Contents<\/span><\/h2>\n<\/section>\n\n\n- Application type<\/a>.<\/li>\n
- Data set<\/a>.<\/li>\n
- Neural network<\/a>.<\/li>\n
- Training strategy<\/a>.<\/li>\n
- Testing analysis<\/a>.<\/li>\n
- Model deployment<\/a>.<\/li>\n<\/ol>\n<\/section>\n
\n1. Application type<\/h2>\n
We will predict the bearing status in the air compressor system, a binary variable (0 or 1). Therefore, this is a classification<\/a> project.<\/p>\nThe goal here is to model the bearings’ status based on the features of the air compressor system for its subsequent use in predictive maintenance.<\/p>\n<\/section>\n\n2. Data set<\/h2>\n
For this study, we use a specialized dataset of air compressor systems to train a neural network for predictive maintenance.<\/p>\n
The dataset includes key parameters, such as motor RPM, power, torque, outlet pressure, and oil pump power, which capture the system’s operating conditions.<\/p>\n
It defines four possible targets\u2014Bearings Status, Water Pump Status, Radiator Status, and Exhaust Valve Status.<\/p>\n
In this work, we focus on predicting the Bearings’ Status, though the same method can be applied to the other components.<\/p>\n
The first step involves preparing the data set<\/a>, which serves as the primary source of information for the problem.<\/p>\nThere are three main components to configure:<\/p>\n
\n- Data source.<\/li>\n
- Variables.<\/li>\n
- Instances.<\/li>\n<\/ul>\n
Data source<\/h3>\n
The data file air_compressor_maintenance.csv<\/a> contains the information for the air compressor example.<\/p>\nThis dataset comprises measurements taken from a compressor system supplying air to a factory production line, with a total of 17 features collected.<\/p>\n
The dataset comprises 17 variables (columns) and 1000 instances (rows).<\/p>\n
Variables<\/h3>\n
The features or variables<\/a> included in the dataset are as follows:<\/p>\nCompressor and motor variables<\/h4>\n<\/section>\n\n- RPM<\/strong> \u2013 Rotations per minute of the motor.<\/li>\n
- Motor Power<\/strong> \u2013 Electric motor power consumption (kW).<\/li>\n
- Torque<\/strong> \u2013 Torque produced by the motor (Nm).<\/li>\n
- Outlet Pressure Bar<\/strong> \u2013 Compressed air outlet pressure (bar).<\/li>\n
- Air Flow<\/strong> \u2013 Compressed air flow rate (m\u00b3\/min).<\/li>\n
- Noise dB<\/strong> \u2013 Noise level of the compressor (dB).<\/li>\n
- Outlet Temp<\/strong> \u2013 Outlet temperature of compressed air (\u00b0C).<\/li>\n<\/ul>\n
Cooling water system variables<\/h4>\n\n- Water Pump Outlet Pressure<\/strong> \u2013 Outlet pressure of the water pump (bar).<\/li>\n
- Water Inlet Temp<\/strong> \u2013 Inlet temperature of cooling water (\u00b0C).<\/li>\n
- Water Outlet Temp<\/strong> \u2013 Outlet temperature of cooling water (\u00b0C).<\/li>\n
- Water Pump Power<\/strong> \u2013 Water pump power consumption (kW).<\/li>\n
- Water Flow<\/strong> \u2013 Cooling water flow rate (m\u00b3\/min).<\/li>\n<\/ul>\n
Oil system variables<\/h4>\n\n- Oil Pump Power<\/strong> \u2013 Oil pump power consumption (kW).<\/li>\n
- Oil Tank Temp<\/strong> \u2013 Oil tank temperature (\u00b0C).<\/li>\n<\/ul>\n
Vibration and acceleration variables<\/h4>\n\n- Ground Acceleration<\/strong> \u2013 Acceleration at the compressor\u2019s mounting point (X, Y, Z in m\/s\u00b2).<\/li>\n
- Head Acceleration<\/strong> \u2013 Acceleration at the compressor head bolt or cooling fin (X, Y, Z in g).<\/li>\n<\/ul>\n
Condition monitoring<\/h4>\n\n- Bearings Status<\/strong> \u2013 Condition of the bearings: Ok<\/em> (normal) or Noise<\/em> (possible wear\/damage).<\/li>\n<\/ul>\n
