Optimizing and Analyzing Performance of Motor Fault Diagnosis Algorithms for Autonomous Vehicles via Cross-Domain Data Fusion

Abstract

Electric motors play a pivotal role in the functioning of autonomous vehicles, necessitating accurate fault diagnosis to ensure vehicle safety and reliability. In this paper, a novel motor fault diagnosis approach grounded in vibration signals to enhance fault detection performance is presented. The method involves capturing vibration signals from the motor across various operational states and frequencies using vibration sensors. Subsequently, the signals undergo transformation into frequency domain representations through fast Fourier transform. This includes normalizing and concatenating the amplitude frequency and phase frequency signals into comprehensive frequency domain information. Leveraging Gramian image-encoding attributes, cross-domain fusion of time-domain and frequency-domain data is achieved. Finally, the fused Gram angle field map is fed into the ConvMixer deep learning model, augmented by the ECA mechanism to facilitate precise motor fault identification. Experimental outcomes underscore the efficacy of cross-domain data fusion, showcasing improved pattern recognition and recognition rates for the models compared to traditional time-domain methods. Additionally, a comparative analysis of various deep learning models highlights the superior performance of the ECA-ConvMixer model. This study makes significant contributions by introducing a cross-domain data fusion method, merging time-domain and frequency-domain information to enhance motor vibration signal analysis. Additionally, the incorporation of the ECA-ConvMixer deep learning model, equipped with attention mechanisms, effectively captures critical features, thus serving as a robust tool for motor fault diagnosis. These innovations not only enhance diagnostic accuracy but also have broad applications in areas like autonomous vehicles and industry, leading to reduced maintenance expenses and enhanced equipment reliability.

1. Introduction

Autonomous driving technology, positioned as a pivotal innovation guiding the future of transportation, has progressively emerged as a central focus of worldwide technological advancement [1]. Nonetheless, to attain secure, streamlined, and dependable autonomous driving, the wellness and fault diagnosis of vehicles hold paramount significance. Scholarly investigations underscore that vehicular malfunctions stand as a chief catalyst for traffic incidents [2]. In the event of an electric motor malfunction within a vehicle, its operational efficacy undergoes substantial deterioration, potentially resulting in erratic driving and heightened accident vulnerability [3]. In light of this, the detection of electric motor faults assumes a pivotal role in the context of autonomous vehicles.

Over the past few decades, remarkable strides have been made in data processing within the realm of fault diagnosis. Wang Bo et al. [4] introduced an innovative approach centered on residual voltage analysis derived from current signals, resulting in a successful diagnosis of open circuit faults within permanent magnet synchronous motor drives. Yutong Song et al. [5] advanced a fault diagnosis methodology employing a multi-scale feature fusion convolutional neural network, grounded in time-domain signals, thereby achieving proficient fault diagnosis for electromechanical actuators. Hong J et al. [6] harnessed the potential of high-frequency detail wavelet components to extract early frequency domain characteristics from fault signals, thereby accomplishing fault prediction and isolation for lithium-ion batteries within electric vehicles. Nonetheless, these research endeavors often prioritize either time-domain or frequency-domain information, inadvertently overlooking the intricate interplay between the two. This oversight may result in incomplete feature extraction and a potential shortfall in accuracy.

In recent years, propelled by the rapid evolution of deep learning technology, an escalating number of research endeavors have embraced its application within the domain of fault diagnosis [7]. For instance, Yang, T et al. [8] pioneered a one-dimensional convolutional spatiotemporal fusion strategy, culminating in an intelligent diagnosis system for aviation hydraulic pipeline networks. In the vehicular context, Gültekin, Ö and other scholars [9] harnessed the potency of the LeNet-5 convolutional neural network (CNN) model, anchoring it as the nucleus of edge artificial intelligence for real-time fault detection and status monitoring in industrial autonomous transfer vehicles. Kaplan, H et al. [10] employed the LSTM model to realize fault diagnosis within the electromechanical conversion chain of electric vehicles. Shang Y studied the elastic vector consensus problem for a set of dynamic agents against mobile malicious attacks [11], which is also worthy of reference in the field of fault diagnosis. Nevertheless, while these deep learning models showcase diversity, some tend to exhibit oversimplified feature extraction, while others manifest heightened complexity, necessitating considerable hardware resources. Moreover, as the volume of training samples for deep learning escalates, the endeavor of enhancing model accuracy while restraining complexity within an acceptable threshold poses a formidable challenge.

