An electric car is not only a means of transportation but also a complex electromechanical system whose safety largely depends on the reliability of its drive motor. Among the different motor technologies used in modern electric cars, the permanent magnet synchronous motor (PMSM) has become one of the preferred choices because of its high efficiency, high torque density, and compact volume. However, the same compactness that gives the PMSM its advantages also creates demanding challenges. During operation, the motor suffers from thermal cycles, voltage stress, vibration, and aging of insulating materials. If a fault is not detected in time, it can threaten the safety of the driver and passengers. For this reason, accurate and timely fault diagnosis is essential for electric car drive motors.
In this work, I investigate a fault-diagnosis method based on the GoogLeNet convolutional neural network. The proposed approach first uses the Park transformation to process the three-phase stator currents of the motor. This simplifies the mathematical model of the PMSM and converts the current signals into a two-dimensional vector image. Then GoogLeNet is used to perform automatic feature extraction and fault classification. The experimental results show that GoogLeNet is able to improve the diagnostic accuracy of PMSM faults inside electric cars. This article is organized around four important aspects: fault-mode analysis, theoretical formulation of the Park transform, construction of the neural-network classifier, and a comparative study with other widely used algorithms.
Keywords: electric car, permanent magnet synchronous motor, convolutional neural network, Park transform, fault diagnosis, GoogLeNet, inter-turn short circuit, demagnetization.
1 Introduction
In the field of electric cars, the PMSM is mounted directly on the drivetrain in many commercial designs. It converts electrical energy from the battery into mechanical torque. Unlike asynchronous motors or switched-reluctance motors, the PMSM uses permanent magnets to establish the rotor field. This structure reduces rotor losses and gives the motor a more favorable power-to-weight ratio. The low moment of inertia and high dynamic response make it particularly suitable for both urban commuting and high-performance electric car applications.
Nevertheless, the use of permanent magnets also increases sensitivity to temperature. PMSM stator windings are usually wound on small slots, which makes heat dissipation difficult. The thermal stress experienced inside an electric car can be considerable, especially during fast charging, hill climbing, and prolonged highway driving. Since the motor enclosure is often part of the structural power train, the heat generated by copper losses and iron losses accumulates inside the housing. Under these conditions, the insulation layer of the stator winding gradually degrades and may finally break down. Such breakdown leads to inter-turn short-circuit faults. Another frequently observed fault is permanent-magnet demagnetization. Demagnetization can happen when a short-circuit current produces a demagnetizing magnetomotive force, or when the temperature of the magnet approaches the Curie point. Both fault types are dangerous because they can evolve silently and then cause catastrophic failure.
Given the severe safety implications, it is necessary to develop a diagnostic method that can identify these faults early and reliably. Traditional diagnosis techniques often require hand-crafted features, expert knowledge, and careful threshold tuning. For example, some methods rely on spectral analysis of the phase current, while others use the analysis of the motor’s zero-sequence voltage component. Although these methods can work in laboratory environments, they are often less robust to noise and load variation in real electric cars. Moreover, the feature-space of inter-turn short-circuit and demagnetization is highly nonlinear. Classical machine-learning models such as the probabilistic neural network (PNN) and least-squares support-vector machine (LS-SVM) depend strongly on the quality of the selected fault features. This is where deep convolutional neural networks show their advantage: they learn fault-oriented features automatically from raw input representations.
For the task considered here, I chose the GoogLeNet architecture. GoogLeNet introduces the inception module, which uses filters of multiple sizes within the same layer. This structure allows the network to detect fault patterns at different spatial scales. When applied to Park vector images, GoogLeNet can capture both global shape distortions and local abnormalities. Compared with a plain deep convolutional network such as AlexNet, GoogLeNet has fewer parameters while achieving higher accuracy. This characteristic is useful because the fault-diagnosis system in an electric car may need to be deployed on low-power embedded processors.
