.9305 | -12.9480 | -0.3965 | 1.5078 | 3.5715 | 15.0807 |
| V13 | 20000.0000 | 1.5805 | 2.8747 | -13.2282 | -0.2235 | 1.6372 | 3.4599 | 15.4196 |
| V14 | 20000.0000 | -0.9506 | 1.7897 | -7.7386 | -2.1707 | -0.9572 | 0.2707 | 5.6707 |
| V15 | 20000.0000 | -2.4150 | 3.3550 | -16.4166 | -4.4153 | -2.3826 | -0.3591 | 12.2465 |
| V16 | 20000.0000 | -2.9252 | 4.2217 | -20.3742 | -5.6342 | -2.6827 | -0.0950 | 13.5832 |
| V17 | 20000.0000 | -0.1343 | 3.3455 | -14.0912 | -2.2156 | -0.0146 | 2.0688 | 16.7564 |
| V18 | 20000.0000 | 1.1893 | 2.5923 | -11.6440 | -0.4039 | 0.8834 | 2.5718 | 13.1799 |
| V19 | 20000.0000 | 1.1818 | 3.3969 | -13.4918 | -1.0502 | 1.2791 | 3.4933 | 13.2377 |
| V20 | 20000.0000 | 0.0236 | 3.6695 | -13.9227 | -2.4330 | 0.0334 | 2.5124 | 16.0523 |
| V21 | 20000.0000 | -3.6113 | 3.5677 | -17.9562 | -5.9304 | -3.5329 | -1.2659 | 13.8405 |
| V22 | 20000.0000 | 0.9518 | 1.6515 | -10.1221 | -0.1181 | 0.9747 | 2.0256 | 7.4099 |
| V23 | 20000.0000 | -0.3661 | 4.0319 | -14.8661 | -3.0988 | -0.2621 | 2.4517 | 14.4587 |
| V24 | 20000.0000 | 1.1344 | 3.9121 | -16.3871 | -1.4681 | 0.9690 | 3.5460 | 17.1633 |
| V25 | 20000.0000 | -0.0022 | 2.0167 | -8.2283 | -1.3652 | 0.0251 | 1.3971 | 8.2234 |
| V26 | 20000.0000 | 1.8738 | 3.4351 | -11.8343 | -0.3379 | 1.9505 | 4.1300 | 16.8364 |
| V27 | 20000.0000 | -0.6124 | 4.3688 | -14.9049 | -3.6523 | -0.8849 | 2.1892 | 17.5604 |
| V28 | 20000.0000 | -0.8832 | 1.9177 | -9.2695 | -2.1712 | -0.8911 | 0.3759 | 6.5276 |
| V29 | 20000.0000 | -0.9856 | 2.6844 | -12.5795 | -2.7874 | -1.1762 | 0.6298 | 10.7221 |
| V30 | 20000.0000 | -0.0155 | 3.0053 | -14.7960 | -1.8671 | 0.1843 | 2.0362 | 12.5058 |
| V31 | 20000.0000 | 0.4868 | 3.4614 | -13.7228 | -1.8178 | 0.4903 | 2.7307 | 17.2551 |
| V32 | 20000.0000 | 0.3038 | 5.5004 | -19.8765 | -3.4205 | 0.0521 | 3.7617 | 23.6332 |
| V33 | 20000.0000 | 0.0498 | 3.5753 | -16.8984 | -2.2429 | -0.0662 | 2.2551 | 16.6925 |
| V34 | 20000.0000 | -0.4627 | 3.1838 | -17.9851 | -2.1370 | -0.2550 | 1.4369 | 14.3582 |
| V35 | 20000.0000 | 2.2296 | 2.9371 | -15.3498 | 0.3362 | 2.0986 | 4.0644 | 15.2911 |
| V36 | 20000.0000 | 1.5148 | 3.8009 | -14.8332 | -0.9438 | 1.5665 | 3.9839 | 19.3296 |
| V37 | 20000.0000 | 0.0113 | 1.7882 | -5.4784 | -1.2558 | -0.1284 | 1.1755 | 7.4670 |
| V38 | 20000.0000 | -0.3440 | 3.9481 | -17.3750 | -2.9876 | -0.3168 | 2.2794 | 15.2899 |
| V39 | 20000.0000 | 0.8907 | 1.7531 | -6.4389 | -0.2723 | 0.9193 | 2.0575 | 7.7599 |
| V40 | 20000.0000 | -0.8756 | 3.0122 | -11.0239 | -2.9402 | -0.9208 | 1.1199 | 10.6543 |
| Target | 20000.0000 | 0.0555 | 0.2290 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 1.0000 |
Observations:¶
Central Tendency & Scale
- All 40 predictor variables (V1–V40) are continuous and numeric.
- Means are close to 0, and medians are also near 0, confirming that the dataset was standardized or z-score transformed.
- Standard deviations vary between ~2 and ~3.5, so the features are roughly on the same scale.
Spread & Ranges
- Min and max values range approximately from -15 to +17 across features.
- Most values fall within [-3, +3], which is consistent with standardized distributions.
- The interquartile ranges (IQR: 25%–75%) are compact, suggesting that the majority of sensor readings are well-clustered around the center.
Outliers
- Almost every variable has extreme values beyond ±10, seen in min/max ranges.
- These are statistical outliers but could represent abnormal sensor readings linked to failures.
- Outlier handling should be cautious—don’t remove them blindly, since they may contain the failure signals you need.
Symmetry & Skewness
- Skewness is generally low, meaning most distributions are fairly symmetric.
- A few features (e.g., V1, V29, V37, V3, V27) show moderate positive skew, with a long right tail.
- Heavy tails suggest rare extreme values which may correspond to operational stress before failure.
The statistical summary suggests the dataset is well-prepared, standardized, and balanced in feature scale, but it is heavily imbalanced in target outcomes. The outliers and skewed features could be key indicators of impending failures, making them valuable for predictive modeling.
# Display the complete statistical summary for the test dataset
print("Complete Statistical Summary for test dataset")
df_test.describe(include="all").T
Complete Statistical Summary for test dataset
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| V1 | 4995.0000 | -0.2776 | 3.4663 | -12.3817 | -2.7437 | -0.7648 | 1.8313 | 13.5044 |
| V2 | 4994.0000 | 0.3979 | 3.1396 | -10.7162 | -1.6492 | 0.4274 | 2.4445 | 14.0791 |
| V3 | 5000.0000 | 2.5518 | 3.3266 | -9.2379 | 0.3149 | 2.2604 | 4.5870 | 15.3145 |
| V4 | 5000.0000 | -0.0489 | 3.4139 | -14.6824 | -2.2927 | -0.1458 | 2.1665 | 12.1402 |
| V5 | 5000.0000 | -0.0801 | 2.1109 | -7.7116 | -1.6152 | -0.1319 | 1.3412 | 7.6728 |
| V6 | 5000.0000 | -1.0421 | 2.0054 | -8.9242 | -2.3689 | -1.0486 | 0.3076 | 5.0677 |
| V7 | 5000.0000 | -0.9079 | 1.7690 | -8.1242 | -2.0543 | -0.9397 | 0.2122 | 7.6162 |
| V8 | 5000.0000 | -0.5746 | 3.3319 | -12.2527 | -2.6421 | -0.3579 | 1.7129 | 10.4147 |
| V9 | 5000.0000 | 0.0301 | 2.1741 | -6.7855 | -1.4557 | -0.0799 | 1.4495 | 8.8507 |
| V10 | 5000.0000 | 0.0185 | 2.1454 | -8.1710 | -1.3533 | 0.1663 | 1.5112 | 6.5987 |
| V11 | 5000.0000 | -2.0086 | 3.1122 | -13.1518 | -4.0504 | -2.0431 | 0.0441 | 9.9564 |
| V12 | 5000.0000 | 1.5764 | 2.9074 | -8.1640 | -0.4497 | 1.4883 | 3.5626 | 12.9836 |
| V13 | 5000.0000 | 1.6225 | 2.8829 | -11.5482 | -0.1260 | 1.7186 | 3.4646 | 12.6200 |
| V14 | 5000.0000 | -0.9211 | 1.8035 | -7.8139 | -2.1110 | -0.8960 | 0.2723 | 5.7341 |
| V15 | 5000.0000 | -2.4522 | 3.3870 | -15.2858 | -4.4791 | -2.4171 | -0.4329 | 11.6734 |
| V16 | 5000.0000 | -3.0185 | 4.2644 | -20.9858 | -5.6483 | -2.7738 | -0.1781 | 13.9758 |
| V17 | 5000.0000 | -0.1037 | 3.3365 | -13.4183 | -2.2277 | 0.0475 | 2.1119 | 19.7766 |
| V18 | 5000.0000 | 1.1956 | 2.5864 | -12.2140 | -0.4089 | 0.8814 | 2.6040 | 13.6422 |
| V19 | 5000.0000 | 1.2105 | 3.3847 | -14.1696 | -1.0264 | 1.2959 | 3.5263 | 12.4280 |
| V20 | 5000.0000 | 0.1384 | 3.6572 | -13.7196 | -2.3255 | 0.1934 | 2.5396 | 13.8706 |
| V21 | 5000.0000 | -3.6644 | 3.5778 | -16.3407 | -5.9444 | -3.6629 | -1.3296 | 11.0469 |
| V22 | 5000.0000 | 0.9620 | 1.6404 | -6.7402 | -0.0477 | 0.9860 | 2.0293 | 7.5053 |
| V23 | 5000.0000 | -0.4222 | 4.0567 | -14.4223 | -3.1627 | -0.2792 | 2.4259 | 13.1809 |
| V24 | 5000.0000 | 1.0888 | 3.9682 | -12.3155 | -1.6232 | 0.9128 | 3.5372 | 17.8060 |
| V25 | 5000.0000 | 0.0612 | 2.0102 | -6.7701 | -1.2984 | 0.0767 | 1.4285 | 6.5569 |
| V26 | 5000.0000 | 1.8473 | 3.4003 | -11.4140 | -0.2425 | 1.9170 | 4.1561 | 17.5282 |
| V27 | 5000.0000 | -0.5524 | 4.4029 | -13.1770 | -3.6626 | -0.8720 | 2.2473 | 17.2902 |
| V28 | 5000.0000 | -0.8677 | 1.9262 | -7.9334 | -2.1598 | -0.9307 | 0.4206 | 7.4157 |
| V29 | 5000.0000 | -1.0958 | 2.6555 | -9.9878 | -2.8614 | -1.3405 | 0.5218 | 14.0395 |
| V30 | 5000.0000 | -0.1187 | 3.0233 | -12.4384 | -1.9967 | 0.1125 | 1.9465 | 10.3150 |
| V31 | 5000.0000 | 0.4688 | 3.4463 | -11.2633 | -1.8224 | 0.4857 | 2.7790 | 12.5589 |
| V32 | 5000.0000 | 0.2326 | 5.5856 | -17.2442 | -3.5563 | -0.0767 | 3.7519 | 26.5394 |
| V33 | 5000.0000 | -0.0801 | 3.5386 | -14.9038 | -2.3481 | -0.1597 | 2.0992 | 13.3235 |
| V34 | 5000.0000 | -0.3927 | 3.1661 | -14.6997 | -2.0096 | -0.1717 | 1.4654 | 12.1463 |
| V35 | 5000.0000 | 2.2112 | 2.9484 | -12.2606 | 0.3218 | 2.1117 | 4.0316 | 13.4892 |
| V36 | 5000.0000 | 1.5948 | 3.7750 | -12.7356 | -0.8661 | 1.7030 | 4.1044 | 17.1161 |
| V37 | 5000.0000 | 0.0229 | 1.7853 | -5.0791 | -1.2405 | -0.1104 | 1.2375 | 6.8099 |
| V38 | 5000.0000 | -0.4057 | 3.9689 | -15.3345 | -2.9845 | -0.3812 | 2.2880 | 13.0650 |
| V39 | 5000.0000 | 0.9388 | 1.7165 | -5.4510 | -0.2080 | 0.9592 | 2.1308 | 7.1822 |
| V40 | 5000.0000 | -0.9324 | 2.9782 | -10.0762 | -2.9866 | -1.0028 | 1.0797 | 8.6985 |
| Target | 5000.0000 | 0.0564 | 0.2307 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 1.0000 |
Observations:¶
Central Tendency & Scale
- Similar to the training set, all 40 predictors are numeric and appear to be standardized/normalized.
- Means are very close to 0 (e.g., V1 = -0.28, V2 = 0.39, V3 = 2.55).
- Medians also hover near 0, confirming symmetry and standardization.
Spread & Ranges
- Standard deviations range roughly 2.0 to 3.5, similar to the training dataset.
- Min/Max values fall within -15 to +15, which aligns with the training dataset ranges.
- Most values are concentrated between -3 and +3 (based on quartiles).
Outliers
- Several features (e.g., V1, V2, V3, V4) include extreme values (< -10 or > 10).
- These outliers are consistent with the training dataset and may represent rare sensor spikes linked to failure events.
Symmetry & Skewness
- Features show low to moderate skewness.
- A few variables (like V1, V2, V3) exhibit slightly longer tails, but the overall distribution remains roughly symmetric.
- This suggests distributions are stable across train and test.
Consistency With Training Dataset
- The statistical properties (mean, std, ranges, skewness) are highly similar between train and test datasets.
- This indicates that the test set is a representative sample, not drawn from a different distribution.
- Ensures models trained on the training set will generalize well.
The test dataset mirrors the training dataset in distribution, scale, and variability. This confirms good dataset preparation, ensuring that models trained on the training set will likely generalize effectively when evaluated on the test set.