The incorporation of attention mechanisms to further refine the feature extraction process is a concept of considerable merit [12]. Leveraging attention mechanisms facilitates automatic weighting of pivotal segments within signals, empowering the model to selectively emphasize crucial information that bolsters fault diagnosis accuracy [13]. In the context of the Squeeze-and-Excitation Network (SENet) introduced by Hu et al. [14], inter-channel attention is established, encapsulating the interdependence among feature channels, thereby facilitating adaptive feature recalibration. This principle was further underscored by Wang Y [15], showcasing the prowess of SE networks in addressing multi-channel neural networks within fault diagnosis. Nevertheless, the SE attention mechanism primarily centers on the channel dimension, precluding attention capture in the spatial dimension. To address this, Wang et al. [16] introduced an efficient channel attention (ECA) module in CVPR 2020, surpassing traditional attention methods by circumventing the detriments of dimensionality reduction on model prediction. Additionally, [17] unveiled a multi-objective tracking approach that seamlessly integrates the efficient channel attention (ECA) module into the backbone network. This augmentation adeptly extracts salient information from images, thereby enhancing object detection accuracy. Consequently, the ECA model stands as a commendable exemplar of attention mechanisms.

In summary, previous fault diagnosis methods have faced challenges concerning incomplete information extraction. For instance, as illustrated in [18,19], these methods typically rely on a single information source without integrating data fusion. Furthermore, certain approaches, as noted in [20,21], lack attention mechanisms and employ overly simplified models, potentially constraining their capability to extract essential features effectively. To surmount the challenges outlined above, this study draws inspiration from signal analysis. It commences by employing vibration sensors to capture the motor’s acceleration signal, subsequently subjecting it to fast Fourier transform to generate a frequency domain signal. The next step involves cross-domain fusion, amalgamating the time-domain and frequency-domain signals using Gram plot angle field encoding. This synthesis culminates in a comprehensive Gram plot angle field, greatly enhancing the capacity to capture intricate motor fault characteristics. In the realm of pattern recognition, the ConvMixer model [22] takes center stage in this study. Thanks to the incorporation of patch embedding layers, the model enables the partitioning of an image into smaller units, thereby facilitating independent feature extraction. This methodology effectively curtails model complexity while ensuring a comprehensive fault analysis. Moreover, the introduction of the efficient channel attention (ECA) mechanism seeks to further augment the precision of motor fault prediction and detection.

The primary contribution of this study lies in the introduction of cross-domain data fusion, which integrates time-domain and frequency-domain information to yield a more comprehensive and precise understanding of motor status. Additionally, we have introduced the ECA-ConvMixer deep learning model, enhancing feature extraction capabilities through attention mechanisms, thereby further elevating the accuracy of motor fault diagnosis. This research’s novelty is grounded in the comprehensive utilization of cross-domain data fusion and deep learning techniques to enhance motor fault diagnosis performance in autonomous vehicles. This innovative approach is seamlessly applied to the domain of motor fault diagnosis in autonomous vehicles. By virtue of meticulously designed experiments and comprehensive result analysis, this article endeavors to empirically substantiate the efficacy and merits of this approach. The ultimate aim is to offer innovative solutions for motor fault diagnosis within the context of autonomous vehicles.

The article’s structure is organized as follows: the second section introduces the fundamental principles. In the third section, a detailed presentation of the cross-domain data fusion algorithm for motor fault diagnosis in autonomous driving vehicles is provided. Moving to the fourth section, the article showcases the experimental design and conducts a thorough result analysis. The final section summarizes the research findings and anticipates potential applications of this study in the field of motor fault diagnosis for autonomous driving vehicles.

