# Intelligent Diagnosis of Bogie Traction Seat Based on PCA-OVO and SVM Optimized by Modified Arithmetic Optimization Algorithm

Authors: Shuli Liu; Yi Liu; Qi Chang; Lin Li; Junfeng Man; Kai Liu; Yiping Shen; Jiaxin Luo
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The bogie traction seat is the main part of urban rail vehicles and its fault status will affect the safe and smooth operation of the vehicles. For the low accuracy of the traditional detection methods, an intelligent fault diagnosis model of the traction seat based on principal component analysis with one versus one (PCA-OVO) and support vector machine (SVM) optimized by modified arithmetic optimization algorithm is proposed. Firstly, for the difficulty of high-frequency data collection under real working conditions, the simulation platform of the bogie of an urban rail vehicle is built, and the vibration signals of the traction seat are collected and processed in different domains, and then the feature extraction and fusion method based on PCA-OVO is used to obtain the sensitive feature set of the traction seat. Finally, the SVM intelligence recognition model is constructed based on the sensitive feature set data, and its parameters are optimally combined and selected by the modified arithmetic optimization algorithm after introducing the cosine factor. The experiments prove the effectiveness of the model. Experimental results show that the model is effective and provides a new model for fault diagnosis of traction seat of urban rail vehicles.