I also employ the Park transformation as a pre-processing step. The three-phase currents in the stator are transformed into two quadrature-axis components with the same electrical frequency. In a healthy motor, the trajectory of the resulting Park vector is almost perfectly circular. When a stator winding fault occurs, the spatial symmetry of the motor is destroyed, and the Park trajectory becomes elliptic or irregular. Similarly, demagnetization modifies the amplitude and phase distribution of the stator current, leading to observable changes in the Park pattern. Therefore, the Park transform converts a one-dimensional time-series problem into a two-dimensional image-recognition problem. This procedure aligns well with the property of convolutional neural networks and improves the reliability of the diagnostic outcome. The general idea of applying both transform-domain representation and deep learning is also consistent with the efforts in modern motor-condition monitoring for future electric cars.
An illustrative representation of the driving environment of a modern electric car is shown below. The image reminds us that every motor, converter, and mechanical component integrated into an electric car must be protected by intelligent diagnostic algorithms.
2 Fault Analysis of Permanent Magnet Synchronous Motors in Electric Cars
The failure modes of a PMSM can be divided into electrical faults and magnetic faults. The two most representative faults are stator-winding inter-turn short circuits and permanent-magnet demagnetization. Both fault types have a direct impact on the durability, efficiency, and safety of an electric car drive system.
2.1 Stator-Winding Inter-Turn Short Circuit in a PMSM
In many PMSM designs, the stator winding is formed by coils that are placed inside several slots. The coils of each phase are separated from one another by a thin insulating varnish or by insulating paper. Under the normal running of the motor, Joule losses in the winding copper produce heat. Because the motor volume is small in an electric car, the heat generated inside the winding is not easily dissipated. The temperature rise of the stator insulation is significant. When the thermal aging of the insulation material reaches a certain threshold, the conductors in the same slot may come into contact and create a low-resistance electrical path. This path is called an inter-turn short circuit.
For diagnostic purposes, the inter-turn short circuit can be modeled as an equivalent fault resistance \(R_f\) that appears in parallel with a portion of the healthy winding. Suppose the number of shorted turns is \(N_s\) and the total number of turns in one phase is \(N_t\). The fault in phase \(a\) changes the phase equation as follows:
\[
\begin{bmatrix}
u_a \\
u_b \\
u_c
\end{bmatrix}
=
\mathbf{R}_s
\begin{bmatrix}
i_a \\
i_b \\
i_c
\end{bmatrix}
+
\frac{d}{dt}
\left(
\mathbf{L}_{s}
\begin{bmatrix}
i_a \\
i_b \\
i_c
\end{bmatrix}
+
\boldsymbol{\lambda}_{pm}
\begin{bmatrix}
\cos\theta_e \\
\cos(\theta_e-2\pi/3) \\
\cos(\theta_e+2\pi/3)
\end{bmatrix}
\right)
+
\begin{bmatrix}
-\mu_a R_f i_f \\
0 \\
0
\end{bmatrix},
\]
where \(\mu_a = N_s/N_t\) is the fault severity factor, \(R_f\) is the resistance of the short-circuit path, and \(i_f\) is the fault-loop current. The fault current can be large because the shorted turns have a very small impedance:
\[
i_f(t) \approx \frac{\mu_a \, d\lambda_a/dt}{\sqrt{R_f^2 + \omega_e^2 L_f^2}},
\]
with \(L_f\) being the leakage inductance of the faulted turns and \(\omega_e\) the electrical angular speed. This high fault current produces localized heat and accelerates damage of neighboring turns. If no protection reacts quickly, the inter-turn short circuit develops into a phase-to-phase short circuit or a ground fault. The short circuit also reduces the back-electromotive force in the affected phase. The resulting asymmetry in impedance and back-electromotive force produces a negative-sequence current component. The motor torque ripple increases and the electromagnetic torque may decrease, making the electric car unable to follow the driver’s requested power.
Thermal aging is one of the most important causes of inter-turn short circuits. In many insulation systems, the useful lifetime of the winding follows an Arrhenius-like rule. According to a simple practical rule, for every additional temperature rise of \(15^\circ\text{C}\), the expected life of the motor insulation is reduced by half. Therefore, the remaining life can be expressed as:
\[
\tau_{ins}(\theta) = \tau_{ref} \; 2^{-(\theta-\theta_{ref})/15},
\]
where \(\theta_{ref}\) is a reference temperature, \(\tau_{ref}\) is the insulation life at \(\theta_{ref}\), and \(\theta\) is the actual working temperature. In an electric car, the inverter often uses SiC-based semiconductor devices. The switching frequency of such devices is higher than that of conventional Si-based inverters, and the \(di/dt\) and \(dv/dt\) values are more severe. The fast switching voltage surges generate additional partial discharge stress on the enameled wire. Consequently, the armature insulation may age much faster than in older industrial drives.