2. Basic Principles

2.1. Gramian Angular Summation Fields

GAF [23] is a technique used to encode one-dimensional time series data into two-dimensional images. Taking into account the feature extraction advantages of ConvMixer in image classification, this paper employs GAF to transform time series data into images using a pole-based matrix. This approach preserves the correlation between the one-dimensional signal and the time series. In the Gramian matrix, each element corresponds to a trigonometric value of an angle. Initially, the original time series is normalized to a range between 0 and 1, as defined in Equation (1):

$${\tilde{x}}_t=\frac{x\left(t\right)-\min \left(X\right)}{\max \left(X\right)-\min \left(X\right)}$$

(1)

Among them, x(t) represents the vibrational signal at the original time t and the scaled signal, ${\tilde{x}}_t$, at that time. X is the original time series. The minimum and maximum values in X are represented by $\min \left(X\right)$ and $\max \left(X\right)$, respectively. Therefore, one can use polar coordinates to represent the rescaled time series, with the timestamp being the radius:

$$\left\{\begin{array}{l}{\Phi }_i=\arccos \left({\tilde{x}}_t\right), -1\le {\tilde{x}}_t\le 1, {\tilde{x}}_t\in X\\ r_i=t_i/N, t_i\in N\end{array}\right.$$

(2)

In the formula, $t_i$ is the timestamp code of the point in time, dividing the interval [0, 1] into N equal parts, where N is a constant factor that adjusts the radial span of polar coordinates and $r_i$ is the polar axis, preserving the temporal relationship; ${\Phi }_i$ represents the polar angle, preserving the numerical relationship. After converting the recalibrated time series into a polar coordinate system, one can use the perspective of angles to identify the time correlation between different time intervals through the triangular sum/difference between each point. Using the GASF encoding, the encoding method is defined by Equation (3):

$$GASF=\left[\begin{array}{ccc}\cos \left({\Phi }_1+{\Phi }_1\right)& \dots & \cos \left({\Phi }_1+{\Phi }_n\right)\\ \cos \left({\Phi }_2+{\Phi }_1\right)& \dots & \cos \left({\Phi }_2+{\Phi }_n\right)\\ ⋮& \cos \left({\Phi }_i+{\Phi }_i\right)& ⋮\\ \cos \left({\Phi }_n+{\Phi }_1\right)& \dots & \cos \left({\Phi }_n+{\Phi }_n\right)\end{array}\right]$$

(3)

In the equation, ${\Phi }_i$ represents the angle value of the i-th sequence. It is evident that after encoding in this way, the order of time from the top left to bottom right on the two-dimensional image is preserved. The original information is retained at the diagonal position, while other regions express relationships between different time sequences. For a vibration signal with an original time series length of n, a numerical matrix with a size of n×n is obtained through GASF encoding.

2.2. ConvMixer Model

The ConvMixer network architecture comprises several key components: patch embedding, the GELU activation function, a batch normalization layer, and multiple ConvMixer layers. Subsequently, a global pooling operation is applied for feature aggregation, followed by a fully connected layer that yields the classification output. The spatial arrangement of the model is visually represented in Figure 1.

Patch embedding, involving a patch size denoted as “p” and an embedding dimension represented as “h”, is accomplished through a convolutional operation. This operation entails c_in input channels, h output channels, a kernel size of “p”, and a step size of “p”, as shown in Formula (4):

$$z_0=\mathrm{BN}\left(\sigma \left\{{\mathrm{Conv}}_{c_{in}\to h}\left(X, \mathrm{stride}=p, \mathrm{kernel}\_\mathrm{size}=p\right)\right\}\right)$$

(4)

The ConvMixer layer is structured with a profound convolutional segment—specifically, a group convolution with the group size matching the channel count “h”. This is succeeded by a subsequent pointwise convolution, employing a kernel size of 1 × 1. As outlined in the source paper, ConvMixer attains optimal performance by utilizing notably substantial kernel sizes in the deep convolution phase. Following each convolution operation, an activation function is applied, and subsequently, batch normalization is performed, enhancing the overall block’s efficacy, as shown in Formulas (5) and (6):

$$z{’}_l=\mathrm{BN}\left(\sigma \left\{\mathrm{ConvDepthwise}\left(z_{l-1}\right)\right\}\right)+z_{l-1}$$

(5)

$$z_{l+1}=\mathrm{BN}\left(\sigma \left\{\mathrm{ConvPointwise}\left(z_l’\right)\right\}\right)$$

(6)

In Equation (5), ConvDepthwise represents depthwise convolution as illustrated in Figure 1. It involves group convolution with the number of groups equal to the number of channels. The purpose of Equation (5) is to perform convolution on the segmented patch embedding images and subsequently apply batch normalization. As for Equation (6), ConvPointwise corresponds to pointwise convolution in Figure 1, involving 1 × 1 convolution. The role of Equation (6) is to merge the data convolved by Equation (5) and apply batch normalization.