All variables in the study are inputs, except for the chosen target variable, Bearings Status, which is the output we aim to extract for this machine learning study.<\/p>\n
However, if desired, the same methodology could be applied to the other three target variables: Water Pump Status, Radiator Status, and Exhaust Valve Status.<\/p>\n\nInstances<\/h3>\n
The instances<\/a> are divided into training, selection, and testing subsets.<\/p>\nThey represent a certain percentage of the original instances and are randomly split.<\/p>\n
The exact percentages depend on the chosen data split approach.<\/p>\n
Variables distributions<\/h3>\n
We can perform a few related analytics once the data set has been set.<\/p>\n
First, we check the provided information and ensure the data is of high quality.<\/p>\n
The data distributions<\/a> show the bearing condition percentages.<\/p>\n![\"\"](\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2024\/02\/bearings-pie-chart.png\")
<\/p>\n
Please note that the actual distributions may vary depending on the nature of the data collected in the air compressor dataset.<\/p>\n
Input-target correlations<\/h3>\n
The input-target correlations<\/a> may indicate which factors strongly influence the status of the motor and compressor system bearings.<\/p>\n![\"\"](\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2023\/08\/bearings-Pearson-correlations-chart.png\")
<\/p>\n
From the chart, we can identify which features have a significant influence on bearing conditions.<\/p>\n
This information can help us better understand the relationships between the variables and the target in the predictive maintenance study.<\/p>\n<\/section>\n\n3. Neural network<\/h2>\n
The second step is to\u00a0select a\u00a0neural network<\/a> that represents<\/span>\u00a0the classification function.
\nFor classification problems, it is composed of:<\/p>\n\n- A scaling layer<\/a>.<\/li>\n
- A dense layer<\/a>.<\/li>\n<\/ul>\n
Scaling layer<\/h3>\n
The scaling layer<\/a> contains the statistics on the input calculated from the data file and the method for scaling the input variables.<\/p>\nThe minimum and maximum scaling methods<\/a> are set here; however, the\u00a0mean and standard deviation scaling methods<\/a> yield<\/span>\u00a0similar results.<\/p>\nDense layer<\/h3>\n
We set just one dense layer with 20 inputs and 1 output, having the logistic activation function.<\/p>\n
Neural network graph<\/h3>\n
The following figure shows the neural network used in this example.<\/p>\n
The yellow circles represent scaling neurons, the blue circles represent perceptron neurons, and the red circles represent probabilistic neurons.<\/p>\n
![\"Neural](\"https:\/\/www.neuraldesigner.com\/images\/bearings)
<\/p>\n
The number of inputs is 20, and the number of outputs is 1.<\/p>\n<\/section>\n\n4. Training strategy<\/h2>\n
The training strategy<\/a> is applied to the neural network to obtain the best possible performance. It is composed of two things:<\/p>\n\n- A loss index.<\/li>\n
- An optimization algorithm.<\/li>\n<\/ul>\n
Loss index<\/h3>\n
The selected loss index<\/a> is the normalized squared error (NSE)<\/a> with L2 regularization<\/a>.<\/p>\nThe normalized squared error is helpful in applications where the targets are balanced, as in this case.<\/p>\n
The error term<\/a> fits the neural network to the training instances of the dataset.<\/p>\nThe regularization term<\/a> makes the model more stable and improves generalization, so our model will be more predictive.<\/p>\nOptimization algorithm<\/h3>\n
The selected optimization algorithm<\/a>, which minimizes the loss index,\u00a0is the quasi-Newton method<\/a>.<\/p>\nTraining<\/h3>\n
