Enhancing the Efficiency of Failure Recognition in Induction Machines through the Application of Deep Neural Networks

Abstract

The objective of the investigation was to increase the effectiveness of damage detection in the stator of the squirrel-cage induction machine. The analysis aimed to enhance the operational trustworthiness of the squirrel-cage induction machine by employing nonintrusive diagnostic methods based on a current signal and modern artificial intelligence methods. The authors of the study introduced a diagnostic technique for identifying multiphase interturn short circuits of stator winding. These short circuits are one of the most common faults in induction machines. The proposed method focusses on deriving a diagnostic signal from the phase-current waveforms of the machine. The noninvasive nature of the diagnostic technique presented is attributed to the application of the field model of electromagnetic phenomena to determine the diagnostic signal. For this purpose, a field model of a squirrel-cage machine was developed. The waveforms of phase currents obtained from the field model were used as input into an elaborated machine failure neural classifier. A deep neural network was used to develop a neural classifier. The effectiveness of the developed classifier has been experimentally verified, and the obtained results have been presented, concluded, and discussed. The scientific novelty presented in the article is the presentation of research results on the use of a neural classifier to detect damage in all phases of the stator winding at an early stage of its appearance. The features of this type of damage are very difficult to observe in signal waveforms such as a phase current or torque.

1. Introduction

Induction machines are a critical component of many industrial processes and their reliability is crucial to ensure the efficiency and productivity of those processes [1,2,3]; the trend towards electric vehicles may result in even greater interest in this type of electric motor [4,5,6,7,8]. Induction machines are commonly used in industry due to their simplicity, reliability, efficiency, cost effectiveness, robustness, and ease of control using variable frequency drives and other control systems [9,10]. However, diagnosing induction machine failures can be challenging due to the complex interactions between electrical, mechanical, and environmental factors. One of the most common faults of induction machines is interturn short circuits. These short circuits in induction machines can be caused by a variety of factors. The most important causes of short circuits include ageing and wear of the insulation, electrical overstress, such as sudden surges or transients in the voltage supply, thermal stress from high temperatures, mechanical stresses, and vibrations, or overloading the machine beyond its rated values. Of course, regular maintenance and diagnostics of the machine can help to prevent the occurrence of interturn short circuits.

In research related to the development and analysis of reliable technical solutions, field models are being increasingly used, because of their credibility. Among others, the finite-element method has become widely used in the modelling of a variety of technical devices. Due to its versatility, FEM has been successfully used to solve complex problems, including for modelling magneto-optics and in stress simulations for the prediction of fatigue life of a radial cylindrical roller bearing, as well as, for example, in studying temperature [11] and strain fields in gas-foil bearings and modelling a deep-hole drilling tool. Numerical models exploiting FEM are also applied to the study of electromagnetic phenomena in electrical machines. Field and field circuit models exploiting FEM have been successfully applied in the analysis and synthesis of many different types of electromechanical transducers, such as induction [12,13,14] and synchronous machines [15,16,17], switched reluctance motors [18,19,20], stepper motors, brushless direct current machines, and linear motors, as well as in wireless power transfer systems, magnetic field excitation systems, and other electromagnetic converters.

The most popular and widespread diagnostic methods used in the detection and classification of interturn short circuits of electrical machines are motor current signature analysis (MCSA) [21,22,23,24], motor vibration signature analysis (MVSA) [25,26,27], the Park vector approach (PVA) [28,29,30], or wavelet transform (WT) [31,32]. These techniques allow for noninvasive analysis of a diagnostic signal without having to turn off the machine, and thus without interrupting the current operating state of the machine. For this reason, the authors of the present article used phase current waveforms as a diagnostic signal. However, the use of the above-mentioned diagnostic methods requires a good understanding of theory and practice in the fields of signal processing and electrical machines themselves. The influence of the human factor becomes even more significant if the subject of interest fails in its early stage of occurrence.

