Neural Networks Detect Inter-Turn Short Circuit Faults Using Inverter Switching Statistics for a Closed-Loop Controlled Motor Drive

Early detection of an inter-turn short circuit fault (ISCF) can reduce repair costs and downtime of an electrical machine. In an induction machine (IM) driven by an inverter with a model predictive control (MPC) algorithm, the controller outputs are influenced by a fault due to the fault-controller interaction. Based on this observation, this study developed neural network models using inverter switching statistics to detect the ISCF of an IM. The method was non-invasive, and it did not require any additional sensors. In the fault detection task, an area under receiver operating characteristics curve value of 0.9950 (95% Confidence Interval: 0.9949 – 0.9951) was obtained. At the rated operating conditions, the neural network model detected and located an ISCF of 2-turns (out of 104 turns per phase) under 0.1 seconds, a speedup of more than two times compared to the thresholding-based method. Moreover, we published the switching vector data collected at various load torque and shaft speed values for healthy and faulty states of the IM, becoming the first publicly available ISCF detection dataset. Together with the dataset, we provided performance baselines for three main neural network architectures, namely, multi-layer perceptron, convolutional neural network, and recurrent neural network.

Neural Networks Detect Inter-Turn Short Circuit Faults Using Inverter Switching Statistics for a Closed-Loop Controlled Motor Drive Mustafa Umit Oner , İlker Şahin , and Ozan Keysan Abstract-Early detection of an inter-turn short circuit fault (ISCF) can reduce repair costs and downtime of an electrical machine.In an induction machine (IM) driven by an inverter with a model predictive control (MPC) algorithm, the controller outputs are influenced by a fault due to the fault-controller interaction.Based on this observation, this study developed neural network models using inverter switching statistics to detect the ISCF of an IM.The method was non-invasive, and it did not require any additional sensors.In the fault detection task, an area under receiver operating characteristics curve value of 0.9950 (95% Confidence Interval: 0.9949 -0.9951) was obtained.At the rated operating conditions, the neural network model detected and located an ISCF of 2-turns (out of 104 turns per phase) under 0.1 seconds, a speedup of more than two times compared to the thresholdingbased method.Moreover, we published the switching vector data collected at various load torque and shaft speed values for healthy and faulty states of the IM, becoming the first publicly available ISCF detection dataset.Together with the dataset, we provided performance baselines for three main neural network architectures, namely, multi-layer perceptron, convolutional neural network, and recurrent neural network.Index Terms-Condition monitoring, fault diagnosis, induction motor, machine learning, motor drives, multi-layer perceptron, neural networks, model predictive control.