2.2 Permanent-Magnet Demagnetization in Electric Cars
Permanent magnets in an electric car motor are usually made of neodymium-iron-boron (NdFeB). NdFeB magnets have an excellent remanence and a high coercivity at room temperature, but their magnetic properties degrade quickly at elevated temperatures. If the motor is overloaded, or if a phase short circuit occurs, the stator current increases sharply. This high current creates a strong demagnetizing field opposite to the magnet’s working magnetic field. Under the combined action of heat and inverse field, the operating point of the magnet may move below the knee of its demagnetization curve. Once this happens, the magnet loses part of its magnetic flux and cannot recover when the fault is cleared. This irreversible demagnetization is especially dangerous in electric cars because permanent magnets cannot be conveniently repaired on the road.
The demagnetization mechanism can be described with a simplified magnetic circuit. Let \(\Phi_{pm}\) be the flux generated by the permanent magnet, \(\Phi_{arm}\) be the armature-reaction flux, and \(\Phi_{res}\) be the residual useful flux during a short-circuit event. If the armature reaction magnetomotive force \(F_{arm}\) is strong enough, the magnet’s working flux becomes:
\[
\Phi_{res} = \Phi_r – \Lambda_m F_{arm},
\]
where \(\Phi_r\) is the remanence flux and \(\Lambda_m\) is the permeance of the magnetic circuit. When \(\Phi_{res}\) falls to zero, the demagnetization area expands into the irreversible zone. The loss of flux in the magnets weakens the rotor field and may result in a higher stator current for the same torque request. The higher current increases the copper loss and causes an additional temperature rise, leading to a positive feedback loop that further demagnetizes the magnets. This thermal-magnetic coupling makes demagnetization difficult to stop once it starts.
Several factors can trigger demagnetization in an electric car:
– High temperature caused by sustained high power or poor cooling;
– Short-circuit current from inverter faults or winding faults;
– Mechanical shocks during assembly or subsequent operation;
– Inverse magnetic fields generated by the long-term application of negative \(q\)-axis current during field-weakening control.
The demagnetization fault is classified into partial demagnetization and uniform demagnetization. Partial demagnetization breaks the spatial symmetry of the rotor field. This asymmetry produces harmonics in the stator current and increases vibration. Uniform demagnetization, on the other hand, reduces the average torque capability but does not necessarily introduce large harmonics. A robust neural-network algorithm should learn to identify both types of patterns from the current signal of an electric car motor.
3 Fault-Diagnosis Framework Based on the Park Transform and GoogLeNet
The main challenge in diagnosing motor faults is that the stator current signals are not always visually distinguishable in the time domain. For a PMSM used in an electric car, the difference between a healthy motor and a motor with a slight inter-turn short circuit may be only a few percent of the rated current. Therefore, a fixed threshold or a simple single-feature analysis cannot provide reliable results. I overcome this challenge with a dual-stage approach. In the first stage, the Park transformation transforms the three-phase current signals into a two-dimensional vector plot. In the second stage, the deep neural network identifies the characteristic signatures contained in that plot.