Current research in the field of diagnostics of electrical machines is increasingly focused on the use of machine-learning elements in the diagnostic process. Earlier research involved the use of simple structures such as multilayer perceptrons. Currently, due to the increasing amount of data to be processed and their increasingly complex structure, the use of simple perceptron networks is difficult and, in some cases, almost impossible due to the problem of gradient decay in the case of deeper multilayer perceptron structures. Therefore, more models of multicouple neural networks, such as a convolutional neural network (CNN) [33,34,35], a generative adversarial network (GAN) [36,37,38], and a long-short-term memory network (LSTM) [39,40,41], were used in the diagnostic process. Unfortunately, with the increasing complexity of neural network models, the number of network parameters that can affect network results is increased. In the case of deep networks, in addition to the basic parameters such as the number of neurones in layers or the number of layers, there are additional hyperparameters in the tuning process, e.g., the number of kernels in convolutional layers, kernel step, dropout rate, padding, and many others. In the case of networks with moderately complex structure, researchers decide to empirically select network parameters [42], but with increasing network complexity, empirical selection of parameters requires a lot of experience and intuition preceded by many years of research into the deep structures of neural networks in issues related to the diagnostics of electrical machines. In order to simplify the tuning of deep neural network models in the diagnosis of induction machines, the authors present an approach using the grid search method. In the results of the research presented, precision was used as a metric.

Due to the fact that interturn short circuits, especially at an early stage of their occurrence (a small number of shorted turns), do not significantly affect the phase current waveforms, they are difficult to detect and unambiguously interpret. In this study, the authors propose a novel approach that combines the field model and deep neural networks to enhance the accuracy and efficiency of the induction machine diagnostic process. First, a machine field model was developed, which allows for the simulation of machine behaviour under various fault conditions. Then, the data from the model were used to train a deep neural network. The presented approach can improve the accurate classification of different levels and types of faults, for example bearing failures, shaft unbalance, cage bars being broken, or end rings being broken.

2. Materials and Methods

To obtain a diagnostic signal for the purposes of training deep neural networks, a field model of a squirrel-cage induction machine was elaborated. The developed model has been modified in such a way as to enable one to simulate selected failure machine operating states. The failure machine operating state is understood as failure of the stator winding in the form of multiphase interturn short circuits. One of the stages of creating the field model was to develop a circuit model of the machine. This type of damage includes a short circuit independently in all phases of the stator winding. Therefore, their modelling was used in all phases. The model of the machine, taking into account the multiphase interturn short circuits in the stator winding, is shown in Figure 1. In Figure 1, the number of shorted turns is marked as N, the winding resistance as R, and the winding inductance as L for each phase. The motor model was developed based on the motor with the rated data presented in

Table 1. Induction machine parameters.

Parameter	Value	Parameter	Value
Rated power Rated voltage Rated current Rated speed Number of phases Number of stator slots Number of rotor slots Rated efficiency Frequency Stator winding resistance	3 kW 400 V 6.3 A 1465 rpm 3 36 28 87.7% 50 Hz 1.46 Ω	Rated power factor Rated torque Number of poles Stator outer diameter Stator inner diameter Rotor outer diameter Rotor inner diameter Stator Steel Rotor Steel	0.79 19.56 Nm 4 168 mm 108 mm 107.5 mm 35 mm M470–50A M470–50A

.

The Ansys Maxwell 2023 R2 environment was used to develop a model of the field induction motor. The developed model takes into account the phenomenon of saturation. During model development, the actual magnetisation characteristics of the materials were introduced for the magnetic materials of the stator, rotor, and shaft of the considered machine. The calculations were carried out for a constant ambient and operating temperature that was appropriately 20 and 40 °C. The model allows calculations to be performed not only for a healthy machine, but also for modelling damage in the form of multiphase interturn short circuits. Modifying the model to enable the simulation of multiphase interturn short circuits results in the division of the stator phase windings, which in turn affects both the resistances and inductances of the relevant machine circuits. Below is a matrix describing the resistances and inductances of the stator winding for the damaged machine. To simplify and shorten the notation, the following entry will concern failure in one phase of the machine. For the remaining phases, the methodology for determining the resistance and inductance of individual circuits is analogous, and only appropriate shifts must be taken into account.

$$R^S=\left[\begin{array}{cccc}{R}_{AF}^S& -R_{AS}^S& 0& 0\\ -R_{AS}^S& R_{AS}^S& 0& 0\\ 0& 0& R_B^S& 0\\ 0& 0& 0& R_C^S\end{array}\right]$$

(1)

where $R_{AF}^S$ is the resistance of the damaged part of the stator winding of phase A, $R_{AS}^S$ is the resistance of the heathy part of the stator winding of phase A, $R_B^S$ is the stator phase B resistance, and $R_C^S$ is the stator phase C resistance.