The following chart shows how the training (blue) and selection (orange) errors decrease with the training epochs.<\/p>\n
![\"\"](\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2023\/08\/Quasi-Newton-method-errors-history.png\")
<\/p>\n
The final training and selection errors are\u00a0a training error\u00a0<\/strong>of\u00a00.001 NSE<\/strong>\u00a0(blue) and\u00a0a selection error\u00a0<\/strong>of<\/span>\u00a00.002 NSE<\/b> (orange), respectively.<\/p>\nConsidering the low values of the training and selection errors, the model already demonstrates good performance.<\/p>\n<\/section>\n\n5. Testing analysis<\/h2>\n
The next step is to perform a test analysis to validate the predictive capability of the neural network.<\/p>\n
The next step is to perform a testing analysis<\/a> to validate the predictive capability of the neural network.<\/p>\nThe testing compares the values provided by this technique to the observed values.<\/p>\n
ROC curve<\/h3>\n
The ROC curve is a good measure of the precision of a binary classification model.<\/p>\n
Our focus is on evaluating the area under the curve (AUC).<\/p>\n
A perfect classifier would have an AUC=1, which implies excellent prediction capabilities, and a random one would have AUC=0.5, indicating no better than random chance.<\/p>\n
![\"\"](\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2023\/08\/ROC-chart.png\")
<\/p>\n
In this case, our model\u00a0achieves an\u00a0AUC\u00a0<\/strong>of\u00a00.998<\/strong>, indicating that it has <\/span>practically perfect classification and prediction capabilities.<\/p>\nConfusion matrix<\/h3>\n
We can also look at the confusion matrix<\/a>.<\/p>\nBelow, we show the elements of this matrix for a decision threshold = 0.43<\/b>.<\/p>\n
![\"\"](\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2023\/08\/Confusion-table.png\")
<\/p>\n
Binary classification metrics<\/h3>\n
From the above confusion matrix, we can calculate the following binary classification tests<\/a>:<\/p>\n
- \n
- Application type<\/a>.<\/li>\n
- Data set<\/a>.<\/li>\n
- Neural network<\/a>.<\/li>\n
- Training strategy<\/a>.<\/li>\n
- Testing analysis<\/a>.<\/li>\n
- Model deployment<\/a>.<\/li>\n<\/ol>\n<\/section>\n
\n 1. Application type<\/h2>\n
We will predict the bearing status in the air compressor system, a binary variable (0 or 1). Therefore, this is a classification<\/a> project.<\/p>\n
The goal here is to model the bearings’ status based on the features of the air compressor system for its subsequent use in predictive maintenance.<\/p>\n<\/section>\n
\n 2. Data set<\/h2>\n
For this study, we use a specialized dataset of air compressor systems to train a neural network for predictive maintenance.<\/p>\n
The dataset includes key parameters, such as motor RPM, power, torque, outlet pressure, and oil pump power, which capture the system’s operating conditions.<\/p>\n
It defines four possible targets\u2014Bearings Status, Water Pump Status, Radiator Status, and Exhaust Valve Status.<\/p>\n
In this work, we focus on predicting the Bearings’ Status, though the same method can be applied to the other components.<\/p>\n
The first step involves preparing the data set<\/a>, which serves as the primary source of information for the problem.<\/p>\n
There are three main components to configure:<\/p>\n
- \n
- Data source.<\/li>\n
- Variables.<\/li>\n
- Instances.<\/li>\n<\/ul>\n
Data source<\/h3>\n
The data file air_compressor_maintenance.csv<\/a> contains the information for the air compressor example.<\/p>\n
