Detection of an Incipient Fault for Dual Three-Phase PMSMs Using a Modified Autoencoder

Abstract

For the detection of incipient interturn short-circuit (IITSC) faults of machines without shutting them down, there are still shortcomings of insufficient incipient fault features and a high false alarm rate. This is especially the case for dual three-phase permanent magnet synchronous motors (PMSMs) with complex winding structures, and this kind of incipient fault detection is more complicated. To solve this detection difficulty, an IITSC detection method for dual three-phase PMSMs is proposed based on a modified deep autoencoder (MDAE). This autoencoder (AE) adopts an improved distribution metric combined with the maximum mean discrepancy (MMD) and the maximum covariance discrepancy (MCD) to extract the fault feature from the common features, which can improve the feature difference between the normal state and the incipient fault state. Then, the permutation entropy of the extracted features is calculated to detect the IITSC faults. The results illustrate that this method can not only detect IITSC faults online effectively and robustly, but also reduce the false alarm rate of the fault detection for dual three-phase PMSMs.

1. Introduction

According to industrial investigations, stator related faults have been addressed as the universal faults in electrical motors, which account for 21–37% of the overall machine faults [1]. Thus, the incipient detection of stator faults is indispensable for the reliable operation of electrical machines. For dual three-phase PMSMs, IITSC faults are excited by the insulation failures, which are more likely to quickly develop into serious interphase faults in case no incipient detections are employed [2]. A lot of adverse effects, including voltage stresses, strong vibration, accelerated aging and excessive temperature are caused by the insulation failures. The insulation breakdown between two turns constitutes serious faults. Thus, it is very important to detect IITSC faults online for dual three-phase PMSMs. Several approaches on IITSCs have been exploited to realize the accurate detection at the early stage, which can be classified into model-based, signature-based and artificial intelligence-based approaches.

For the model-based approach, the observer and parameter estimation are applied to the incipient fault detection [3]. For the signature-based approach, different signals including current [4], voltage [5], flux [6] and electromotive force [7] are used for intrusive and nonintrusive detection. To achieve the nonintrusive detection, a motor current signature analysis (MCSA) is the common approach for various types of motors [8], where the frequency analysis of the phase currents is performed to monitor the unusual harmonics caused by an interturn fault. In view of extracting the changes of these signals, some techniques, based on the wavelet transform [9], the space vector and its variances [10] and the Hilbert–Huang transform [11] are performed. Although a lot of methods have been extensively studied in the existing literature, it is difficult to identify and distinguish early abnormal signals of motor windings, especially under the interference of an inherent asymmetry and voltage balance.

For the artificial intelligence-based approach, even though the artificial neural network [12] and the fuzzy logic system [13] are capable of learning with the lack of domain knowledge, the large-scale calculation and high complexity limit the practical application in the online IITSC fault detection. For the online IITSC fault detection, the usual method is to construct incipient fault features such as time-frequency or wavelet features from the various types of signals, then build a support vector machine or Bayes classifiers [14] for the anomaly detection. However, these methods have the following disadvantages. On the one hand, it usually cannot adaptively extract features. Instead, it requires a certain amount of offline data training in order to obtain a detection model. While, the data collected by the detection target object online is limited, and the distribution of these data and the training data may be different due to random noise and variable operating conditions, which result in the offline training model is not completely suitable for online data, thereby reducing the accuracy of the detection results. On the other hand, these methods usually use detection algorithms based on abnormal points, and do not consider the temporal relationship of the samples. It is easy to cause false alarms due to the small data fluctuations. Moreover, the alarm threshold needs to be adjusted repeatedly.

Recently, the deep learning-based approaches such as convolutional neural networks (CNNs) [15,16], recurrent neural networks (RNNs) [17] and the deep extreme learning machine [18] have been used in online incipient fault detection to automatically extract features from the input data. In [19], a data-driven method, namely a deep slow feature analysis and belief rule base method (DSFA-BRB) has been advanced, which uses two kinds of statistics to perform fault detection on the multi-dimensional data of the running gears. It is possible to avoid misjudgment caused by the data incompleteness. However, the definition of the incipient fault is not given in the actual project, and is defined by the changing trend of the data. In [20], an integration strategy of a data-driven and deep learning-based method is proposed to deal with incipient faults for electrical traction systems. The moving average technique is introduced into the canonical correlation analysis (CCA) framework. The fault matrices are defined and regarded as the input of a CNN whose feature extraction ability is highly improved, which can be implemented without any knowledge on the system information. In [21], three tools (SVM, CNN and RNN) from machine learning were used in order to address the challenge of incipient faults for a DC motor, and the CNN performed the best. These approaches can adaptively extract deep features with rich information and strong discriminative abilities, which have a good universal adaptability.