Following the iterative application of this block, the model incorporates a global pooling layer to extract a feature vector of dimension “h”. This resultant feature vector is then fed into a softmax classifier for further processing.

2.3. Efficient Channel Attention

To further enhance feature extraction, this model introduces an attention mechanism—ECA. ECA is a model derived from the analysis and enhancement of Squeeze-and-Excitation Network (SENet) [24]. It is an efficient channel attention module designed to improve the expressive power of target features by capturing inter-channel relationships [25]. In this study, the ECA module is employed to enhance the correlation between channels after convolutional layers, facilitating the extraction of effective features.

Figure 2 illustrates the structure of the ECA module. Under equivalent conditions, the feature map X is first subjected to global average pooling, followed by learning using weight-shared one-dimensional convolution. During this process, inter-channel correlations are taken into account to capture cross-channel interactions, significantly reducing the model’s complexity. Subsequently, the sigmoid activation function is applied. Finally, the information output by the activation function is multiplied with the feature map X to produce X′. Formula (7) represents the method for adaptively selecting the size of the one-dimensional convolutional kernel in ECA. Here, k denotes the size of the one-dimensional convolutional kernel, γ = 2, b = 1, and C represents the number of channels. Using this formula, the coverage range for local cross-channel interaction is determined, thereby establishing the value of k.

$$k=\psi \left(C\right)=\left|\frac{{\log }_2\left(C\right)}{\gamma }+\frac{b}{\gamma }\right|$$

(7)

3. Optimized Algorithm for Motor Fault Diagnosis in Autonomous Driving Vehicles Based on Multi-Domain Data Fusion

This section offers an in-depth introduction to the research methodology employed for the diagnosis of motor faults in autonomous vehicles. Specifically, it centers around a multi-domain data fusion algorithm designed for motor fault diagnosis in autonomous vehicles. This algorithm encompasses the integration of both time-domain and frequency-domain information, coupled with the implementation of the ECA-ConvMixer model. A comprehensive elaboration of the content details is visually presented in Figure 3.

3.1. Integration of Time-Domain and Frequency-Domain Data Fusion

In this study, considering the distinct characteristics of autonomous vehicles, the research team devised an experimental platform aimed at achieving fault diagnosis for electric motors. Given the significant role that vibration signals play in motor fault diagnosis, offering crucial insights into the internal operational status and potential faults of the motor, vibration sensors were employed to gather vibration signals from simulated electric motors within autonomous vehicles under various operational scenarios. Nonetheless, these signals frequently encompass a wealth of features in both the time and frequency domains, and researchers often concentrate on one aspect while inadvertently neglecting the other. To ensure a more comprehensive capture of these features, this study strategically employs a fusion approach that integrates both time-domain and frequency-domain information.

3.1.1. Application of Fast Fourier Transform to Frequency Domain Data

For the extraction of frequency domain characteristics from vibration signals, this study harnessed the fast Fourier transform (FFT) technology. The fast Fourier transform empowers the conversion of time-domain signals into frequency domains, facilitating the generation of spectral maps. Within this spectrum, each distinct frequency component corresponds to specific vibration characteristics. These attributes rooted in the frequency domain serve as valuable indicators of the motor’s internal operation and potential faults.

Illustrated in Figure 4, the juxtaposition of time-domain signals, representative of any given set of vibration signals, is accompanied by the presentation of frequency-domain signals subsequent to the fast Fourier transform. The time-domain signal consists of a total of 4096 points, while the amplitude frequency and phase frequency signals each comprise 2048 points. Notably, the unequal count of frequency-domain and time-domain signals poses a challenge in the process of information fusion.

As a result, the subsequent section of this paper will delve into an elucidation of the procedures involved in handling frequency-domain signals, as well as their harmonious integration with time-domain signals.

3.1.2. Fusion of Time-Domain and Frequency-Domain Information Using Gram Map Encoding

To harness the full potential of both time-domain and frequency-domain information, this study employs the Gram map-encoding method for achieving cross-domain fusion of these two types of data. Leveraging the inherent symmetry of the Gram angle field graph, signals of equal length are merged. However, it was previously highlighted that the length of the amplitude frequency signal and the phase frequency signal within the frequency-domain data is not congruent with that of the time-domain signal. Acknowledging that these two components of the frequency-domain signal are precisely half the length of the time-domain signal, this paper adopts a splicing approach to concatenate these signals, thus establishing a corresponding relationship. For instance, as depicted in Figure 4, two frequency-domain signals, each with a length of 2048, are seamlessly concatenated, culminating in a collective length of 4096 data points to correspond with the time-domain signal.