Exploratory Data Analysis¶
# Function to plot a boxplot and a histogram along the same scale.
def histogram_boxplot(data, feature, figsize=(12, 7), kde=False, bins=None):
"""
Boxplot and histogram combined with a title
data: dataframe
feature: dataframe column
figsize: size of figure (default (12,7))
kde: whether to show the density curve (default False)
bins: number of bins for histogram (default None)
"""
f2, (ax_box2, ax_hist2) = plt.subplots(
nrows=2, # Number of rows of the subplot grid= 2
sharex=True, # x-axis will be shared among all subplots
gridspec_kw={"height_ratios": (0.25, 0.75)},
figsize=figsize,
) # creating the 2 subplots
# Add a title to the figure
f2.suptitle(f"Distribution of {feature}", fontsize=16)
# Boxplot creation
sns.boxplot(
data=data,
x=feature,
ax=ax_box2,
showmeans=True,
palette="Oranges",
)
# Histogram creation
sns.histplot(
data=data,
x=feature,
kde=kde,
ax=ax_hist2,
bins=bins if bins else 50,
color="orange",
)
# Add mean and median lines
ax_hist2.axvline(data[feature].mean(), color="green", linestyle="--", label="Mean")
ax_hist2.axvline(
data[feature].median(), color="black", linestyle="-", label="Median"
)
# Add a legend for the mean and median lines
ax_hist2.legend()
plt.show() # Show the plot
# Copying data to another variable to avoid any changes to original data
df_eda = df.copy()
Univariate analysis¶
# Selecting all numerical columns ('int64', 'float64')
num_cols = df_eda.select_dtypes(include=["int64", "float64"]).columns
# Iterate through each numerical column and plot the histogram and boxplot combined
for column in num_cols:
print(f"Distribution of '{column}'")
print(df_eda[column].describe())
histogram_boxplot(df_eda, column, bins=50, kde=True)
print("-" * 100)
Distribution of 'V1' count 19982.0000 mean -0.2720 std 3.4416 min -11.8765 25% -2.7371 50% -0.7479 75% 1.8401 max 15.4930 Name: V1, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V2' count 19982.0000 mean 0.4404 std 3.1508 min -12.3200 25% -1.6407 50% 0.4715 75% 2.5440 max 13.0893 Name: V2, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V3' count 20000.0000 mean 2.4847 std 3.3890 min -10.7081 25% 0.2069 50% 2.2558 75% 4.5662 max 17.0909 Name: V3, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V4' count 20000.0000 mean -0.0832 std 3.4316 min -15.0821 25% -2.3477 50% -0.1352 75% 2.1306 max 13.2364 Name: V4, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V5' count 20000.0000 mean -0.0538 std 2.1048 min -8.6034 25% -1.5356 50% -0.1020 75% 1.3405 max 8.1338 Name: V5, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V6' count 20000.0000 mean -0.9954 std 2.0410 min -10.2271 25% -2.3472 50% -1.0005 75% 0.3803 max 6.9758 Name: V6, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V7' count 20000.0000 mean -0.8793 std 1.7616 min -7.9497 25% -2.0309 50% -0.9172 75% 0.2237 max 8.0061 Name: V7, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V8' count 20000.0000 mean -0.5482 std 3.2958 min -15.6576 25% -2.6427 50% -0.3891 75% 1.7230 max 11.6795 Name: V8, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V9' count 20000.0000 mean -0.0168 std 2.1606 min -8.5963 25% -1.4950 50% -0.0676 75% 1.4092 max 8.1376 Name: V9, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V10' count 20000.0000 mean -0.0130 std 2.1932 min -9.8540 25% -1.4112 50% 0.1010 75% 1.4770 max 8.1085 Name: V10, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V11' count 20000.0000 mean -1.8954 std 3.1243 min -14.8321 25% -3.9224 50% -1.9212 75% 0.1189 max 11.8264 Name: V11, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V12' count 20000.0000 mean 1.6048 std 2.9305 min -12.9480 25% -0.3965 50% 1.5078 75% 3.5715 max 15.0807 Name: V12, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V13' count 20000.0000 mean 1.5805 std 2.8747 min -13.2282 25% -0.2235 50% 1.6372 75% 3.4599 max 15.4196 Name: V13, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V14' count 20000.0000 mean -0.9506 std 1.7897 min -7.7386 25% -2.1707 50% -0.9572 75% 0.2707 max 5.6707 Name: V14, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V15' count 20000.0000 mean -2.4150 std 3.3550 min -16.4166 25% -4.4153 50% -2.3826 75% -0.3591 max 12.2465 Name: V15, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V16' count 20000.0000 mean -2.9252 std 4.2217 min -20.3742 25% -5.6342 50% -2.6827 75% -0.0950 max 13.5832 Name: V16, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V17' count 20000.0000 mean -0.1343 std 3.3455 min -14.0912 25% -2.2156 50% -0.0146 75% 2.0688 max 16.7564 Name: V17, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V18' count 20000.0000 mean 1.1893 std 2.5923 min -11.6440 25% -0.4039 50% 0.8834 75% 2.5718 max 13.1799 Name: V18, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V19' count 20000.0000 mean 1.1818 std 3.3969 min -13.4918 25% -1.0502 50% 1.2791 75% 3.4933 max 13.2377 Name: V19, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V20' count 20000.0000 mean 0.0236 std 3.6695 min -13.9227 25% -2.4330 50% 0.0334 75% 2.5124 max 16.0523 Name: V20, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V21' count 20000.0000 mean -3.6113 std 3.5677 min -17.9562 25% -5.9304 50% -3.5329 75% -1.2659 max 13.8405 Name: V21, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V22' count 20000.0000 mean 0.9518 std 1.6515 min -10.1221 25% -0.1181 50% 0.9747 75% 2.0256 max 7.4099 Name: V22, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V23' count 20000.0000 mean -0.3661 std 4.0319 min -14.8661 25% -3.0988 50% -0.2621 75% 2.4517 max 14.4587 Name: V23, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V24' count 20000.0000 mean 1.1344 std 3.9121 min -16.3871 25% -1.4681 50% 0.9690 75% 3.5460 max 17.1633 Name: V24, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V25' count 20000.0000 mean -0.0022 std 2.0167 min -8.2283 25% -1.3652 50% 0.0251 75% 1.3971 max 8.2234 Name: V25, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V26' count 20000.0000 mean 1.8738 std 3.4351 min -11.8343 25% -0.3379 50% 1.9505 75% 4.1300 max 16.8364 Name: V26, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V27' count 20000.0000 mean -0.6124 std 4.3688 min -14.9049 25% -3.6523 50% -0.8849 75% 2.1892 max 17.5604 Name: V27, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V28' count 20000.0000 mean -0.8832 std 1.9177 min -9.2695 25% -2.1712 50% -0.8911 75% 0.3759 max 6.5276 Name: V28, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V29' count 20000.0000 mean -0.9856 std 2.6844 min -12.5795 25% -2.7874 50% -1.1762 75% 0.6298 max 10.7221 Name: V29, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V30' count 20000.0000 mean -0.0155 std 3.0053 min -14.7960 25% -1.8671 50% 0.1843 75% 2.0362 max 12.5058 Name: V30, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V31' count 20000.0000 mean 0.4868 std 3.4614 min -13.7228 25% -1.8178 50% 0.4903 75% 2.7307 max 17.2551 Name: V31, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V32' count 20000.0000 mean 0.3038 std 5.5004 min -19.8765 25% -3.4205 50% 0.0521 75% 3.7617 max 23.6332 Name: V32, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V33' count 20000.0000 mean 0.0498 std 3.5753 min -16.8984 25% -2.2429 50% -0.0662 75% 2.2551 max 16.6925 Name: V33, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V34' count 20000.0000 mean -0.4627 std 3.1838 min -17.9851 25% -2.1370 50% -0.2550 75% 1.4369 max 14.3582 Name: V34, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V35' count 20000.0000 mean 2.2296 std 2.9371 min -15.3498 25% 0.3362 50% 2.0986 75% 4.0644 max 15.2911 Name: V35, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V36' count 20000.0000 mean 1.5148 std 3.8009 min -14.8332 25% -0.9438 50% 1.5665 75% 3.9839 max 19.3296 Name: V36, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V37' count 20000.0000 mean 0.0113 std 1.7882 min -5.4784 25% -1.2558 50% -0.1284 75% 1.1755 max 7.4670 Name: V37, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V38' count 20000.0000 mean -0.3440 std 3.9481 min -17.3750 25% -2.9876 50% -0.3168 75% 2.2794 max 15.2899 Name: V38, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V39' count 20000.0000 mean 0.8907 std 1.7531 min -6.4389 25% -0.2723 50% 0.9193 75% 2.0575 max 7.7599 Name: V39, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'V40' count 20000.0000 mean -0.8756 std 3.0122 min -11.0239 25% -2.9402 50% -0.9208 75% 1.1199 max 10.6543 Name: V40, dtype: float64
---------------------------------------------------------------------------------------------------- Distribution of 'Target' count 20000.0000 mean 0.0555 std 0.2290 min 0.0000 25% 0.0000 50% 0.0000 75% 0.0000 max 1.0000 Name: Target, dtype: float64
----------------------------------------------------------------------------------------------------
Obserations:¶
General Characteristics
- All 40 predictors are continuous numeric (float).
- Most features are centered around 0 (mean ~0), consistent with standardized or ciphered transformation.
- Standard deviations range mostly between 2.0 – 3.5, indicating moderate variability.
Skewness
- None of the 40 predictors show high skewness (|skew| > 1).
- Most distributions are approximately symmetric or mildly skewed.
- This is consistent with transformed data where distributions were normalized.
Outliers
- Many predictors show values beyond 3× standard deviation (e.g., V1–V15 confirmed).
- This suggests sensor anomalies or rare extreme readings.
- Outliers are scattered rather than concentrated, indicating natural system variability rather than data corruption.
Spread
- Example ranges:
- V1: -11.9 to +15.5
- V3: -10.7 to +17.1
- V5: -8.6 to +8.1
- Some variables cover wide ranges, others are more compact.
- This mix of wide/narrow distributions may influence model interpretability.
- Example ranges:
Key Observations (Across All Predictors)
- Balanced Feature Distributions → Most predictors resemble bell-shaped curves with moderate variance.
- No heavily skewed features → Good for algorithms assuming normality (e.g., Logistic Regression).
- Outliers are common across features (esp. V1–V15 tested) → May require robust scaling or outlier-tolerant models (Random Forest, XGBoost).
- No missing values issue → Only 36 missing values in total, negligible at dataset scale.
In summary:
The dataset is well-prepared, symmetric, and standardized, but has rare outliers and a severe class imbalance. These will be the two main EDA findings guiding preprocessing and model design.
Bivariate Analysis¶
# Calculate the correlation matrix
corr_matrix = df_eda[num_cols].corr()
# Visual representation of the correlation matrix
plt.figure(figsize=(25, 25))
sns.heatmap(corr_matrix, annot=True, fmt='.2f', cbar=False, cmap='Spectral')
plt.title("Correlation Heatmap")
plt.xlabel("Features")
plt.ylabel("Features")
plt.show()
Observations:¶
Correlation with Target
- Most predictors (V1–V40) show low-to-moderate correlation with Target (values are generally within ±0.1 to ±0.3).
- No single variable stands out as highly correlated with failures (no |corr| > 0.5).
- Observation → Failures are multi-factorial and likely need combinations of features (non-linear models will be helpful).
Inter-feature Correlation
- Several predictors are strongly correlated with each other (|corr| > 0.7).
- Example clusters visible in the heatmap:
- V1–V4 group shows moderate inter-correlation.
- V13–V16 are highly correlated.
- V26–V29 show notable correlation.
- Example clusters visible in the heatmap:
- Observation → There is multicollinearity in the dataset.
- Linear models may suffer (unstable coefficients).
- Tree-based models handle this better.
- Several predictors are strongly correlated with each other (|corr| > 0.7).
Overall Patterns
- The correlation matrix is dense, with many weak-to-moderate correlations spread across variables.
- This suggests that the data is not sparse — most features carry some information.
- No single dominant predictor → classification may benefit from ensemble learning rather than simple univariate thresholds.
Modeling Implications
- Feature Selection / Dimensionality Reduction
- Since many features are correlated, PCA or feature importance methods (Random Forest/XGBoost) can help reduce redundancy.
- Alternatively, L1 regularization (Lasso) can help shrink correlated features.
- Model Choice
- Tree-based methods (Random Forest, XGBoost, LightGBM) will handle correlated predictors and interactions effectively.
- Logistic Regression/SVM may need regularization to avoid instability.
- Failure Detection Difficulty
- Low correlation with target → linear separability is weak.
- Models that capture non-linear boundaries and feature interactions will perform better.
- Feature Selection / Dimensionality Reduction
Summary:
- No single “hero feature” strongly predicts failures.
- Several feature clusters are inter-correlated, introducing multicollinearity.
- Failures depend on complex feature interactions, requiring non-linear, ensemble-based models with feature importance ranking.
# Function to create distribution plot
def distribution_plot_wrt_target(data, predictor, target):
fig, axs = plt.subplots(2, 2, figsize=(12, 10))
target_uniq = data[target].unique()
axs[0, 0].set_title(f"Distribution of target for target={str(target_uniq[0])}")
sns.histplot(
data=data[data[target] == target_uniq[0]],
x=predictor,
kde=True,
ax=axs[0, 0],
color="green",
stat="density",
)
axs[0, 1].set_title(f"Distribution of target for target={str(target_uniq[1])}")
sns.histplot(
data=data[data[target] == target_uniq[1]],
x=predictor,
kde=True,
ax=axs[0, 1],
color="blue",
stat="density",
)
axs[1, 0].set_title("Boxplot w.r.t target")
sns.boxplot(data=data, x=target, y=predictor, ax=axs[1, 0], palette="gist_rainbow")
axs[1, 1].set_title("Boxplot (without outliers) w.r.t target")
sns.boxplot(
data=data,
x=target,
y=predictor,
ax=axs[1, 1],
showfliers=False,
palette="gist_rainbow",
)
plt.tight_layout()
plt.show()
# Selecting all numerical columns ('int64', 'float64')
num_cols = df_eda.select_dtypes(include=["int64", "float64"]).columns[:-1]
# Iterate through each numerical column and distribution plot
for column in num_cols:
distribution_plot_wrt_target(df_eda, column, "Target")
print("-" * 150)
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Observations:¶
The target variable shows only weak correlations with the predictors overall. The features with the strongest associations to the target are:
- V7: 0.24
- V15: 0.25
- V16: 0.23
- V21: 0.26
Observations of V7 and Target
Higher values of V7 appear to be strongly associated with failures. For Target = 1, the distribution is roughly symmetric but shifted to the right, with a mean closer to 2. In addition, the median value of V7 under Target = 1 is clearly higher than under Target = 0.
These patterns suggest that V7 is an effective discriminator between failures and non-failures, particularly given its positive correlation with the target.
Observations of V15 and Target
Similar to V7, higher values of V15 are linked to failures. This feature may serve as another strong predictor for distinguishing between failures and non-failures, given that failures consistently occur at higher V15 values.
Observations of V15 and Target
Failures are characterized by higher values of V16, continuing the pattern observed in the previous variables. This feature may also contribute to the model’s ability to effectively identify failure events.
Observations of V21 and Target
As with the other variables, higher values of V21 are associated with failure events. The separation between the two groups is evident, with failures displaying both higher and more dispersed values, making V21 a useful feature for distinguishing between failure and non-failure cases.
Data Preprocessing¶
# Copying data to another variable to avoid any changes to original data
df_model = df_eda.copy()
# Outlier detection using boxplot
# Creating a list of numerical columns
numeric_columns = df_model.select_dtypes(include=np.number).columns.tolist()
# Calculate the number of rows needed for the subplots
num_plots = len(num_cols)
num_rows = (num_plots // 3) + (num_plots % 3 > 0)
# Create subplots
plt.figure(figsize=(15, num_rows * 5))
for i, variable in enumerate(num_cols):
plt.subplot(num_rows, 3, i + 1)
sns.boxplot(data=df_model, x=variable)
plt.tight_layout(pad=2)
plt.show()
# Check for outliers in continuous variables
outliers = df_model[num_cols].describe()
print("\nSummary of the numerical features, including outliers:")
display(outliers)
Summary of the numerical features, including outliers:
| V1 | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 | V10 | V11 | V12 | V13 | V14 | V15 | V16 | V17 | V18 | V19 | V20 | V21 | V22 | V23 | V24 | V25 | V26 | V27 | V28 | V29 | V30 | V31 | V32 | V33 | V34 | V35 | V36 | V37 | V38 | V39 | V40 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | 19982.0000 | 19982.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 | 20000.0000 |
| mean | -0.2720 | 0.4404 | 2.4847 | -0.0832 | -0.0538 | -0.9954 | -0.8793 | -0.5482 | -0.0168 | -0.0130 | -1.8954 | 1.6048 | 1.5805 | -0.9506 | -2.4150 | -2.9252 | -0.1343 | 1.1893 | 1.1818 | 0.0236 | -3.6113 | 0.9518 | -0.3661 | 1.1344 | -0.0022 | 1.8738 | -0.6124 | -0.8832 | -0.9856 | -0.0155 | 0.4868 | 0.3038 | 0.0498 | -0.4627 | 2.2296 | 1.5148 | 0.0113 | -0.3440 | 0.8907 | -0.8756 |
| std | 3.4416 | 3.1508 | 3.3890 | 3.4316 | 2.1048 | 2.0410 | 1.7616 | 3.2958 | 2.1606 | 2.1932 | 3.1243 | 2.9305 | 2.8747 | 1.7897 | 3.3550 | 4.2217 | 3.3455 | 2.5923 | 3.3969 | 3.6695 | 3.5677 | 1.6515 | 4.0319 | 3.9121 | 2.0167 | 3.4351 | 4.3688 | 1.9177 | 2.6844 | 3.0053 | 3.4614 | 5.5004 | 3.5753 | 3.1838 | 2.9371 | 3.8009 | 1.7882 | 3.9481 | 1.7531 | 3.0122 |
| min | -11.8765 | -12.3200 | -10.7081 | -15.0821 | -8.6034 | -10.2271 | -7.9497 | -15.6576 | -8.5963 | -9.8540 | -14.8321 | -12.9480 | -13.2282 | -7.7386 | -16.4166 | -20.3742 | -14.0912 | -11.6440 | -13.4918 | -13.9227 | -17.9562 | -10.1221 | -14.8661 | -16.3871 | -8.2283 | -11.8343 | -14.9049 | -9.2695 | -12.5795 | -14.7960 | -13.7228 | -19.8765 | -16.8984 | -17.9851 | -15.3498 | -14.8332 | -5.4784 | -17.3750 | -6.4389 | -11.0239 |
| 25% | -2.7371 | -1.6407 | 0.2069 | -2.3477 | -1.5356 | -2.3472 | -2.0309 | -2.6427 | -1.4950 | -1.4112 | -3.9224 | -0.3965 | -0.2235 | -2.1707 | -4.4153 | -5.6342 | -2.2156 | -0.4039 | -1.0502 | -2.4330 | -5.9304 | -0.1181 | -3.0988 | -1.4681 | -1.3652 | -0.3379 | -3.6523 | -2.1712 | -2.7874 | -1.8671 | -1.8178 | -3.4205 | -2.2429 | -2.1370 | 0.3362 | -0.9438 | -1.2558 | -2.9876 | -0.2723 | -2.9402 |
| 50% | -0.7479 | 0.4715 | 2.2558 | -0.1352 | -0.1020 | -1.0005 | -0.9172 | -0.3891 | -0.0676 | 0.1010 | -1.9212 | 1.5078 | 1.6372 | -0.9572 | -2.3826 | -2.6827 | -0.0146 | 0.8834 | 1.2791 | 0.0334 | -3.5329 | 0.9747 | -0.2621 | 0.9690 | 0.0251 | 1.9505 | -0.8849 | -0.8911 | -1.1762 | 0.1843 | 0.4903 | 0.0521 | -0.0662 | -0.2550 | 2.0986 | 1.5665 | -0.1284 | -0.3168 | 0.9193 | -0.9208 |
| 75% | 1.8401 | 2.5440 | 4.5662 | 2.1306 | 1.3405 | 0.3803 | 0.2237 | 1.7230 | 1.4092 | 1.4770 | 0.1189 | 3.5715 | 3.4599 | 0.2707 | -0.3591 | -0.0950 | 2.0688 | 2.5718 | 3.4933 | 2.5124 | -1.2659 | 2.0256 | 2.4517 | 3.5460 | 1.3971 | 4.1300 | 2.1892 | 0.3759 | 0.6298 | 2.0362 | 2.7307 | 3.7617 | 2.2551 | 1.4369 | 4.0644 | 3.9839 | 1.1755 | 2.2794 | 2.0575 | 1.1199 |
| max | 15.4930 | 13.0893 | 17.0909 | 13.2364 | 8.1338 | 6.9758 | 8.0061 | 11.6795 | 8.1376 | 8.1085 | 11.8264 | 15.0807 | 15.4196 | 5.6707 | 12.2465 | 13.5832 | 16.7564 | 13.1799 | 13.2377 | 16.0523 | 13.8405 | 7.4099 | 14.4587 | 17.1633 | 8.2234 | 16.8364 | 17.5604 | 6.5276 | 10.7221 | 12.5058 | 17.2551 | 23.6332 | 16.6925 | 14.3582 | 15.2911 | 19.3296 | 7.4670 | 15.2899 | 7.7599 | 10.6543 |
# Step 1: Define and Prepare the Data
X = df_model.drop("Target", axis=1)
y = df_model["Target"]
display(X.head())
display(y.head())
| V1 | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 | V10 | V11 | V12 | V13 | V14 | V15 | V16 | V17 | V18 | V19 | V20 | V21 | V22 | V23 | V24 | V25 | V26 | V27 | V28 | V29 | V30 | V31 | V32 | V33 | V34 | V35 | V36 | V37 | V38 | V39 | V40 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | -4.4646 | -4.6791 | 3.1015 | 0.5061 | -0.2211 | -2.0325 | -2.9109 | 0.0507 | -1.5224 | 3.7619 | -5.7147 | 0.7359 | 0.9813 | 1.4179 | -3.3758 | -3.0473 | 0.3062 | 2.9141 | 2.2700 | 4.3949 | -2.3883 | 0.6464 | -1.1905 | 3.1330 | 0.6653 | -2.5108 | -0.0367 | 0.7262 | -3.9822 | -1.0726 | 1.6671 | 3.0597 | -1.6904 | 2.8463 | 2.2352 | 6.6675 | 0.4438 | -2.3692 | 2.9506 | -3.4803 |
| 1 | 3.3659 | 3.6534 | 0.9097 | -1.3675 | 0.3320 | 2.3589 | 0.7326 | -4.3321 | 0.5657 | -0.1011 | 1.9145 | -0.9515 | -1.2553 | -2.7065 | 0.1932 | -4.7694 | -2.2053 | 0.9077 | 0.7569 | -5.8337 | -3.0651 | 1.5966 | -1.7573 | 1.7664 | -0.2671 | 3.6250 | 1.5003 | -0.5857 | 0.7830 | -0.2012 | 0.0249 | -1.7955 | 3.0328 | -2.4675 | 1.8946 | -2.2978 | -1.7310 | 5.9088 | -0.3863 | 0.6162 |
| 2 | -3.8318 | -5.8244 | 0.6340 | -2.4188 | -1.7738 | 1.0168 | -2.0989 | -3.1732 | -2.0819 | 5.3926 | -0.7707 | 1.1067 | 1.1443 | 0.9433 | -3.1638 | -4.2478 | -4.0389 | 3.6885 | 3.3112 | 1.0590 | -2.1430 | 1.6501 | -1.6606 | 1.6799 | -0.4508 | -4.5507 | 3.7388 | 1.1344 | -2.0335 | 0.8408 | -1.6004 | -0.2571 | 0.8035 | 4.0862 | 2.2921 | 5.3608 | 0.3520 | 2.9400 | 3.8392 | -4.3094 |
| 3 | 1.6181 | 1.8883 | 7.0461 | -1.1473 | 0.0831 | -1.5298 | 0.2073 | -2.4936 | 0.3449 | 2.1186 | -3.0530 | 0.4597 | 2.7045 | -0.6361 | -0.4537 | -3.1740 | -3.4043 | -1.2815 | 1.5821 | -1.9518 | -3.5166 | -1.2060 | -5.6279 | -1.8177 | 2.1241 | 5.2946 | 4.7481 | -2.3085 | -3.9630 | -6.0287 | 4.9488 | -3.5844 | -2.5775 | 1.3638 | 0.6227 | 5.5501 | -1.5268 | 0.1389 | 3.1014 | -1.2774 |
| 4 | -0.1114 | 3.8725 | -3.7584 | -2.9829 | 3.7927 | 0.5450 | 0.2054 | 4.8490 | -1.8549 | -6.2200 | 1.9983 | 4.7238 | 0.7091 | -1.9894 | -2.6327 | 4.1844 | 2.2454 | 3.7345 | -6.3128 | -5.3799 | -0.8867 | 2.0617 | 9.4456 | 4.4900 | -3.9451 | 4.5821 | -8.7804 | -3.3830 | 5.1065 | 6.7875 | 2.0442 | 8.2659 | 6.6292 | -10.0687 | 1.2230 | -3.2298 | 1.6869 | -2.1639 | -3.6446 | 6.5103 |
| Target | |
|---|---|
| 0 | 0 |
| 1 | 0 |
| 2 | 0 |
| 3 | 0 |
| 4 | 0 |
Observations:¶
In classification problems with imbalanced target classes, it is recommended to use stratified sampling to maintain the relative class frequencies across the training and test sets. This can be achieved by setting the stratify parameter in the train_test_split function.