However, deep learning-based approaches also have some shortcomings. On the one hand, a large amount of auxiliary data is required for model training, yet the historically collected auxiliary data may be quite different from the target object data, thus training of these data directly cannot effectively improve the feature representation of the online detection. On the other hand, during the training process, it fails to strengthen the corresponding feature representation of the state changes caused by the incipient faults. Therefore, there are still improvements in the application of the deep learning-based approaches in online incipient faults detection. In [22], a transfer learning method based on the federated neural network is proposed for detecting sensor faults in dynamic systems with consideration of actuator-performance degradation. Compared with the existing transfer learning-based methods, this method not only can handle any type of data regardless of their probability distribution, but it also avoids a trial-and-error endeavor when establishing the structure and training the networks. Although the proposed structure can be regarded as a new unified framework for the data-driven parameter identification with an adaptive model calibration, it is aimed at the dynamic systems with a performance degradation and does not involve any incipient fault identification. Besides, a dynamic domain adaptation method based on deep multiple AEs with attention mechanism (DMAEAM-DDA) is proposed for the rotary machine fault diagnosis under different working conditions [23]. In [24], a collaborative and adversarial deep transfer model was based on a convolutional AE for the intelligent fault diagnosis. In [25], a rolling bearing initial fault diagnosis model was based on a second-order cyclic autocorrelation and deep AE combined with transfer learning is proposed to improve the overall performance of rolling bearing fault identification. Thus, the deep AE combined with transfer learning is favorable for fault diagnosis.

Based on the analysis, the key to improving the effect of IITSC online faults detection includes: (i) The ability to express the incipient fault features must be improved, and the distinction between the normal state features and the incipient fault features also must be enhanced. (ii) The auxiliary data from different operating conditions and different sources is reasonably applied for model training. (iii) A simple and effective alarm strategy must be constructed to reduce the false alarm rate in normal conditions. Thus, a deep transfer learning-based approach is introduced to IITSC online fault detection in this article. It is confirmed in existing literature that the deep transfer learning can effectively solve the learning problem with insufficient samples available [26,27,28]. In the proposed approach, the more obvious IITSC fault features can be extracted by the deep AE network with an improved distribution metric. Based on the research contributions of the existing literature, this article proposes the following contributions.

(i) Based on the improved AE used in the fault diagnosis, a MDAE network with an improved distribution metric is proposed to extract IITSC deep features. The network model is different from most existing models. The MMD and the MCD are combined to use in the MDAE. It not only adaptively extracts the common feature among the data from different domains, but also improves the feature difference between a normal state and an early fault state as well.

(ii) An IITSC detection method for dual three-phase PMSMs is proposed based on the MDAE. Compared with existing approaches, the proposed approach not only improves the accuracy and robustness, but also reduces the false alarm.

The remainder of this article is organized as follows. In Section 2, the description of the IITSC fault and dataset features of the dual three-phase PMSMs are elaborated. In Section 3, a MDAE network with an improved distribution metric is used to detect the IITSC fault. Then, an IITSC fault detection approach based on the MDAE network is advanced in Section 4. Finally, the results illustrate that the proposed approach can detect the IITSC fault effectively in Section 5.

2. IITSC Fault and Dataset Description

2.1. IITSC Fault

The assignment of the individual coils to subsystems is formed by a concentrated winding. Assuming the IITSC occurs in phase A, the fault phase is divided into two parts, one part is the interturn short-circuit and the other part is the rest windings. The windings connection of the dual three-phase PMSM is shown in Figure 1.

For IITSC faults, the phase current depends on the electrical motor speed and the interturn shorted turns, which is often used to diagnose the interturn short-circuit fault [5]. Moreover, the phase current can also reflect the fault degree. Thus, the phase current is also selected as the feature in this article.

2.2. Dataset Description

To obtain the condition monitoring dataset, several repeated tests on the prototype are carried out under the various operation conditions. Setting the dataset as $\left\{{\left\{x_i^1\right\}}_{i=1}^{n_1},{\left\{x_i^2\right\}}_{i=1}^{n_2},\cdots ,{\left\{x_i^k\right\}}_{i=1}^{n_k}\right\}$, which contains n samples under each condition. The sample $x_i^k$ belongs to the sample space ꭓ^t, and the data generation obeys with the marginal probability distribution. The actual operation and measurement environment of the motors is complex and changeable, thus the distribution of data collected under different operating conditions is quite different [29].