Due to notable disparities in the amplitudes of the two frequency-domain signals, a preliminary step involves their individual normalization, followed by concatenation. An illustrative instance of the resultant spliced signal is depicted in Figure 5. Subsequently, this study employs the Gram angle and field methodology for encoding both the time-domain signal and the sorted frequency-domain signal. Ultimately, the two encoded signals are merged within a Gram angle field map, culminating in the process as illustrated in Figure 3.

3.2. ECA-ConvMixer Model

Enhanced Channel Attention Network (ECAnet) represents a deep learning model grounded in the attention mechanism, dedicated to extracting pivotal features from data. Central to its philosophy is the objective of capturing correlations among various channels, thereby augmenting the model’s expressive prowess. The architecture of ECAnet is fashioned from a sequence of stacked attention modules, each comprising both a channel attention mechanism and a position attention mechanism. The channel attention mechanism delves into the correlations between diverse channels, fostering an enriched understanding of their interplay. Meanwhile, the positional attention mechanism concentrates on delineating relationships between distinct positions within the same channel. This multi-tiered attention framework equips ECAnet with the capability to effectively discern and encapsulate critical data attributes.

ConvMixer represents an innovative deep learning model, drawing parallels in concept with ViT and MLP Mixer. Distinguishing itself, this model accepts patches as input and undertakes a segregated approach for modeling spatial and channel dimensions, all the while preserving consistent resolution across the entirety of the network. This capacity for multi-channel feature extraction significantly contributes to bolstering the model’s prowess in articulating and accommodating diverse datasets.

4. Motor Fault Diagnosis Experiment and Analysis

4.1. Principles of Establishing an Experimental Platform for Autonomous Vehicle Fault Diagnosis

In line with the content outlined in the first white paper on autonomous driving safety, the verification and validation of auto drive systems and vehicles hold paramount importance [26]. Rigorous testing and related endeavors are imperative to ensure meticulous adherence to system design and vehicle safety standards. As elucidated in the referenced literature [27], motors constitute the pivotal components within electric vehicles, serving the purpose of converting electrical energy into mechanical power. However, as operational time accumulates, the susceptibility to motor failures across diverse operational scenarios amplifies, thereby impinging upon the reliability and safety of electric vehicles. Consequently, the diagnosis of motor faults within autonomous vehicles assumes substantial significance. Notably, Tesla, a prominent proponent in the realm of electric vehicles, has undertaken pioneering research and practical implementation of autonomous driving technology [28].

Based on the available autonomous vehicle data, an array of motor types such as AC motors and variable frequency drive motors are integrated onboard [29]. Furthermore, the power system encompasses additional components like gearboxes and braking systems. In alignment with this premise, the present study employs electric motors, variable speed gearboxes, magnetic particle brakes, among other elements, to emulate the operational conditions of autonomous vehicles. The comprehensive layout of the experimental platform is delineated in Section 4.2.

4.2. Experimental Platform

Building upon the foundational framework elucidated in Section 4.1, this article describes an experimental platform tailored for the diagnosis of motor faults in autonomous driving vehicles, as exemplified in Figure 6. The composition of this experimental platform encompasses three-phase asynchronous motors, gearbox reducers, frequency converters, and magnetic particle brakes, collectively aimed at mimicking genuine operational scenarios. The vibration signal acquisition system is orchestrated with a YE6231 acquisition card, complemented by a CAYD051V acceleration sensor and the corresponding acquisition software. To initiate the setup, the three-phase asynchronous motor, gearbox, and magnetic particle brake are securely affixed to the testing apparatus. The three-phase asynchronous motor establishes its link with the power supply via a frequency converter, while a pulley mechanism interconnects the motor and gearbox. Within the experimental context, vibration acceleration sensors are judiciously positioned at both the drive end and fan end of the motor, thereby facilitating the capture of pertinent vibration signals. The experimental design unfolds across four distinctive states—namely, health, rotor bar breakage, inter-turn short circuit, and end ring cracking—coupled with two operational speeds, namely 30 Hz and 40 Hz, governing the operation of the three-phase asynchronous motor. These fault states are thoughtfully delineated in Figure 7.