# Splitting train dataset into training and validation set (75% train, 25% validation), using stratify to maintain target distribution
X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.25, random_state=1, stratify=y)
# Checking the number of rows and columns in the X_train data
print("There are", X_train.shape[0], "rows and", X_train.shape[1], "columns in the Training set.", X_train.shape,)
# Checking the number of rows and columns in the X_val data
print("There are", X_val.shape[0], "rows and", X_val.shape[1], "columns in the Test set.", X_val.shape,)
There are 15000 rows and 40 columns in the Training set. (15000, 40) There are 5000 rows and 40 columns in the Test set. (5000, 40)
print("Percentage of classes in training set:")
print(y_train.value_counts(normalize=True) * 100)
print("")
print("Percentage of classes in validation set:")
print(y_val.value_counts(normalize=True) * 100)
Percentage of classes in training set: Target 0 94.4533 1 5.5467 Name: proportion, dtype: float64 Percentage of classes in validation set: Target 0 94.4400 1 5.5600 Name: proportion, dtype: float64
# Dividing test data into X_test and y_test
X_test = df_test.drop(["Target"], axis=1)
y_test = df_test["Target"]
display(X_test.head())
display(y_test.head())
| V1 | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 | V10 | V11 | V12 | V13 | V14 | V15 | V16 | V17 | V18 | V19 | V20 | V21 | V22 | V23 | V24 | V25 | V26 | V27 | V28 | V29 | V30 | V31 | V32 | V33 | V34 | V35 | V36 | V37 | V38 | V39 | V40 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | -0.6135 | -3.8196 | 2.2023 | 1.3004 | -1.1849 | -4.4960 | -1.8358 | 4.7230 | 1.2061 | -0.3419 | -5.1229 | 1.0170 | 4.8185 | 3.2690 | -2.9843 | 1.3874 | 2.0320 | -0.5116 | -1.0231 | 7.3387 | -2.2422 | 0.1555 | 2.0538 | -2.7723 | 1.8514 | -1.7887 | -0.2773 | -1.2551 | -3.8329 | -1.5045 | 1.5868 | 2.2912 | -5.4114 | 0.8701 | 0.5745 | 4.1572 | 1.4281 | -10.5113 | 0.4547 | -1.4484 |
| 1 | 0.3896 | -0.5123 | 0.5271 | -2.5768 | -1.0168 | 2.2351 | -0.4413 | -4.4057 | -0.3329 | 1.9668 | 1.7965 | 0.4105 | 0.6383 | -1.3896 | -1.8834 | -5.0179 | -3.8272 | 2.4181 | 1.7623 | -3.2423 | -3.1930 | 1.8575 | -1.7080 | 0.6334 | -0.5879 | 0.0837 | 3.0139 | -0.1823 | 0.2239 | 0.8652 | -1.7822 | -2.4749 | 2.4936 | 0.3152 | 2.0593 | 0.6839 | -0.4855 | 5.1284 | 1.7207 | -1.4882 |
| 2 | -0.8749 | -0.6406 | 4.0842 | -1.5905 | 0.5259 | -1.9576 | -0.6954 | 1.3473 | -1.7323 | 0.4665 | -4.9282 | 3.5651 | -0.4493 | -0.6562 | -0.1665 | -1.6302 | 2.2919 | 2.3965 | 0.6013 | 1.7935 | -2.1202 | 0.4820 | -0.8407 | 1.7902 | 1.8744 | 0.3639 | -0.1691 | -0.4838 | -2.1190 | -2.1566 | 2.9073 | -1.3189 | -2.9975 | 0.4597 | 0.6198 | 5.6315 | 1.3235 | -1.7522 | 1.8083 | 1.6757 |
| 3 | 0.2384 | 1.4586 | 4.0145 | 2.5345 | 1.1970 | -3.1173 | -0.9240 | 0.2695 | 1.3224 | 0.7023 | -5.5783 | -0.8507 | 2.5905 | 0.7674 | -2.3908 | -2.3420 | 0.5719 | -0.9338 | 0.5087 | 1.2107 | -3.2595 | 0.1046 | -0.6589 | 1.4981 | 1.1003 | 4.1430 | -0.2484 | -1.1365 | -5.3558 | -4.5459 | 3.8087 | 3.5179 | -3.0741 | -0.2842 | 0.9546 | 3.0293 | -1.3672 | -3.4121 | 0.9060 | -2.4509 |
| 4 | 5.8282 | 2.7683 | -1.2345 | 2.8093 | -1.6416 | -1.4067 | 0.5686 | 0.9650 | 1.9184 | -2.7749 | -0.5300 | 1.3745 | -0.6509 | -1.6795 | -0.3792 | -4.4431 | 3.8939 | -0.6076 | 2.9449 | 0.3672 | -5.7891 | 4.5975 | 4.4503 | 3.2249 | 0.3967 | 0.2478 | -2.3620 | 1.0794 | -0.4731 | 2.2428 | -3.5914 | 1.7738 | -1.5016 | -2.2267 | 4.7768 | -6.5597 | -0.8056 | -0.2760 | -3.8582 | -0.5377 |
| Target | |
|---|---|
| 0 | 0 |
| 1 | 0 |
| 2 | 0 |
| 3 | 0 |
| 4 | 0 |
# Checking the number of rows and columns in the X_test data
print("There are", X_test.shape[0], "rows and", X_test.shape[1], "columns in the Test set.", X_test.shape,)
There are 5000 rows and 40 columns in the Test set. (5000, 40)
print("Percentage of classes in test set:")
print(y_test.value_counts(normalize=True) * 100)
Percentage of classes in test set: Target 0 94.3600 1 5.6400 Name: proportion, dtype: float64
# Creating an instance of the imputer to be used
imputer = SimpleImputer(strategy="median")
# Fit and transform the train data
X_train = pd.DataFrame(imputer.fit_transform(X_train), columns=X_train.columns)
# Transform the validation data without data leakage (using the same imputer trained on X_train)
X_val = pd.DataFrame(imputer.transform(X_val), columns=X_train.columns)
# Transform the test data without data leakage
X_test = pd.DataFrame(imputer.transform(X_test), columns=X_train.columns)
# Checking that no column has missing values in train, validation, or test sets
print("Missing values on the Train dataset")
print(X_train.isna().sum())
print("-" * 50)
print("Missing values on the Validation dataset")
print(X_val.isna().sum()) # Checking missing values in validation set
print("-" * 50)
print("Missing values on the Test dataset")
print(X_test.isna().sum()) # Checking missing values in test set
Missing values on the Train dataset V1 0 V2 0 V3 0 V4 0 V5 0 V6 0 V7 0 V8 0 V9 0 V10 0 V11 0 V12 0 V13 0 V14 0 V15 0 V16 0 V17 0 V18 0 V19 0 V20 0 V21 0 V22 0 V23 0 V24 0 V25 0 V26 0 V27 0 V28 0 V29 0 V30 0 V31 0 V32 0 V33 0 V34 0 V35 0 V36 0 V37 0 V38 0 V39 0 V40 0 dtype: int64 -------------------------------------------------- Missing values on the Validation dataset V1 0 V2 0 V3 0 V4 0 V5 0 V6 0 V7 0 V8 0 V9 0 V10 0 V11 0 V12 0 V13 0 V14 0 V15 0 V16 0 V17 0 V18 0 V19 0 V20 0 V21 0 V22 0 V23 0 V24 0 V25 0 V26 0 V27 0 V28 0 V29 0 V30 0 V31 0 V32 0 V33 0 V34 0 V35 0 V36 0 V37 0 V38 0 V39 0 V40 0 dtype: int64 -------------------------------------------------- Missing values on the Test dataset V1 0 V2 0 V3 0 V4 0 V5 0 V6 0 V7 0 V8 0 V9 0 V10 0 V11 0 V12 0 V13 0 V14 0 V15 0 V16 0 V17 0 V18 0 V19 0 V20 0 V21 0 V22 0 V23 0 V24 0 V25 0 V26 0 V27 0 V28 0 V29 0 V30 0 V31 0 V32 0 V33 0 V34 0 V35 0 V36 0 V37 0 V38 0 V39 0 V40 0 dtype: int64
Model Building¶
Model Evaluation Criterion¶
Write down the model evaluation criterion with rationale
Interpretation of Predictions
- True Positives (TP): Actual failures that the model correctly identifies.
- False Negatives (FN): Actual failures that the model fails to detect (most costly).
- False Positives (FP): Cases where the model predicts a failure, but the generator is actually fine.
Metric We Should Optimize
Since missed failures (FN) are far more expensive than unnecessary inspections (FP), our priority is to correctly capture as many real failures as possible.
- Recall is the most appropriate metric to optimize.
- Maximizing Recall reduces false negatives, ensuring that potential failures are flagged in advance.
- This aligns with the business objective of minimizing costly generator replacements by enabling timely repairs.
def plot(history, name):
"""
Function to plot loss/accuracy
history: an object which stores the metrics and losses.
name: can be one of Loss or Accuracy
"""
fig, ax = plt.subplots() #Creating a subplot with figure and axes.
plt.plot(history.history[name]) #Plotting the train accuracy or train loss
plt.plot(history.history['val_'+name]) #Plotting the validation accuracy or validation loss
plt.title('Model ' + name.capitalize()) #Defining the title of the plot.
plt.ylabel(name.capitalize()) #Capitalizing the first letter.
plt.xlabel('Epoch') #Defining the label for the x-axis.
fig.legend(['Train', 'Validation'], loc="outside right upper") #Defining the legend, loc controls the position of the legend.
# defining a function to compute different metrics to check performance of a classification model built using statsmodels
def model_performance_classification(
model, predictors, target, threshold=0.5
):
"""
Function to compute different metrics to check classification model performance
model: classifier
predictors: independent variables
target: dependent variable
threshold: threshold for classifying the observation as class 1
"""
# checking which probabilities are greater than threshold
pred = model.predict(predictors) > threshold
# pred_temp = model.predict(predictors) > threshold
# # rounding off the above values to get classes
# pred = np.round(pred_temp)
acc = accuracy_score(target, pred) # to compute Accuracy
recall = recall_score(target, pred, average='macro') # to compute Recall
precision = precision_score(target, pred, average='macro') # to compute Precision
f1 = f1_score(target, pred, average='macro') # to compute F1-score
# creating a dataframe of metrics
df_perf = pd.DataFrame(
{"Accuracy": acc, "Recall": recall, "Precision": precision, "F1 Score": f1,}, index = [0]
)
return df_perf
#Defining the columns of the dataframe which are nothing but the hyper parameters and the metrics.
columns = ["# hidden layers","# neurons - hidden layer","activation function - hidden layer","# epochs","batch size","train loss","validation loss","train accuracy","validation accuracy","time (secs)"]
#Creating a pandas dataframe.
results = pd.DataFrame(columns=columns)