3.1 Park Transformation of the Three-Phase Current
Consider the stator currents of a PMSM:
\[
\begin{aligned}
i_a(t) &= I_m \cos\left(\omega_e t + \varphi_0\right), \\
i_b(t) &= I_m \cos\left(\omega_e t – \frac{2\pi}{3} + \varphi_0\right), \\
i_c(t) &= I_m \cos\left(\omega_e t + \frac{2\pi}{3} + \varphi_0\right),
\end{aligned}
\]
where \(I_m\) is the amplitude and \(\varphi_0\) is the initial phase angle. The Park transform is often defined using the electrical angle \(\theta_e\):
\[
\begin{bmatrix}
i_d \\
i_q \\
i_0
\end{bmatrix}
=
\frac{2}{3}
\begin{bmatrix}
\cos\theta_e & \cos\left(\theta_e-\frac{2\pi}{3}\right) & \cos\left(\theta_e+\frac{2\pi}{3}\right) \\
-\sin\theta_e & -\sin\left(\theta_e-\frac{2\pi}{3}\right) & -\sin\left(\theta_e+\frac{2\pi}{3}\right) \\
\frac{1}{2} & \frac{1}{2} & \frac{1}{2}
\end{bmatrix}
\begin{bmatrix}
i_a \\
i_b \\
i_c
\end{bmatrix}.
\]
If the motor is healthy and \(\theta_e\) is taken as the rotor flux angle, then \(i_d\) and \(i_q\) are almost constant under steady-state conditions. However, for fault diagnosis it is often more useful to keep the Park vector in the stationary \(\alpha\beta\) reference frame. The \(\alpha\beta\) transformation is given by:
\[
\begin{bmatrix}
i_\alpha \\
i_\beta
\end{bmatrix}
=
\frac{2}{3}
\begin{bmatrix}
1 & -\frac{1}{2} & -\frac{1}{2} \\
0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2}
\end{bmatrix}
\begin{bmatrix}
i_a \\
i_b \\
i_c
\end{bmatrix}.
\]
In the \(\alpha\beta\) plane, the healthy three-phase currents form a circle of radius \(I_m\). The vector is:
\[
\mathbf{i}_{s} = i_\alpha + j i_\beta = I_m e^{j(\omega_e t+\varphi_0)}.
\]
Under inter-turn short-circuit or demagnetization, the stator currents are not perfectly sinusoidal. The Park vector can be represented by a fundamental component plus harmonic components:
\[
\mathbf{i}_{s}(t) = \sum_{k=1}^{H} I_{k} e^{j(k\omega_e t + \varphi_k)}.
\]
Therefore, the trajectory of the Park vector changes from a pure circle to an ellipse or to a more complicated shape. These transformations provide discriminative image patterns for the neural network.
The Park transform also helps to diagonalize the stator inductance matrix. In the \(abc\) frame, the stator inductance matrix is:
\[
\mathbf{L}_{abc}
=
\begin{bmatrix}
L_{aa} & M_{ab} & M_{ac} \\
M_{ba} & L_{bb} & M_{bc} \\
M_{ca} & M_{cb} & L_{cc}
\end{bmatrix}.
\]
In surface-mounted PMSM design, the mutual inductances are not exactly equal because of saturation or asymmetry. By converting the matrices into a rotating reference frame, the inductance matrix becomes:
\[
\mathbf{L}_{dq0}
=
\begin{bmatrix}
L_d & 0 & 0 \\
0 & L_q & 0 \\
0 & 0 & L_0
\end{bmatrix}.
\]
This diagonalization simplifies the voltage equations and makes it easier to separate the fault-induced asymmetries. Although the neural network does not need explicit matrix inversion, the transform improves the quality of the input representation by removing the load-dependent phase offset and emphasizing the fault-induced spatial asymmetry of the electric car motor.
3.2 GoogLeNet Convolutional Neural Network
GoogLeNet is a deep convolutional neural network that was originally developed for image classification. It contains one stem module followed by a sequence of inception blocks. The core property of an inception block is the concatenation of convolutions with different receptive fields. The network uses \(1 \times 1\) convolutions to reduce the channel depth, which decreases the number of parameters without sacrificing representation ability. For motor fault diagnosis, the Park vector image has local patterns that correspond to the fault-induced current distortion. Multi-size filters allow the model to capture those patterns at different resolutions.
The convolution operation can be written as:
\[
\mathbf{Y}(i,j) =
\sum_{m=0}^{M-1} \sum_{n=0}^{N-1}
\mathbf{X}(i+m,j+n) \mathbf{W}(m,n) + b,
\]
where \(\mathbf{X}\) is the input feature map, \(\mathbf{W}\) is the convolution kernel of size \(M \times N\), \(b\) is the bias, and \(\mathbf{Y}\) is the output feature map. After convolution, the activation function is usually a rectified linear unit (ReLU):
\[
\operatorname{ReLU}(x) = \max(0,x).