4.3. Experimental Data Description

The vibration signals on the experimental platform are sampled at a frequency of 12,000 Hz. To guarantee comprehensive coverage of fault-related information, each sample consists of 1024 data points, resulting in a total of 800 samples. This configuration ensures the incorporation of fault frequencies from both the rotor and stator. Additional details regarding the data setup are elucidated in

Table 1. Data Introduction.

Encoding	Category	Number of Training Sets	Number of Validation Sets	Number of Test Sets
0	End ring cracking 30 Hz	400 × 1024	160 × 1024	240 × 1024
1	End ring cracking 40 Hz	400 × 1024	160 × 1024	240 × 1024
2	Broken rotor bar 30 Hz	400 × 1024	160 × 1024	240 × 1024
3	Broken rotor bar 40 Hz	400 × 1024	160 × 1024	240 × 1024
4	Health 30 Hz	400 × 1024	160 × 1024	240 × 1024
5	Health 40 Hz	400 × 1024	160 × 1024	240 × 1024
6	Turn-to-turn short circuit 30 Hz	400 × 1024	160 × 1024	240 × 1024
7	Turn-to-turn short circuit 30 Hz	400 × 1024	160 × 1024	240 × 1024

.

Table 1 illustrates the random partitioning of datasets into training, validation, and experimental sets, utilizing a ratio of 5:2:3. This allocation translates to 400 training sets, 160 validation sets, and 240 testing sets, encompassing each individual sensor state for testing. The data compilation process resulted in a total of 3200 training samples, 1280 validation samples, and 1920 test samples, spanning across eight distinct states. For each sample, containing 1024 data points, the training set assumes dimensions of 3200 × 1024, the validation set is configured as 1280 × 1024, and the test set assumes dimensions of 1920 × 1024. Prior to training, each sample undergoes a transformation into a Gram angle field map via the cross-domain fusion technique. The resultant Gram angle field maps corresponding to each state’s cross-domain fusion are visualized in Figure 7.

4.4. Analysis of Performance for Multi-Domain Data Fusion Fault Diagnosis Algorithms

This study employs cross-domain fused data in conjunction with the ECA-ConvMixer deep learning model to facilitate efficient motor fault diagnosis. To underscore the merits of the ECA-ConvMixer deep learning model and cross-domain data fusion, two distinct experiments are conducted.

For all models, the chosen optimizer is Adam, utilizing a cross-entropy loss function with an initial learning rate of 0.0001. The training process concludes upon reaching a designated iteration count of 10, with parameter optimization assessed based on the stipulated loss criteria. Furthermore, all networks are implemented within the TensorFlow 2.6.1 deep learning framework. The hardware configuration entails an 11th Gen Intel Core i7-11800H@2.30 GHz, Nvidia GeForce RTX 3070 GPU, and 16 GB of RAM.

4.4.1. Analysis of Results from Various Deep Learning Models on Single-Domain Data

To underscore the superior attributes of the proposed deep learning model, this subsection describes a comparative analysis involving CNN, ResNet, ConvMixer, and ECA-ConvMixer. The subsequent subsections of this article will comprehensively examine the model’s performance from two distinctive vantage points: the training process and accuracy.

In reference to Figure 8a, notable observations emerge during the model training phase. The “Time domain + CNN” configuration exhibits swift loss reduction at the initial training stage. Nevertheless, the eventual training loss value is relatively high, signaling a potential overfitting to the training data. Conversely, the “Time domain + ResNet” model showcases a favorable trajectory in loss reduction, culminating in a relatively lower final training loss value. This effect could be attributed to the incorporation of residual connections, which contribute to a more effective capture of data features. Continuing the analysis, the loss value of the “Time domain + ConvMixer” configuration demonstrates a steady and consistent decline throughout the training process, portraying commendable stability and performance. Meanwhile, the training loss value of “Time domain + ECA-ConvMixer” registers a gradual descent, albeit slight. This subtle decrease attests to the model’s robustness and stability, particularly evident in the later stages of training.

In the context of model validation, insights can be gleaned from Figure 8b. Notably, the validation loss trajectory of “Time domain + CNN” exhibits marked fluctuations, implying a compromised ability to generalize to unfamiliar data. This erratic behavior suggests potential overfitting concerns. Conversely, “Time domain + ResNet” displays relatively stable performance during validation, showcasing improved generalization compared to CNN. The validation loss curve for “Time domain + ConvMixer” maintains consistent stability, indicative of a model that consistently performs well on novel data and exhibits robust generalization capabilities. Similarly, “Time domain + ECA-ConvMixer” demonstrates unwavering performance across the validation phase, affirming strong generalization abilities and robustness, aligning with its counterpart “Time domain + ConvMixer”.