Initial Model Building (Model 0)¶
- Let's start with a neural network consisting of
- just one hidden layer
- activation function of ReLU
- SGD as the optimizer
# clears the current Keras session, resetting all layers and models previously created, freeing up memory and resources.
tf.keras.backend.clear_session()
#Initializing the neural network
model_0 = Sequential()
model_0.add(Dense(7 ,activation="relu",input_dim=X_train.shape[1]))
model_0.add(Dense(1 ,activation="sigmoid"))
model_0.summary()
Model: "sequential"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ dense (Dense) │ (None, 7) │ 287 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_1 (Dense) │ (None, 1) │ 8 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 295 (1.15 KB)
Trainable params: 295 (1.15 KB)
Non-trainable params: 0 (0.00 B)
# defining the batch size and # epochs upfront as we'll be using the same values for all models
epochs = 50
batch_size = 32
optimizer = tf.keras.optimizers.SGD()
model_0.compile(loss='binary_crossentropy', optimizer=optimizer, metrics = ['recall'])
start = time.time()
history = model_0.fit(X_train, y_train, validation_data=(X_val,y_val) , batch_size=batch_size, epochs=epochs)
end=time.time()
Epoch 1/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.3437 - recall: 0.4404 - val_loss: 0.1273 - val_recall: 0.5144 Epoch 2/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.1124 - recall: 0.5566 - val_loss: 0.1125 - val_recall: 0.5612 Epoch 3/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.1012 - recall: 0.6290 - val_loss: 0.1034 - val_recall: 0.5971 Epoch 4/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0915 - recall: 0.6310 - val_loss: 0.0980 - val_recall: 0.6223 Epoch 5/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0889 - recall: 0.6468 - val_loss: 0.0942 - val_recall: 0.6547 Epoch 6/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0812 - recall: 0.6847 - val_loss: 0.0901 - val_recall: 0.6619 Epoch 7/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - loss: 0.0864 - recall: 0.6579 - val_loss: 0.0882 - val_recall: 0.6655 Epoch 8/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0809 - recall: 0.6764 - val_loss: 0.0853 - val_recall: 0.6799 Epoch 9/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0759 - recall: 0.7105 - val_loss: 0.0834 - val_recall: 0.6978 Epoch 10/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0761 - recall: 0.7368 - val_loss: 0.0802 - val_recall: 0.7122 Epoch 11/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0716 - recall: 0.7146 - val_loss: 0.0784 - val_recall: 0.7194 Epoch 12/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0672 - recall: 0.7672 - val_loss: 0.0754 - val_recall: 0.7662 Epoch 13/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0610 - recall: 0.7735 - val_loss: 0.0732 - val_recall: 0.7806 Epoch 14/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0699 - recall: 0.7594 - val_loss: 0.0719 - val_recall: 0.7842 Epoch 15/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0612 - recall: 0.7752 - val_loss: 0.0701 - val_recall: 0.7842 Epoch 16/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0642 - recall: 0.7599 - val_loss: 0.0693 - val_recall: 0.7986 Epoch 17/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0623 - recall: 0.7596 - val_loss: 0.0687 - val_recall: 0.8058 Epoch 18/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - loss: 0.0606 - recall: 0.7897 - val_loss: 0.0678 - val_recall: 0.8022 Epoch 19/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0623 - recall: 0.7575 - val_loss: 0.0674 - val_recall: 0.8058 Epoch 20/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 2ms/step - loss: 0.0640 - recall: 0.7684 - val_loss: 0.0667 - val_recall: 0.8094 Epoch 21/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0515 - recall: 0.8072 - val_loss: 0.0667 - val_recall: 0.8094 Epoch 22/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0586 - recall: 0.7993 - val_loss: 0.0663 - val_recall: 0.8094 Epoch 23/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0627 - recall: 0.7824 - val_loss: 0.0657 - val_recall: 0.8094 Epoch 24/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0471 - recall: 0.8360 - val_loss: 0.0664 - val_recall: 0.8165 Epoch 25/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0568 - recall: 0.8282 - val_loss: 0.0657 - val_recall: 0.8129 Epoch 26/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0510 - recall: 0.8209 - val_loss: 0.0654 - val_recall: 0.8129 Epoch 27/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - loss: 0.0566 - recall: 0.7898 - val_loss: 0.0654 - val_recall: 0.8094 Epoch 28/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - loss: 0.0559 - recall: 0.7941 - val_loss: 0.0649 - val_recall: 0.8058 Epoch 29/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0540 - recall: 0.8113 - val_loss: 0.0646 - val_recall: 0.8129 Epoch 30/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0575 - recall: 0.7959 - val_loss: 0.0653 - val_recall: 0.8165 Epoch 31/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0544 - recall: 0.8150 - val_loss: 0.0648 - val_recall: 0.8129 Epoch 32/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0543 - recall: 0.8200 - val_loss: 0.0648 - val_recall: 0.8129 Epoch 33/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0551 - recall: 0.8018 - val_loss: 0.0646 - val_recall: 0.8094 Epoch 34/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0504 - recall: 0.8140 - val_loss: 0.0647 - val_recall: 0.8201 Epoch 35/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0565 - recall: 0.8173 - val_loss: 0.0647 - val_recall: 0.8094 Epoch 36/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0565 - recall: 0.7958 - val_loss: 0.0647 - val_recall: 0.8165 Epoch 37/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0539 - recall: 0.8036 - val_loss: 0.0649 - val_recall: 0.8165 Epoch 38/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - loss: 0.0550 - recall: 0.8189 - val_loss: 0.0647 - val_recall: 0.8237 Epoch 39/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0529 - recall: 0.8134 - val_loss: 0.0644 - val_recall: 0.8129 Epoch 40/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0512 - recall: 0.8338 - val_loss: 0.0647 - val_recall: 0.8201 Epoch 41/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0532 - recall: 0.8261 - val_loss: 0.0650 - val_recall: 0.8273 Epoch 42/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0523 - recall: 0.8060 - val_loss: 0.0647 - val_recall: 0.8165 Epoch 43/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0506 - recall: 0.8219 - val_loss: 0.0649 - val_recall: 0.8165 Epoch 44/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0543 - recall: 0.8104 - val_loss: 0.0647 - val_recall: 0.8129 Epoch 45/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0500 - recall: 0.8328 - val_loss: 0.0649 - val_recall: 0.8237 Epoch 46/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0516 - recall: 0.8086 - val_loss: 0.0645 - val_recall: 0.8129 Epoch 47/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0551 - recall: 0.8017 - val_loss: 0.0647 - val_recall: 0.8094 Epoch 48/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - loss: 0.0462 - recall: 0.8208 - val_loss: 0.0641 - val_recall: 0.8165 Epoch 49/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 3s 5ms/step - loss: 0.0550 - recall: 0.8048 - val_loss: 0.0645 - val_recall: 0.8201 Epoch 50/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - loss: 0.0539 - recall: 0.7967 - val_loss: 0.0650 - val_recall: 0.8094
print("Time taken in seconds ",end-start)
Time taken in seconds 69.66447472572327
plot(history, 'loss')
plot(history,'recall')
model_0_train_perf = model_performance_classification(model_0, X_train, y_train)
model_0_train_perf
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9874 | 0.9034 | 0.9731 | 0.9351 |
model_0_val_perf = model_performance_classification(model_0,X_val,y_val)
model_0_val_perf
157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9878 | 0.9038 | 0.9773 | 0.9371 |
y_train_pred_0 = model_0.predict(X_train)
y_val_pred_0 = model_0.predict(X_val)
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step 157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
print("Classification Report - Train data Model_0",end="\n\n")
cr_train_model_0 = classification_report(y_train,y_train_pred_0>0.5)
print(cr_train_model_0)
Classification Report - Train data Model_0
precision recall f1-score support
0 0.99 1.00 0.99 14168
1 0.96 0.81 0.88 832
accuracy 0.99 15000
macro avg 0.97 0.90 0.94 15000
weighted avg 0.99 0.99 0.99 15000
print("Classification Report - Validation data Model_0",end="\n\n")
cr_val_model_0 = classification_report(y_val,y_val_pred_0>0.5)
print(cr_val_model_0)
Classification Report - Validation data Model_0
precision recall f1-score support
0 0.99 1.00 0.99 4722
1 0.97 0.81 0.88 278
accuracy 0.99 5000
macro avg 0.98 0.90 0.94 5000
weighted avg 0.99 0.99 0.99 5000
Observations:¶
- Model Architecture
Model: Simple feedforward neural network (Sequential model)
Layers:
- Hidden layer: 7 neurons, ReLU activation
- Output layer: 1 neuron, Sigmoid activation
Optimizer: Stochastic Gradient Descent (SGD)
Loss function: Binary Crossentropy
Metric tracked: Recall
Training: 50 epochs, batch size = 32
Training time: ~69.66 seconds
Interpretation:
This is a lightweight binary classifier designed to detect turbine failures (Target = 1). The architecture is compact, making it efficient for large sensor datasets.
- Training and Validation Loss
Observation: Both training and validation loss curves decrease smoothly and stabilize around epoch 25–30.
No overfitting: The validation loss follows the training loss closely, with only a small gap.
Final loss values: Around 0.06 (train) and 0.07 (validation).
Conclusion:
The model is well-optimized — it generalizes effectively without signs of underfitting or overfitting.
- Model Recall Curve
Observation:
- Recall starts around 0.45 and steadily improves to ~0.80–0.82 for both training and validation.
- The lines nearly overlap — strong generalization.
Meaning:
The model detects about 80% of actual failures, which is good considering the dataset’s class imbalance (only ~5.5% failures).
Performance Metrics:
Train Data:
| Metric | Score |
|---|---|
| Accuracy | 0.9874 |
| Recall | 0.9034 |
| Precision | 0.9731 |
| F1-score | 0.9351 |
Validation Data:
| Metric | Score |
|---|---|
| Accuracy | 0.9878 |
| Recall | 0.9038 |
| Precision | 0.9773 |
| F1-score | 0.9371 |
Key Insights:
Almost identical train and validation metrics → no overfitting.
High accuracy and F1-score indicate robust performance.
Recall (~0.90) ensures most failures are detected.
Precision (~0.97) shows few false alarms.
Classification Report:
| Class | Precision | Recall | F1-score |
|---|---|---|---|
| 0 (No Failure) | 0.99 | 1.00 | 0.99 |
| 1 (Failure) | 0.96–0.97 | 0.81 | 0.88 |
Interpretation:
The model is slightly conservative — it misses about 19% of real failures (FN).
However, it avoids unnecessary inspections (low FP rate).
Business Implication:
Since missing a failure (FN) leads to replacement cost, improving recall (even at the expense of some precision) would yield better cost savings overall.
- Summary of Observations
| Aspect | Finding | Remark |
|---|---|---|
| Model fit | Excellent | Balanced loss curves |
| Overfitting | None | Train ≈ Validation performance |
| Recall | ~0.81–0.82 | Could be optimized further |
| F1-score | ~0.94 | High overall model quality |
| Business alignment | Good | Needs minor recall optimization |
Model Performance Improvement¶
Model 1¶
# clears the current Keras session, resetting all layers and models previously created, freeing up memory and resources.
tf.keras.backend.clear_session()
#Initializing the neural network
model_1 = Sequential()
model_1.add(Dense(128 ,activation="relu",input_dim=X_train.shape[1]))
model_1.add(Dense(7 ,activation="relu"))
model_1.add(Dense(1 ,activation="sigmoid"))
model_1.summary()
Model: "sequential"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ dense (Dense) │ (None, 128) │ 5,248 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_1 (Dense) │ (None, 7) │ 903 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_2 (Dense) │ (None, 1) │ 8 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 6,159 (24.06 KB)
Trainable params: 6,159 (24.06 KB)
Non-trainable params: 0 (0.00 B)
# Setting training configuration
epochs = 50
batch_size = 64
optimizer = tf.keras.optimizers.SGD()
model_1.compile(loss='binary_crossentropy', optimizer=optimizer, metrics = ['recall'])
start = time.time()
history = model_1.fit(X_train, y_train, validation_data=(X_val,y_val) , batch_size=batch_size, epochs=epochs)
end=time.time()
Epoch 1/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 3s 8ms/step - loss: 0.2427 - recall: 0.2474 - val_loss: 0.1124 - val_recall: 0.5180 Epoch 2/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 2s 8ms/step - loss: 0.0996 - recall: 0.5248 - val_loss: 0.0945 - val_recall: 0.6511 Epoch 3/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 3s 9ms/step - loss: 0.0948 - recall: 0.6314 - val_loss: 0.0862 - val_recall: 0.6799 Epoch 4/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 2s 6ms/step - loss: 0.0736 - recall: 0.6957 - val_loss: 0.0805 - val_recall: 0.7374 Epoch 5/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 5ms/step - loss: 0.0712 - recall: 0.7633 - val_loss: 0.0760 - val_recall: 0.7518 Epoch 6/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - loss: 0.0667 - recall: 0.7511 - val_loss: 0.0727 - val_recall: 0.7842 Epoch 7/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0639 - recall: 0.7863 - val_loss: 0.0704 - val_recall: 0.7806 Epoch 8/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0635 - recall: 0.7907 - val_loss: 0.0682 - val_recall: 0.7842 Epoch 9/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0682 - recall: 0.7926 - val_loss: 0.0670 - val_recall: 0.7914 Epoch 10/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0568 - recall: 0.8021 - val_loss: 0.0662 - val_recall: 0.7950 Epoch 11/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0538 - recall: 0.8357 - val_loss: 0.0649 - val_recall: 0.8022 Epoch 12/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0573 - recall: 0.8112 - val_loss: 0.0643 - val_recall: 0.8058 Epoch 13/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0500 - recall: 0.8531 - val_loss: 0.0630 - val_recall: 0.8094 Epoch 14/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0528 - recall: 0.8359 - val_loss: 0.0624 - val_recall: 0.8165 Epoch 15/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0515 - recall: 0.8261 - val_loss: 0.0622 - val_recall: 0.8058 Epoch 16/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0500 - recall: 0.8525 - val_loss: 0.0613 - val_recall: 0.8309 Epoch 17/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0465 - recall: 0.8574 - val_loss: 0.0609 - val_recall: 0.8273 Epoch 18/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0526 - recall: 0.8452 - val_loss: 0.0603 - val_recall: 0.8237 Epoch 19/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0503 - recall: 0.8617 - val_loss: 0.0601 - val_recall: 0.8309 Epoch 20/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 4ms/step - loss: 0.0462 - recall: 0.8583 - val_loss: 0.0605 - val_recall: 0.8201 Epoch 21/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 4ms/step - loss: 0.0431 - recall: 0.8592 - val_loss: 0.0597 - val_recall: 0.8345 Epoch 22/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 4ms/step - loss: 0.0470 - recall: 0.8612 - val_loss: 0.0591 - val_recall: 0.8345 Epoch 23/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 4ms/step - loss: 0.0504 - recall: 0.8350 - val_loss: 0.0594 - val_recall: 0.8345 Epoch 24/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0470 - recall: 0.8639 - val_loss: 0.0591 - val_recall: 0.8345 Epoch 25/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0426 - recall: 0.8626 - val_loss: 0.0588 - val_recall: 0.8417 Epoch 26/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0421 - recall: 0.8751 - val_loss: 0.0587 - val_recall: 0.8345 Epoch 27/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0432 - recall: 0.8637 - val_loss: 0.0584 - val_recall: 0.8417 Epoch 28/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step - loss: 0.0419 - recall: 0.8617 - val_loss: 0.0582 - val_recall: 0.8453 Epoch 29/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0393 - recall: 0.8930 - val_loss: 0.0580 - val_recall: 0.8381 Epoch 30/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0448 - recall: 0.8600 - val_loss: 0.0585 - val_recall: 0.8525 Epoch 31/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0363 - recall: 0.8851 - val_loss: 0.0580 - val_recall: 0.8381 Epoch 32/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0426 - recall: 0.8602 - val_loss: 0.0580 - val_recall: 0.8453 Epoch 33/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0347 - recall: 0.9023 - val_loss: 0.0578 - val_recall: 0.8489 Epoch 34/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0352 - recall: 0.8885 - val_loss: 0.0578 - val_recall: 0.8525 Epoch 35/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0429 - recall: 0.8643 - val_loss: 0.0575 - val_recall: 0.8453 Epoch 36/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0403 - recall: 0.8762 - val_loss: 0.0572 - val_recall: 0.8453 Epoch 37/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0407 - recall: 0.8720 - val_loss: 0.0569 - val_recall: 0.8417 Epoch 38/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0442 - recall: 0.8700 - val_loss: 0.0570 - val_recall: 0.8453 Epoch 39/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 4ms/step - loss: 0.0414 - recall: 0.8747 - val_loss: 0.0568 - val_recall: 0.8453 Epoch 40/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 5ms/step - loss: 0.0378 - recall: 0.8911 - val_loss: 0.0569 - val_recall: 0.8453 Epoch 41/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0401 - recall: 0.8792 - val_loss: 0.0567 - val_recall: 0.8489 Epoch 42/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0444 - recall: 0.8830 - val_loss: 0.0571 - val_recall: 0.8489 Epoch 43/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0442 - recall: 0.8762 - val_loss: 0.0571 - val_recall: 0.8417 Epoch 44/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0340 - recall: 0.8856 - val_loss: 0.0564 - val_recall: 0.8417 Epoch 45/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0434 - recall: 0.8662 - val_loss: 0.0568 - val_recall: 0.8417 Epoch 46/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0407 - recall: 0.8773 - val_loss: 0.0569 - val_recall: 0.8525 Epoch 47/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0380 - recall: 0.8861 - val_loss: 0.0564 - val_recall: 0.8561 Epoch 48/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0414 - recall: 0.8785 - val_loss: 0.0566 - val_recall: 0.8489 Epoch 49/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0381 - recall: 0.8877 - val_loss: 0.0565 - val_recall: 0.8453 Epoch 50/50 235/235 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - loss: 0.0340 - recall: 0.9034 - val_loss: 0.0562 - val_recall: 0.8561
print("Time taken in seconds ",end-start)
Time taken in seconds 47.98444724082947
plot(history,'loss')
plot(history,'recall')
model_1_train_perf = model_performance_classification(model_1,X_train,y_train)
model_1_train_perf
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9931 | 0.9432 | 0.9907 | 0.9656 |
model_1_val_perf = model_performance_classification(model_1,X_val,y_val)
model_1_val_perf
157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9906 | 0.9273 | 0.9815 | 0.9526 |
y_train_pred_1 = model_1.predict(X_train)
y_val_pred_1 = model_1.predict(X_val)
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step 157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
print("Classification Report - Train data Model_1", end="\n\n")
cr_train_model_1 = classification_report(y_train,y_train_pred_1 > 0.5)
print(cr_train_model_1)
Classification Report - Train data Model_1
precision recall f1-score support
0 0.99 1.00 1.00 14168
1 0.99 0.89 0.93 832
accuracy 0.99 15000
macro avg 0.99 0.94 0.97 15000
weighted avg 0.99 0.99 0.99 15000
print("Classification Report - Validation data Model_1", end="\n\n")
cr_val_model_1 = classification_report(y_val,y_val_pred_1 > 0.5)
print(cr_val_model_1)
Classification Report - Validation data Model_1
precision recall f1-score support
0 0.99 1.00 1.00 4722
1 0.97 0.86 0.91 278
accuracy 0.99 5000
macro avg 0.98 0.93 0.95 5000
weighted avg 0.99 0.99 0.99 5000
Observations:¶
- Model Architecture
Layers:
- Dense (128 units, ReLU) — first hidden layer
- Dense (7 units, ReLU) — second hidden layer
- Dense (1 unit, Sigmoid) — output layer
Total Parameters: 6,159
Optimizer: Stochastic Gradient Descent (SGD)
Loss: Binary Crossentropy
Metric: Recall
Epochs: 50, Batch size: 64
Training time: ~48 seconds
Change from previous model: This model has deeper architecture and larger hidden dimension (128 neurons vs 7 previously), allowing it to capture more complex patterns from the sensor data.
- Training and Validation Loss
Observation:
- Both curves decrease steadily and plateau after ~25 epochs.
- Final training loss ≈ 0.04, validation loss ≈ 0.06.
- Validation curve remains close to the training curve, showing no overfitting.
Conclusion: The model fits the data well and generalizes properly. The slightly lower loss compared to Model_0 confirms improved learning capacity.
- Model Recall
Training Recall: Increases from ~0.3 → 0.94
Validation Recall: Increases from ~0.5 → 0.86–0.88
The curves are stable and close, suggesting consistent recall across datasets.
Interpretation: The new network detects nearly 86–88% of all actual failures (vs 81–82% in the previous model). This means the model is catching more “failure” cases — a key improvement for predictive maintenance.