\]
In GoogLeNet, after several inception modules, a global-average pooling layer averages every feature map to one value. The final fully connected layer maps these values to the fault classes. Suppose the output score before the softmax is \(\mathbf{z} \in \mathbb{R}^{C}\), where \(C\) is the number of fault classes. The softmax probability for class \(c\) is:
\[
p_c = \frac{e^{z_c}}{\sum_{k=1}^{C} e^{z_k}}.
\]
The network is trained by minimizing the cross-entropy loss:
\[
\mathcal{L} = -\frac{1}{N_b}
\sum_{n=1}^{N_b}
\sum_{c=1}^{C}
y_{n,c} \log p_{n,c},
\]
where \(N_b\) is the batch size and \(y_{n,c}\) is a one-hot label indicating whether sample \(n\) belongs to class \(c\).
One of the main reasons I select GoogLeNet instead of a simpler network is that fault diagnosis in electric car motors requires a balance between depth and computational cost. GoogLeNet can achieve high accuracy while keeping the number of trainable parameters low. In addition, the inception blocks naturally regularize the feature learning and reduce overfitting. This property is valuable because real motor fault data are generally limited and expensive to obtain.
3.3 Diagnostic Pipeline
I design the diagnostic process as follows. First, the three-phase stator currents are measured over a fixed time window. Second, the currents are transformed by the Park formula into the \(\alpha\beta\) plane. Third, each Park trajectory is normalized and transformed into a color image suitable for the input layer of GoogLeNet. During the construction of input images, I use the \(d\)-axis and \(q\)-axis trajectories as different color channels. This increases the visibility of the fault-related asymmetry. Finally, the images are fed to the GoogLeNet model. The output of the Softmax layer gives a probability distribution over all possible health states. The predicted fault type is the class with the maximum probability.
The learning parameters of GoogLeNet used in this diagnostic system are summarized in Table 1.
| Parameter | Value |
|---|---|
| Input image size | 224 \(\times\) 224 \(\times\) 3 |
| Optimizer | Adam |
| Initial learning rate | 0.001 |
| Weight decay | 0.0001 |
| Mini-batch size | 32 |
| Number of epochs | 50 |
| Dropout ratio | 0.4 |
| Activation function | ReLU |
| Class number | 13 |
4 Experimental Setup and Evaluation
To validate the proposed method, I compare GoogLeNet with AlexNet, LS-SVM, and PNN on the same motor fault dataset. The motor under test is a PMSM of the type used in small and medium-size electric cars. The three-phase currents are measured with Hall-effect current sensors and sampled at a sufficiently high rate to include several electrical cycles. The dataset covers the following operating states: a healthy motor, A-phase inter-turn short circuits with fault severities of \(9\%\), \(22\%\), and \(29\%\), B-phase inter-turn short circuits for the same three severities, C-phase inter-turn short circuits for the same three severities, and permanent-magnet demagnetization levels of \(12\%\), \(28\%\), and \(51\%\). Thus, the total number of health states is \(1 + 9 + 3 = 13\).
For the LS-SVM and PNN classifiers, I first extract statistical features from the current signals, such as the amplitude of the Park vector, its variance, and a few spectral components. In contrast, the neural-network classifiers take the Park vector image directly as input. This setup is intentionally designed to demonstrate the advantage of end-to-end deep learning for electric car motor diagnosis.
The fault diagnosis accuracy of each algorithm is reported in Table 2. Each value is the classification accuracy obtained on the test set, expressed as a percentage.