I. INTRODUCTION
O WING to its value and significance, fault diagnosis of electrical machines has been a focus of intensive research, as reflected by a plethora of publications over the past years [1], [2], [3], [4].The early detection of an incipient fault can enable repair cost and downtime reduction benefits.Furthermore, provided that the machine is fault-tolerant by design and proper identification of the inflicting fault is made, the continuum of operation with a reduced rating is also possible.Mustafa Umit Oner is with the Artificial Intelligence Engineering Department, Bahcesehir University, 34349 Istanbul, Turkey (e-mail: mustafaumit.oner@eng.bau.edu.tr).
Ozan Keysan is with the Electrical and Electronics Engineering Department, Middle East Technical University, 06800 Ankara, Turkey (e-mail: keysan@metu.edu.tr).
Color versions of one or more figures in this article are available at https://doi.org/10.1109/TEC.2023.3274052.
Digital Object Identifier 10.1109/TEC.2023.3274052 Several fault detection methods that address induction motors (IM) have been reported [5], [6], [7] as the IM is the most commonly used AC machine type due to its low cost and ruggedness.It is estimated that the stator faults constitute 21% of all the faults [8].Stator faults usually start as inter-turn short circuit faults (ISCF) [9] and quickly develop further into complete phase-to-phase or phase-to-ground faults, which implies the total malfunctioning of the machine.Depending on the machine and the fault's structure, the time between ISCF occurrence and the total loss of insulation is in the order of seconds [10].Therefore, a swift and effective identification of an incipient ISCF is crucial.
An important distinction regarding the fault detection studies is the control method assumed for the motor.The motor can be line-fed (uncontrolled, open-loop) or closed-loop controlled via an inverter.There exists a complex interaction between the fault and the controller [11], [12], [13], [14].The controller inherently tries to negate the fault's effect.The bandwidth of the controller, hence the current regulating performance, emerges as an important parameter influencing fault-controller interaction [13], [14].It is shown in [15] that an IM drive implemented with finite control set model predictive control (FCS-MPC) continues to exhibit perfectly balanced phase currents under an ISCF of 3-turns (out of 104 turns per phase).However, a significant unbalance is observed for the line-fed operation under the same fault condition.This example implies that most fault detection methods developed considering line-fed machines (such as motor current signature analysis) would be less effective (if not totally useless) for a high-performance control case.Therefore, it is essential to develop a fault detection method in conjunction with the main control algorithm.
Recently, the utilization of artificial intelligence (AI) techniques, such as neural networks (NN), has been gaining increasing momentum in power electronics [32], [33].A particular area for which the NN approach is very suitable is the fault diagnosis of electrical machines.Several studies have developed AI-based fault detection methods as reviewed in [34], [35], [36], [37].They mostly use stator currents or vibration signals from additional sensors to extract the fault data.
While most of these studies are for bearing fault diagnosis [34], few are for ISCF [38], [39], [40], [41], [42], [43], [44], [45].Studies [38], [39], [40], [41] use neural networks to detect ISCFs in permanent magnet synchronous machines (PMSMs).Convolutional neural networks using stator phase currents, voltages, or flux as input, for example, are utilized for ISCF detection in [38], which requires additional sensors.Similarly, an NN-based method detects ISCFs down to 4.2% using phase currents and speed information in a closed-loop controlled machine in [41].However, no details regarding the controller structure or the controller-fault interaction are provided.For IMs, a data-driven online detection method utilizing multiple classifiers is proposed in [42].The fault information is acquired from phase currents and voltages.ISCFs down to 2% could have been detected.A multi-layer perceptron is trained to detect ISCFs down to 0.6% in [43].The three-phase shifts are utilized as the input data.An unsupervised learning-based NN using phase currents for fault detection is reported in [44].Similarly, ISCF detection is achieved in [45] using an NN-based method on stator currents of an IM driven by an inverter via open-loop scalar V/f control.While these studies [42], [43], [44], [45] consider IMs that work in an open-loop fashion, a closed-loop controlled IM, driven by a model predictive control structure is considered in this article, which constitutes a fundamental difference.
The voltage vectors of a two-level voltage source inverter (2L-VSI) are depicted in Fig. 1(a).In the standard FCS-MPC, the controller finds the optimum voltage vector in view of the control outcomes and applies it at the next switching instant.Hence, the controller outcomes are discrete voltage vectors and convenient for statistical approaches.
The evident benefits of achieving fault detection by examining controller outcomes are being non-invasive and requiring no additional sensor or circuit contrary to studies [25], [26], [27].Hence, no extra cost or complexity is introduced since switching vectors produced by the controller are readily available for analysis.
To the authors' knowledge, the utilization of inverter switching statistics for ISCF diagnosis was first proposed by [31].Later, it was utilized in [15] for ISCF detection in an IM driven by FCS-MPC using a simple thresholding-based approach with a manually set threshold level.This article employs NNs for ISCF diagnosis using inverter switching vectors of the same experimental setup of [15].With the utilization of NNs, improved fault detection performance over a broader range on the torque-speed plane is achieved in this study.A motor drive inverter with model predictive control produces an (almost) uniform distribution of active switching vectors while driving a healthy induction machine.However, an interturn short circuit in the stator changes the distribution of active switching vectors since the driver tries to compensate for the fault's influence for the proper operation of the motor (Fig. 1(b)).This observation constitutes the basis for this study.Our primary approach is to train a neural network with the switching vector data collected for healthy and faulty cases so that the trained structure can identify and locate an ISCF.The detection performance results prove the effectiveness of the proposed approach.
There are three main contributions of this article.1) A machine learning-based, non-invasive ISCF detection method using inverter switching statistics is introduced.
2) The first publicly available ISCF detection dataset containing switching vector data collected at various load torque and shaft speed values for healthy and faulty states of an induction machine is released.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.3) Performance baselines on the released dataset for three main neural network architectures, namely, multi-layer perceptron, convolutional neural network, and recurrent neural network are provided.