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## Body

## 1. Introduction

Urban rail vehicles can effectively relieve the traffic tension in modern cities and promote the rapid development of cities. With the rapid increase in speed and mileage as well as the continuous increase of vehicles, the maintenance services need to be improved gradually. In this context, the fault diagnosis of vehicles is a crucial field of research. Bogie is the core component and its main function is to guide the vehicle along the track, support the vehicle, transfer the load between the vehicle and the track, and mitigate its impact. The traction seat is on the side beam of the bottom frame of the vehicle, which is a connecting part between the car body and the bogie. It bears and transmits the longitudinal force of the vehicle and is the key part of the vehicle body. Its fault diagnosis seriously threatens the safe running of the city rail vehicle. Under the conditions of alternating variable speed and load, long-term overload, etc., once the traction car seat cracks, it will directly affect the connection between the car body and bogie, which can lead to derailment of urban rail vehicles in serious cases. Because of the frequent occurrence of traction seat cracks, it is necessary to study the fault type analysis and fault diagnosis technology of traction seat [1, 2]. The detection of crack faults of key components of rail vehicles mostly adopts ultrasonic flaw detection and magnetic particle flaw detection. As the structure of the components becomes more and more complex and the specific location of the cracks cannot be determined, the above detection methods cannot detect the cracks. To the demand for early fault detection of bogie traction seat and the development of fault trend evolution analysis technology, paper [3] proposes a research on the identification of bogie traction seat crack faults by using vibration diagnosis method, collecting vibration signal data in different states by using experimental simulation platform, and combining with machine learning for pattern recognition to achieve certain results.At present, the research on mechanical equipment fault diagnosis is emerging, and the development trend is unstoppable. Fault diagnosis can improve maintenance efficiency and reduce maintenance costs in the field of vehicles. In the field of rail transit, a lot of achievements have been made in equipment fault diagnosis methods [4, 5]. Darong et al. proposed an improved hidden Markov model (HMM) algorithm, which was applied to fault diagnosis of rail vehicle motor drive system to avoid disaster events to the maximum extent [4]. Feng et al. discussed intelligent sensors and proposed sensor signal sensing technology, mainly from sensor data acquisition, processing technology, and voltage-based sensor fault diagnosis technology, which put forward ideas for the future research of rail transit train sensors [6]. For the bogie fault diagnosis of rail transit vehicles, the adaptive synthetic sampling approach, gradient boosting decision tree, is proposed [7], and it is helpful to detect bogie faults. Based on the uncertainty fault of the rail vehicle door system, Zhao et al. proposed an algorithm based on a Bayesian network to reason the faults of the rail vehicle door system, providing a new scheme for fault diagnosis and maintenance of vehicle doors [8]. Considering that traditional diagnostic methods are difficult to diagnose bogies under variable working conditions and data imbalance often exists in actual data collection, Geng et al. proposed a new loss function-imbalance weighted cross entropy (IWCE) for network training to solve the data imbalance problem and improve the diagnostic accuracy [9]. For the problem that it is difficult to establish the vibration data characteristics and vibration mechanism model of rolling bearing components of railroad trains, a long-term fault diagnosis method based on exponential smoothing prediction segmentation and an improved integrated learning algorithm are proposed, which is effective for fault diagnosis of bearings by experimental result [5]. Given the previous research results, based on the currently commonly used feature engineering diagnosis method, the traction seat fault diagnosis based on principal component analysis with one versus one (PCA-OVO) is proposed from two aspects of information acquisition and feature extraction.Adopting an effective feature extraction scheme can improve the generalization and accuracy of machinery and equipment fault diagnosis. Bharti and Singh proposed a modified joint method to apply jointly to the top-ranked features and apply intersection to the remaining features, which reduces the dimensionality of the feature space and solves the computational complexity, but only the key feature information is retained and the feature information is incomplete [10]. Based on two classic dimensionality reduction methods (feature selection and feature extraction), He et al. studied the use of selected and extracted features to approximate data and obtain the best feature characterization method [11]. Haq et al. used linear correlation coefficients and information gain to jointly characterize feature information, selected the highest ranked feature from each cluster as a representative, and then used a union operation to merge all representatives from, the three ranked lists, into the final feature set [12]. Zebari et al. discussed and analyzed two common feature processing methods in feature extraction, namely, feature selection and feature extraction [13]. Wang et al. studied an adaptive spectral mode extraction method for fault feature extraction of rolling bearings that consists of spectral segmentation, pattern extraction, and feedback adjustment [14]. The empirical mode decomposition (EMD) was used to identify and purify vibration signal waveforms and approximate coefficients of various fault signals were obtained [15]. Based on the traditional single fractal dimension, to distinguish different health states of bearings, Li et al. proposed a generalized multiple fractal dimension algorithm to extract the features of bearing vibration signals [16]. Hu et al. used kernel principal component analysis (KPCA) to eliminate irrelevant and redundant information in the original feature set and obtain the feature set affecting the classification, which solved the problem of insufficient feature parameters of rotating machinery faults and the limitation of fault information [17]. Given a large number of studies, and the complexity of vibration signals caused by different degrees of cracks in traction seat is difficult to analyze, this experiment proposed PCA-OVO feature extraction and fusion algorithm to extract the state information of the traction seat. Pattern recognition is the most common method for fault diagnosis at this stage. Recently, machine learning has been successfully applied to pattern recognition tasks, and many experiments have demonstrated their applicability to fault diagnosis problems [18, 19]. Considering the correlation between threshold levels and signals, a fault detection method based on HMM for mechanical components of wind turbines is proposed, which achieves a detection success rate of 95% [20]. Luo et al. combined random signal analysis and generalized hidden Markov model (GHMM), applied it to simulated fault diagnosis, and verified the finiteness [21]. A method based on the weighted K nearest neighbor (KNN) algorithm is proposed to classify different gear cracks, which can automatically and reliably identify this crack level by selecting sensitive features and eliminating irrelevant features [22]. Wu et al. developed a convolutional neural network to learn features directly from the raw gearbox vibration signal, and then perform fault diagnosis [23]. Eren et al. mentioned that when targeting relatively small training/testing datasets, where feature extraction, feature selection, and classification are usually encapsulated into separate blocks, the proposed system takes the raw time-series sensor data directly as input and it can learn the best features efficiently with proper training [24]. Considering relatively large data sets, a convolutional neural network (CNN) classifier is used [25]. However, most of the existing studies assume that the training and test data have the same distribution, which is not consistent with the actual diagnosis task. Han et al. proposed a migration learning framework based on pretrained CNNs, which uses the knowledge learned from the training data to help diagnose a new but similar task [26]. To solve the problem of insufficient samples in rotating machinery fault diagnosis, Li et al. proposed an improved unsupervised data augmentation method that generates multimode samples simultaneously to assist in training deep learning fault diagnosis models [27]. Xiao el al. designs a new joint transmission network for unsupervised bearing fault diagnosis, which makes full use of bearing simulation data containing rich fault marker information to construct the source domain and reduce the dependence on laboratory test bench resources [28]. Given the previous studies, it can be found that the selection of the classifier should take into account the characteristics of the sample class itself. Support vector machine (SVM) was suitable for solving small-scale samples and nonlinear and high-dimensional pattern recognition. It has high stability in finding the optimal solution based on the complexity of the limited sample information present among the models and the learning ability and is used in the field of industrial equipment and mechanical equipment [19, 29], photovoltaic power prediction [30], medical engineering [31], and so on, which have advantages in practical applications. The choice of parameters has a great degree of influence on the model performance of SVM, and failure to choose parameters correctly may have negative effects on the performance. Therefore finding the most suitable combination of parameters to construct the best SVM model is worth investigating. The arithmetic optimization algorithm (AOA) was proposed by Abualigah et al. in 2021 [32]. It was inspired by heuristic arithmetic problem solving, this algorithm can solve the optimization problem without calculating the derivatives solving optimization problems [33], and thus can be applied to practical engineering problems. In this research, we propose to classify and diagnose faults in the state of the traction seat using SVM with optimized parameters by modified AOA for the typical properties of the traction seat collection data.For the fault diagnosis of bogies of urban rail vehicles, we propose the first SVM model optimized by a modified arithmetic optimization algorithm of traction seat based on PCA-OVO multifeature extraction and fusion. The training and test data sampling of the diagnostic model are based on the simulation under actual working conditions. The experiments verify the effectiveness of the method and have value for real-world engineering applications.