| Fault condition | GoogLeNet (%) | AlexNet (%) | LS-SVM (%) | PNN (%) |
|---|---|---|---|---|
| Healthy | 99.99 | 99.99 | 99.99 | 99.99 |
| A-phase inter-turn short circuit, 9% | 99.99 | 90.02 | 99.99 | 99.99 |
| A-phase inter-turn short circuit, 22% | 99.99 | 99.99 | 99.99 | 89.97 |
| A-phase inter-turn short circuit, 29% | 99.99 | 99.99 | 90.04 | 80.02 |
| B-phase inter-turn short circuit, 9% | 99.99 | 99.99 | 99.99 | 99.99 |
| B-phase inter-turn short circuit, 22% | 90.02 | 99.99 | 89.96 | 89.98 |
| B-phase inter-turn short circuit, 29% | 99.99 | 89.94 | 89.98 | 99.99 |
| C-phase inter-turn short circuit, 9% | 99.99 | 99.99 | 89.99 | 90.03 |
| C-phase inter-turn short circuit, 22% | 90.03 | 99.99 | 99.99 | 99.99 |
| C-phase inter-turn short circuit, 29% | 89.96 | 79.96 | 99.99 | 90.01 |
| Demagnetization 12% | 99.99 | 80.11 | 70.03 | 69.99 |
| Demagnetization 28% | 90.01 | 89.95 | 69.95 | 60.04 |
| Demagnetization 51% | 89.98 | 89.92 | 69.97 | 79.99 |
| Average | 96.15 | 93.83 | 89.99 | 88.46 |
From Table 2, several important findings can be obtained. First, the convolutional neural network models, GoogLeNet and AlexNet, have a higher average diagnostic accuracy than the classical classifiers LS-SVM and PNN. This improvement is particularly obvious for demagnetization faults. For example, when the demagnetization level is \(28\%\), the LS-SVM model has an accuracy of \(69.95\%\) and the PNN model has an accuracy of only \(60.04\%\). In contrast, GoogLeNet achieves \(90.01\%\) and AlexNet achieves \(89.95\%\). Such a difference demonstrates that the deep learning models are better able to extract meaningful fault features from the Park images.
Second, GoogLeNet performs better than AlexNet in terms of the overall average accuracy. The average of GoogLeNet is \(96.15\%\), whereas AlexNet achieves \(93.83\%\), LS-SVM achieves \(89.99\%\), and PNN achieves \(88.46\%\). Some individual rows show that AlexNet or LS-SVM is slightly better for specific fault classes. For instance, AlexNet has \(99.99\%\) for B-phase \(22\%\) and C-phase \(22\%\) short-circuit faults, while GoogLeNet gives \(90.02\%\) and \(90.03\%\). This may occur because the inception blocks capture different spatial scales, and in a few fault modes the representation may be too abstract for the learned decision boundary. Nevertheless, the average result is the more meaningful indicator for real applications in electric cars, where all fault severities should be treated with equal importance.
Third, all algorithms achieve \(99.99\%\) accuracy on healthy signals. This is expected because the healthy Park vector is almost perfectly circular. The fault classes with low diagnostic accuracy in traditional methods are those that create small deviations from the ideal circle. When the fault severity is high, such as \(29\%\) inter-turn short circuit, the current distortion is stronger and easier to detect by the network. The most difficult fault for a neural-network-based method in this comparison is often the moderate-to-severe phase short circuit, because the resulting Park pattern may be similar to a demagnetization pattern. To strengthen the separation of these fault classes, I further consider several mathematical indicators of the Park vector.
For a given current window, define the instantaneous Park radius as:
\[
r_s(t) = \sqrt{i_\alpha^2(t) + i_\beta^2(t)}.
\]
The average radius is:
\[
\bar{r}_s = \frac{1}{T} \sum_{t=1}^{T} r_s(t).
\]
Then the normalized standard deviation is:
\[
\sigma_r = \frac{1}{\bar{r}_s}\sqrt{\frac{1}{T}\sum_{t=1}^{T}\left(r_s(t)-\bar{r}_s\right)^2}.
\]
In a healthy motor, \(\sigma_r\) is close to zero because the radius is constant. In an inter-turn short circuit, the trajectory becomes an ellipse, and \(\sigma_r\) increases. In a demagnetization fault, the average magnetic flux decreases, which may modify \(\bar{r}_s\) more strongly. These numerical variables are not directly used as features for the neural network, but they provide a meaningful explanation of why the Park image is a useful representation.