II. NEURAL NETWORK BASED ISCF DETECTION
This study designs neural network models detecting interturn short circuit faults in an induction machine driven by an inverter with model predictive control (Fig. 1(c) and Fig. 2).We formulate ISCF detection as a classification problem using inverter switching statistics.

A. Problem Formulation
Let X = {x 1 , . . ., x N } be a set of training samples such that each sample x i ∈ R D has a corresponding ground-truth label We train a model end-to-end using categoricalcross entropy as the loss function (1).

B. Neural Network Model Architectures
We constructed three different models using multi-layer perceptron (MLP), convolutional neural network (CNN), and recurrent neural network (RNN) architectures.Models are designed such that they have almost the same number of learnable parameters, i.e. 'capacity' (MLP: 4612, CNN: 4417, and RNN: 4418 learnable parameters).A model accepts a histogram of inverter switching statistics at the input and predicts the machine's status (healthy or faulty) at the output.
The multi-layer perceptron model consists of an input layer with 4 nodes, two hidden layers with 64 nodes, and an output layer with 2 nodes (Fig. 1(c)).Each layer computes a weighted sum of its inputs (s j = i w ji x i + b j , where s = [s j ] is the output vector, x = [x i ] is the input vector, W = [w ji ] is the learnable weight matrix, and b = [b j ] is the learnable bias vector), followed by a non-linear activation function.Hidden layers have a ReLU activation function (f (s) = max(0, s)) followed by a dropout with a rate of 0.5.The output layer has a softmax activation function producing normalized probability values, i.e., adding up to 1.
The convolutional neural network model consists of three convolutional layers with 32, 64, and 2 filters, respectively (Fig. 2(a)).Each convolutional layer computes a crosscorrelation of its inputs and filter weights (s j = i w i x j+i + b, where W = [w ji ] is the learnable and shared filter weights and b is the learnable bias).Except the last layer, each convolutional layer is followed by a ReLU activation function and a dropout with a rate of 0.5.Similar to the MLP model, outputs at the last layer are normalized using a softmax activation function.
The recurrent neural network model consists of a recurrent cell containing 64 hidden nodes and a fully connected layer as a linear classifier on top (Fig. 2(b)).A recurrent cell computes an affine transformation of the input and the previous hidden state, adds them up and passes through a non-linear activation function to compute the current hidden state (h t = f (W ih x + b ih + W hh h t−1 + b hh ), where W ih and W hh are learnable weight matrices, and b ih and b hh are learnable bias vectors).Note that non-linear activation function is ReLU, and after each recurrent step a dropout with a rate of 0.5 is applied on hidden state.

C. Experimental Setup and Preparation of the Machine Learning Dataset
The switching vectors of the motor drive inverter were collected from the same experimental setup utilized in [15].A photo of the setup is provided in Fig. 3.The parameters of the IM, on which intentional ISCFs of 2, 3, and 5 turns can be created for tests, are given in Table I as utilized in the MPC loop.The motor drive development kit TMDXIDDK379D from Texas Instruments is used as the motor drive inverter.The interested reader is referred to [46] for detailed descriptions regarding the FCS-MPC structure and equations, the laboratory implementation, and various test results including motor drive operation and the ISCF detection through switching vector analysis based on a simple thresholding method.
For several different combinations of speed and torque at healthy and faulty states (see Table II), the voltage vectors (decided by the controller and executed by the inverter) are recorded as time series of 22000 elements.The FCS-MPC algorithm has a control frequency of 40 kHz, therefore the record for the switching vector array of 22000 elements corresponds to a total of 0.55 s time interval.In the creation of Table II, frequency and torque