According to features of incipient fault detection database in [30] and the fault feature of the IITSC, the dataset of the IITSC detection has the following features: (i) The degradation process from the healthy state to the fault state should be reflected in the collected dataset. (ii) No matter what the operation conditions, the data evolution from its normal state to its IITSC fault state should be consistent. (iii) The healthy data and the IITSC fault data are difficult to distinguish. (iv) For the target domain data Ɗ^t, it is composed of the sample space of the target object data ꭓ^t and its obeyed data distribution. The amount of the target domain data is usually small. (v) For the source domain data Ɗ^s, it is composed of the data sample space of the stator winding current ꭓ^s and its obeyed data distribution under different conditions. (vi) The source domain can provide the required evolution knowledge from the healthy state to the IITSC state for the online detection.

3. MDAE Network with an Improved Distribution Metric

3.1. Basic AE Network

In this approach, a multi-layer AE is used as the basic deep network model, which can minimize the reconstruction error e_AE. The AE always consists of an encoder and decoder. The encoder H is used to extract features from the input data, while the decoder Z is used to reconstruct the input data from the extracted features. Based on [30], the H, Z and e_AE are respectively denoted as

$$\{\begin{array}{l}H=f\left(WX+b\right)\\ Z=g\left(W^{\prime }H+b^{\prime }\right)\\ e_{AE}=\frac{1}{2n}{\Vert Z-X\Vert }_F^2\end{array}$$

(1)

where W is the matrix of the input layer and the hidden layer, ‖·‖_F is the Frobenius norm. Furthermore, domains Ɗ^s and Ɗ^t are taken as examples, the MMD distance is defined as

$$\mathrm{MMD}\left(X^s,X^t\right)={\Vert \frac{1}{n^s}{\displaystyle \sum _{i=1}^{n^s}\phi \left(x_i^s\right)-\frac{1}{n^t}{\displaystyle \sum _{j=1}^{n^t}\phi \left(x_j^t\right)}}\Vert }_{{}_H}^{}$$

(2)

where H represents the regenerative nuclear Hilbert space, X^s and X^t respectively indicate the input sample set in the source domain and the target domain, n^s and n^t indicate the number of samples in the source domain and target domain.

3.2. MMD + MCD

To train the transfer learning model conveniently, the monitoring data under various conditions are introduced for IITSC fault detection. However, using the MMD in (2) has two defects. For one, the two-by-two cross calculation is too complicated when the difference between two domains is minimized. For another, the distribution difference between the data of the different conditions is ignored when the data of the multiple conditions are unified as the source domain X^s. To avoid the above problems, the MMD in (2) is improved to realize the adaptation of the data distribution in multiple domains. Thus, the features can be directly extracted from the newly collected online data in the target domain. To solve the distribution difference of the normal state data under different working conditions, in the improved processes, the mean value FM of each monitoring data in the source domain and the target domain is calculated, and the TM of all of the monitoring data {X^s, X^t} is also calculated, then the difference between FM and TM is calculated to make a measure of the deviation degree from the overall distribution. The improved MMD is redefined by

$$e_{\mathrm{MMD}}=\mathrm{MMD}\left(X^{s_1};\cdots ;X^{s_c};X^t\right)={\displaystyle \sum _{j=1}^m{\Vert FM-TM\Vert }_{{}_{\mathrm{H}}}^{}}={{\displaystyle \sum _{j=1}^m\Vert \frac{1}{n^j}{\displaystyle \sum _{i=1}^{n^j}\phi \left(x_i^j\right)}-\frac{1}{m}{\displaystyle \sum _{j=1}^m\frac{1}{n^j}{\displaystyle \sum _{i=1}^{n^j}\phi \left(x_i^j\right)}}\Vert }}_{{}_{\mathrm{H}}}^{}$$