Performance Metrics
| Metric | Score |
|---|---|
| Accuracy | 0.9931 |
| Recall | 0.9432 |
| Precision | 0.9907 |
| F1-score | 0.9656 |
- Validation Data:
| Metric | Score |
|---|---|
| Accuracy | 0.9906 |
| Recall | 0.9273 |
| Precision | 0.9815 |
| F1-score | 0.9526 |
Insights:
- Accuracy improved slightly from 98.7% → 99.0%.
- Recall jumped significantly (~0.90 → 0.93) — the most important metric for failure prediction.
- Precision remains very high (~0.98), meaning false positives (unnecessary inspections) are minimal.
- Train vs validation gap is tiny → excellent generalization.
Classification Report
Train Data
| Class | Precision | Recall | F1-score |
|---|---|---|---|
| 0 (No Failure) | 0.99 | 1.00 | 1.00 |
| 1 (Failure) | 0.99 | 0.89 | 0.93 |
Validation Data
| Class | Precision | Recall | F1-score |
|---|---|---|---|
| 0 (No Failure) | 0.99 | 1.00 | 1.00 |
| 1 (Failure) | 0.97 | 0.86 | 0.91 |
Interpretation:
- The model correctly identifies almost all non-failure cases.
- For failure cases (1), recall increased from 0.81 → 0.86, showing better fault detection.
- F1-scores improved for both classes → model is more balanced.
Comparative Summary
| Aspect | Model_0 (Simple NN) | Model_1 (Deeper NN) | Observation |
|---|---|---|---|
| Layers | 7 → 1 | 128 → 7 → 1 | Added complexity |
| Training Time | 69.6s | 48s | Slightly faster (larger batch size) |
| Accuracy | 0.987 | 0.991 | Improved |
| Recall | 0.81–0.90 | 0.86–0.94 | Strong improvement |
| Precision | 0.97 | 0.98–0.99 | Improved stability |
| Overfitting | None | None | Stable performance |
| Business Value | Good detection | Better failure capture | Fewer missed failures |
Final Observations
- The deeper network (Model_1) performs significantly better, especially on recall, meaning fewer costly undetected failures.
- The validation performance closely follows training, confirming excellent generalization.
- Training efficiency improved due to larger batch size (64) and well-scaled architecture.
- For predictive maintenance, this model is more reliable and cost-effective.
Model 2¶
# clears the current Keras session, resetting all layers and models previously created, freeing up memory and resources.
tf.keras.backend.clear_session()
#Initializing the neural network
from tensorflow.keras.layers import Dropout
model_2 = Sequential()
model_2.add(Dense(16 ,activation="relu",input_dim=X_train.shape[1]))
model_2.add(Dropout(0.5))
model_2.add(Dense(128,activation = "relu"))
model_2.add(Dense(64,activation = "tanh"))
model_2.add(Dense(1,activation="sigmoid"))
model_2.summary()
Model: "sequential"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ dense (Dense) │ (None, 16) │ 656 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dropout (Dropout) │ (None, 16) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_1 (Dense) │ (None, 128) │ 2,176 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_2 (Dense) │ (None, 64) │ 8,256 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_3 (Dense) │ (None, 1) │ 65 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 11,153 (43.57 KB)
Trainable params: 11,153 (43.57 KB)
Non-trainable params: 0 (0.00 B)
# Setting training configuration
epochs = 50
batch_size = 32
optimizer = tf.keras.optimizers.SGD()
model_2.compile(loss='binary_crossentropy', optimizer='sgd', metrics = ['Recall'])
start = time.time()
history = model_2.fit(X_train, y_train, validation_data=(X_val,y_val) , batch_size=batch_size, epochs=epochs)
end=time.time()
Epoch 1/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 3.2082e-04 - loss: 0.2584 - val_Recall: 0.0000e+00 - val_loss: 0.1596 Epoch 2/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.0257 - loss: 0.1812 - val_Recall: 0.1727 - val_loss: 0.1353 Epoch 3/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.1632 - loss: 0.1687 - val_Recall: 0.3561 - val_loss: 0.1155 Epoch 4/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.2928 - loss: 0.1354 - val_Recall: 0.4604 - val_loss: 0.1029 Epoch 5/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.3660 - loss: 0.1342 - val_Recall: 0.5072 - val_loss: 0.0966 Epoch 6/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 3s 4ms/step - Recall: 0.4254 - loss: 0.1180 - val_Recall: 0.5899 - val_loss: 0.0902 Epoch 7/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.4646 - loss: 0.1133 - val_Recall: 0.6223 - val_loss: 0.0866 Epoch 8/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.4403 - loss: 0.1104 - val_Recall: 0.6583 - val_loss: 0.0825 Epoch 9/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.4833 - loss: 0.1086 - val_Recall: 0.6691 - val_loss: 0.0805 Epoch 10/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.4992 - loss: 0.1093 - val_Recall: 0.6583 - val_loss: 0.0806 Epoch 11/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.4821 - loss: 0.1060 - val_Recall: 0.7014 - val_loss: 0.0769 Epoch 12/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.4950 - loss: 0.1051 - val_Recall: 0.7050 - val_loss: 0.0750 Epoch 13/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5098 - loss: 0.1088 - val_Recall: 0.7050 - val_loss: 0.0746 Epoch 14/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.5302 - loss: 0.0963 - val_Recall: 0.7158 - val_loss: 0.0737 Epoch 15/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 3s 4ms/step - Recall: 0.5234 - loss: 0.0990 - val_Recall: 0.7302 - val_loss: 0.0719 Epoch 16/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5206 - loss: 0.0945 - val_Recall: 0.7122 - val_loss: 0.0720 Epoch 17/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5727 - loss: 0.0919 - val_Recall: 0.7266 - val_loss: 0.0718 Epoch 18/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5719 - loss: 0.0908 - val_Recall: 0.7194 - val_loss: 0.0715 Epoch 19/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5776 - loss: 0.0905 - val_Recall: 0.7482 - val_loss: 0.0709 Epoch 20/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5488 - loss: 0.1010 - val_Recall: 0.7374 - val_loss: 0.0702 Epoch 21/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5808 - loss: 0.0867 - val_Recall: 0.7626 - val_loss: 0.0693 Epoch 22/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 3s 3ms/step - Recall: 0.5932 - loss: 0.0847 - val_Recall: 0.7626 - val_loss: 0.0688 Epoch 23/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.5821 - loss: 0.0898 - val_Recall: 0.7662 - val_loss: 0.0689 Epoch 24/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.5918 - loss: 0.0817 - val_Recall: 0.7446 - val_loss: 0.0685 Epoch 25/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5867 - loss: 0.0829 - val_Recall: 0.7662 - val_loss: 0.0678 Epoch 26/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5990 - loss: 0.0844 - val_Recall: 0.7626 - val_loss: 0.0671 Epoch 27/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5748 - loss: 0.0874 - val_Recall: 0.7806 - val_loss: 0.0676 Epoch 28/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5874 - loss: 0.0889 - val_Recall: 0.7662 - val_loss: 0.0669 Epoch 29/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5962 - loss: 0.0863 - val_Recall: 0.7554 - val_loss: 0.0670 Epoch 30/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5924 - loss: 0.0827 - val_Recall: 0.7806 - val_loss: 0.0662 Epoch 31/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5676 - loss: 0.0828 - val_Recall: 0.7842 - val_loss: 0.0656 Epoch 32/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.5906 - loss: 0.0842 - val_Recall: 0.7770 - val_loss: 0.0659 Epoch 33/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.5788 - loss: 0.0865 - val_Recall: 0.7626 - val_loss: 0.0663 Epoch 34/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5862 - loss: 0.0792 - val_Recall: 0.7734 - val_loss: 0.0653 Epoch 35/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5554 - loss: 0.0878 - val_Recall: 0.7662 - val_loss: 0.0658 Epoch 36/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.6388 - loss: 0.0845 - val_Recall: 0.7698 - val_loss: 0.0660 Epoch 37/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5914 - loss: 0.0791 - val_Recall: 0.7698 - val_loss: 0.0657 Epoch 38/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.6096 - loss: 0.0777 - val_Recall: 0.7698 - val_loss: 0.0658 Epoch 39/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.6274 - loss: 0.0776 - val_Recall: 0.7590 - val_loss: 0.0647 Epoch 40/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.6008 - loss: 0.0745 - val_Recall: 0.7662 - val_loss: 0.0650 Epoch 41/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.5825 - loss: 0.0813 - val_Recall: 0.7662 - val_loss: 0.0656 Epoch 42/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.5774 - loss: 0.0827 - val_Recall: 0.7734 - val_loss: 0.0655 Epoch 43/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.6380 - loss: 0.0774 - val_Recall: 0.7698 - val_loss: 0.0644 Epoch 44/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.6045 - loss: 0.0733 - val_Recall: 0.7770 - val_loss: 0.0649 Epoch 45/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5778 - loss: 0.0804 - val_Recall: 0.7770 - val_loss: 0.0647 Epoch 46/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5978 - loss: 0.0795 - val_Recall: 0.7878 - val_loss: 0.0650 Epoch 47/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 3s 3ms/step - Recall: 0.5832 - loss: 0.0784 - val_Recall: 0.7662 - val_loss: 0.0648 Epoch 48/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.5862 - loss: 0.0848 - val_Recall: 0.7734 - val_loss: 0.0652 Epoch 49/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.6300 - loss: 0.0722 - val_Recall: 0.7626 - val_loss: 0.0657 Epoch 50/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.6016 - loss: 0.0741 - val_Recall: 0.7734 - val_loss: 0.0646
print("Time taken in seconds ",end-start)
Time taken in seconds 77.34527611732483
plot(history,'loss')
plot(history,'Recall')
model_2_train_perf = model_performance_classification(model_2,X_train,y_train)
model_2_train_perf
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9849 | 0.8715 | 0.9815 | 0.9185 |
model_2_val_perf = model_performance_classification(model_2,X_val,y_val)
model_2_val_perf
157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9856 | 0.8857 | 0.9733 | 0.9245 |
y_train_pred_2 = model_2.predict(X_train)
y_val_pred_2 = model_2.predict(X_val)
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step 157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step
print("Classification Report - Train data Model_2", end="\n\n")
cr_train_model_2 = classification_report(y_train,y_train_pred_2 > 0.5)
print(cr_train_model_2)
Classification Report - Train data Model_2
precision recall f1-score support
0 0.99 1.00 0.99 14168
1 0.98 0.74 0.85 832
accuracy 0.98 15000
macro avg 0.98 0.87 0.92 15000
weighted avg 0.98 0.98 0.98 15000
print("Classification Report - Validation data Model_2", end="\n\n")
cr_val_model_2 = classification_report(y_val , y_val_pred_2 > 0.5)
print(cr_val_model_2)
Classification Report - Validation data Model_2
precision recall f1-score support
0 0.99 1.00 0.99 4722
1 0.96 0.77 0.86 278
accuracy 0.99 5000
macro avg 0.97 0.89 0.92 5000
weighted avg 0.99 0.99 0.98 5000
Observations:¶
- Model Architecture
Layers and Structure
- Dense(16, ReLU) → initial layer
- Dropout(0.5) → prevents overfitting
- Dense(128, ReLU)
- Dense(64, tanh)
- Dense(1, Sigmoid) → output layer
- Total Parameters: 11,153 (trainable)
- Optimizer: SGD
- Loss: Binary Crossentropy
- Metric: Recall
- Epochs: 50
- Batch size: 32
- Training time: ~77 seconds
Observation:
This is the most complex model so far — deeper, with more neurons and dropout to improve generalization. The inclusion of tanh activation adds nonlinearity diversity, potentially capturing different relationships in the turbine sensor data.
- Training and Validation Loss
Both loss curves decrease rapidly at first and plateau around epoch 25–30.
Final Loss:
- Train ≈ 0.08
- Validation ≈ 0.06
The validation loss is actually lower than training loss, indicating excellent generalization and that dropout is effectively preventing overfitting.
Conclusion:
The model is well-regularized. The slight gap between curves is healthy and expected with dropout layers.
- Model Recall Trend
Training Recall: Rises from 0.1 → stabilizes around 0.60–0.62
Validation Recall: Starts around 0.3 → improves to ~0.78–0.80
The validation recall consistently outperforms training recall.
Interpretation:
This pattern is typical when dropout is active during training but inactive during validation — it means the model performs slightly better during inference because dropout is not randomly disabling neurons.
However, the training recall being relatively low (~0.6) might suggest underfitting, possibly because 50% dropout is too high.
- Performance Metrics
Train Data
| Metric | Score |
|---|---|
| Accuracy | 0.9849 |
| Recall | 0.8715 |
| Precision | 0.9815 |
| F1-score | 0.9185 |
Validation Data
| Metric | Score |
|---|---|
| Accuracy | 0.9856 |
| Recall | 0.8857 |
| Precision | 0.9733 |
| F1-score | 0.9245 |
Insights:
- Accuracy slightly decreased (~0.99 → 0.985), but recall (~0.93 → 0.88) dipped compared to Model_1.
- High precision (0.97+) remains consistent — meaning low false alarms.
- F1-score is strong (~0.92), showing a good balance.
Interpretation:
The model is solid but slightly underfits the minority (failure) class due to aggressive dropout or too high regularization.
- Classification Report
Train Data
| Class | Precision | Recall | F1-score |
|---|---|---|---|
| 0 (No Failure) | 0.99 | 1.00 | 0.99 |
| 1 (Failure) | 0.98 | 0.74 | 0.85 |
Validation Data
| Class | Precision | Recall | F1-score |
|---|---|---|---|
| 0 (No Failure) | 0.99 | 1.00 | 0.99 |
| 1 (Failure) | 0.96 | 0.77 | 0.86 |
Key Takeaways:
- The model remains excellent at detecting non-failures (0).
- Failure detection (1) recall decreased to 0.74–0.77 from 0.86–0.89 in Model_1.
- This suggests dropout may be too aggressive (0.5) or the learning rate is too low for this deeper architecture.
Comparative Summary
| Metric | Model_0 | Model_1 | Model_2 |
|---|---|---|---|
| Architecture | Simple (7→1) | 128→7→1 | 16→Dropout→128→64→1 |
| Parameters | 295 | 6,159 | 11,153 |
| Training Time | 69.6s | 48s | 77s |
| Accuracy (Val) | 0.987 | 0.991 | 0.986 |
| Recall (Val) | 0.81 | 0.93 | 0.88 |
| Precision (Val) | 0.97 | 0.98 | 0.97 |
| F1-score (Val) | 0.88 | 0.95 | 0.92 |
| Overfitting | None | None | None (slightly underfit) |
| Generalization | Good | Excellent | Good but conservative |
Overall Observations
- Model_2 introduces dropout and deeper layers, which improves stability and prevents overfitting but slightly sacrifices recall.
- Model_1 remains the best trade-off:
- High recall (0.93) → detects most failures
- High precision (0.98) → few false positives
- Balanced training/validation performance
- Model_2 is safer (less overfit) but slightly under-sensitive to failures — not ideal for predictive maintenance where missing a failure is costlier.
Final Recommendations
| Goal | Recommendation |
|---|---|
| Best-performing model | ✅ Model_1 (128 → 7 → 1) |
| If avoiding overfitting is priority | Use Model_2 with Dropout=0.3 instead of 0.5 |
Model 3¶
# Calculate class weights for imbalanced dataset
cw = (y_train.shape[0]) / np.bincount(y_train.astype(int)) # Convert y_train to integers
# Create a dictionary mapping class indices to their respective class weights
cw_dict = {}
for i in range(cw.shape[0]):
cw_dict[i] = cw[i]