TABLE I INDUCTION MACHINE (IM) PARAMETERS
values are read from the waveform analyzer and torque sensor respectively, which are involved in the experimental setup shown in Fig. 3. ISCFs were introduced over 2 out of 104 turns in a phase winding of a star connected IM.Short circuits were created over an external cable, which introduces an additional resistance of 0.13 Ω and no additional resistance was utilized to resemble the fault resistance.Experimental results depicting successful fault detection performance with the simple thresholding approach for additional external fault resistances of 0.2 Ω and 0.33 Ω are provided in [46].
Collected data series (healthy: 30, faulty: 34) were segregated into two sets such that the first set (healthy: 16, faulty: 18) was for training and validation, and the second set (healthy: 14, faulty: 16) was for the test.Each data series in the first set was further split into two.The first 70% of data points constituted a data series for training, and the remaining 30% constituted a data series for validation.Then, machine learning datasets of training, validation, and test were prepared by creating sample and label pairs over respective data series.The dataset details are available with the released code [47].
Over a data series, multiple samples were created in a sliding window fashion with a step size of one.A sample was created by calculating the histogram of switching vectors over a window of five electrical periods (≈ 92 ms at the rated speed and torque)  ).The machine's status (i.e., healthy or faulty) was assigned as the sample's label.

D. Training and Testing of the NN Model
A neural network model was trained on samples created from training data series using the loss function given in (1).Early stopping based on loss in the validation dataset was employed to avoid overfitting.Finally, the model's performance was evaluated on the unseen test dataset.Please note that all models were trained and tested offline.They require neither storing the current dataset nor collecting new data during operation to identify ISCFs.
The area under the receiver operating characteristic curve (AUROC) was used as the performance metric.We also calculated the 95% confidence interval (CI) of the AUROC using the percentile bootstrap method [48].

E. Data and Code Availability
All original code and the dataset have been deposited at Zenodo under the https://doi.org/10.5281/zenodo.6774360and made publicly available [47].The dataset, code, and performance baselines are valuable resources to the research community for enabling reproducible and comparable experiments.

A. NNs Detect ISCF
We checked the performance of neural network models on ISCF detection.For each sample in the test set, we obtained a prediction from each trained model and plotted the receiver operating characteristic curves.We obtained AUROC values of 0.9946 (95% CI: 0.9945 -0.9947), 0.9942 (95% CI: 0.9940 -0.9943), and 0.9950 (95% CI: 0.9949 -0.9951) for the MLP, CNN, and RNN models, respectively.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.We also compared our models' performances with the performances of the models in [38] (Table III).Our models were about 1.3 to 7 times smaller, and our test set was about 74 times bigger than the models and test set in [38], respectively.Our models performed better than the models of [38] using stator currents and voltages.On the other hand, the model using the axial flux signal in [38] had a better performance than ours.However, it required an additional sensor for flux measurements, which was not the case for our models.
To check our models' generalization ability, we excluded data series collected at w = 2250 rpm and w = 3750 rpm from the training set (Table II).We retrained our MLP model from scratch.Similar to the performance of our MLP model trained on the whole training set, an AUROC value of 0.9946 (95% CI: 0.9945 -0.9947) was obtained on the test set.Furthermore, the model achieved an AUROC value of 0.9998 (95% CI: 0.9998 -0.9998) on data series collected at w = 2250 rpm and w = 3750 rpm in the test set (Table II), showing our model's generalization ability.Please note that the model had never seen data from a data series at these speeds.
We also analyzed the effect of training set size on the model's performance.We excluded some of the data series having similar speed and torque values from the training set (i.e., data series 6, 8, 11, 13, 15, 21, 23, 26, 28, 30, 32, and 34 were excluded (Table II)).Our MLP model was retrained from scratch and tested on the test set.Although the model was trained on less than 65% of the original training set, it achieved an AUROC value of 0.9944 (95% CI: 0.9943 -0.9945) on the test set, which was similar to the performance of the model trained on the whole training set.
To determine the MLP model's architecture, we conducted a hyperparameter search on hidden-layer sizes in the MLP model.By varying the hidden layer sizes (16,32, or 64 nodes in each hidden layer), we analyzed the effect of the model's capacity on its performance.As expected, we observed that the model's performance decreased with decreasing model capacity (Fig. 4).Therefore, we performed our experiments using the MLP model with 64 nodes in its two hidden layers.Nevertheless, the performance decrease was not drastic in the smaller networks, which could be preferable for real-world deployment since they require less computational power.
Besides, we checked the model's performance on identifying if a data series was collected at the healthy or faulty state of the machine.Prediction for a data series was obtained as the Fig. 4. The neural network models detect ISCF.Different NN models using the same architecture with different number of nodes in the hidden layers were trained and tested on the ISCF detection task.The area under receiver operating characteristics curve (AUROC) calculated on the test set was used as performance metric.We trained and tested the models using histogram of all vectors (0-vector included) and active vectors only (0-vector excluded).average of predictions of all samples created from the data series.Although we observed wrong predictions at the sample level in the few data series, the model perfectly identified the machine's status at the data series level (Fig. 5).