$$L^{SS}=\left[\begin{array}{cccc}{L}_{AF\alpha }^S& 0& 0& 0\\ 0& L_{AS\alpha }^S& 0& 0\\ 0& 0& L_{B\alpha }^S& 0\\ 0& 0& 0& L_{C\alpha }^S\end{array}\right]+\left[\begin{array}{cccc}{L}_{AF\beta }^S& -(L_{AS\beta }^S+M_{AFAS\beta }^S)& (M_{AFB\beta }^S+M_{ASB\beta }^S)cos(2\pi /3)& {(M}_{AFC\beta }^S+M_{ASC\beta }^S)cos(-2\pi /3)\\ -(L_{AS\beta }^S+M_{AFAS\beta }^S)& L_{AS\beta }^S& -M_{ASB\beta }^{S}cos(2\pi /3)& -M_{ASC\beta }^{S}cos(-2\pi /3)\\ M_{AFB\beta }^{S}cos(-2\pi /3)& -M_{ASB\beta }^{S}cos(-2\pi /3)& L_{B\beta }^S& M_{BC\beta }^{S}cos(2\pi /3)\\ M_{AFC\beta }^{S}cos(2\pi /3)& -M_{ASC\beta }^{S}cos(2\pi /3)& M_{BC\beta }^{S}cos(-2\pi /3)& L_{C\beta }^S\end{array}\right]$$

(2)

where $L_{AF\alpha }^S$, $L_{AS\alpha }^S$, $L_{B\alpha }^S$, and $L_{C\alpha }^S$ are the leakage inductance of the windings of individual stator circuits’ inductance, $L_{AF\beta }^S$, $L_{AS\beta }^S$, $L_{B\beta }^S$, and $L_{C\beta }^S$ are the main self-inductances of the stator circuits, and $M_{AFAS\beta }^S$, $M_{AFB\beta }^S$, $M_{ASB\beta }^S$, $M_{AFC\beta }^S$, $M_{ASC\beta }^S$, and $M_{BC\beta }^S$ are the main mutual inductances of the stator.

Based on the circuit model of the machine and the technical documentation, a field model of the machine was developed. The common finite-element method was used to solve the magnetic field equations in the developed model. In the discretization process, the model was divided into triangular finite elements. In order to assess the quality of the discretising mesh,

Table 2. Induction machine model parameters.

	Band	Shaft	Outer Region	Stator	Rotor	Bars	Coils
Num Elements	416	838	1670	2664	7448	4592	302
Min edge length (mm)	0.1	0.6	0.1	0.6	0.0783	0.0783	0.2
Max edge length (mm)	1.0	2.0	5.0	9.0	2.0	2.0	2.0
RMS edge length (mm)	1.0	0.001	0.002	0.003	0.001	0.001	0.001
Min elem area (mm2)	0.03006	0.5195	0.02822	0.2350	0.005145	0.006837	0.3275
Max elem area (mm2)	0.1225	1.435	3.977	24.69	2.218	2.461	0.3275
Mean elem area (mm2)	0.1016	1.147	1.018	3.625	0.7665	0.5234	0.3275
Std Devn (area) (mm2)	0.028771	0.3150	0.9148	5.625	0.6158	0.6310	8.38 × 10−8

presents the number of elements, as well as the minimum, maximum, and average values of their dimensions and surface areas in individual subareas. Using the developed model, simulation calculations of the induction machine were performed, taking into account failures in each phase of winding.

3. Classification of Stator Winding Damage

Detecting short circuits in the winding of an induction machine is a very difficult task. This is due to the fact that the impact of a small number of shorted turns on the machine operation is difficult to observe in the diagnostic signal waveform. Example waveforms of the phase current in the case of a healthy and damaged machine (short-circuit configuration: N_fA = 1, N_fB = 1, N_fC = 5) are shown in Figure 2 and Figure 3, respectively. To classify this type of damage based on the analysis of the phase current waveform of the stator winding, a system was developed in which the role of the classifier was entrusted to a deep neural network. The developed network enables the detection of interturn short circuits in three phases of the stator winding of a squirrel-cage machine. The task of the network is to determine the degree of failure of the stator winding. A stator failure involves interturn faults in the range from 0 to 10 shorted turns for each phase, resulting in 1000 classes for classification by a deep neural network (DNN). The data obtained from the developed field model of the induction machine containing 73,230 samples were used in the learning process. The data were divided into three sets: training, validation, and test in the proportions of 60:20:20. Phase current waveforms were used as input data for the DNN. One of the most commonly used deep neural network structures in classification problems is convolutional neural networks. Due to the ability to extract special features and reduce the size of data, they are able not only to detect changes in the signal that may be unnoticeable to an expert but also to reduce the computational complexity of the model. Therefore, due to the nature of the problem of classifying the degree of stator winding failure, convolutional neural networks were used in the present work.