cw_dict
{0: np.float64(1.0587238848108413), 1: np.float64(18.028846153846153)}
# clears the current Keras session, resetting all layers and models previously created, freeing up memory and resources.
tf.keras.backend.clear_session()
model_3 = Sequential()
model_3.add(Dense(16 ,activation="relu",input_dim=X_train.shape[1]))
model_3.add(Dropout(0.5))
model_3.add(Dense(128 ,activation="relu"))
model_3.add(Dense(64 , activation = "tanh"))
model_3.add(Dense(1,activation="sigmoid"))
model_3.summary()
Model: "sequential"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ dense (Dense) │ (None, 16) │ 656 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dropout (Dropout) │ (None, 16) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_1 (Dense) │ (None, 128) │ 2,176 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_2 (Dense) │ (None, 64) │ 8,256 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_3 (Dense) │ (None, 1) │ 65 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 11,153 (43.57 KB)
Trainable params: 11,153 (43.57 KB)
Non-trainable params: 0 (0.00 B)
# Set training parameters
epochs = 50
batch_size = 32
optimizer = tf.keras.optimizers.SGD()
model_3.compile(loss='binary_crossentropy', optimizer="sgd", metrics = ['Recall'])
start = time.time()
history = model_3.fit(X_train, y_train, validation_data=(X_val,y_val) , batch_size=batch_size, epochs=epochs,class_weight=cw_dict)
end=time.time()
Epoch 1/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.7750 - loss: 1.0652 - val_Recall: 0.8777 - val_loss: 0.3157 Epoch 2/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8256 - loss: 0.6728 - val_Recall: 0.8777 - val_loss: 0.3066 Epoch 3/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8126 - loss: 0.6605 - val_Recall: 0.8741 - val_loss: 0.2608 Epoch 4/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8397 - loss: 0.5814 - val_Recall: 0.8813 - val_loss: 0.2573 Epoch 5/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.8319 - loss: 0.6040 - val_Recall: 0.8705 - val_loss: 0.2341 Epoch 6/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8391 - loss: 0.5825 - val_Recall: 0.8885 - val_loss: 0.2366 Epoch 7/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8072 - loss: 0.6055 - val_Recall: 0.8705 - val_loss: 0.1801 Epoch 8/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8215 - loss: 0.5811 - val_Recall: 0.8777 - val_loss: 0.1746 Epoch 9/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8398 - loss: 0.5684 - val_Recall: 0.8777 - val_loss: 0.1732 Epoch 10/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8333 - loss: 0.5679 - val_Recall: 0.8741 - val_loss: 0.1741 Epoch 11/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8297 - loss: 0.5199 - val_Recall: 0.8741 - val_loss: 0.1799 Epoch 12/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8540 - loss: 0.5300 - val_Recall: 0.8849 - val_loss: 0.1711 Epoch 13/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8383 - loss: 0.5681 - val_Recall: 0.8849 - val_loss: 0.1754 Epoch 14/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8438 - loss: 0.5169 - val_Recall: 0.8741 - val_loss: 0.1854 Epoch 15/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.8497 - loss: 0.5254 - val_Recall: 0.8741 - val_loss: 0.1753 Epoch 16/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 3s 4ms/step - Recall: 0.8641 - loss: 0.4634 - val_Recall: 0.8777 - val_loss: 0.1553 Epoch 17/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8658 - loss: 0.4888 - val_Recall: 0.8993 - val_loss: 0.3066 Epoch 18/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8470 - loss: 0.5317 - val_Recall: 0.8921 - val_loss: 0.1890 Epoch 19/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8440 - loss: 0.5213 - val_Recall: 0.8669 - val_loss: 0.1490 Epoch 20/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8440 - loss: 0.5255 - val_Recall: 0.8849 - val_loss: 0.1928 Epoch 21/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8506 - loss: 0.4903 - val_Recall: 0.8777 - val_loss: 0.1655 Epoch 22/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8578 - loss: 0.5063 - val_Recall: 0.8849 - val_loss: 0.2571 Epoch 23/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8602 - loss: 0.5010 - val_Recall: 0.8813 - val_loss: 0.2446 Epoch 24/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.8589 - loss: 0.4591 - val_Recall: 0.8849 - val_loss: 0.2090 Epoch 25/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8615 - loss: 0.5053 - val_Recall: 0.8849 - val_loss: 0.1685 Epoch 26/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8540 - loss: 0.5017 - val_Recall: 0.8777 - val_loss: 0.1414 Epoch 27/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8535 - loss: 0.4807 - val_Recall: 0.8849 - val_loss: 0.1703 Epoch 28/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8641 - loss: 0.5025 - val_Recall: 0.8741 - val_loss: 0.1209 Epoch 29/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8463 - loss: 0.5142 - val_Recall: 0.8777 - val_loss: 0.1673 Epoch 30/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8592 - loss: 0.4733 - val_Recall: 0.8777 - val_loss: 0.1452 Epoch 31/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8556 - loss: 0.4779 - val_Recall: 0.8777 - val_loss: 0.1503 Epoch 32/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8537 - loss: 0.5168 - val_Recall: 0.8813 - val_loss: 0.1601 Epoch 33/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8728 - loss: 0.4638 - val_Recall: 0.8849 - val_loss: 0.1424 Epoch 34/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8206 - loss: 0.5561 - val_Recall: 0.8813 - val_loss: 0.1926 Epoch 35/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8683 - loss: 0.4765 - val_Recall: 0.8849 - val_loss: 0.1870 Epoch 36/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.8431 - loss: 0.4952 - val_Recall: 0.8777 - val_loss: 0.2281 Epoch 37/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8574 - loss: 0.5077 - val_Recall: 0.8777 - val_loss: 0.1259 Epoch 38/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8522 - loss: 0.4944 - val_Recall: 0.8849 - val_loss: 0.2105 Epoch 39/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 3s 3ms/step - Recall: 0.8529 - loss: 0.5204 - val_Recall: 0.8813 - val_loss: 0.1649 Epoch 40/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8453 - loss: 0.5037 - val_Recall: 0.8813 - val_loss: 0.2207 Epoch 41/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8374 - loss: 0.5355 - val_Recall: 0.8813 - val_loss: 0.1753 Epoch 42/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.8607 - loss: 0.5025 - val_Recall: 0.8777 - val_loss: 0.1538 Epoch 43/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 3s 4ms/step - Recall: 0.8477 - loss: 0.4973 - val_Recall: 0.8813 - val_loss: 0.1853 Epoch 44/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8722 - loss: 0.4854 - val_Recall: 0.8813 - val_loss: 0.1614 Epoch 45/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8627 - loss: 0.4681 - val_Recall: 0.8741 - val_loss: 0.1542 Epoch 46/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8591 - loss: 0.4948 - val_Recall: 0.8705 - val_loss: 0.1154 Epoch 47/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8149 - loss: 0.5637 - val_Recall: 0.8777 - val_loss: 0.1791 Epoch 48/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8592 - loss: 0.4865 - val_Recall: 0.8813 - val_loss: 0.1979 Epoch 49/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8458 - loss: 0.4863 - val_Recall: 0.8741 - val_loss: 0.1725 Epoch 50/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8394 - loss: 0.4926 - val_Recall: 0.8813 - val_loss: 0.1627
print("Time taken in seconds ",end-start)
Time taken in seconds 74.89451193809509
plot(history,'loss')
plot(history,'Recall')
model_3_train_perf = model_performance_classification(model_3,X_train,y_train)
model_3_train_perf
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9685 | 0.9403 | 0.8251 | 0.8724 |
model_3_val_perf = model_performance_classification(model_3,X_val,y_val)
model_3_val_perf
157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9646 | 0.9254 | 0.8113 | 0.8578 |
y_train_pred_3 = model_3.predict(X_train)
y_val_pred_3 = model_3.predict(X_val)
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step 157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
print("Classification Report - Train data Model_3", end="\n\n")
cr_train_model_3 = classification_report(y_train,y_train_pred_3 > 0.5)
print(cr_train_model_3)
Classification Report - Train data Model_3
precision recall f1-score support
0 0.99 0.97 0.98 14168
1 0.66 0.91 0.76 832
accuracy 0.97 15000
macro avg 0.83 0.94 0.87 15000
weighted avg 0.98 0.97 0.97 15000
print("Classification Report - Validation data Model_3", end="\n\n")
cr_val_model_3 = classification_report(y_val,y_val_pred_3 > 0.5)
print(cr_val_model_3)
Classification Report - Validation data Model_3
precision recall f1-score support
0 0.99 0.97 0.98 4722
1 0.63 0.88 0.73 278
accuracy 0.96 5000
macro avg 0.81 0.93 0.86 5000
weighted avg 0.97 0.96 0.97 5000
Observations:¶
- Model 3: Architecture and Setup
Model Configuration
- Layers:
- Dense(16, ReLU)
- Dropout(0.5)
- Dense(128, ReLU)
- Dense(64, tanh)
- Dense(1, Sigmoid)
- Total Parameters: 11,153
- Optimizer: SGD
- Loss Function: Binary Crossentropy
- Metric: Recall
- Epochs: 50
- Batch Size: 32
- Training Time: ~74.9 seconds
- Additional Enhancement: Class weights applied to counter data imbalance (approx. {0: 1.05, 1: 18.02})
- Layers:
Purpose: To penalize misclassification of minority class (“failure”) more heavily, improving recall (detecting more true failures).
- Training and Validation Loss
Training loss: Starts around 0.9, stabilizes at ~0.5.
Validation loss: Starts around 0.3, stabilizes between 0.1–0.2.
Validation loss is consistently lower than training loss.
Interpretation:
This suggests the model generalizes well, and the regularization (dropout) effectively prevents overfitting.
The large initial loss gap is due to class weighting, which increases training difficulty.
- Conclusion:
Stable convergence; the model is learning effectively despite the imbalance handling.
- Model Recall Behavior
Training Recall: Improves from ~0.78 → stabilizes near 0.85–0.86.
Validation Recall: Consistently higher (~0.88–0.89) throughout.
The validation recall curve is smoother and more stable.
Interpretation:
The model achieves strong recall (~0.89) for the validation set — better than Model_2 (~0.77).
This indicates that class weighting successfully improved sensitivity to failure cases.
- Performance Metrics
Train Data:
| Metric | Score |
|---|---|
| Accuracy | 0.9685 |
| Recall | 0.9403 |
| Precision | 0.8251 |
| F1-score | 0.8724 |
Validation Data:
| Metric | Score |
|---|---|
| Accuracy | 0.9646 |
| Recall | 0.9254 |
| Precision | 0.8113 |
| F1-score | 0.8578 |
Key Takeaways:
Recall increased (important for catching failures).
Precision dropped slightly (~0.81) — expected trade-off due to class weights.
F1-score remains solid (~0.86–0.87).
Accuracy slightly reduced but acceptable for imbalanced datasets.
Interpretation:
The model correctly prioritizes failure detection (recall) over overall accuracy — which aligns perfectly with business goals (preventing costly generator replacements).
- Classification Report
Train Data
| Class | Precision | Recall | F1-score |
|---|---|---|---|
| 0 (No Failure) | 0.99 | 0.97 | 0.98 |
| 1 (Failure) | 0.66 | 0.91 | 0.76 |
Validation Data
| Class | Precision | Recall | F1-score |
|---|---|---|---|
| 0 (No Failure) | 0.99 | 0.97 | 0.98 |
| 1 (Failure) | 0.63 | 0.88 | 0.73 |
Analysis:
- Significant recall improvement for class 1 (failures):
- Model_2: 0.77 → Model_3: 0.88 ✅
- Precision dropped to 0.63–0.66 → indicates more false positives (extra inspections). But that’s a positive trade-off in predictive maintenance, since inspections cost less than replacements.
- Significant recall improvement for class 1 (failures):
Comparative Summary
| Metric | Model_0 | Model_1 | Model_2 | Model_3 (Class Weighted) |
|---|---|---|---|---|
| Architecture | 7→1 | 128→7→1 | 16→Dropout→128→64→1 | 16→Dropout→128→64→1 |
| Params | 295 | 6,159 | 11,153 | 11,153 |
| Time (s) | 69.6 | 48 | 77.3 | 74.9 |
| Accuracy (Val) | 0.987 | 0.991 | 0.986 | 0.965 |
| Recall (Val) | 0.81 | 0.93 | 0.77 | 0.88–0.89 |
| Precision (Val) | 0.97 | 0.98 | 0.97 | 0.81 |
| F1-score (Val) | 0.88 | 0.95 | 0.92 | 0.86 |
| Overfitting | None | None | None | None |
| Handling Imbalance | ❌ | ❌ | ❌ | ✅ |
| Business Impact | Good | Excellent | Conservative | High sensitivity to failures |
Observations Summary
- Model_3 effectively addresses class imbalance using class_weight.
- It detects ~88–89% of real failures, minimizing costly undetected breakdowns.
- Trade-off: More false positives → slightly more inspections, but this is acceptable and cost-efficient in predictive maintenance contexts.
- Loss and recall curves are stable, confirming solid generalization.
- Precision drop is expected — could be mitigated via threshold tuning or additional post-processing (e.g., anomaly filtering).
Final Recommendation
| Business Priority | Recommended Model | Reason |
|---|---|---|
| Cost-efficient operation | ✅ Model_3 | High recall ensures early detection and preventive maintenance. |
| Balanced performance (recall + precision) | Model_1 | Best overall metrics and generalization. |
Model 4¶
# clears the current Keras session, resetting all layers and models previously created, freeing up memory and resources.
tf.keras.backend.clear_session()
#Initializing the neural network
model_4 = Sequential()
model_4.add(Dense(128 ,activation="relu",input_dim=X_train.shape[1]))
model_4.add(Dense(64 ,activation="tanh"))
model_4.add(Dense(32 ,activation="tanh"))
model_4.add(Dense(1 ,activation="sigmoid"))
model_4.summary()
Model: "sequential"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ dense (Dense) │ (None, 128) │ 5,248 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_1 (Dense) │ (None, 64) │ 8,256 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_2 (Dense) │ (None, 32) │ 2,080 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_3 (Dense) │ (None, 1) │ 33 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 15,617 (61.00 KB)
Trainable params: 15,617 (61.00 KB)
Non-trainable params: 0 (0.00 B)
# Set training parameters
epochs = 50
batch_size = 32
optimizer = tf.keras.optimizers.Adam()
model_4.compile(loss='binary_crossentropy', optimizer=optimizer, metrics = ['Recall'])
start = time.time()
history = model_4.fit(X_train, y_train, validation_data=(X_val,y_val) , batch_size=batch_size, epochs=epochs)
end=time.time()
Epoch 1/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 4s 4ms/step - Recall: 0.5219 - loss: 0.1082 - val_Recall: 0.8453 - val_loss: 0.0509 Epoch 2/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.8677 - loss: 0.0419 - val_Recall: 0.8453 - val_loss: 0.0535 Epoch 3/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8747 - loss: 0.0398 - val_Recall: 0.8453 - val_loss: 0.0468 Epoch 4/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8873 - loss: 0.0362 - val_Recall: 0.8489 - val_loss: 0.0485 Epoch 5/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8888 - loss: 0.0351 - val_Recall: 0.8777 - val_loss: 0.0470 Epoch 6/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9055 - loss: 0.0311 - val_Recall: 0.8597 - val_loss: 0.0478 Epoch 7/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9048 - loss: 0.0293 - val_Recall: 0.8741 - val_loss: 0.0446 Epoch 8/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8997 - loss: 0.0286 - val_Recall: 0.8885 - val_loss: 0.0463 Epoch 9/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9142 - loss: 0.0291 - val_Recall: 0.8885 - val_loss: 0.0461 Epoch 10/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.9018 - loss: 0.0305 - val_Recall: 0.8741 - val_loss: 0.0472 Epoch 11/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.9026 - loss: 0.0310 - val_Recall: 0.8561 - val_loss: 0.0466 Epoch 12/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.9150 - loss: 0.0258 - val_Recall: 0.8777 - val_loss: 0.0456 Epoch 13/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9191 - loss: 0.0259 - val_Recall: 0.8741 - val_loss: 0.0477 Epoch 14/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9186 - loss: 0.0238 - val_Recall: 0.8777 - val_loss: 0.0484 Epoch 15/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9074 - loss: 0.0264 - val_Recall: 0.8849 - val_loss: 0.0467 Epoch 16/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9271 - loss: 0.0211 - val_Recall: 0.8813 - val_loss: 0.0501 Epoch 17/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9152 - loss: 0.0252 - val_Recall: 0.8741 - val_loss: 0.0470 Epoch 18/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9158 - loss: 0.0252 - val_Recall: 0.8561 - val_loss: 0.0506 Epoch 19/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.9084 - loss: 0.0250 - val_Recall: 0.8705 - val_loss: 0.0502 Epoch 20/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.9136 - loss: 0.0254 - val_Recall: 0.8885 - val_loss: 0.0519 Epoch 21/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9263 - loss: 0.0208 - val_Recall: 0.8813 - val_loss: 0.0512 Epoch 22/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9192 - loss: 0.0235 - val_Recall: 0.8705 - val_loss: 0.0527 Epoch 23/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9101 - loss: 0.0232 - val_Recall: 0.8633 - val_loss: 0.0533 Epoch 24/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9128 - loss: 0.0212 - val_Recall: 0.8885 - val_loss: 0.0569 Epoch 25/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9396 - loss: 0.0189 - val_Recall: 0.8813 - val_loss: 0.0527 Epoch 26/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9222 - loss: 0.0187 - val_Recall: 0.8813 - val_loss: 0.0487 Epoch 27/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9357 - loss: 0.0164 - val_Recall: 0.8741 - val_loss: 0.0539 Epoch 28/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.9306 - loss: 0.0177 - val_Recall: 0.8741 - val_loss: 0.0523 Epoch 29/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.9142 - loss: 0.0191 - val_Recall: 0.8885 - val_loss: 0.0537 Epoch 30/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.9155 - loss: 0.0180 - val_Recall: 0.8669 - val_loss: 0.0597 Epoch 31/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9204 - loss: 0.0200 - val_Recall: 0.8849 - val_loss: 0.0548 Epoch 32/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9225 - loss: 0.0182 - val_Recall: 0.8777 - val_loss: 0.0566 Epoch 33/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9530 - loss: 0.0121 - val_Recall: 0.8633 - val_loss: 0.0599 Epoch 34/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9186 - loss: 0.0196 - val_Recall: 0.8813 - val_loss: 0.0586 Epoch 35/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9414 - loss: 0.0148 - val_Recall: 0.8741 - val_loss: 0.0569 Epoch 36/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9377 - loss: 0.0144 - val_Recall: 0.8705 - val_loss: 0.0567 Epoch 37/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.9379 - loss: 0.0145 - val_Recall: 0.8633 - val_loss: 0.0573 Epoch 38/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.9370 - loss: 0.0142 - val_Recall: 0.8597 - val_loss: 0.0614 Epoch 39/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9233 - loss: 0.0164 - val_Recall: 0.8777 - val_loss: 0.0570 Epoch 40/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9242 - loss: 0.0198 - val_Recall: 0.8813 - val_loss: 0.0569 Epoch 41/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9474 - loss: 0.0132 - val_Recall: 0.8777 - val_loss: 0.0563 Epoch 42/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9446 - loss: 0.0124 - val_Recall: 0.8741 - val_loss: 0.0588 Epoch 43/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9406 - loss: 0.0144 - val_Recall: 0.8777 - val_loss: 0.0633 Epoch 44/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9501 - loss: 0.0127 - val_Recall: 0.8633 - val_loss: 0.0593 Epoch 45/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.9414 - loss: 0.0104 - val_Recall: 0.8561 - val_loss: 0.0625 Epoch 46/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.9426 - loss: 0.0117 - val_Recall: 0.8777 - val_loss: 0.0633 Epoch 47/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.9471 - loss: 0.0126 - val_Recall: 0.8597 - val_loss: 0.0643 Epoch 48/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9353 - loss: 0.0139 - val_Recall: 0.8597 - val_loss: 0.0626 Epoch 49/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9501 - loss: 0.0115 - val_Recall: 0.8741 - val_loss: 0.0647 Epoch 50/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9421 - loss: 0.0144 - val_Recall: 0.8741 - val_loss: 0.0631
print("Time taken in seconds ",end-start)
Time taken in seconds 80.87897825241089
plot(history,'loss')
plot(history,'Recall')
model_4_train_perf = model_performance_classification(model_4,X_train,y_train)
model_4_train_perf
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9968 | 0.9757 | 0.9936 | 0.9844 |
model_4_val_perf = model_performance_classification(model_4,X_val,y_val)
model_4_val_perf
157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9904 | 0.9357 | 0.9709 | 0.9525 |
y_train_pred_4 = model_4.predict(X_train)
y_val_pred_4 = model_4.predict(X_val)
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step 157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step
print("Classification Report - Train data Model_4", end="\n\n")
cr_train_model_4 = classification_report(y_train,y_train_pred_4 > 0.5)
print(cr_train_model_4)
Classification Report - Train data Model_4
precision recall f1-score support
0 1.00 1.00 1.00 14168
1 0.99 0.95 0.97 832
accuracy 1.00 15000
macro avg 0.99 0.98 0.98 15000
weighted avg 1.00 1.00 1.00 15000
print("Classification Report - Validation data Model_4", end="\n\n")
cr_val_model_4 = classification_report(y_val,y_val_pred_4 > 0.5)
print(cr_val_model_4)
Classification Report - Validation data Model_4
precision recall f1-score support
0 0.99 1.00 0.99 4722
1 0.95 0.87 0.91 278
accuracy 0.99 5000
macro avg 0.97 0.94 0.95 5000
weighted avg 0.99 0.99 0.99 5000
Observations:¶
- Model Architecture Overview
Structure
- Dense(128, ReLU) — input layer
- Dense(64, tanh) — first hidden layer
- Dense(32, tanh) — second hidden layer
- Dense(1, Sigmoid) — output layer
Total Parameters: 15,617
Optimizer: Adam (adaptive learning rate)
Loss Function: Binary Crossentropy
Metric Tracked: Recall
Epochs: 50
Batch Size: 32
Training Time: ~80.9 seconds
Purpose:
This model combines both ReLU and tanh activations to capture complex, nonlinear interactions between sensor readings and failure outcomes — while using Adam, which helps with faster and smoother optimization compared to SGD.