B. 0-Vectors Help the NN Detect ISCF
We know that the proportion of 0-vectors provides information about the speed and torque of the machine, which can be valuable for the model.To test the effect of 0-vectors on the performance of the neural network model, we excluded 0-vectors from histogram calculation and reran our experiments.As expected, we observed a performance decrease (Fig. 4).Hence, we concluded that 0-vectors helped the neural network models detect ISCF.Furthermore, we observed a decrease in fault detection performance for the speed values beyond 3750 rpm (Fig. 5).This region corresponds to the verge of overmodulation in an inverter control system with a carrier-based modulation, where the percentage of zero vectors significantly decreases.The switching vector statistics were also not as responsive to the occurrence of the fault as they were at the slower speeds.Fig. 5. Sample-level ISCF predictions on the data series in the test dataset.At each point of a data series (i.e., for a sample), inter-turn short circuit fault (ISCF) probability was obtained from the trained model.ISCF probability and predicted machine status (MS) obtained by thresholding the predicted probability value with 0.5 are presented for data series.For each data series, id, speed (rpm), torque (N • m), and MS ((H)ealthy, (F)aulty) are also given.

C. Statistics Over Longer Intervals Improve Performance
We trained and tested our models with sample and label pairs.A sample was created by calculating the histogram of switching vectors over a window of five electrical periods (≈ 92 ms at the rated speed and torque).In an ideal system (where there is no noise), an ISCF can be detected using inverter switching statistics calculated over one electrical period.However, the system is noisy in practice, and the noise directly affects the model's performance.
We investigated the effects of the interval length, over which switching vector histograms were calculated, on the performance of neural network models.We observed that as the length of the interval decreased (multiples of electrical period: 5, 4, 3, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Fig. 6.Statistics over longer intervals improve performance.Switching vector histograms were calculated over an interval of multiples of electrical period (5, 4, 3, 2, and 1) while training the NN models.We compared the effect of interval length on the model's performance using AUROC on the test set both for 0-vector included and 0-vector excluded cases.
2, and 1), the model's performance also decreased (Fig. 6).In short, we concluded that statistics over longer intervals improved the model's performance.
One interesting observation was that the performance decay was gradual from five to two periods.Nevertheless, it was drastic from two periods to a single period.Our observation was also consistent with the findings of [15], which uses a thresholding-based method over switching vector statistics.Besides, the contribution of 0-vectors in the model's performance was evident (Fig. 6).