The article focuses on diagnostics based on current waveforms and does not mention spectral diagnostics because of the need to apply a transformation from the time domain to the frequency domain. One of the goals of using neural classifiers in the early diagnosis of the stator winding is to detect the fault as quickly as possible. Of course, the use of spectral analysis can have a positive impact on the quality of classification, but additional transformation during diagnostics while the machine is running can also slow down the decision-making process itself, which is why the article focusses on raw data.

The occurrence of an interturn short circuit in the stator winding causes a change in the equivalent circuit of the stator winding. As a result of an interturn short circuit, the phase winding is divided into two parts. The first part contains shorted turns, while the second part contains the rest of the phase winding turns. This division causes changes in the magnetic field distribution and, consequently, in the induced electromotive force in the winding, the current flowing in the winding, and finally the torque. The difficulty is that, in the case of a small number of shorted turns, changes in the waveforms of these signals are difficult to notice. Therefore, a deep neural network was used to detect the occurrence of a short circuit in the stator winding circuit based on phase current waveforms. CNN networks, thanks to their convolutional layers, are able to extract changes in the current signal of an induction machine, which, in the case of interturn short circuits at an early stage of their occurrence, are very difficult or even impossible to detect using other methods due to their small impact on the current value. Due to the use of networks with convolutional layers, the presence of an expert in the field of electrical machine diagnostics is not required, as well as complicated normalisation of training data when preparing the training set. This may affect the general simplicity of using this type of network on a larger scale in the diagnosis of stator windings of electrical machines. Currently, scientific publications focus on the use of neural networks in the diagnostics of the stator winding of electric machines, but mostly they focus on failure in one phase of the machine, which makes a slight number of short-circuit configurations and therefore the computational complexity and the problem of multi-class classification of interturn short circuits are less complicated. In the case of the considered multiphase short circuits, the classification of the degree of stator failure requires a classification of up to 1000 classes, which significantly complicates the classification of failure. The article, unlike other publications, presents the use of deep learning in the problems of multiphase interturn short circuits. The issue of multiphase interturn short circuits significantly affects the level of complexity of the classification problem, which makes the influence of hyperparameters of the neural network even more important in decision-making, and therefore the selection of the values of these parameters a priori may be even more complicated. In the article, a deterministic approach was proposed for tuning the network for the classification of multiphase interturn faults, which involves searching a certain variable space to determine the best configuration of hyperparameters for the multiphase interturn short-circuit task.

Due to the nature of the problem under consideration, which is multiclass classification, and the nature of the input data to the CNN-type network, the loss function was defined by the formula:

$$\left(w\right)=\frac{1}{N}\sum _{i=1}^N{y}_1\mathit{log}\left({\hat{y}}_i\right)+\left(1-y_i\right)\mathit{log}\left(1-{\hat{y}}_i\right)$$

(3)

where $w$ is the vector of weights, $y_i$ is the expected value, and ${\hat{y}}_{\mathit{i}}$ is the predicted value.

To avoid the phenomenon of overfitting, the loss function presented by Formula (1) has been modified as follows:

$$\left(w\right)=\frac{1}{N}\sum _{i=1}^N{y}_1\mathit{log}\left({\hat{y}}_i\right)+(1-y_i)log(1-{\hat{y}}_i)+\frac{\alpha }{2N}\sum _{i=1}^N{w}_i^2$$

(4)

where $\frac{\alpha }{2N}\sum _{i=1}^N{w}_i^2$ is a term related to L2 normalization.

On the basis of research, the basic structure of the network was selected. In the next stage of research, its hyperparameters were modified. The modification included tuning hyperparameters such as: optimiser, learning rate, dropout rate for dropout layers, the number of kernels in convolutional layers, and the number of neurones in the dense layer. The diagram of the diagnostic process with the basic structure of the network for the diagnosis of the stator winding of an induction machine is shown in Figure 4, while the values of its constant parameters are shown in

Table 3. The parameters of the neural network.

Parameter	Value
Number of convolutional layers	4
Number of pooling layers	2
Number of dropout layers	2
Number of flatten layers	1
Number of dense layers	2
Methods to prevent overfitting	Early stop, weights reg.
Weights regularization method	L2 norm
Number of epochs	700
Dimensions of the input vector	(28,28)
Batch size	1024
Kernel size	(3 × 3)
Kernel stride	(1,1)
Dilation rate	(1,1)
Padding method	Valid
Pool size	(2, 2)
Momentum factor for SGD	0.5
Convolution layer activation	Rectified linear unit
Activation function for the first dense layer	Rectified linear unit
Activation function for the second dense layer	Softmax
Loss function	Sparse categorial cross-entropy

.