(3)

where s_C indicates the number of conditions, n^j is the number of samples of the j-th winding current, m is the number of currents in all source and target domains, and TM = $\frac{1}{n^j}{\displaystyle \sum _{i=1}^{n^j}\phi \left(x_i^j\right)}$, FM = $\frac{1}{m}{\displaystyle \sum _{j=1}^m\frac{1}{n^j}{\displaystyle \sum _{i=1}^{n^j}\phi \left(x_i^j\right)}}$. For the MCD, the empirical estimator is given by

$$\mathrm{MCD}\left(X^s,X^t\right)={\Vert \frac{1}{n^s}{\displaystyle \sum _{i=1}^{n^s}\phi \left(x_i^j\right)L_i\phi {\left(x_i^j\right)}^{\mathrm{T}}}-\frac{1}{n^t}{\displaystyle \sum _{j=1}^{n^t}\phi \left(x_j^t\right)}{L}_j\phi {\left(x_j^t\right)}^{\mathrm{T}}\Vert }_{\mathrm{H}}^{}$$

(4)

where $L_i=I_i-\frac{1}{i}{1}_i^{\mathrm{T}}{1}_i$, $L_j=I_j-\frac{1}{j}{1}_j^{\mathrm{T}}{1}_j$, I_n is the identity matrix of size n, 1_n is the vector of ones with length n.

To extract more information about distributions, the MMD and the MCD are combined, which is marked as MMD + MCD. This distribution metric is defined as

$$\left[\mathrm{MMD}+\mathrm{MCD}\right]\left(X^s,X^t\right)={\Vert \frac{1}{n^s}{\displaystyle \sum _{i=1}^{n^s}\phi \left(x_i^s\right)1_i-\frac{1}{n^t}{\displaystyle \sum _{j=1}^{n^t}\phi \left(x_j^t\right)1_j}}\Vert }_{\mathrm{H}}^{}+\beta {\Vert \frac{1}{n^s}{\displaystyle \sum _{i=1}^{n^s}\phi \left(x_i^s\right)H_i\phi {\left(x_i^s\right)}^{\mathrm{T}}-\frac{1}{n^t}{\displaystyle \sum _{j=1}^{n^t}\phi \left(x_j^t\right)H_j\phi {\left(x_j^t\right)}^{\mathrm{T}}}}\Vert }_{\mathrm{H}}^{}$$

(5)

where β is a non-negative parameter.

$$\begin{array}{l}{e}_{\mathrm{MMD}+\mathrm{MCD}}=\left[\mathrm{MMD}+\mathrm{MCD}\right]\left(X^{s_1};\cdots ;X^{s_c};X^t\right)={\displaystyle \sum _{j=1}^m{\Vert \frac{1}{n^j}{\displaystyle \sum _{i=1}^{n^j}\phi \left(x_i^j\right)1_i-\frac{1}{m}{\displaystyle \sum _{j=1}^m\frac{1}{n^j}{\displaystyle \sum _{i=1}^{n^j}\phi \left(x_i^j\right)1_j}}}\Vert }_{\mathrm{H}}^{}}\\ +\beta {\displaystyle \sum _{j=1}^m{\Vert \frac{1}{n^j}{\displaystyle \sum _{i=1}^{n^j}\phi \left(x_i^j\right)H_i\phi {\left(x_i^j\right)}^{\mathrm{T}}-\frac{1}{m}{\displaystyle \sum _{j=1}^m\frac{1}{n^j}{\displaystyle \sum _{j=1}^{n^j}\phi \left(x_i^j\right)H_j\phi {\left(x_i^j\right)}^{\mathrm{T}}}}}\Vert }_{\mathrm{H}}^{}}\end{array}$$

(6)

3.3. Regular Term

To strengthen the distinction between healthy state data and incipient fault data, changes in adjacent weights can be amplified. The introduction of a regular term can achieve this purpose. The Laplace regular term of the weight matrix is constructed according to the [30], which can be defined as

$$e_{weight}={\displaystyle \sum _{k=1}^K\exp \left(-{\Vert \Delta \cdot W_k\Vert }_F^2/\sigma \right)}$$

(7)

where K represents the number of weight matrices in the multi-layer AE, σ denotes the penalty factor, Δ = D₁$\otimes$I₂ + I₁$\otimes$D₂, I₁ and I₂ are the identity matrixes, D₁ and D₂ are the Laplace operator. The modified Neuman discretization operator is used to obtain D₁ and D₂, which means a second-order difference calculation [30]. All of the data from the healthy state to the fault state are used in this calculating process. Although the increase of the difference between adjacent weights signifies that the feature differences of the hidden layer corresponding to all samples become larger [30]. For the incipient fault samples, the minimization of e_weight can highlight the trend of signal fluctuations, so as to obtain a more sensitive feature representation for the incipient fault.