## 2. Problem and Solution

Concerning the development of the country’s “new infrastructure,” the scale of investment in the field of rail transportation cannot be underestimated. To respond to the national call, in-depth research on the fault diagnosis of urban rail vehicles was carried out. The bogie is subjected to high frequency and random changes of load when the urban rail vehicle is in operation, and it is easy to have structural failure. At present, the research on vehicle bogie traction seat has just started, and there are few related literature studies and limited access to information. Secondly, the diagnosis of the vehicle relies too much on traditional signal processing technology, expert experience, etc., and the generality and real-time are not strong. The state data of the traction seat under actual working conditions are difficult to collect, and the data cannot be fully analyzed leading to low diagnostic accuracy. Due to the current difficulty in diagnosing traction seat of vehicle bogie faults, taking the traction seat as the research object, the corresponding solutions are put forward one by one. Firstly, the urban rail vehicle bogie simulation experiment platform (including the traction seat simulation experiment platform) was built to solve the difficulty of insufficient experimental data at present. Secondly, effective signal processing and information extraction were carried out for the traction seat data collected and variational modal decomposition (VMD) and PCA-OVO information extraction architectures were established. Finally, pattern recognition based on SVM optimized by the modified arithmetic optimization algorithm after introducing the cosine factor (named CAOA-SVM) is constructed for state diagnosis. A fault diagnosis model was constructed on the simulation experimental platform of the traction seat. Figure1 shows the online intelligent diagnosis process, which can be described as follows:(1)
Data Acquisition of vibration signals is performed on the experimental simulation equipment of the bogie traction seat.(2)
Effective signal processing and information extraction are performed on the collected data. PCA-OVO algorithm is used to obtain effective feature vectors to characterize the traction seat state features.(3)
The data set calculated by step 3 is divided into two groups, which are used as training data set and test data set, respectively. The training data set are input into CAOA-SVM for training to produce the classifier model, while the test data set are input into the completed training classifier to identify the traction seat fault types.Figure 1
Traction seat fault diagnosis process.


## 3. Establishment of Fault Model for Bogie Traction Seat

### 3.1. Experimental Equipment Construction and Data Acquisition

Data analysis and mining are essential to work in fault diagnosis. Reliable data is the basis of establishing a fault diagnosis model. The state data of the bogie traction seat under actual operating conditions are not easy to obtain, and the lack of data leads to the difficulty of fault diagnosis. This experiment refers to the bogie overhaul standard of urban rail vehicle bogies, the health status of traction seat is divided into three kinds: normal crack, small crack, and large crack. The grading of traction seat status is shown in Table1. The experiment builds the simulation platform (Figure 2); the experimental device consists of six parts: signal generation device, power output device, transmission device, detection device, acquisition device, and signal processing device (Figure 3), and the sensors related to the parameters of vibration, noise, temperature, and speed, which have a great influence on the state, are selected and installed on the key points of the experimental object to obtain the real and reliable data source.Table 1
The state of the traction seat.
StateNormalSmall crackLarge crackJudgmentNo set fault1 mm × 3 mm2 mm × 8 mmFigure 2
Traction seat model. (a) Real model; (b) experimental model; (c) experimental model-small crack; and (d) experimental model-large crack.
(a)(b)(c)(d)Figure 3
Traction seat vibration test device. (a) Vibration test equipment and (b) data acquisition equipment.
(a)(b)Acceleration and deceleration of vehicles will cause the vibration of the traction seat to change. Therefore, the combination of experimental instruments and vibration sensors provides a data source for bogie running state prediction. According to the vibration frequency of trains running at low speeds and the natural frequency of vehicle body parts, the experimental excitation frequency range is determined to be 100 Hz∼2500 Hz. The excitation output mode of frequency sweep is set to constant frequency output to reflect the dynamic change process of traction seat vibration, and the output signal is a steady sinusoidal signal. To cover the range of frequency variation, the output frequency of the sweep is fixed, and the output excitation signal is from 100 Hz to 2500 Hz. The parameters of the data acquisition system include sampling frequency, sampling time, trigger mode, etc. The sampling frequency is set toFs = 12 kHz, sampling time t = 5 s, and sampling interval t = 1 h. Three groups of different states of data are collected each time, and each group of data is 6000 sampling points. Experimentally, 1200 groups of data were collected, with 400 groups of sample data for each state (normal, small crack, and large crack). 70% of the data were randomly selected as the training set and the remaining 30% of the data were used as the test set as shown in Table 2.Table 2
Experimental data of traction seat.
StateNormalSmall crackLarge crackLabel namingNSLSample points in a single group600060006000Number of training data groups280280280Number of test data groups120120120Number of sample groups400400400