D. NN Identifies Faulty Phase in a Machine With ISCF
After we showed that a neural network model successfully detected ISCF, we also checked if it could identify the faulty phase.We prepared a small dataset using data series collected at the rated speed (w = 3000 rpm) and around the rated torque (T = 1.20 N • m) of the induction machine.Training, validation, and test sets were prepared similar to the previous data segregation.Two healthy and three faulty (one for each phase) data series were used for preparing data samples in each set.The dataset details are available with the released code [47].
We modified the neural network architecture used in ISCF detection to a multi-class classification model with four classes corresponding to the machine's status of healthy, faulty (A), faulty (B), and faulty (C).Then, we trained the model on the training set with early stopping based on loss in the validation set and evaluated its performance on the test set.The model successfully detected ISCF and identified the faulty phase (Table IV).It achieved an accuracy of 0.9995.As in the ISCF detection task, our neural network model perfectly detected ISCF and identified the faulty phase at the data series

NN Outperforms Based
The duration of high electrical currents passing through shorted turns during an is critical for the repair and possible fault-tolerant operation of the machine.As the detection time takes longer, the ISCF condition will evolve further into the unmanageable situations such as complete phase to phase or phase to ground shorts.Therefore, we compared the performance of our neural network model with the thresholding-based method of [15] in terms of ISCF detection time.At various load torque and shaft speed values, while the thresholding-based method detected ISCF in between 0.5 to 2 seconds, the neural network model detected ISCF in between 0.074 to 0.196 seconds.There was a speedup of more than two times at the rated operating conditions (≈ 0.2 second for the thresholding-based method in [46] and 0.092 seconds for our neural network model).

IV. CONCLUSION
Early detection of an ISCF in an electrical machine is vital for its maintenance.This study developed neural network models that detect an ISCF in an IM driven by an inverter with an MPC algorithm.The models accepted the histogram of inverter switching vectors, which are readily available, as input and predicted the machine's status (healthy or faulty) at the output (Fig. 1).An ISCF in the IM was successfully detected under 0.1 seconds with an almost perfect performance (Fig. 4).Besides, the faulty phase was identified with an accuracy of 0.9995 (Table IV).
In our experiments, while the large networks performed slightly better in the ISCF detection task, the performance of the smaller networks were also good enough for real-world deployment (Fig. 4).Moreover, a small network requires less memory and computational resources, facilitating its deployment in the same processor alongside the controller algorithm.
Our experiments validated that 0-vectors contained valuable information for ISCF detection (Fig. 4), and statistics over longer intervals improved the performance (Fig. 6).Nevertheless, there was a trade-off between better performance and faster ISCF detection in determining the optimum interval for statistics calculation.We concluded that an interval of three to five electrical periods was reasonable.
Lastly, the proposed approach evaluates the inverter switching vectors that are already available as controller outputs, i.e., it is non-invasive.Besides, different than some online signalprocessing-based techniques requiring extra sensors [25], [26], [27], our method does not require any extra sensors.Hence, no significant cost or complexity is introduced.

A. Limitations and Future Work
To avoid data leakage in our experiments, we used data series collected at different runs in training and test sets (Table II), i.e., we tested the models on unseen data [49].Besides, our model successfully detected ISCFs in data series collected at speed and torque values that were different from the speed and torque values of the data series in the model's training set, showing our model's generalization ability.Our model could perform quite well for machines of the same manufacturer with similar specifications.However, it might require fine-tuning for machines of different manufacturers or specifications, known as domain adaptation and a hot topic in machine learning research [50], [51].Therefore, it would have been better to test the trained model on data from another machine, which we have kept as future work.
Furthermore, we observed that the model's performance started to degrade beyond the rated speed and torque values (Fig. 5), which corresponds to the operation on the verge of overmodulation, where the utilization of zero vectors significantly decreases.This could be due to the limited available data around these operation regions of the IM.We had around 300 k samples in our training set; however, they were created from only 26 independent data series (Table II).Since data collection is quite expensive, our dataset was minimal compared to traditional deep learning datasets containing millions of independent samples [52].Besides, all healthy data points in our dataset were collected in a short period of time relative to lifetime of a machine, so our dataset did not capture the aging effects, such as the change of motor parameters or insulator degradation over time.Hence, the collection of an extensive dataset and the real-world deployment of our ISCF detection models are reserved for future work.The prospective dataset should broadly cover the IM's operation regions, including different operating scenarios, temperatures, and DC-bus voltages, over a sufficiently long time interval to include the aging effects.
Lastly, this study focused on detecting ISCF of ∼2% of turns (2 out of 104).It did not consider severe cases, like ISCFs of high percentages or phase-to-phase and phase-to-ground short circuits.Nevertheless, their effects on the input variables would be more evident, and NNs would have easily identified them.Similarly, this study did not consider rotor and bearing faults.Although controller-fault interactions would be anticipated for the rotor and bearing faults, an ISCF can be discriminated from these fault types by their characteristics.A rotor fault's influence would be effective on each phase equally, and the bearing fault's rate of progression would be considerably slower compared to the ISCF case.In addition to detecting a fault independent of the inflicting fault type, identification of fault type would be valuable.Hence, preparing an extensive dataset including different fault types and operating scenarios is essential in future work.