In summary, while CNN demonstrates rapid convergence during training, its validation phase is characterized by notable volatility, potentially indicating susceptibility to overfitting. Conversely, ResNet showcases steady performance across both training and validation, underscoring its reliability and competence. The ConvMixer model maintains stability in validation and demonstrates favorable generalization, thus showcasing advantages over conventional deep learning architectures. The “Time domain + ECA-ConvMixer” configuration stands out for its robustness throughout both training and validation stages, underscoring the efficacy of incorporating attention mechanisms. This attribute positions it as superior among the evaluated models, affirming the value brought about by attention mechanisms in enhancing model performance.

Next, the recognition performance of various models in Experiment 1 on the time-domain dataset was visualized using a confusion matrix. The computed results are presented in Figure 9.

Figure 9 illustrates the outcomes of a comprehensive confusion matrix analysis conducted on eight distinct motor states. This meticulous evaluation juxtaposes the classification performance of four distinct deep learning models. The intention behind this analysis is to foster a deeper comprehension of their respective capabilities in the realm of fault diagnosis.

In the context of Figure 9a, the CNN model demonstrates an overall classification accuracy of 73.80%, as observed from

Table 2. Accuracy of each model.

Model	Time Domain Data Accuracy	Cross Domain Data Accuracy
CNN	73.80%	97.08%
ResNet	76.30%	97.55%
ConvMixer	97.14%	98.91%
ECA-ConvMixer	98.39%	99.68%

. Notably, numerous misclassifications are evident across various operational states. These inaccuracies could be attributed to the model’s difficulty in effectively extracting features from this specific category. To achieve enhanced outcomes, the model might necessitate deeper feature extraction capabilities tailored to these categories. Moving to Figure 9b, the ResNet model exhibits an overall classification accuracy of 76.30%. While an improvement is noted compared to the CNN model, the enhancement is moderate. Figure 9c showcases the remarkable performance of the ConvMixer model, boasting an impressive overall classification accuracy of 97.14%. This high accuracy permeates all categories, with no accuracy dipping below 96.13%. This underscores the model’s substantial accomplishments in feature extraction and classification. Importantly, this model showcases a substantial increase of 23.34% and 20.84% over the CNN and ResNet models, respectively, signifying significant advancement. In Figure 9d, the ECA-ConvMixer model exhibits an accuracy of 99.79%. Similar to the “Time Domain + ConvMixer” model, this configuration also maintains accuracy surpassing 96.68% across all categories. Notably, the most significant errors occur solely in label 4 (Health 30 Hz), resulting in a total of 16 recognition errors. This outcome accentuates the model’s exceptional aptitude for the task. The incorporation of the attention mechanism further amplifies the ConvMixer model’s accuracy, as evidenced by the superior performance of ECA-ConvMixer.

In conclusion, the time-domain ECA-ConvMixer model demonstrates robust performance across various fault types, exhibiting enhanced discrimination capability and classification accuracy. Its strengths are particularly evident when addressing fault features that share similarities and in complex scenarios. The model showcases exceptional performance in terms of training convergence and stability validation. The insights garnered from this study offer valuable guidance for both research endeavors and practical implementations in the realm of motor fault diagnosis. Furthermore, the findings can contribute to the refinement of predictive maintenance strategies, thereby enhancing the formulation and optimization of such strategies.

4.4.2. Analysis of Results from Cross-Domain Data

To accentuate the advantages of the proposed multi-domain data fusion approach, this subsection employs the CNN, ResNet, ConvMixer, and ECA-ConvMixer deep models for training and contrasts their performance with that of single-domain data. The accuracy of each model under distinct data conditions is presented in Table 2.

Based on the data presented in Table 2, it becomes evident that the utilization of cross-domain data yields advantages across all models. In this context, the CNN model attains a cross-domain data accuracy of 97.08%, marking a noteworthy increase of 23.28% compared to its accuracy on time-domain data. Similarly, the ResNet model showcases commendable performance, achieving an accuracy of 97.55% on cross-domain data—an improvement of approximately 21.25% over time-domain data accuracy. The ConvMixer model also exhibits substantial progress, achieving an impressive cross-domain data accuracy of 98.91%. Remarkably, the ECA-ConvMixer model stands out with exceptional prowess, boasting a cross-domain data accuracy of 99.68%. This accomplishment underscores its remarkable capacity to adeptly manage previously unseen data distributions.