### 3.2. Feature Extraction and Fusion of Traction Seat Based on PCA-OVO

The status identification and problem diagnosis of bogie depend on efficient signal processing and information extraction. The time domain, frequency domain, and time-frequency domain are the most frequently utilized signal feature extraction techniques. Time-domain analysis can directly see the changes in signals over time. When the equipment fails, it can simply judge whether the equipment fails by observing the time domain waveform or time-domain index of the signal. Time-domain signals are transformed into frequency domain signals after Fourier transform, and a complex signal is decomposed into multiple harmonic signals of different frequencies, and then a certain harmonic signal is analyzed [34]. Time-frequency analysis can know the instantaneous frequency and amplitude of signals at different moments. Common time-frequency analysis methods include empirical mode decomposition (EMD), ensemble EMD, energy entropy wavelet transform (EEWT) [35, 36], empirical wavelet transform (EWT), VMD, etc. Literatures [37, 38] can prove VMD’s obvious advantage in number decomposition. The vibration signal of the traction seat collected in this experiment will contain a lot of interference information. Only by filtering out the invalid and redundant information, the effective characteristic information of the traction seat state can be efficiently extracted. Based on the popular signal analysis and extraction methods, a PCA-OVO algorithm is suggested, which can efficiently propose the sensitive feature set and fully represent the state of the traction seat.The PCA-OVO feature extraction and fusion algorithm is used to eliminate the redundant and invalid information of the device and retain the key feature information, which means that the dimensionality and computational complexity of the feature space can be reduced, and yet the state information of the device is characterized to the maximum extent. The process is as follows: after PCA reduces the dimensionality of the feature parameters obtained from the time domain, frequency domain, and time-frequency domain analysis, a total of 3n feature values are assumed to be selected. These 3n feature values are divided into two pairs and transformed into a binary classification problem after two pairs: first, the training samples of feature values T1 and F1 are selected to train the classifiers of T1 and F1, then the samples of T1 and F2 are selected to train the classifiers of classesT1 and F2, then the samples of classes T2 and F1 are selected to train the classifiers of classes T2 and F1, and so on, until the samples of Tn and Fn are selected to train the classifiers of Tn and Fn. The 3 classes of n eigenvalue samples are introduced into the optimized SVM classifier, respectively, and the accuracy of fault identification is compared, and those with accuracy higher than 90% are put into the sensitive feature set, and vice versa, those with less than 90% are put into the insensitive feature set. Figure 4 shows the schematic diagram of the PCA-OVO feature extraction and fusion algorithm.Figure 4
Schematic diagram of PCA-OVO feature extraction and fusion algorithm.