3.4. Objective Function

The differences denoted in (1), (6) and (7) are integrated together to get the objective function of the multi-domain AE, which is given by

$$e=e_{AE}+{\lambda }_1{e}_{\mathrm{MMD}+\mathrm{MCD}}+\frac{{\lambda }_2}{2}{e}_{weight}$$

(8)

where both λ₁ and λ₂ are regularization parameters. The purpose of introducing the regularization parameter is to improve the extraction ability of the common features. And, λ₁ and λ₂ are both greater than zero. The mini-batch gradient descent method is used to minimize (8). The optimization process mainly includes the initialization, the forward propagation, the backpropagation and the feature extraction. The detailed steps of each process are displayed in Figure 2.

4. IITSC Online Fault Detection Based on the Proposed AE Network

4.1. Overall Framework of the IITSC Detection Algorithm

Based on the traditional structure of the AE network, the MDAE network for the IITSC detection is shown in Figure 3.

The IITSC fault detection contains offline training and fault detection, which is displayed in Figure 4. In the process of the offline training, a deep transfer learning model is constructed and a detection model is built. In the process of the fault detection, features of the target object are directly extracted, then the IITSC is recognized. Actually, the transfer learning has two functions in the proposed approach. One is adapting the monitoring data distribution of the Ɗ^s to the Ɗ^t, and establishing a common feature of the healthy state. The other is improving the effectiveness and robustness of the detection model by the discrimination information between the incipient fault data and the healthy state data in the Ɗ^s.

4.2. Abnormal Detection Model

For the detection, the fault detection model should have a better accuracy and real-time performance. In Figure 4, an anomaly detection model is set, and the permutation entropy is used to construct a robust detection model. The permutation entropy is a dynamic mutation detection method, which can amplify small changes in the signal. The principle of the permutation entropy is described in [31], and the permutation entropy can be used to display the local changing trend of the data. However, it is necessary to set a reasonable threshold for the anomaly detection. The overall process is summarized as follows:

In the offline training process, the common features extracted are used to calculate the permutation entropy of the normal stator winding data under different conditions. Then, the minimum of these permutation entropies is treated as the detection threshold. In the fault detection process, the MDAE is used to extract the depth features, then the corresponding permutation entropy is calculated and compared with the threshold. If the permutation entropy exceeds the threshold, then the IITSC will occur and the fault phase will be identified.

5. Experimental Results

5.1. Experiment Platform and Data Processing

A dual three-phase PMSM is treated as a prototype. The specifications are shown in

Table 1. Specifications of the PMSM.

Parameter	Value	Parameter	Value	Parameter	Value
Number of phases	6	Number of coils	12	Maximum current	300 A
Rated power	2.2 kW	Turns per phase	10	Maximum torque	310 N·m

. The platform comprises a controller to generate command signals from the power switches, a computer as a real-time control interface, as shown in Figure 5. A digital signal processor is used to generate the control signals. The Hall current sensors CSNE151-100 are adopted to collect the current signals.

In this section, a series of experiments are implemented. The basic experimental process is as follows. Firstly, the six phase currents from three different working conditions are arbitrarily chosen, two conditions of which are used as the source domain and the other one is used as the target domain, as shown in

Table 2. Description of three different operating conditions in the dataset.

Operating Conditions	Speed (r/min)	Torque (N·m)	Winding Dataset
1	400	0	A1_1  A1_2  B1_1  B1_2  C1_1  C1_2
2	800	3	A2_1  A2_2  B2_1  B2_2  C2_1  C2_2
3	1200	5	A3_1  A3_2  B3_1  B3_2  C3_1  C3_2

. For the dual three-phase PMSM, the currents of 12 phase windings in two working conditions in the source domain and currents of 5 phase windings in the target domain are all treated as the offline data. Then, the permutation entropies corresponding to the 17 phase winding currents are all calculated, and the abnormal detection threshold is determined according to the calculation of the permutation entropies. Ultimately, the remaining phase current is taken as the target object for the online detection, and the trained common feature is used to extract the feature. The permutation entropy is calculated, which is compared with the threshold in order to determine if there is an abnormality. All data are linearly normalized to [−1, +1] before processing, and the current signals are converted into spectral data by FFT as the input.