Fig. 1 .
Fig. 1.Inverter switching statistics and neural network model.(a) The voltage vectors of a two-level voltage source inverter.The controller finds the optimum voltage vector in view of the control outcomes, and applies it at the next switching instant.(b) Histograms of switching vectors over a period for a healthy machine and a machine with inter-turn short circuit fault are given.While aggregated 0-vectors is represented as 0, aggregated active vectors are represented as A, B and C. (c) The neural network model is a multi-layer perceptron consisting of an input layer (with 4 nodes), two hidden layers (Layer1 and Layer2 -each with 64 nodes) and an output layer (with 2 nodes).The model takes a histogram of switching vectors at the input and predicts whether the machine is healthy or faulty at the output.

Fig. 3 .
Fig. 3. Experimental setup.An FCS-MPC driven IM is used in the experiments.The ISCF condition corresponds to a short-circuiting of 2-turns out of 104-turns in a phase winding.

TABLE II DATA
FOR ISCF DETECTION.INVERTER SWITCHING VECTORS WERE COLLECTED FOR DIFFERENT CONDITIONS (H: HEALTHY AND F: FAULTY) OF AN INDUCTION MACHINE WITH A RATED SPEED OF w = 3000 RPM AND A RATED TORQUE OF T = 1.20 N • M. THE COLLECTED DATA SERIES WERE SEGREGATED INTO TWO SETS SUCH THAT THE FIRST SET (H:16, F:18) WAS FOR TRAINING AND VALIDATION, AND THE SECOND SET (H:14, F:16) WAS FOR THE TEST.SPEED (w), TORQUE (T ), MEASURED ELECTRICAL FREQUENCY (f e ), AND THE NUMBER OF HEALTHY AND FAULTY DATA SERIES IN THE MACHINE LEARNING DATASET ARE PRESENTED.EACH DATA SERIES IN THE FIRST SET WAS DIVIDED INTO TWO SUCH THAT THE FIRST 70% AND THE REMAINING 30% WERE USED TO CREATE SAMPLES FOR THE TRAINING AND VALIDATION SETS, RESPECTIVELY.DATA SERIES IN THE SECOND SET WERE USED TO CREATE SAMPLES FOR THE TEST SET

TABLE III ISCF
DETECTION PERFORMANCE COMPARISON.WE COMPARED OUR MODELS' PERFORMANCES ON ISCF DETECTION TASK WITH THE PERFORMANCES OF THE MODELS IN [38].WE ALSO PRESENTED THE TYPE OF NEURAL NETWORK MODELS, THE NUMBER OF LEARNABLE PARAMETERS IN EACH MODEL, INPUT SIGNALS TO THE MODELS, AND THE NUMBER OF HEALTHY AND FAULTY SAMPLES IN THE TEST SETS.IF THERE IS AN EXTRA SENSOR REQUIREMENT FOR AN INPUT SIGNAL, IT IS ALSO INDICATED

TABLE IV FAULTY
PHASE DETECTION.THE SAME NN ARCHITECTURE WAS MODIFIED TO A MULTI-CLASS CLASSIFICATION MODEL DETECTING FAULTY PHASE AS WELL.THE CONFUSION MATRIX OBTAINED ON THE TEST SET IS PRESENTED