### 3.3. CAOA-SVM-Based Traction Seat Pattern Recognition

#### 3.3.1. Arithmetic Optimization Algorithm Modification

Abualigah et al. [32] proposed the arithmetic optimization algorithm (AOA) in 2021, inspired by the use of arithmetic operators (i.e., multiplication, division, subtraction, and addition) in solving arithmetic problems, which discusses the behavior of arithmetic operators and reveals their impact in the algorithm. The AOA algorithm is simple to operate and has a short search time.The population-based optimization algorithm starts its optimization process from a randomly generated set of candidate solutions, improves incrementally on this generated set of solutions by a set of optimization rules, and iteratively evaluates them by a specific objective function. AOA is a novel population-based metaheuristic algorithm that uses both exploration and development phases to elucidate its optimization process. The algorithm mechanism is shown in Figure5.Figure 5
AOA algorithm mechanism.(1) Initialization. AOA generates random numbers for population initialization by using the following equation:(1)X=x1,1⋯x1,jx1,nx2,1⋯x2,1x2,n⋮⋮⋮xm,1⋯xm,jxm,n,where m is the number of populations, n is the exploration space dimension, and xij is the position of the i-th solution in the j-th dimension.Before the AOA starts optimization, the value of math optimizer accelerated (MOA) is calculated to decide whether to enter the exploration or exploitation. A random numberr1∈0,1 is selected, if r1>MOA, the exploration is executed, or else if r1≤MOA the exploitation is executed.(2)MOAc_t=Min+c_tMax−Minm_t,Where c_t is the current number of iteration, m_t is the maximum number of iteration, and Max and Min denote the maximum and minimum values of MOA functions, respectively.(2) Exploration Phase. In this phase, AOA uses multiplication (M) and division (D), D and M have high dispersion, which is beneficial to the global survey exploration. The mathematical model of this stage is as follows:(3)xi,jc_t+1=bestxj÷MOPc_t+ε×D,r2<0.5,bestxj×MOPc_t×D,r2≥0.5,(4)D=μUBj−LBj+LBj,MOPc_t=1−ct1/αct1/α,where xi,jc_t+1 is the i-th solution of the c_t+1 iterations; bestxj is the position of the best solution in the j-th dimension during the iteration; UBj,DBj denote the upper and lower bounds of the optimal value in the j-th dimension, respectively; ε is the minimum constant; μ is the control parameter to adjust the exploration process; math optimizer probability (MOP) is a coefficient number; and r2∈0,1 is a random number.(3) Exploitation Phase. In this phase, AOA uses addition (A) and subtraction (S). A and S have significantly low dispersion and can easily approach the goal. Therefore, strengthening the connection between S and A to support the exploitation phase is faster. The mathematical model of this phase is as follows:(5)xi,jc_t+1=bestxj−MOPct+ε+D,r3<0.5,bestxj+MOPc_t+D,r3≥0.5,where r3∈0,1 is a random number. This phase utilizes the search space by performing a deep search.(4) Modification. Similar to other algorithms, AOA encounters the problem of global search and local search imbalance in the process of finding the best. MOA is linearly growing, which determines the exploration phase or exploitation phase of the algorithm, the larger the MOA, the stronger the local search capability, and the smaller the MOA, the stronger the global search capability. As shown in Figure 5, the optimization search process of AOA is nonlinear, and the linearly growing MOA cannot accurately express the actual iterative process of AOA. For exploration and exploitation, the MOA growth interval defined by AOA is [0.2, 1], and the MOA with the introduction of cosine factor is smaller and increases slowly to fully perform a global search in the early stage of AOA iteration and increases rapidly to perform a local search in the late stage of iteration.The balance of global search and local search affects the performance of AOA. The MOA formula is reconstructed according to the characteristics of Figure5, and the cosine factor is introduced to dynamically adjust the balance of the global and local search to improve the algorithm’s search accuracy and stability, and the MOA value changes as shown in Figure 6.(6)MOAc_t=Min+Max−Mincosc_tm_t·π2+π+1.Figure 6
Change of MOA.


#### 3.3.2. SVM Parameter Optimization

SVM adopts the principle of structural risk minimization, has good generalization ability, and can better solve small sample and nonlinear problems. The selection of SVM parameters including penalty factor and kernel function parameters is sensitive, and finding the best parameters is a key step to improving the classification ability of SVM models. The traditional method uses the grid-search, but due to many combinations of parameters, this method is very slow and cannot achieve satisfactory results [39], and more metaheuristic algorithms are currently used to find the parameters of SVM. For example, Tao et al. [40] used a genetic algorithm (GA) combined with SVM to solve the multi-classification problem; Zhu et al. [19] used improved particle swarm optimization (PSO) to select the parameters of SVM to get better results. To solve the problem of accurate identification of tool wear status in titanium machining, Kong et al. [41] optimized SVM using the whale optimization algorithm (WOA). Eswaramoorthy et al. [42] used gray wolf optimization (GWO) to find a better combination of internal parameters of SVM. Houssein et al. [43] combine Harris Hawks optimization (HHO) metaheuristics with SVM and used it for chemical description and compound activity. Although scholars have conducted a lot of research on SVM parameter selection, different data sets affect the classification accuracy of SVM, and different optimization algorithms are used to search the parameters of SVM for different data sets. Therefore, we try to use modified AOA to select the parameters of SVM based on the urban rail bogie traction seat data set.We assume that the training samples arexi,yi, where i=1,2,...,n,x∈Rd,y is the class label. SVM realizes the optimization of the problem under limited conditions. Let the optimal classification function and constraints be as follows:(7)fx=sgn∑i=1naiyikxi,x+b,ai≠0,min12ω+C∑i=1nξi,where xi is the support vector, x is the classification vector, k· is the kernel function, a and b are the coefficients to determine the optimal hyperplane, C is the penalty coefficient, and ξi is the relaxation coefficient. Through the Lagrange functional algorithm, this problem is transformed into a quadratic optimization problem as follows:(8)max∑i=1nai−12∑i,j=1naiajyiyjkxi,x,s.t.∑i=1nyiai=0,0≤aj≤C,i=1,2,...,n,b is obtained by equation (9)(9)yi∑i=1naiyikxi,x+b−1=0.A Gaussian function represents the kernel function as follows:(10)kx,y=exp−xi−xj2σ2.Obviously, in the SVM parameter selection, the penalty factorC and the kernel function parameter σ are more critical for constructing the optimal classifier. We use C,σ as the optimized combination optimized by modified AOA, and the classification accuracy of the training set is selected as the evaluation basis to evaluate the best . The classification model is built, and its flowchart is shown in Figure 7.Figure 7
The flow chart of modified AOA-SVM.