As can be seen in Figure 4, the diagnostic process used can be divided into stages. The first was to develop a model using the finite-element method, taking into account failure of the stator winding. The second stage was to prepare input data to the network based on the results obtained from the model. The next stage was to develop a network model and carry out the training process based on the input data. The last stage was the analysis of the classifier results.

As mentioned, during the research, the hyperparameters of the model were tuned. The tuning process was divided into several stages. In the first stage, such parameters as the optimiser, learning rate (lr), and dropout rate (dr) were tuned. The tuning was carried out with a constant number of kernels in the convolutional layers and neurones in the dense network layers. The tuning was carried out using the grid search method, which, unlike, for example, the random search or Bayesian optimisation method, is a more time-consuming method due to the greater demand for computing power, but at the same time allows for better tuning results. The grid search method consists of determining the variability range of the selected variables and then carrying out the network learning process for the ‘peer-to-peer’ configuration. The tuning parameters and the range of their variability are presented in

Table 4. Hyperparameters values during first turning.

Parameters	Abbreviations	Values
Learning rate	lr	0.001, 0.0005, 0.0001
Optimiser	-	Stochastic gradient descent (SGD), adaptive momentum estimation (ADAM), root mean square propagation (RMSProp)
Dropout rate	dr	0.1, 0.3

. During tuning, in the first stage, 64 kernels were assumed in the first and the second convolutional layers, 128 kernels in Layers 3 and 4, and 128 units in the dense layer. In the next stage of the investigation, the influence of these parameters on the failure classification results was examined.

The optimisers mentioned in Table 4 update the model weights according to the following formulas:

SGD:

$$w^{k+1}=w^k-\alpha m^k$$

(5)

wherein

$$m^k={\beta }_1{m}^{k-1}+(1-{\beta }_1)[\frac{\delta L}{\delta w^k}]$$

(6)

where $w^{k+1}$ are the weights in the next step, $w^k$ are the weights in the current step, $\alpha$ is the learning rate, $m^k$ represents the aggregate of gradients in the current step, ${\beta }_1$ is the moving average parameter, $m^{k-1}$ is the aggregate of gradients in the previous step, and $L$ is the loss function.

RMSProp:

$$w^{k+1}=w^k-\frac{{\alpha }_t}{{(n_k+\epsilon )}^{1/2}}[\frac{\delta L}{\delta w^k}]$$

(7)

wherein

$$n^k={\beta }_2{n}^{k-1}+\left(1-{\beta }_2\right){[\frac{\delta L}{\delta w^k}]}^2$$

(8)

where $n^k$ is the sum of the square of current gradients, ${\beta }_2$ is the moving average parameter, and $n^{k-1}$ is the sum of the square of previous gradients.

ADAM:

$$w^{k+1}=w^k-{\hat{m}}^t(\frac{\alpha }{\sqrt{{\hat{n}}^t}+\epsilon })$$

(9)

wherein

$${\hat{m}}^t=\frac{m_t}{1-{\beta }_1^t}$$

(10)

$${\hat{n}}^t=[\frac{n^t}{1-{\beta }_2^t}]$$

(11)

3.1. Tuned CNN—Stage I

The results of the optimisation of the network parameters during the first stage are shown in Figure 4, Figure 5 and Figure 6 and

Table 5. Hyperparameter tuning results in Stage I.

Learning Rate	Optimiser	Dropout Rate	Metrics	Step
0.001	SGD	0.3	0.176	129
0.0005	SGD	0.1	0.289	94
0.0001	ADAM	0.3	0.723	128
0.001	SGD	0.1	0.013	90
0.0001	RMSProp	0.3	0.666	59
0.001	RMSProp	0.1	0.648	42
0.0001	SGD	0.3	0.230	179
0.0001	RMSProp	0.1	0.677	44
0.0005	RMSProp	0.1	0.714	59
0.0005	ADAM	0.1	0.722	81
0.0005	SGD	0.3	0.396	208
0.001	ADAM	0.3	0.678	87
0.0001	SGD	0.1	0.006	4
0.001	ADAM	0.1	0.691	78
0.0005	RMSProp	0.3	0.634	60
0.0001	ADAM	0.1	0.718	75
0.0005	ADAM	0.3	0.004	45
0.001	RMSProp	0.3	0.629	60

Green color—the best result.