This dataset comprises measurements taken from a compressor system supplying air to a factory production line, with a total of 17 features collected.<\/p>\n
The dataset comprises 17 variables (columns) and 1000 instances (rows).<\/p>\n
Variables<\/h3>\n
The features or variables<\/a> included in the dataset are as follows:<\/p>\n
Compressor and motor variables<\/h4>\n<\/section>\n
- \n
- RPM<\/strong> \u2013 Rotations per minute of the motor.<\/li>\n
- Motor Power<\/strong> \u2013 Electric motor power consumption (kW).<\/li>\n
- Torque<\/strong> \u2013 Torque produced by the motor (Nm).<\/li>\n
- Outlet Pressure Bar<\/strong> \u2013 Compressed air outlet pressure (bar).<\/li>\n
- Air Flow<\/strong> \u2013 Compressed air flow rate (m\u00b3\/min).<\/li>\n
- Noise dB<\/strong> \u2013 Noise level of the compressor (dB).<\/li>\n
- Outlet Temp<\/strong> \u2013 Outlet temperature of compressed air (\u00b0C).<\/li>\n<\/ul>\n
Cooling water system variables<\/h4>\n
- \n
- Water Pump Outlet Pressure<\/strong> \u2013 Outlet pressure of the water pump (bar).<\/li>\n
- Water Inlet Temp<\/strong> \u2013 Inlet temperature of cooling water (\u00b0C).<\/li>\n
- Water Outlet Temp<\/strong> \u2013 Outlet temperature of cooling water (\u00b0C).<\/li>\n
- Water Pump Power<\/strong> \u2013 Water pump power consumption (kW).<\/li>\n
- Water Flow<\/strong> \u2013 Cooling water flow rate (m\u00b3\/min).<\/li>\n<\/ul>\n
Oil system variables<\/h4>\n
- \n
- Oil Pump Power<\/strong> \u2013 Oil pump power consumption (kW).<\/li>\n
- Oil Tank Temp<\/strong> \u2013 Oil tank temperature (\u00b0C).<\/li>\n<\/ul>\n
Vibration and acceleration variables<\/h4>\n
- \n
- Ground Acceleration<\/strong> \u2013 Acceleration at the compressor\u2019s mounting point (X, Y, Z in m\/s\u00b2).<\/li>\n
- Head Acceleration<\/strong> \u2013 Acceleration at the compressor head bolt or cooling fin (X, Y, Z in g).<\/li>\n<\/ul>\n
Condition monitoring<\/h4>\n
- \n
- Bearings Status<\/strong> \u2013 Condition of the bearings: Ok<\/em> (normal) or Noise<\/em> (possible wear\/damage).<\/li>\n<\/ul>\n
All variables in the study are inputs, except for the chosen target variable, Bearings Status, which is the output we aim to extract for this machine learning study.<\/p>\n
However, if desired, the same methodology could be applied to the other three target variables: Water Pump Status, Radiator Status, and Exhaust Valve Status.<\/p>\n
\n Instances<\/h3>\n
The instances<\/a> are divided into training, selection, and testing subsets.<\/p>\n
They represent a certain percentage of the original instances and are randomly split.<\/p>\n
The exact percentages depend on the chosen data split approach.<\/p>\n
Variables distributions<\/h3>\n
We can perform a few related analytics once the data set has been set.<\/p>\n
First, we check the provided information and ensure the data is of high quality.<\/p>\n
The data distributions<\/a> show the bearing condition percentages.<\/p>\n
<\/p>\nPlease note that the actual distributions may vary depending on the nature of the data collected in the air compressor dataset.<\/p>\n
Input-target correlations<\/h3>\n
The input-target correlations<\/a> may indicate which factors strongly influence the status of the motor and compressor system bearings.<\/p>\n
<\/p>\nFrom the chart, we can identify which features have a significant influence on bearing conditions.<\/p>\n
This information can help us better understand the relationships between the variables and the target in the predictive maintenance study.<\/p>\n<\/section>\n
\n 3. Neural network<\/h2>\n
The second step is to\u00a0select a\u00a0neural network<\/a> that represents<\/span>\u00a0the classification function.