## 3.1. Experimental Equipment Construction and Data Acquisition

Data analysis and mining are essential to work in fault diagnosis. Reliable data is the basis of establishing a fault diagnosis model. The state data of the bogie traction seat under actual operating conditions are not easy to obtain, and the lack of data leads to the difficulty of fault diagnosis. This experiment refers to the bogie overhaul standard of urban rail vehicle bogies, the health status of traction seat is divided into three kinds: normal crack, small crack, and large crack. The grading of traction seat status is shown in Table1. The experiment builds the simulation platform (Figure 2); the experimental device consists of six parts: signal generation device, power output device, transmission device, detection device, acquisition device, and signal processing device (Figure 3), and the sensors related to the parameters of vibration, noise, temperature, and speed, which have a great influence on the state, are selected and installed on the key points of the experimental object to obtain the real and reliable data source.Table 1
The state of the traction seat.
StateNormalSmall crackLarge crackJudgmentNo set fault1 mm × 3 mm2 mm × 8 mmFigure 2
Traction seat model. (a) Real model; (b) experimental model; (c) experimental model-small crack; and (d) experimental model-large crack.
(a)(b)(c)(d)Figure 3
Traction seat vibration test device. (a) Vibration test equipment and (b) data acquisition equipment.
(a)(b)Acceleration and deceleration of vehicles will cause the vibration of the traction seat to change. Therefore, the combination of experimental instruments and vibration sensors provides a data source for bogie running state prediction. According to the vibration frequency of trains running at low speeds and the natural frequency of vehicle body parts, the experimental excitation frequency range is determined to be 100 Hz∼2500 Hz. The excitation output mode of frequency sweep is set to constant frequency output to reflect the dynamic change process of traction seat vibration, and the output signal is a steady sinusoidal signal. To cover the range of frequency variation, the output frequency of the sweep is fixed, and the output excitation signal is from 100 Hz to 2500 Hz. The parameters of the data acquisition system include sampling frequency, sampling time, trigger mode, etc. The sampling frequency is set toFs = 12 kHz, sampling time t = 5 s, and sampling interval t = 1 h. Three groups of different states of data are collected each time, and each group of data is 6000 sampling points. Experimentally, 1200 groups of data were collected, with 400 groups of sample data for each state (normal, small crack, and large crack). 70% of the data were randomly selected as the training set and the remaining 30% of the data were used as the test set as shown in Table 2.Table 2
Experimental data of traction seat.
StateNormalSmall crackLarge crackLabel namingNSLSample points in a single group600060006000Number of training data groups280280280Number of test data groups120120120Number of sample groups400400400


## 3.2. Feature Extraction and Fusion of Traction Seat Based on PCA-OVO

The status identification and problem diagnosis of bogie depend on efficient signal processing and information extraction. The time domain, frequency domain, and time-frequency domain are the most frequently utilized signal feature extraction techniques. Time-domain analysis can directly see the changes in signals over time. When the equipment fails, it can simply judge whether the equipment fails by observing the time domain waveform or time-domain index of the signal. Time-domain signals are transformed into frequency domain signals after Fourier transform, and a complex signal is decomposed into multiple harmonic signals of different frequencies, and then a certain harmonic signal is analyzed [34]. Time-frequency analysis can know the instantaneous frequency and amplitude of signals at different moments. Common time-frequency analysis methods include empirical mode decomposition (EMD), ensemble EMD, energy entropy wavelet transform (EEWT) [35, 36], empirical wavelet transform (EWT), VMD, etc. Literatures [37, 38] can prove VMD’s obvious advantage in number decomposition. The vibration signal of the traction seat collected in this experiment will contain a lot of interference information. Only by filtering out the invalid and redundant information, the effective characteristic information of the traction seat state can be efficiently extracted. Based on the popular signal analysis and extraction methods, a PCA-OVO algorithm is suggested, which can efficiently propose the sensitive feature set and fully represent the state of the traction seat.The PCA-OVO feature extraction and fusion algorithm is used to eliminate the redundant and invalid information of the device and retain the key feature information, which means that the dimensionality and computational complexity of the feature space can be reduced, and yet the state information of the device is characterized to the maximum extent. The process is as follows: after PCA reduces the dimensionality of the feature parameters obtained from the time domain, frequency domain, and time-frequency domain analysis, a total of 3n feature values are assumed to be selected. These 3n feature values are divided into two pairs and transformed into a binary classification problem after two pairs: first, the training samples of feature values T1 and F1 are selected to train the classifiers of T1 and F1, then the samples of T1 and F2 are selected to train the classifiers of classesT1 and F2, then the samples of classes T2 and F1 are selected to train the classifiers of classes T2 and F1, and so on, until the samples of Tn and Fn are selected to train the classifiers of Tn and Fn. The 3 classes of n eigenvalue samples are introduced into the optimized SVM classifier, respectively, and the accuracy of fault identification is compared, and those with accuracy higher than 90% are put into the sensitive feature set, and vice versa, those with less than 90% are put into the insensitive feature set. Figure 4 shows the schematic diagram of the PCA-OVO feature extraction and fusion algorithm.Figure 4
Schematic diagram of PCA-OVO feature extraction and fusion algorithm.