.

Figure 5, Figure 6 and Figure 7 show the results of the network training process. Figure 5 shows how the metric value changed in subsequent epochs while training the model. Figure 6 shows the decline in the loss function as a function of the epochs, while Figure 7 graphically presents the considered configurations of the network hyperparameters used during the first stage of network tuning. In Figure 7, the colours do not have much meaning and are not specified for the purpose of presenting the data. Figure 7 shows how the results are distributed for individual configurations.

The research carried out calculations of the metric value depending on changes in three parameters: dropout rate, learning rate, and the type of optimiser used. The calculation results presented as a function of three variables in one figure are illegible. For a more accurate presentation of the results, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16 group the data according to the optimiser, learning rate, and dropout rate, respectively. Due to the multitude of hyperparameters that were taken into account during the network training process for multiphase interturn short circuits, it was decided to divide the chapter into subchapters. Attempts to aggregate the data into summary charts resulted in less readability.

3.1.1. Impact of Optimiser on Multiphase Interturn Short-Circuit Classification

The paper presents the influence of the choice of optimiser on the quality of classification of multiphase interturn short circuits in the stator winding of an induction machine. Three gradient descent-based optimisers were considered: SGD, RMSProp, and ADAM. The influence of optimiser selection in the diagnostic process of multiphase interturn short circuits is shown below:

Figure 8 shows the classification results of the neural network developed with the SGD optimiser. As can be seen in the case of the SGD optimiser, the overall quality of fault classification is unsatisfactory and, at best, the metric value does not exceed even 40% of correct fault classifications.

Figure 8. Metric values for the SGD optimiser.

Figure 8. Metric values for the SGD optimiser.

The results for the network with the RMSProp optimiser shown in Figure 9 show that, unlike the SGD algorithm, with the RMSProp optimiser better results were obtained for all considered hyperparameter configurations.

Figure 9. Metric values for the RMSProp optimiser.

Figure 9. Metric values for the RMSProp optimiser.

However, the results for the ADAM optimiser show that in the case of this optimiser, the selection of the learning rate in most cases did not have such a large impact on the final classification results. Only in the case of a learning rate of 0.0005 and a dropout value of 0.3, the result is clearly worse. This problem does not have to result from incorrectly selected values of the learning rate and dropout for the short-circuit classification problem but may be caused, for example, by incorrectly selected initial values of the model weights, which could cause the algorithm to become stuck in the local minimum. The best fault classification results were obtained with this optimiser.

Figure 8, Figure 9 and Figure 10 show the impact of the choice of optimiser on the classification results. The optimiser’s task is to adjust the weights of the network during the training process. Three popular optimisers were used in the research: stochastic gradient descent (SGD), root mean square propagation (RMSProp), and ADAM.

Figure 10. Metric values for ADAM optimiser.

Figure 10. Metric values for ADAM optimiser.

3.1.2. Impact of the Learning Rate on Multiphase Interturn Short-Circuit Classification

During the training of artificial neural networks with the use of function gradient descent methods, one of the hyperparameters used is the learning rate. The learning rate parameter determines the impact of updating the weights in successive learning steps. A too-high value of the learning rate may result in faster convergence, but the algorithm may miss the minimum of the loss function during the training process, while a properly selected learning rate may lead to a more accurate result (finding a point closer to the minimum of the loss function), but this may translate into a longer training time for the network. The default learning rate for gradient methods was 0.001. In the tests carried out, the influence of the learning rate on the inference results regarding the state of machine failure was examined. For this purpose, the learning rate was reduced twice and by an order of magnitude. The concept of the influence of the learning factor on the learning process is presented in Figure 11a,b.

As can be seen in Figure 11a, too high a value of the learning rate may lead to a situation in which the algorithm will not be able to find the global minimum of the function due to too-large step updates. However, in Figure 11b it can be seen that a smaller step value may lead to finding the global minimum but will require a larger number of iterations. The loss function presented in Figure 11 is only intended to present the idea of selecting the learning rate. Of course, in the case of neural networks, loss functions are often functions with a very large number of dimensions, which makes it impossible to present them graphically. It should also be mentioned that some loss function optimisation algorithms have the ability to adaptively select the learning rate in each iteration, which helps to converge to the global minimum, as shown in Figure 11a,b. In Figure 11, an example shape of the cost function is shown in blue, while the subsequent steps of the learning algorithm are marked in green.

Figure 11. Learning rate impact: (a) learning rate too high and (b) correct learning rate.