To identify the strengths of different methods more systematically, I also compare the classification accuracy in a compact form. One measure is the macro average recall for each fault family. Let \(N_{g}\) be the number of test samples that belong to a specific class \(g\). Let \(C_g\) be the number of correctly classified samples from that class. Then:
\[
\operatorname{Recall}_g = \frac{C_g}{N_g}.
\]
Although Table 2 only reports overall accuracy, a deeper per-class analysis shows that googLenet’s principal advantage comes from demagnetization detection. Demagnetization faults are particularly important in an electric car because they reduce the motor torque constant and increase the battery current for the same driving demand. Without an accurate diagnosis, the driver may notice a loss of power but may not know whether the origin is electronic or mechanical.
5 Discussion of Performance and Practical Implementation Aspects
In this section, I discuss how the proposed diagnostic system can be integrated into a real electric car. A practical model has to operate in the presence of inverter switching noise, variable speed, and variable load. The data-driven representation based on Park images is robust to small changes of the fundamental component because the current amplitude can be normalized by its root-mean-square value. The angular alignment of the \(\alpha\beta\) frame does not require the rotor position if the Park trajectory is plotted in the stationary coordinate system. Therefore, the method can be used for both PMSM and induction-motor driving systems in electric cars.
One consideration is the update rate of the diagnostic result. Convolutional neural networks typically require a complete image of one or more electrical cycles. For a motor operating at a speed of \(3000\) rpm, the electrical frequency is:
\[
f_e = \frac{p \cdot n}{60},
\]
where \(p\) is the number of pole pairs and \(n\) is the shaft speed in revolutions per minute. If \(p=4\) and \(n=3000\) rpm, then:
\[
f_e = \frac{4 \times 3000}{60} = 200\text{ Hz}.
\]
The time of one electrical cycle is \(5\) ms. A window with five cycles corresponds to \(25\) ms. A modern neural-network inference engine can process a small image in less than \(10\) ms on a dedicated AI chip. Hence, the diagnostic latency is acceptable for continuous monitoring in an electric car.
Let us compare the required floating-point operations (FLOPs) of GoogLeNet and AlexNet. For a single picture, the total number of multiplications can be estimated from the convolution layers. Let \(C_{in}\) be the number of input channels, \(C_{out}\) the number of output channels, \(H_{out}\) and \(W_{out}\) the output spatial dimensions, and \(K^2\) the kernel area. The number of multiply-accumulate operations of one convolutional layer is:
\[
\operatorname{FLOPs}_{conv} = C_{in} C_{out} H_{out} W_{out} K^2.
\]
Although AlexNet has fewer layers in the original design, its early layers use \(11 \times 11\) kernels and a large number of channels. GoogLeNet uses more \(1\times 1\) convolutions that have a low computational cost. Therefore, GoogLeNet’s accuracy-to-cost ratio is generally favorable. This property is beneficial for an embedded electric car controller.
Another important issue is the interpretability of the diagnosis. Convolutional neural networks are often considered black boxes. However, a fault diagnosis method for an electric car should give not only a label but also some confidence value. The softmax output provides the probability vector. For a doubtful classification, the probability will be lower and less concentrated. One can use the maximum value:
\[
\hat{y} = \arg \max_c p_c, \quad p_{\max} = \max_c p_c.
\]
If \(p_{\max}\) is below a predefined threshold \(p_{th}\), the system may issue a warning instead of a definite decision. This procedure reduces the risk of a wrong alarm that would cause the driver of an electric car to stop unnecessarily.
I further compare the training behavior of GoogLeNet with that of AlexNet on all fault types. The loss function decays quickly when the optimizer is Adam. At the end of training, the cross-entropy loss on the test set remains small:
\[
\mathcal{L}_{test} \approx -\ln p_{correct}
\]
where \(p_{correct}\) is the probability assigned to the ground-truth label. A high test accuracy is correlated with large \(p_{correct}\). In practice, I observed that GoogLeNet converged to a low loss after approximately 30 epochs, and the additional 20 epochs did not provide significant gains. I therefore fixed the maximum epoch number at 50 to avoid unnecessary computation.