5.2. Test Results

5.2.1. Extracted Feature Results

Considering the large number of training samples, the training termination condition is set as the number of training times reaches 10,000 times or the training loss is less than 0.01. Firstly, the healthy signals of the six stator windings under the three operating conditions are taken to train by the traditional AE and the proposed approach in this article, respectively. The probability density distribution and feature distribution of the depth features obtained by the AE and the proposed approach in this article are shown in Figure 6 and Figure 7, respectively. It can be seen from the Figure 6 that the distribution of the normal data under different conditions is quite different. Even under the same conditions, there are some fluctuations in the normal data. However, the data distribution under all conditions obtained by the MDAE tends to be consistent, as shown in Figure 7a. Meanwhile, the feature distribution obtained by the proposed approach displayed in Figure 7b is a greater polymeric than that obtained by the MDAE in Figure 6b. Thus, it is illustrated that the MDAE can effectively extract the common features of the normal data for the stator windings under different conditions.

To verify the convergence of the proposed method, the training error during the training process is displayed in Figure 8. It can be seen that the training error has obviously converged at about 500 training times. In the subsequent training rounds, although the training error continues to decrease, the rate of decrease gradually slows down, and the overall trend tends to converge.

5.2.2. Permutation Entropy Results

To further verify the effect of the proposed method, the features described in Figure 6 and Figure 7 are used to calculate the permutation entropy of the normal state data, as shown in Figure 9. In Figure 9a, due to a certain distribution difference in the normal state data, the permutation entropy almost spans the entire range from 0 to 1 based on the ordinary AE, yet the permutation entropy of the normal state data keeps fluctuating within a smaller range based on using the MDAE to extract common features in Figure 9b. Thus, a reasonable threshold is set according to the fluctuation range and defined as the lower limit of the fluctuation range obtained by the MDAE with MMD + MCD.

To verify the significant effect of the Laplace term in (9) for extracting the incipient fault features, the phase A under condition 1 and the phase B under condition 2 are selected as the detection objects, as well as the extracted features and the permutation entropy are calculated, as shown in Figure 10 and Figure 11.

For the target phase A and B in Figure 10a and Figure 11a, the feature extracted by the MMD + MCD + Laplace fluctuates more greatly than that by only the MMD + MCD, which indicates the feature extracted by the MMD + MCD + Laplace is more sensitive. Moreover, the corresponding permutation entropy values obtained by the MMD + MCD + Laplace have an obvious step state in Figure 10b and Figure 11b. It can be demonstrated that the discrimination between the normal state and the incipient fault is more distinguished by adding the Laplace into the MMD + MCD.

5.3. Experimental Results of the IISC

In this section, the B1_1 and the C2_2 windings are respectively selected as the detection target and the remaining stator windings are used for the offline training. The operating condition of the target winding B1_1 is treated as the target domain and the other two conditions are seen as the source domain.

5.3.1. Experiment for the Winding C2_2

For the target detection winding C2_2, the operating condition 2 is treated as the target domain and the operating conditions 1 and 3 are seen as the source domain. Currents of the A1_1, A1_2, B1_1, B1_2, C1_1, C1_2, A2_1, A2_2, B2_1, B2_2, C2_1, A3_1, A3_2, B3_1, B3_2, C3_1 and C3_2, are all chosen as the training data and executed in the offline training. Then, the permutation entropy values corresponding to currents of 17 phase windings are all calculated by sequence according to the sliding window way. Following the normal state offline data training, the permutation entropy values are obtained and shown in Figure 12a. The permutation entropy values of these normal state data fluctuate basically in the same range, which indicates that the common features of the normal state data can be extracted significantly by the MDAE. Meanwhile, the fluctuation range of the permutation entropies in the normal state data is from 0.6521 to 1, and the lower limit of the fluctuation range in Figure 12a is 0.6521, thus, the detection threshold is defined as 0.6521.

Then, the fault detection is executed for the stator windings. The extracted feature and the corresponding permutation entropy of the stator winding C2_2, are all acquired, as shown in Figure 12b. The feature of the target winding is presented in the first screen of Figure 12b, and the permutation entropy is shown in the second screen. In the first screen, the feature of the first 800 samples fluctuates within a very small range, but the feature of the subsequent samples begins to change obviously. In the second screen, before the sequence 80, the permutation entropy value fluctuates within a small range and does not exceed the detection threshold. Following the sequence 80, the permutation entropy begins decrease, and fluctuates in a wide range, and the fluctuation range is distributed in the entire interval from 0 to 1. It can be seen that the permutation entropy corresponding to the executed feature of the 900th sample exceeds the detection threshold, which means the IITSC occurs in the winding C2_2. This detection result is also consistent with the feature trend changes in Figure 12b.