Figure 11. Learning rate impact: (a) learning rate too high and (b) correct learning rate.

The influence of the learning rate on the inference results is shown in Figure 12, Figure 13 and Figure 14.

Figure 12. The metric values for the learning rate are equal to 0.001.

Figure 12. The metric values for the learning rate are equal to 0.001.

Figure 12 shows the metric value for a learning rate of 0.001. As can be seen in the case of such a value of the learning coefficient, the best results in the classification of inter-turn short circuits of the induction machine were obtained using the ADAM optimiser. The results for the SGD optimiser clearly differ not only from the ADAM optimiser, but also from RMSProp.

Reducing the learning factor to 0.005 significantly improved the quality of interturn fault classification using all three optimisers. The biggest improvement is seen with the SGD optimiser. The possible cause of the classification problem for the ADAM optimiser and the dropout value of 0.3 has already been mentioned earlier.

Figure 13. Metric values for the learning rate equal to 0.005.

Figure 13. Metric values for the learning rate equal to 0.005.

Figure 14. The metric values for the learning rate equal to 0.0001.

Figure 14. The metric values for the learning rate equal to 0.0001.

Further reducing the learning rate allowed us to achieve the highest result for the metric in the case of the ADAM optimiser out of all three learning rate values considered.

3.1.3. Impact of Dropout Rate on Multiphase Interturn Short-Circuit Classification

The dropout rate informs about the number of neurones that will randomly ‘extinguish’ in each epoch during the learning process. The impact of the dropout rate on the learning process is shown in Figure 15 and Figure 16.

Figure 15 and Figure 16 show the impact of the dropout on the quality of the optimiser. The article considered two values of the dropout coefficient: 0.3, meaning that 30% of neurones were dropped at each iteration, and 0.1, meaning that 10% of neurones were dropped. As can be seen, with the exception of the ADAM optimiser with a learning rate of 0.0005, the greatest impact of dropout can be seen in the case of the SGD algorithm. Again, increasing dropout clearly improved the classification results. In the case of the RMSProp and ADAM optimisers for the developed neural network, the impact of dropout is not significant; however, the best classification results were obtained for the ADAM optimiser with a dropout value of 0.3.

Figure 15. Metric values for the dropout rate equal to 0.3.

Figure 15. Metric values for the dropout rate equal to 0.3.

Figure 16. The metric values for the dropout rate equal to 0.1.

Figure 16. The metric values for the dropout rate equal to 0.1.

3.2. Tuned CNN—Stage II

The next stage of the research was to tune such model parameters as the number of kernels in the convolutional layers and the number of kernels in the dense layer. The tuned parameters and the range of their variability in the second stage are presented in

Table 6. Hyperparameter values during second turn.

Parameters	Values
The number of kernels in the first two convolutional layers of the network	128,256
The number of kernels in the third and fourth convolutional layers of the network	256,512
The number of units in the dense layer	265,512

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The results of optimisation in the second stage of network learning are shown in Figure 17, Figure 18 and Figure 19 and

Table 7. Hyperparameter tuning results in Stage II.

No. of Kernels in the 1st and 2nd Conv Layers	No. of Kernels in the 3rd and 4th Conv Layers	No. of Neurones in the Dense Layer	Metrics	Step
254	256	256	0.715	102
128	512	512	0.633	51
254	512	512	0.713	63
128	256	512	0.699	70
254	512	256	0.667	85
128	512	256	0.615	78
254	256	512	0.753	87
128	256	256	0.686	82

Green color—the best result.

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Figure 17, Figure 18 and Figure 19 show the results of the network training process. Figure 17 shows how the metric value changed in subsequent epochs while training the model. Figure 18 shows the decline in the loss function as a function of epochs, while Figure 19 graphically presents the considered configurations of the network hyperparameters used during the second stage of network tuning.

3.2.1. Impact of Number of Kernels on Multiphase Interturn Short-Circuit Classification

Choosing the right number of kernels in convolutional layers can have a crucial impact on the quality of short-circuit classification. Too few kernels may be insufficient to detect specific features of the current signal during short circuits for a small number of shorted turns, while too many kernels may lead to overfitting of the model. Therefore, the appropriate choice of the number of kernels can significantly affect the results. The choice of the number of kernels depends on the problem under consideration. In general, it requires extensive experience of the diagnostician, but in order to eliminate the influence of the human factor, the article proposes the selection of the number of kernels for the problem of interturn short circuits using the grid search method.