## 3.3. CAOA-SVM-Based Traction Seat Pattern Recognition

### 3.3.1. Arithmetic Optimization Algorithm Modification

Abualigah et al. [32] proposed the arithmetic optimization algorithm (AOA) in 2021, inspired by the use of arithmetic operators (i.e., multiplication, division, subtraction, and addition) in solving arithmetic problems, which discusses the behavior of arithmetic operators and reveals their impact in the algorithm. The AOA algorithm is simple to operate and has a short search time.The population-based optimization algorithm starts its optimization process from a randomly generated set of candidate solutions, improves incrementally on this generated set of solutions by a set of optimization rules, and iteratively evaluates them by a specific objective function. AOA is a novel population-based metaheuristic algorithm that uses both exploration and development phases to elucidate its optimization process. The algorithm mechanism is shown in Figure5.Figure 5
AOA algorithm mechanism.(1) Initialization. AOA generates random numbers for population initialization by using the following equation:(1)X=x1,1⋯x1,jx1,nx2,1⋯x2,1x2,n⋮⋮⋮xm,1⋯xm,jxm,n,where m is the number of populations, n is the exploration space dimension, and xij is the position of the i-th solution in the j-th dimension.Before the AOA starts optimization, the value of math optimizer accelerated (MOA) is calculated to decide whether to enter the exploration or exploitation. A random numberr1∈0,1 is selected, if r1>MOA, the exploration is executed, or else if r1≤MOA the exploitation is executed.(2)MOAc_t=Min+c_tMax−Minm_t,Where c_t is the current number of iteration, m_t is the maximum number of iteration, and Max and Min denote the maximum and minimum values of MOA functions, respectively.(2) Exploration Phase. In this phase, AOA uses multiplication (M) and division (D), D and M have high dispersion, which is beneficial to the global survey exploration. The mathematical model of this stage is as follows:(3)xi,jc_t+1=bestxj÷MOPc_t+ε×D,r2<0.5,bestxj×MOPc_t×D,r2≥0.5,(4)D=μUBj−LBj+LBj,MOPc_t=1−ct1/αct1/α,where xi,jc_t+1 is the i-th solution of the c_t+1 iterations; bestxj is the position of the best solution in the j-th dimension during the iteration; UBj,DBj denote the upper and lower bounds of the optimal value in the j-th dimension, respectively; ε is the minimum constant; μ is the control parameter to adjust the exploration process; math optimizer probability (MOP) is a coefficient number; and r2∈0,1 is a random number.(3) Exploitation Phase. In this phase, AOA uses addition (A) and subtraction (S). A and S have significantly low dispersion and can easily approach the goal. Therefore, strengthening the connection between S and A to support the exploitation phase is faster. The mathematical model of this phase is as follows:(5)xi,jc_t+1=bestxj−MOPct+ε+D,r3<0.5,bestxj+MOPc_t+D,r3≥0.5,where r3∈0,1 is a random number. This phase utilizes the search space by performing a deep search.(4) Modification. Similar to other algorithms, AOA encounters the problem of global search and local search imbalance in the process of finding the best. MOA is linearly growing, which determines the exploration phase or exploitation phase of the algorithm, the larger the MOA, the stronger the local search capability, and the smaller the MOA, the stronger the global search capability. As shown in Figure 5, the optimization search process of AOA is nonlinear, and the linearly growing MOA cannot accurately express the actual iterative process of AOA. For exploration and exploitation, the MOA growth interval defined by AOA is [0.2, 1], and the MOA with the introduction of cosine factor is smaller and increases slowly to fully perform a global search in the early stage of AOA iteration and increases rapidly to perform a local search in the late stage of iteration.The balance of global search and local search affects the performance of AOA. The MOA formula is reconstructed according to the characteristics of Figure5, and the cosine factor is introduced to dynamically adjust the balance of the global and local search to improve the algorithm’s search accuracy and stability, and the MOA value changes as shown in Figure 6.(6)MOAc_t=Min+Max−Mincosc_tm_t·π2+π+1.Figure 6
Change of MOA.