\nFor classification problems, it is composed of:<\/p>\n- \n
- A scaling layer<\/a>.<\/li>\n
- A dense layer<\/a>.<\/li>\n<\/ul>\n
Scaling layer<\/h3>\n
The scaling layer<\/a> contains the statistics on the input calculated from the data file and the method for scaling the input variables.<\/p>\n
The minimum and maximum scaling methods<\/a> are set here; however, the\u00a0mean and standard deviation scaling methods<\/a> yield<\/span>\u00a0similar results.<\/p>\n
Dense layer<\/h3>\n
We set just one dense layer with 20 inputs and 1 output, having the logistic activation function.<\/p>\n
Neural network graph<\/h3>\n
The following figure shows the neural network used in this example.<\/p>\n
The yellow circles represent scaling neurons, the blue circles represent perceptron neurons, and the red circles represent probabilistic neurons.<\/p>\n
The number of inputs is 20, and the number of outputs is 1.<\/p>\n<\/section>\n
\n 4. Training strategy<\/h2>\n
The training strategy<\/a> is applied to the neural network to obtain the best possible performance. It is composed of two things:<\/p>\n
- \n
- A loss index.<\/li>\n
- An optimization algorithm.<\/li>\n<\/ul>\n
Loss index<\/h3>\n
The selected loss index<\/a> is the normalized squared error (NSE)<\/a> with L2 regularization<\/a>.<\/p>\n
The normalized squared error is helpful in applications where the targets are balanced, as in this case.<\/p>\n
The error term<\/a> fits the neural network to the training instances of the dataset.<\/p>\n
The regularization term<\/a> makes the model more stable and improves generalization, so our model will be more predictive.<\/p>\n
Optimization algorithm<\/h3>\n
The selected optimization algorithm<\/a>, which minimizes the loss index,\u00a0is the quasi-Newton method<\/a>.<\/p>\n
Training<\/h3>\n
The following chart shows how the training (blue) and selection (orange) errors decrease with the training epochs.<\/p>\n
<\/p>\nThe final training and selection errors are\u00a0a training error\u00a0<\/strong>of\u00a00.001 NSE<\/strong>\u00a0(blue) and\u00a0a selection error\u00a0<\/strong>of<\/span>\u00a00.002 NSE<\/b> (orange), respectively.<\/p>\n
Considering the low values of the training and selection errors, the model already demonstrates good performance.<\/p>\n<\/section>\n
\n 5. Testing analysis<\/h2>\n
The next step is to perform a test analysis to validate the predictive capability of the neural network.<\/p>\n
The next step is to perform a testing analysis<\/a> to validate the predictive capability of the neural network.<\/p>\n
The testing compares the values provided by this technique to the observed values.<\/p>\n
ROC curve<\/h3>\n
The ROC curve is a good measure of the precision of a binary classification model.<\/p>\n
Our focus is on evaluating the area under the curve (AUC).<\/p>\n
A perfect classifier would have an AUC=1, which implies excellent prediction capabilities, and a random one would have AUC=0.5, indicating no better than random chance.<\/p>\n
<\/p>\nIn this case, our model\u00a0achieves an\u00a0AUC\u00a0<\/strong>of\u00a00.998<\/strong>, indicating that it has <\/span>practically perfect classification and prediction capabilities.<\/p>\n
Confusion matrix<\/h3>\n
We can also look at the confusion matrix<\/a>.<\/p>\n
Below, we show the elements of this matrix for a decision threshold = 0.43<\/b>.<\/p>\n
<\/p>\nBinary classification metrics<\/h3>\n
From the above confusion matrix, we can calculate the following binary classification tests<\/a>:<\/p>\n
- A dense layer<\/a>.<\/li>\n<\/ul>\n
- A scaling layer<\/a>.<\/li>\n
- Head Acceleration<\/strong> \u2013 Acceleration at the compressor head bolt or cooling fin (X, Y, Z in g).<\/li>\n<\/ul>\n
- Oil Tank Temp<\/strong> \u2013 Oil tank temperature (\u00b0C).<\/li>\n<\/ul>\n
- Water Inlet Temp<\/strong> \u2013 Inlet temperature of cooling water (\u00b0C).<\/li>\n
- Motor Power<\/strong> \u2013 Electric motor power consumption (kW).<\/li>\n
- RPM<\/strong> \u2013 Rotations per minute of the motor.<\/li>\n
- Data set<\/a>.<\/li>\n