Notably, the ECA-ConvMixer model excels in both cross-domain and time-domain data accuracy. It not only attains high accuracy within the same data distribution but also demonstrates exceptional performance when faced with unfamiliar data distributions. To provide a more comprehensive assessment of the model, we present the classification outcomes of “Cross-domain data + ECA-ConvMixer” using a confusion matrix, as visualized in Figure 10.

As depicted in the above figure, each category comprises 240 samples, and the analysis of the confusion matrix sheds light on the model’s classification performance across distinct fault categories.

Firstly, the “End ring cracking 30 Hz” and “End ring cracking 40 Hz” categories exhibit impeccable accuracy of 100%, signifying the model’s adeptness in accurately classifying these cases. Nevertheless, slight misclassifications occur in the “Broken rotor bar 30 Hz” and “Broken rotor bar 40 Hz” categories, indicating the model’s potential oversight of certain samples within these classes. Moving on, the “Health 30 Hz” and “Health 40 Hz” categories demonstrate higher accuracy. In the “Health 30 Hz” category, six samples are misclassified into other categories, potentially due to the similarity of specific features. Remarkably, unlike Figure 9d, no misclassifications of fault states as health categories are observed, underscoring the model’s formidable ability to distinguish fault states and thus offer reliable support for practical fault diagnosis. Moreover, the “Turn-to-turn short circuit 30 Hz” and “Turn-to-turn short circuit 40 Hz” categories exhibit outstanding accuracy of 100%, further affirming the model’s capacity to accurately detect these conditions.

Overall, the ECA-ConvMixer model excels, particularly in the cross-domain data scenario, where accuracy is enhanced and faults are not misconstrued as health cases. This achievement enhances the safety of autonomous driving vehicles. Future research avenues could explore feature engineering, model refinement, and other facets to elevate classification performance and effectively address real-world applications’ requisites.

5. Conclusions

Addressing the challenges posed by low accuracy of deep learning models in discerning intricate operating conditions and the paucity of information in single-domain data for diagnosing motor faults in autonomous driving vehicles, this study conducted an extensive comparative analysis encompassing four distinct deep learning models: CNN, ResNet, ConvMixer, and ECA-ConvMixer. The examination focused on the accuracy of these models in both time-domain and cross-domain data settings, with the objective of assessing their performance in terms of data generalization and practical applicability.

The outcomes of this research affirm that each model displays remarkable prowess under cross-domain data simulation. Notably, the cross-domain data + ECA-ConvMixer model excels in fault state classification, achieving zero error classification across multiple categories within the confusion matrix. Furthermore, the model refrains from erroneously categorizing samples from other fault categories as healthy, highlighting its robust reliability and accuracy in classifying motor faults in autonomous vehicles. These findings establish a strong foundation for real-world implementation.

Moreover, this study unveils a noteworthy observation: the performance of models generally improves in terms of cross-domain data accuracy. Specifically, the CNN model witnesses an enhancement of 23.28% in cross-domain data accuracy over its time-domain counterpart, while the ResNet model experiences a 21.25% improvement, and the ConvMixer model undergoes a 1.77% enhancement. However, it is the ECA-ConvMixer model that emerges as a standout performer, excelling across both time- and cross-domain data settings, thus showcasing its pronounced advantage in data generalization.

In summation, the research findings underscore the significance of cross-domain data classification tasks within the ambit of autonomous vehicle fault diagnosis. The exceptional performance of the ECA-ConvMixer model in this context further reinforces its competence. While this study delves into cross-domain data and deep learning performance, an array of promising avenues remain to be explored. Future research endeavors could encompass evaluating model performance in scenarios with enhanced data acquisition, comparing various feature extraction techniques, and exploring advanced algorithms. Various fields have harnessed advanced optimization algorithms as solutions, including the adaptive polyploid memetic algorithm [30], exact and metaheuristic algorithms [31], and ant-based pheromone spaces [32], among others. We anticipate that these forthcoming investigations will enrich the body of knowledge in the domain of autonomous vehicle fault diagnosis, offering robust support and guidance for practical engineering applications.