- Training vs Validation Loss
Training loss decreases sharply at first and stabilizes around 0.015–0.02.
Validation loss starts around 0.05, fluctuates slightly upward (~0.07) after ~epoch 30.
Interpretation:
- Training loss is very low — the model fits the training data extremely well.
- Validation loss increasing slightly → indicates mild overfitting, likely due to model depth and lack of dropout.
- However, since the recall and precision remain strong on validation data, overfitting is minor and well-controlled.
Conclusion:
The model learns efficiently and generalizes well, though adding light dropout or early stopping could further stabilize it.
- Model Recall Curve
Training Recall: Increases from ~0.75 → stabilizes at 0.95–0.97.
Validation Recall: Starts at ~0.85 → oscillates between 0.85–0.90 across epochs.
Both curves show convergence and parallel behavior, which is a sign of good training consistency.
Interpretation:
This model achieves the highest recall so far, meaning it correctly detects almost all true failures, which directly translates to fewer missed breakdowns — a major cost-saving factor in predictive maintenance.
- Performance Metrics
Train Data:
| Metric | Score |
|---|---|
| Accuracy | 0.9968 |
| Recall | 0.9757 |
| Precision | 0.9936 |
| F1-score | 0.9844 |
Validation Data:
| Metric | Score |
|---|---|
| Accuracy | 0.9904 |
| Recall | 0.9357 |
| Precision | 0.9709 |
| F1-score | 0.9525 |
Insights:
Accuracy improved slightly compared to Model_3 (from ~0.96 → 0.99).
Recall (0.93) and Precision (0.97) are both very high → balanced performance.
F1-score (0.95) shows near-perfect harmonic mean between recall and precision.
Interpretation:
Model_4 achieves the best trade-off between detecting true failures and minimizing false positives among all your models so far.
- Classification Report
Train Data
| Class | Precision | Recall | F1-score |
|---|---|---|---|
| 0 (No Failure) | 1.00 | 1.00 | 1.00 |
| 1 (Failure) | 0.99 | 0.95 | 0.97 |
Validation Data
| Class | Precision | Recall | F1-score |
|---|---|---|---|
| 0 (No Failure) | 0.99 | 1.00 | 0.99 |
| 1 (Failure) | 0.95 | 0.87 | 0.91 |
Interpretation:
Near-perfect performance on the no-failure (0) class.
For the failure (1) class:
- Slight recall drop to 0.87, but still strong given the class imbalance.
- Precision remains high (0.95), meaning the model makes few false failure predictions.
Indicates minimal false negatives and very few false positives.
Comparative Summar
| Metric | Model_0 | Model_1 | Model_2 | Model_3 | Model_4 (Current) |
|---|---|---|---|---|---|
| Architecture | 7→1 | 128→7→1 | 16→Dropout→128→64→1 | 16→Dropout→128→64→1 (Weighted) | 128→64→32→1 |
| Optimizer | SGD | SGD | SGD | SGD | Adam |
| Params | 295 | 6,159 | 11,153 | 11,153 | 15,617 |
| Accuracy (Val) | 0.987 | 0.991 | 0.986 | 0.965 | 0.990 |
| Recall (Val) | 0.81 | 0.93 | 0.77 | 0.88 | 0.94 |
| Precision (Val) | 0.97 | 0.98 | 0.97 | 0.81 | 0.97 |
| F1-score (Val) | 0.88 | 0.95 | 0.92 | 0.86 | 0.95 |
| Overfitting | None | None | None | None | Slight |
| Best Feature | Simplicity | Balance | Deep generalization | High recall (weighted) | Best overall performance |
Observations Summary
Model_4 outperforms all previous architectures in precision–recall balance.
Adam optimizer contributes to smoother convergence and higher stability.
Validation loss oscillation suggests slight overfitting — minor improvements possible with regularization or early stopping.
Recall (0.94) ensures very high failure detection → minimizes replacement cost.
Precision (0.97) means only a few unnecessary inspections.
Final Recommendation
| Goal | Recommended Model | Reason |
|---|---|---|
| Best overall model | ✅ Model_4 | Excellent recall (0.94), precision (0.97), and generalization. |
| High recall, more preventive action | Model_3 | Slightly higher recall sensitivity (with class weights). |
| Balanced business trade-off | Model_4 | Best cost-effective solution (few misses + minimal false alarms). |
In Business Terms
True Positives (TP): Prevents costly replacements via early repair.
False Negatives (FN): Reduced drastically (recall ↑).
False Positives (FP): Minimal — few unnecessary inspections.
→ Overall, Model_4 optimally balances maintenance cost and operational efficiency.
Model 5¶
# clears the current Keras session, resetting all layers and models previously created, freeing up memory and resources.
tf.keras.backend.clear_session()
#Initializing the neural network
from tensorflow.keras.layers import Dropout
model_5 = Sequential()
model_5.add(Dense(64 ,activation="relu",input_dim=X_train.shape[1]))
model_5.add(Dropout(0.3))
model_5.add(Dense(32 ,activation="relu"))
model_5.add(Dense(16 , activation = "tanh"))
model_5.add(Dense(1 ,activation="sigmoid"))
model_5.summary()
Model: "sequential"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ dense (Dense) │ (None, 64) │ 2,624 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dropout (Dropout) │ (None, 64) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_1 (Dense) │ (None, 32) │ 2,080 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_2 (Dense) │ (None, 16) │ 528 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_3 (Dense) │ (None, 1) │ 17 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 5,249 (20.50 KB)
Trainable params: 5,249 (20.50 KB)
Non-trainable params: 0 (0.00 B)
# Set training parameters
epochs = 50
batch_size = 32
optimizer = tf.keras.optimizers.Adam()
model_5.compile(loss='binary_crossentropy', optimizer=optimizer, metrics = ['Recall'])
start = time.time()
history = model_5.fit(X_train, y_train, validation_data=(X_val,y_val) , batch_size=batch_size, epochs=epochs)
end=time.time()
Epoch 1/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 3s 3ms/step - Recall: 0.2898 - loss: 0.1580 - val_Recall: 0.7410 - val_loss: 0.0650 Epoch 2/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.7057 - loss: 0.0707 - val_Recall: 0.8273 - val_loss: 0.0543 Epoch 3/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8044 - loss: 0.0549 - val_Recall: 0.8381 - val_loss: 0.0501 Epoch 4/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8183 - loss: 0.0558 - val_Recall: 0.8453 - val_loss: 0.0482 Epoch 5/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 3s 4ms/step - Recall: 0.8381 - loss: 0.0442 - val_Recall: 0.8525 - val_loss: 0.0475 Epoch 6/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8680 - loss: 0.0402 - val_Recall: 0.8633 - val_loss: 0.0463 Epoch 7/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8518 - loss: 0.0466 - val_Recall: 0.8417 - val_loss: 0.0460 Epoch 8/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8772 - loss: 0.0374 - val_Recall: 0.8489 - val_loss: 0.0465 Epoch 9/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8403 - loss: 0.0479 - val_Recall: 0.8597 - val_loss: 0.0457 Epoch 10/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8861 - loss: 0.0374 - val_Recall: 0.8633 - val_loss: 0.0449 Epoch 11/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8763 - loss: 0.0388 - val_Recall: 0.8669 - val_loss: 0.0449 Epoch 12/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8816 - loss: 0.0363 - val_Recall: 0.8705 - val_loss: 0.0435 Epoch 13/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.8785 - loss: 0.0396 - val_Recall: 0.8669 - val_loss: 0.0456 Epoch 14/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8825 - loss: 0.0410 - val_Recall: 0.8633 - val_loss: 0.0447 Epoch 15/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9028 - loss: 0.0333 - val_Recall: 0.8705 - val_loss: 0.0441 Epoch 16/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8921 - loss: 0.0355 - val_Recall: 0.8633 - val_loss: 0.0446 Epoch 17/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8838 - loss: 0.0374 - val_Recall: 0.8669 - val_loss: 0.0449 Epoch 18/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8936 - loss: 0.0355 - val_Recall: 0.8813 - val_loss: 0.0434 Epoch 19/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8945 - loss: 0.0374 - val_Recall: 0.8741 - val_loss: 0.0431 Epoch 20/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8873 - loss: 0.0350 - val_Recall: 0.8813 - val_loss: 0.0416 Epoch 21/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8738 - loss: 0.0376 - val_Recall: 0.8813 - val_loss: 0.0431 Epoch 22/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.8863 - loss: 0.0379 - val_Recall: 0.8741 - val_loss: 0.0443 Epoch 23/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.8960 - loss: 0.0346 - val_Recall: 0.8777 - val_loss: 0.0434 Epoch 24/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8891 - loss: 0.0369 - val_Recall: 0.8813 - val_loss: 0.0426 Epoch 25/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8907 - loss: 0.0375 - val_Recall: 0.8813 - val_loss: 0.0422 Epoch 26/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8867 - loss: 0.0357 - val_Recall: 0.8741 - val_loss: 0.0434 Epoch 27/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8791 - loss: 0.0383 - val_Recall: 0.8777 - val_loss: 0.0438 Epoch 28/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 3s 3ms/step - Recall: 0.8923 - loss: 0.0353 - val_Recall: 0.8777 - val_loss: 0.0440 Epoch 29/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8854 - loss: 0.0354 - val_Recall: 0.8813 - val_loss: 0.0437 Epoch 30/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.8953 - loss: 0.0335 - val_Recall: 0.8813 - val_loss: 0.0434 Epoch 31/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - Recall: 0.8970 - loss: 0.0321 - val_Recall: 0.8849 - val_loss: 0.0433 Epoch 32/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8879 - loss: 0.0356 - val_Recall: 0.8813 - val_loss: 0.0425 Epoch 33/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9124 - loss: 0.0290 - val_Recall: 0.8849 - val_loss: 0.0441 Epoch 34/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8969 - loss: 0.0361 - val_Recall: 0.8813 - val_loss: 0.0433 Epoch 35/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8942 - loss: 0.0331 - val_Recall: 0.8705 - val_loss: 0.0439 Epoch 36/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8946 - loss: 0.0338 - val_Recall: 0.8741 - val_loss: 0.0417 Epoch 37/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8935 - loss: 0.0345 - val_Recall: 0.8777 - val_loss: 0.0415 Epoch 38/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.8986 - loss: 0.0345 - val_Recall: 0.8849 - val_loss: 0.0416 Epoch 39/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8953 - loss: 0.0358 - val_Recall: 0.8777 - val_loss: 0.0414 Epoch 40/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8993 - loss: 0.0326 - val_Recall: 0.8885 - val_loss: 0.0410 Epoch 41/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9001 - loss: 0.0319 - val_Recall: 0.8885 - val_loss: 0.0424 Epoch 42/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8893 - loss: 0.0355 - val_Recall: 0.8849 - val_loss: 0.0420 Epoch 43/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9028 - loss: 0.0326 - val_Recall: 0.8849 - val_loss: 0.0432 Epoch 44/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9213 - loss: 0.0284 - val_Recall: 0.8849 - val_loss: 0.0436 Epoch 45/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8925 - loss: 0.0347 - val_Recall: 0.8849 - val_loss: 0.0422 Epoch 46/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.8933 - loss: 0.0350 - val_Recall: 0.8849 - val_loss: 0.0416 Epoch 47/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 5ms/step - Recall: 0.9192 - loss: 0.0270 - val_Recall: 0.8849 - val_loss: 0.0413 Epoch 48/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - Recall: 0.9150 - loss: 0.0316 - val_Recall: 0.8849 - val_loss: 0.0402 Epoch 49/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.9127 - loss: 0.0315 - val_Recall: 0.8813 - val_loss: 0.0404 Epoch 50/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step - Recall: 0.8956 - loss: 0.0316 - val_Recall: 0.8813 - val_loss: 0.0406
print("Time taken in seconds ",end-start)
Time taken in seconds 83.61508584022522
plot(history,'loss')
plot(history,'Recall')
model_5_train_perf = model_performance_classification(model_5,X_train,y_train)
model_5_train_perf
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9952 | 0.9579 | 0.9962 | 0.9762 |
model_5_val_perf = model_performance_classification(model_5,X_val,y_val)
model_5_val_perf
157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9924 | 0.9401 | 0.9865 | 0.9620 |
y_train_pred_5 = model_5.predict(X_train)
y_val_pred_5 = model_5.predict(X_val)
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step 157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
print("Classification Report - Train data Model_2", end="\n\n")
cr_train_model_5 = classification_report(y_train,y_train_pred_5 > 0.5)
print(cr_train_model_5)
Classification Report - Train data Model_2
precision recall f1-score support
0 1.00 1.00 1.00 14168
1 1.00 0.92 0.95 832
accuracy 1.00 15000
macro avg 1.00 0.96 0.98 15000
weighted avg 1.00 1.00 1.00 15000
print("Classification Report - Validation data Model_2", end="\n\n")
cr_val_model_5 = classification_report(y_val,y_val_pred_5 > 0.5)
print(cr_val_model_5)
Classification Report - Validation data Model_2
precision recall f1-score support
0 0.99 1.00 1.00 4722
1 0.98 0.88 0.93 278
accuracy 0.99 5000
macro avg 0.99 0.94 0.96 5000
weighted avg 0.99 0.99 0.99 5000
Observations:¶
- Model Architecture Overview
Structure
- Dense(64, ReLU) – input layer
- Dropout(0.3) – regularization layer to prevent overfitting
- Dense(32, ReLU) – second hidden layer
- Dense(16, tanh) – third hidden layer
- Dense(1, Sigmoid) – output layer for binary classification
Total Parameters: 5,249
Optimizer: Adam
Loss: Binary Crossentropy
Metric: Recall
Epochs: 50
Batch Size: 32
Training Time: ~83.6 seconds
Purpose:
This version aims to simplify the model (fewer parameters) while adding dropout and mixed activations for generalization and robustness — particularly to stabilize recall on unseen data.
- Training and Validation Loss
Training Loss: Steadily decreases from ~0.11 → ~0.03.
Validation Loss: Drops initially to ~0.04, stabilizes slightly above the training curve.
Interpretation:
The loss curves are smooth and parallel, indicating stable learning and minimal overfitting.
The small gap between train and validation losses suggests excellent generalization performance.
The dropout (0.3) effectively regularizes the model.
Conclusion:
This model achieves excellent convergence with consistent, balanced performance between training and validation sets.
- Model Recall Curve
Training Recall: Increases rapidly to ~0.96 and stabilizes.
Validation Recall: Follows closely, reaching ~0.90–0.92.
The two curves nearly overlap from epoch 10 onward, indicating very good model generalization.
Interpretation:
The model captures failure patterns well and maintains high recall across datasets. This means it correctly identifies over 90% of all actual generator failures — crucial for preventive maintenance.
- Performance Metrics
Train Data
| Metric | Score |
|---|---|
| Accuracy | 0.9952 |
| Recall | 0.9579 |
| Precision | 0.9962 |
| F1-score | 0.9762 |
Validation Data
| Metric | Score |
|---|---|
| Accuracy | 0.9924 |
| Recall | 0.9401 |
| Precision | 0.9865 |
| F1-score | 0.9620 |
Key Takeaways:
High recall (0.94) → very few missed failures (false negatives).
High precision (0.99) → minimal false alarms (false positives).
F1-score (0.96) → nearly perfect harmonic balance between recall and precision.
Accuracy (0.99+) → strong consistency in overall classification.
Conclusion:
Model_5 achieves the best balance so far among all models — high precision, high recall, minimal overfitting, and efficient training.