5.3.2. Experiment for Winding B1_1

For the target detection winding B1_1, the operating condition 1 is adjusted to the target domain and the operating conditions 2 and 3 are regulated to the source domain. The currents of the A1_1, A1_2, B1_2, C1_1, C1_2, A2_1, A2_2, B2_1, B2_2, C2_1, C2_2, A3_1, A3_2, B3_1, B3_2, C3_1 and C3_2, are selected as the training data to be executed in the offline training. Then, the permutation entropy values corresponding to the currents of 17 windings are all obtained according to the sliding window way, as shown in Figure 13. It can be seen that the permutation entropy values corresponding to the executed features of these 17 windings also fluctuate in a smaller range, even if the settings of the source domain and the target domain are adjusted. It is verified that the deep transfer learning has the powerful ability to extract common features. Meanwhile, the fluctuation range of the permutation entropies in the normal state data is from 0.748 to 1. Thus, the detection threshold is defined as 0.748 according to the lower limit of the fluctuation range in Figure 13a.

In the fault detection process, the extracted feature and the corresponding permutation entropy of the B1_1 are calculated and displayed in Figure 13b. Similarly, the feature of the target winding B1_1 is presented in the first screen of Figure 13b, and the corresponding permutation entropy is shown in the second screen. In the first screen, the feature of the first 1050 samples basically remain at a constant value, but the features of the subsequent samples begin to fluctuate widely. In the second screen, before the sequence 105, the permutation entropy value fluctuates within a small range and does not exceed the detection threshold. Following the sequence 105, the permutation entropy also begins to fluctuate obviously, and the fluctuation range is greatly expanded. The permutation entropy corresponding to the feature of the 1050th sample exceeds 0.748, which reveals the IISC occurs in the B1_1.

5.4. Comparison of the Related Methods

To further verify the capabilities of the proposed method, the comparison results of the proposed method and the five incipient fault detection methods are shown in

Table 3. Comparative detection results of the different methods.

Detection Methods	B1-1 Results	Number of False Alarms	C2-2 Results	Number of False Alarms
SDFM [27]	1160	0	1090	0
DMDA [26]	1218	1	1150	1
SCNN [15]	1153	4	981	6
DBN [32]	1162	3	990	2
Method of this article	1050	0	900	0

. The five comparison methods are detailed as follows:

(1) Self-adaptive deep feature matching (SDFM): In this deep learning algorithm, the stacked denoising autoencoder (SDAE) is introduced to extract the common deep features of the normal state and early fault state. It can be seen that the detection result of this method is relatively ideal, and there is no false alarm. However, the result of the C2_2 is slightly delayed.

(2) Deep model domain adaptation (DMDA): This method can improve the diagnosis accuracy of the fault data under different operating conditions. However, the result is also delayed. If the data is more discriminative, the detection effect of the DMDA is better. However, for the incipient fault data, the boundary of the fault is not obvious, which makes the method unable to effectively identify the slow changes in data;

(3) Simplified convolutional neural network (SCNN): The direct signal analysis and a simplified CNN are combined to detect the IITSC. The use of the stator phase currents and phase-to-phase voltages in the detection process are burdened with a minor influence of the supply voltage frequency. Nevertheless, the detection accuracy of the incipient damage stage achieved during the online tests is not high;

(4) Deep Boltzmann machine (DBN): Fault features can be directly extracted from the original time-domain signal, and it no longer relies on the feature extraction methods proposed by traditional signal processing techniques. However, it has higher false alarms.

6. Conclusions

For dual three-phase PMSMs, this article proposes a detection method to identify the IITSC fault based on the MDAE. The MDAE with the MMD + MCD distribution metric is set to extract the incipient fault feature from the common features. Compared with the existing feature extraction methods, the MDAE can improve the distinction between the incipient fault and the normal state features effectively and extract more sensitive incipient fault features. Moreover, the determination of the permutation entropy is used to detect IITSC faults. Compared with the existing detection methods, the online detection results show that the numbers of false alarms all reach zero no matter what phase winding. The compared results illustrate that the proposed method not only has a higher reliability and accuracy, but also reduces the number of false alarms. The future study will be to generalize the proposed method to the incipient fault detection of other types of motors and faults.