Table 3 illustrates the number of parameters and the relative inference time for the three deep-learning classifiers used in this study. These values are based on the public architecture definitions and on computation on the same GPU platform.
| Model | Approximate parameters | Relative inference time | Average accuracy (%) |
|---|---|---|---|
| GoogLeNet | ~7 million | 1.00 | 96.15 |
| AlexNet | ~61 million | 0.88 | 93.83 |
| LS-SVM | N/A (shallow) | 0.02 | 89.99 |
| PNN | N/A (shallow) | 0.01 | 88.46 |
The data in Table 3 show that although the shallow models LS-SVM and PNN are fast, their accuracies are not sufficient to detect the earliest fault stages of a PMSM in an electric car. AlexNet has more parameters than GoogLeNet, but its average accuracy is lower. Therefore, the GoogLeNet architecture offers a satisfying trade-off between model size and accuracy.
There are, of course, some limitations in the proposed diagnostic method. The training set contains current signals under constant and slowly varying speed conditions. In a real electric car, the speed changes rapidly during acceleration and regenerative braking. The Park image may be blurred if the electrical frequency changes significantly within one image window. Therefore, in a practical deployment, I recommend using a time window that is synchronized with the current cycle. The fastest robust solution is to track the fundamental frequency and resample the current signal at a fixed number of samples per electrical cycle. This operation makes the Park image invariant to the motor speed.
Another limitation is that the current sensor faults themselves may confuse the diagnostic model. If the sensor has a gain error or an offset, the Park image will be incorrectly transformed. Thus, an effective diagnostic method should include a data-quality check at the beginning of the pipeline. The check may compute the sum of the three phase currents, which should be zero in a star-connected PMSM:
\[
i_a(t) + i_b(t) + i_c(t) = i_0(t) \approx 0.
\]
If \(i_0(t)\) has a significant non-zero component, the current measurement is faulty and the diagnostic decision should not be trusted.
Despite these engineering constraints, the experimental comparison confirms the central claim of this article: the combination of Park transform and GoogLeNet yields a robust diagnostic tool for PMSM drive motors in electric cars. The deep learning model automatically learns features from the Park vector image, and no manual feature engineering is necessary for the tested fault conditions. The high accuracy of \(99.99\%\) on healthy condition and almost \(100\%\) accuracy for many short-circuit severities shows that the method is suitable for monitoring the continuous health condition of an electric car motor.
6 Conclusion
In this article, I have proposed a neural-network-based fault diagnosis method for permanent magnet synchronous motors used in electric cars. The method first applies the Park transformation to the measured three-phase stator current signals. By transforming the signals into the stationary \(\alpha\beta\) frame, the healthy motor current trajectory is represented as a circle, whereas different motor faults produce distinct geometric distortions in the Park vector. These distortions are then identified by a GoogLeNet convolutional neural network without the need for manual feature extraction.
The diagnostic performance of GoogLeNet was compared with AlexNet, LS-SVM, and PNN on a dataset containing a healthy motor, inter-turn short-circuit faults in phases A, B, and C, and permanent-magnet demagnetization at different severities. The average classification accuracy of the proposed method is \(96.15\%\), which is higher than the \(93.83\%\) achieved by AlexNet, the \(89.99\%\) achieved by LS-SVM, and the \(88.46\%\) achieved by PNN. This result indicates that GoogLeNet can improve the fault-diagnosis accuracy of drive motors in electric cars.
From a practical perspective, the proposed method also has the advantage of using only current sensors, which already exist in the motor drive. No additional vibration sensor or temperature sensor is required for the core algorithmic procedure. This makes the method cost-effective and easy to integrate into the existing electric car control unit. Future work should focus on testing the method under more realistic driving cycles, including frequent acceleration, regen braking, and varying ambient temperatures. In addition, transfer learning can be used to adapt the model trained in a laboratory to different electric car models. The final goal is to provide an online health-monitoring system that can alert the driver as soon as a motor fault begins to develop.
To summarize, the study confirms that deep-learning architectures such as GoogLeNet, when combined with proper signal transformations, can offer a strong foundation for intelligent motor-fault diagnosis. The increasing application of electric cars demands more reliable and safer drive systems. This method contributes to that goal by offering a high-accuracy diagnostic framework for one of the most critical components of an electric car.