The main goal is to understand how voltage and current influence car performance and motor temperature.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<\/section>\n The first step is to prepare the data set<\/a>, which is the source of information for the approximation problem. It is composed of:<\/p>\n The file permanent_magnet_synchronous_motor.csv<\/a> contains the data for this example.<\/p>\n Here, the number of variables (columns) is 14, and the number of instances (rows) is 107.<\/p>\n In that way, this problem has the following variables<\/a>:<\/p>\n<\/section>\n In this study, we use several environmental, electrical, and current variables as inputs to predict motor performance and internal temperatures.<\/p>\n The goal is to model motor behavior and prevent overheating.<\/p>\n The data is randomly split into 60% training<\/a> (65 samples), 20% selection<\/a> (21 samples), and 20% testing<\/a> (21 samples).<\/p>\n Once we establish the data set information, we perform analytics to check the data quality.<\/p>\n For instance, we can calculate the data distribution<\/a>. The following figure depicts the histogram for one of the target variables.<\/p>\n This diagram shows a normal distribution of the stator tooth temperature, one of the stator components.<\/p>\n The distribution appears normal because the output depends on many input variables, which vary constantly during the experiment.<\/p>\n The following figure depicts input-target correlations<\/a>. This might help us see the different inputs’ influence on the motor temperature.<\/p>\n As this machine learning study has various target variables, we show the correlation diagram of one.<\/p>\n The above chart shows that a few instances have a critical dependency on the variable ‘torque’. As we can see, an instance is highly correlated to this target, as seen in the input ‘current_quadrature’.<\/p>\n At first sight, we could have predicted this behavior simply by looking at the data set and realizing the torque is induced by the current, in this case, by the quadrature coordinate of the current.<\/p>\n We can also plot a scatter chart<\/a> with the stator winding temperature versus the ambient temperature.<\/p>\n Logically, the higher the ambient temperature, the higher the stator winding temperature.<\/p>\n<\/section>\n The neural network<\/a> outputs the different motor temperatures as a function of the current, voltage, coolant, and ambient temperature.<\/p>\n Approximation models usually contain the following layers:<\/p>\n The scaling layer<\/a> transforms the original inputs to normalized values.<\/p>\n Here, we set the mean and standard deviation scaling method<\/a>\u00a0so that the input values have a mean of 0 and a standard deviation of 1.<\/p>\n Here, two perceptron layers<\/a> are added to the neural network. This number of layers is enough for most applications. The first layer has eight inputs and three neurons. The second layer has three inputs and five neurons.<\/p>\n The unscaling layer<\/a> transforms the normalized values from the neural network into the original outputs.<\/p>\n Here, we also use the mean and standard deviation unscaling method<\/a>.<\/p>\n The following figure shows the resulting network architecture.<\/p>\n The next step is\u00a0to select an appropriate\u00a0training strategy<\/a> that defines<\/span>\u00a0what the neural network will learn. A general training strategy is composed of two concepts:<\/p>\n The loss index<\/a> chosen is the\u00a0normalized squared error<\/a> with\u00a0L2 regularization<\/a>. This loss index is the default in approximation applications.<\/p>\n The optimization algorithm<\/a> chosen is the\u00a0quasi-Newton method<\/a>. This optimization algorithm is the default for medium-sized applications like this one.<\/p>\n Once the strategy has been set, we can train the neural network.<\/p>\n The following chart shows how the training (blue) and selection (orange) errors decrease with the training epoch during the training process.<\/p>\n The key training result is the final selection error, which measures the neural network\u2019s generalization ability.<\/p>\n In this case, the final selection error is 0.083 NSE.<\/p>\n<\/section>\n The objective of model selection<\/a> is to find the network architecture with the best generalization properties. We want to improve the final selection error obtained before (0.083 NSE).<\/p>\n The best selection error is achieved using a model whose complexity is the most appropriate to produce a good data fit. Order selection<\/a> algorithms are responsible for finding the optimal number of perceptrons in the neural network.<\/p>\n <\/p>\n The final training error continuously decreases with the number of neurons. However, the final selection error takes a minimum value at some point. Here, the optimal number of neurons is 9, corresponding to a selection error of 0.043<\/b>.<\/p>\n The following figure shows the optimal network architecture for this application.<\/p>\n The objective of the testing analysis<\/a> is to validate the generalization performance of the trained neural network. The testing compares the values provided by this technique to the observed values.<\/p>\n A standard testing technique in approximation problems is to perform a\u00a0linear regression analysis<\/a> between the predicted and the real values using an independent testing set. The following figure illustrates a graphical output provided by this testing analysis.<\/p>\n The above chart shows that the neural network is predicting the entire range of temperature data well. The correlation value is R2 = 0.990<\/b>, indicating the model has a reliable prediction capability.<\/p>\n<\/section>\n2. Data set<\/h2>\n
\n
Data source<\/h3>\n
Variables<\/h3>\n
Environmental variables<\/h4>\n
\n
Electrical variables<\/h4>\n
\n
Performance variables<\/h4>\n
\n
Thermal variables<\/h4>\n
\n
Instances<\/h3>\n
Variables distribution<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/electric-car-pm_distribution.webp\")
<\/p>\nInputs-targets correlations<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/electric-car-inputs-targets-correlation.webp\")
<\/p>\nScatter charts<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/stator_winding-vs-ambient-scatter-chart.webp\")
<\/p>\n3. Neural network<\/h2>\n
\n
Scaling layer<\/h3>\n
Dense layers<\/h3>\n
Unscaling layer<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/electric-car-neuron-layer.webp\")
<\/p>\n<\/section>\n4. Training strategy<\/h2>\n
\n
![](\"https:\/\/www.neuraldesigner.com\/images\/electric-car-training-strategy.webp\")
<\/p>\n5. Model selection<\/h2>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/electric-motor-final-neuron-layer.webp\")
<\/p>\n<\/section>\n6. Testing analysis<\/h2>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/electric-motor-linear-regression-chart.webp\")
<\/p>\n7. Model deployment<\/h2>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/electric-car-directional-output.webp\")
<\/p>\n