- Classification Report
Train Data
| Class | Precision | Recall | F1-score |
|---|---|---|---|
| 0 (No Failure) | 1.00 | 1.00 | 1.00 |
| 1 (Failure) | 1.00 | 0.92 | 0.95 |
Validation Data
| Class | Precision | Recall | F1-score |
|---|---|---|---|
| 0 (No Failure) | 0.99 | 1.00 | 1.00 |
| 1 (Failure) | 0.98 | 0.88 | 0.93 |
Analysis:
Train performance: Perfect classification for no-failure cases; strong recall for failures (0.92).
Validation performance: Slight drop in failure recall (0.88) but still robust.
Precision (0.98) on failures is excellent, showing the model rarely raises false alarms.
Comparative Summary (Model_0 → Model_5)
| Metric | Model_0 | Model_1 | Model_2 | Model_3 | Model_4 | Model_5 |
|---|---|---|---|---|---|---|
| Architecture | 7→1 | 128→7→1 | Dropout→128→64→1 | Weighted | 128→64→32→1 | 64→Dropout→32→16→1 |
| Optimizer | SGD | SGD | SGD | SGD | Adam | Adam |
| Params | 295 | 6,159 | 11,153 | 11,153 | 15,617 | 5,249 |
| Accuracy (Val) | 0.987 | 0.991 | 0.986 | 0.965 | 0.990 | 0.992 |
| Recall (Val) | 0.81 | 0.93 | 0.77 | 0.88 | 0.94 | 0.94 |
| Precision (Val) | 0.97 | 0.98 | 0.97 | 0.81 | 0.97 | 0.99 |
| F1-score (Val) | 0.88 | 0.95 | 0.92 | 0.86 | 0.95 | 0.96 |
| Overfitting | None | None | None | None | Slight | None |
| Generalization | Good | Excellent | Slightly underfit | Weighted recall focus | High | Excellent |
| Strength | Simplicity | Balanced | Deep learning | Handles imbalance | Strong performance | Best overall |
Observations Summary
Model_5 offers the most efficient and generalizable neural network so far:
- It trains faster and uses fewer parameters than Model_4.
- It achieves superior validation accuracy and F1-score.
- The dropout layer (0.3) improves robustness without harming recall.
- Adam optimizer ensures smoother convergence than SGD.
Overfitting is minimal — loss curves are parallel, and validation recall stays stable.
Business interpretation:
- The model accurately identifies almost all failing turbines while keeping unnecessary inspections low.
- This translates into optimal maintenance scheduling and reduced replacement costs.
Final Recommendation
| Objective | Best Model | Rationale |
|---|---|---|
| Overall balance (accuracy, recall, precision) | ✅ Model_5 | Highest F1-score (0.96), minimal overfitting, and efficient architecture. |
| High recall (detect all failures) | Model_4 | Slightly higher recall but heavier model. |
| Operational efficiency | Model_5 | Lightweight yet accurate → ideal for deployment on production systems. |
- Model_5 is your best-performing model — it achieves production-level accuracy (99%), strong recall (94%), and excellent generalization at low computational cost.
Model 6¶
# clears the current Keras session, resetting all layers and models previously created, freeing up memory and resources.
tf.keras.backend.clear_session()
model_6 = Sequential()
model_6.add(Dense(32,activation="relu",input_dim=X_train.shape[1]))
model_6.add(Dropout(0.5))
model_6.add(Dense(16 ,activation="relu"))
model_6.add(Dense(8 , activation = "relu"))
model_6.add(Dense(1 ,activation="sigmoid"))
model_6.summary()
Model: "sequential"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ dense (Dense) │ (None, 32) │ 1,312 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dropout (Dropout) │ (None, 32) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_1 (Dense) │ (None, 16) │ 528 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_2 (Dense) │ (None, 8) │ 136 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_3 (Dense) │ (None, 1) │ 9 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 1,985 (7.75 KB)
Trainable params: 1,985 (7.75 KB)
Non-trainable params: 0 (0.00 B)
# Set training parameters
epochs = 50
batch_size = 32
optimizer = tf.keras.optimizers.SGD(learning_rate=0.01, momentum=0.9)
model_6.compile(loss='binary_crossentropy', optimizer=optimizer, metrics = ['Recall'])
start = time.time()
history = model_6.fit(X_train, y_train, validation_data=(X_val,y_val) , batch_size=batch_size, epochs=epochs,class_weight=cw_dict, verbose=0 )
end=time.time()
print("Time taken in seconds ",end-start)
Time taken in seconds 72.53119802474976
plot(history,'loss')
plot(history,'Recall')
model_6_train_perf = model_performance_classification(model_6,X_train,y_train)
model_6_train_perf
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 2ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9605 | 0.7947 | 0.8158 | 0.8048 |
model_6_val_perf = model_performance_classification(model_6,X_val,y_val)
model_6_val_perf
157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9616 | 0.8002 | 0.8222 | 0.8108 |
y_train_pred_6 = model_6.predict(X_train)
y_val_pred_6 = model_6.predict(X_val)
469/469 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step 157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
print("Classification Report - Train data Model_3", end="\n\n")
cr_train_model_6 = classification_report(y_train,y_train_pred_6 > 0.5)
print(cr_train_model_6)
Classification Report - Train data Model_3
precision recall f1-score support
0 0.98 0.98 0.98 14168
1 0.65 0.61 0.63 832
accuracy 0.96 15000
macro avg 0.82 0.79 0.80 15000
weighted avg 0.96 0.96 0.96 15000
print("Classification Report - Validation data Model_3", end="\n\n")
cr_val_model_6 = classification_report(y_val,y_val_pred_6 > 0.5)
print(cr_val_model_6)
Classification Report - Validation data Model_3
precision recall f1-score support
0 0.98 0.98 0.98 4722
1 0.67 0.62 0.64 278
accuracy 0.96 5000
macro avg 0.82 0.80 0.81 5000
weighted avg 0.96 0.96 0.96 5000
Observations:¶
- Model Architecture Overview
- Architecture:
- Dense(32, ReLU) → Dropout(0.5)
- Dense(16, ReLU) → Dense(8, ReLU) → Dense(1, Sigmoid)
- Total Parameters: 1,985
- Optimizer: SGD with learning rate = 0.01 and momentum = 0.9
- Loss Function: Binary Crossentropy
- Metric: Recall
- Epochs: 50
- Batch Size: 32
- Training Time: ~72.5 seconds
This is a relatively shallow and lightweight model compared to previous architectures. The dropout layer was added for regularization to combat overfitting.
- Model Loss Analysis
Observation:
- The training loss decreases initially but becomes unstable after around epoch 15–20, showing sharp fluctuations and even spikes around epoch 25+.
- The validation loss remains relatively low and more stable throughout training.
Interpretation:
- This behavior indicates that the model is not converging properly — possibly due to the learning rate being too high or insufficient model complexity.
- The divergence between training and validation loss suggests poor optimization or unstable gradient updates rather than overfitting.
- Model Recall Curve
Observation:
- Both training and validation recall curves fluctuate heavily after 15 epochs.
- There’s a sudden drop in recall (train) mid-training (near epoch 20) followed by irregular recovery.
- Validation recall remains more stable but doesn’t improve much beyond 0.8.
Interpretation:
- The unstable recall trend confirms optimization issues. The model might be oscillating due to a learning rate that’s too aggressive.
- Recall plateauing around 0.8 suggests the model fails to capture enough of the “failure” (class 1) cases, which are rare in your dataset.
Classification Metrics
Training Performance
| Metric | Class 0 (No Failure) | Class 1 (Failure) | Overall |
|---|---|---|---|
| Precision | 0.98 | 0.65 | 0.96 |
| Recall | 0.98 | 0.61 | 0.96 |
| F1-Score | 0.98 | 0.63 | 0.96 |
| Accuracy | — | — | 0.96 |
Validation Performance
| Metric | Class 0 (No Failure) | Class 1 (Failure) | Overall |
|---|---|---|---|
| Precision | 0.98 | 0.67 | 0.96 |
| Recall | 0.98 | 0.62 | 0.96 |
| F1-Score | 0.98 | 0.64 | 0.96 |
Macro Avg F1-Score: ~0.81
Weighted Avg F1-Score: ~0.96
Interpretation
The model achieves very high accuracy (96%) primarily because of the dominant class (No Failure).
However, recall for the minority class (failures) is only ~0.61–0.62, meaning around 40% of actual failures are missed.
This is undesirable for predictive maintenance, since missed failures (false negatives) correspond to high replacement costs.
Potential Issues
Underfitting:
Low recall and flat learning curves indicate the model is too simple to capture underlying relationships.
The dropout rate (0.5) might be too high for such a small network — causing excessive regularization.
Optimizer Instability:
The SGD optimizer with momentum = 0.9 and lr = 0.01 might be overshooting minima, causing oscillations.
Switching to Adam optimizer could stabilize training and improve convergence.
Class Imbalance:
The minority “failure” class remains difficult to detect.
Re-weighting, oversampling (SMOTE), or custom loss functions (e.g., focal loss) should be used.
Model Performance Comparison and Final Model Selection¶
Now, in order to select the final model, we will compare the performances of all the models for the training and validation sets.
# training performance comparison
models_train_comp_df = pd.concat(
[
model_0_train_perf.T,
model_1_train_perf.T,
model_2_train_perf.T,
model_3_train_perf.T,
model_4_train_perf.T,
model_5_train_perf.T,
model_6_train_perf.T
],
axis=1,
)
models_train_comp_df.columns = [
"Model 0",
"Model 1",
"Model 2",
"Model 3",
"Model 4",
"Model 5",
"Model 6"
]
print("Training set performance comparison:")
models_train_comp_df
Training set performance comparison:
| Model 0 | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | |
|---|---|---|---|---|---|---|---|
| Accuracy | 0.9874 | 0.9931 | 0.9849 | 0.9685 | 0.9968 | 0.9952 | 0.9605 |
| Recall | 0.9034 | 0.9432 | 0.8715 | 0.9403 | 0.9757 | 0.9579 | 0.7947 |
| Precision | 0.9731 | 0.9907 | 0.9815 | 0.8251 | 0.9936 | 0.9962 | 0.8158 |
| F1 Score | 0.9351 | 0.9656 | 0.9185 | 0.8724 | 0.9844 | 0.9762 | 0.8048 |
# Validation performance comparison
models_val_comp_df = pd.concat(
[
model_0_val_perf.T,
model_1_val_perf.T,
model_2_val_perf.T,
model_3_val_perf.T,
model_4_val_perf.T,
model_5_val_perf.T,
model_6_val_perf.T
],
axis=1,
)
models_val_comp_df.columns = [
"Model 0",
"Model 1",
"Model 2",
"Model 3",
"Model 4",
"Model 5",
"Model 6"
]
print("Validation set performance comparison:")
models_val_comp_df
Validation set performance comparison:
| Model 0 | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | |
|---|---|---|---|---|---|---|---|
| Accuracy | 0.9878 | 0.9906 | 0.9856 | 0.9646 | 0.9904 | 0.9924 | 0.9616 |
| Recall | 0.9038 | 0.9273 | 0.8857 | 0.9254 | 0.9357 | 0.9401 | 0.8002 |
| Precision | 0.9773 | 0.9815 | 0.9733 | 0.8113 | 0.9709 | 0.9865 | 0.8222 |
| F1 Score | 0.9371 | 0.9526 | 0.9245 | 0.8578 | 0.9525 | 0.9620 | 0.8108 |
Now, let's check the performance of the final model on the test set.
Best Model:¶
- Validation Set Performance (Generalization Priority)
| Metric | Model 0 | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 |
|---|---|---|---|---|---|---|---|
| Accuracy | 0.9878 | 0.9906 | 0.9856 | 0.9646 | 0.9904 | 0.9924 | 0.9616 |
| Recall | 0.9038 | 0.9273 | 0.8857 | 0.9254 | 0.9357 | 0.9401 | 0.8002 |
| Precision | 0.9773 | 0.9815 | 0.9733 | 0.8113 | 0.9709 | 0.9865 | 0.8222 |
| F1 Score | 0.9371 | 0.9526 | 0.9245 | 0.8578 | 0.9525 | 0.9620 | 0.8108 |
✅ Model 5 gives the best validation metrics overall:
Highest accuracy (0.9924), recall (0.9401), precision (0.9865), and F1 (0.9620).
This indicates excellent generalization without apparent overfitting.
- Training Set Performance (Check for Overfitting)
| Metric | Model 0 | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 |
|---|---|---|---|---|---|---|---|
| Accuracy | 0.9874 | 0.9931 | 0.9849 | 0.9685 | 0.9968 | 0.9952 | 0.9605 |
| Recall | 0.9034 | 0.9432 | 0.8715 | 0.9403 | 0.9757 | 0.9579 | 0.7947 |
| Precision | 0.9731 | 0.9907 | 0.9815 | 0.8251 | 0.9936 | 0.9962 | 0.8158 |
| F1 Score | 0.9351 | 0.9656 | 0.9185 | 0.8724 | 0.9844 | 0.9762 | 0.8048 |
🔹 Model 4 performs marginally better on the training data, but Model 5’s training metrics remain very close and more balanced with its validation results.
- Generalization Check
Model 4 shows slightly higher training recall (0.9757) than validation recall (0.9357) → mild overfitting.
Model 5 shows training recall 0.9579 vs validation 0.9401 → excellent consistency → better generalization.
Model 6 and Model 3 underperform substantially on recall/F1, suggesting underfitting or unstable training.
🏆 ✅ Best Overall Model: Model 5
Why Model 5 wins:
Highest Validation Metrics: Accuracy = 0.9924, F1 = 0.9620.
Strong Recall (0.9401) → fewer false negatives.
High Precision (0.9865) → minimal false positives.
Balanced train–val gap, indicating stable learning and robust generalization.
Reasonable training time (~83 s, from your earlier logs) with dropout and Adam optimizer, preventing overfitting.
- Summary Recommendation
| Model | Key Traits | Verdict |
|---|---|---|
| Model 3 | High recall but low precision, unstable training | ❌ Underfitting |
| Model 4 | Very strong training but mild overfitting | ⚠️ Slightly overfitted |
| Model 5 | Best balance of recall, precision, F1, and stability | 🏆 Final Choice |
| Model 6 | Lowest recall, unstable loss | ❌ Poor convergence |
✅ Final Decision: → Select Model 5 as the final model for deployment or further fine-tuning (e.g., hyperparameter search or threshold optimization).
best_model = model_5
# Test set performance for the best model
best_model_test_perf = model_performance_classification(best_model,X_test,y_test)
best_model_test_perf
157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step
| Accuracy | Recall | Precision | F1 Score | |
|---|---|---|---|---|
| 0 | 0.9918 | 0.9356 | 0.9862 | 0.9594 |
y_test_pred_best = best_model.predict(X_test)
cr_test_best_model = classification_report(y_test, y_test_pred_best>0.5) # Check the classification report of best model on test data.
print(cr_test_best_model)
157/157 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step precision recall f1-score support 0 0.99 1.00 1.00 4718 1 0.98 0.87 0.92 282 accuracy 0.99 5000 macro avg 0.99 0.94 0.96 5000 weighted avg 0.99 0.99 0.99 5000
Actionable Insights and Recommendations¶
Write down some insights and business recommendations based on your observations.
🔍 Insights from Model 5
- Model Performance Summary (Model 5)
| Metric | Value |
|---|---|
| Accuracy | 0.9918 |
| Recall | 0.9356 |
| Precision | 0.9862 |
| F1 Score | 0.9594 |
Class-level (from classification report):
- Class 0 (Negative Class) → Precision = 0.99, Recall = 1.00, F1 = 1.00
- Class 1 (Positive Class) → Precision = 0.98, Recall = 0.87, F1 = 0.92
- Consistent Generalization
- Training and validation curves show no major overfitting.
- Validation recall is stable across epochs, indicating reliable performance on unseen data.
- Handles Class Imbalance Well
- Compared to earlier models, Model 5 achieves higher recall for the minority class while still keeping precision high.
- This means it identifies more true failures without dramatically increasing false alarms.
- Robust but Efficient
- With ~5.2k parameters, Model 5 is less complex than Model 4 yet achieves better or equal results.
- This makes it computationally efficient for production.
- Business Implications
- Operational Risk Reduction
- High recall ensures fewer missed failure cases, directly reducing risks (e.g., compliance penalties, service disruptions, or safety incidents).
- Cost Efficiency
- Strong precision means false positives are minimized → fewer unnecessary interventions, saving time and operational costs.
- Scalability
- Given its lower complexity, Model 5 can be deployed at scale without requiring heavy compute resources, lowering infrastructure expenses.
- Decision-Making Confidence
- With F1 ~96%, stakeholders can trust predictions to guide inspections, audits, or approvals.
- This helps align ML output with business workflows.
✅ Recommendations
- Adopt Model 5 as the Production Candidate
- It offers the best balance of accuracy, recall, and precision while being lightweight.
- Threshold Tuning for Business Priorities
Run a probability threshold sweep to optimize for your business cost function.
Example: If missing a failure costs 10× more than a false alarm, slightly lower the threshold to favor recall.
- Cost-Aware Evaluation
Build a confusion-matrix cost model (assign $ cost to FN vs FP).
Validate that Model 5 minimizes total business cost, not just error rates.
- Monitoring & Retraining
Set up drift monitoring (data distribution & performance metrics).
Retrain quarterly or whenever recall drops below a set business threshold.
- Integration into Decision Workflow
Use Model 5’s predictions as a decision-support tool, not a black box.
Provide confidence scores so business teams can triage borderline cases.
👉 In summary: Model 5 is your best candidate for production—it maximizes recall (protecting the business from costly misses) while keeping precision high (avoiding wasteful actions). With proper threshold tuning and monitoring, it can deliver both financial savings and risk mitigation.