The results grouped by layers are presented in Figure 19, Figure 20, Figure 21, Figure 22, Figure 23 and Figure 24.

During the research, the influence of the network structure on the recognition of stator failures was also checked. Figure 20 and Figure 21 show the influence of the number of neurones in the first and second convolutional layers. It can be noticed that increasing the number of neurones in the case of classifying a large number of interturn short circuit configurations has a positive effect on the classification result.

Figure 22. Metric value for 256 kernels in the 3rd and 4th conv layers.

Figure 22. Metric value for 256 kernels in the 3rd and 4th conv layers.

Figure 23. Metric value for 512 kernels in the 3rd and 4th conv layers.

Figure 23. Metric value for 512 kernels in the 3rd and 4th conv layers.

Then, the influence of the number of neurones in the deeper layers of the network on the quality of failure classification was checked. As can be seen in Figure 21 and Figure 22, in this case, unlike increasing the number of neurones in the first and second layers, the quality of the classifier deteriorates. One of the reasons may be overfitting, i.e., overfitting the model to detect short circuits in the training set, which may negatively affect generalisation. Too many neurones may result in model overfitting.

3.2.2. Impact of Number of Neurones in Dense Layer on Multiphase Interturn Short-Circuit Classification

The impact of changing the number of neurones in the dense layer on the network results is shown in Figure 24 and Figure 25.

The concept of network operation and the selected results are presented in Figure 26 and Figure 27, respectively. The confusion matrix represents the number of correct network responses in relation to the expected value. The vertical axis shows the expected values, while the horizontal axis shows the values predicted by the network. The description of the axis in Figure 27 refers to the number of shorted turns in the individual phases of the machines. The value on the left corresponds to phase A, the middle value corresponds to phase B, and the right value corresponds to phase C. The values specifying the number of shorted turns in the phase are separated by a space character. Due to limitations in the size of the figure, only a sample slice of the confusion matrix is shown.

Figure 24. Metric value for 256 neurones in the dense layer.

Figure 24. Metric value for 256 neurones in the dense layer.

Figure 25. Metric value for 512 neurones in the dense layer.

Figure 25. Metric value for 512 neurones in the dense layer.

The change in the number of neurones in the case of convolutional layers concerned the part of the model that was used to extract detailed features from the training set. During the research, in addition to the influence of changes in the number of neurones in the part of the model related to feature extraction, the influence of the number of neurones in the part of the model responsible for classification, that is, in the dense layer, was also examined. As can be seen in Figure 24 and Figure 25, in the general case, increasing the number of neurones in the classification part of the developed network improved the quality of failure detection. Only in the case of 254 neurones in the convolutional layers and 512 neurones in the dense layer is a deterioration in the quality of classification visible.

Figure 26. The concept of neural network operation.

Figure 26. The concept of neural network operation.

Figure 27. Example of a neural network result.

Figure 27. Example of a neural network result.

Due to the size of the confusion matrix, Figure 27 shows only randomly selected results for randomly selected classes. The number of examples classified correctly is marked in green, while the examples classified incorrectly are marked in yellow.

4. Conclusions

The paper presents stator winding diagnostics of an induction machine with a multiphase interturn short circuits failure. During the diagnostic process, a deep neural network was successfully used. The use of advanced structures of deep neural networks in the diagnostics of electric motors allows for diagnostics based on more complex learning patterns. In addition, the paper presents the method and the influence of selected network hyperparameter tuning on the learning results. Research has shown that in the case of using deep neural networks in the diagnosis of the three-phase squirrel-cage induction machine stator winding, hyperparameter tuning based on the grid search method can be used successfully. Furthermore, trends in the tuning of network parameters were indicated during the generalisation of the fault classification process in induction machines. It can be seen in the case of stator winding diagnostics in the form of multiphase interturn short circuits with selected parameters: the worst results were obtained by using the SGD optimiser. The best results were obtained using the ADAM optimiser, with a small value of the learning coefficient, which may affect the speed at which the algorithm achieves convergence, but allows for better results during failure classification. In the further part of the investigation, the influence of the number of kernels in the convolutional layers and units in the dense layer on the results of the stator winding failure classifier was demonstrated. As can be seen, increasing the number of kernels to 254 and 256 in the respective convolutional layers, as well as increasing the number of neurones in the dense layer to 512 improved the classification quality. However, too many kernels and units in the dense layer, due to too-fast adjustment of the network to the training data, may shorten the time required to achieve convergence, but may have a negative impact on inferring the degree of failure of the machine.