### 3.3.2. SVM Parameter Optimization

SVM adopts the principle of structural risk minimization, has good generalization ability, and can better solve small sample and nonlinear problems. The selection of SVM parameters including penalty factor and kernel function parameters is sensitive, and finding the best parameters is a key step to improving the classification ability of SVM models. The traditional method uses the grid-search, but due to many combinations of parameters, this method is very slow and cannot achieve satisfactory results [39], and more metaheuristic algorithms are currently used to find the parameters of SVM. For example, Tao et al. [40] used a genetic algorithm (GA) combined with SVM to solve the multi-classification problem; Zhu et al. [19] used improved particle swarm optimization (PSO) to select the parameters of SVM to get better results. To solve the problem of accurate identification of tool wear status in titanium machining, Kong et al. [41] optimized SVM using the whale optimization algorithm (WOA). Eswaramoorthy et al. [42] used gray wolf optimization (GWO) to find a better combination of internal parameters of SVM. Houssein et al. [43] combine Harris Hawks optimization (HHO) metaheuristics with SVM and used it for chemical description and compound activity. Although scholars have conducted a lot of research on SVM parameter selection, different data sets affect the classification accuracy of SVM, and different optimization algorithms are used to search the parameters of SVM for different data sets. Therefore, we try to use modified AOA to select the parameters of SVM based on the urban rail bogie traction seat data set.We assume that the training samples arexi,yi, where i=1,2,...,n,x∈Rd,y is the class label. SVM realizes the optimization of the problem under limited conditions. Let the optimal classification function and constraints be as follows:(7)fx=sgn∑i=1naiyikxi,x+b,ai≠0,min12ω+C∑i=1nξi,where xi is the support vector, x is the classification vector, k· is the kernel function, a and b are the coefficients to determine the optimal hyperplane, C is the penalty coefficient, and ξi is the relaxation coefficient. Through the Lagrange functional algorithm, this problem is transformed into a quadratic optimization problem as follows:(8)max∑i=1nai−12∑i,j=1naiajyiyjkxi,x,s.t.∑i=1nyiai=0,0≤aj≤C,i=1,2,...,n,b is obtained by equation (9)(9)yi∑i=1naiyikxi,x+b−1=0.A Gaussian function represents the kernel function as follows:(10)kx,y=exp−xi−xj2σ2.Obviously, in the SVM parameter selection, the penalty factorC and the kernel function parameter σ are more critical for constructing the optimal classifier. We use C,σ as the optimized combination optimized by modified AOA, and the classification accuracy of the training set is selected as the evaluation basis to evaluate the best . The classification model is built, and its flowchart is shown in Figure 7.Figure 7
The flow chart of modified AOA-SVM.


## 3.3.1. Arithmetic Optimization Algorithm Modification

Abualigah et al. [32] proposed the arithmetic optimization algorithm (AOA) in 2021, inspired by the use of arithmetic operators (i.e., multiplication, division, subtraction, and addition) in solving arithmetic problems, which discusses the behavior of arithmetic operators and reveals their impact in the algorithm. The AOA algorithm is simple to operate and has a short search time.The population-based optimization algorithm starts its optimization process from a randomly generated set of candidate solutions, improves incrementally on this generated set of solutions by a set of optimization rules, and iteratively evaluates them by a specific objective function. AOA is a novel population-based metaheuristic algorithm that uses both exploration and development phases to elucidate its optimization process. The algorithm mechanism is shown in Figure5.Figure 5
AOA algorithm mechanism.(1) Initialization. AOA generates random numbers for population initialization by using the following equation:(1)X=x1,1⋯x1,jx1,nx2,1⋯x2,1x2,n⋮⋮⋮xm,1⋯xm,jxm,n,where m is the number of populations, n is the exploration space dimension, and xij is the position of the i-th solution in the j-th dimension.Before the AOA starts optimization, the value of math optimizer accelerated (MOA) is calculated to decide whether to enter the exploration or exploitation. A random numberr1∈0,1 is selected, if r1>MOA, the exploration is executed, or else if r1≤MOA the exploitation is executed.(2)MOAc_t=Min+c_tMax−Minm_t,Where c_t is the current number of iteration, m_t is the maximum number of iteration, and Max and Min denote the maximum and minimum values of MOA functions, respectively.(2) Exploration Phase. In this phase, AOA uses multiplication (M) and division (D), D and M have high dispersion, which is beneficial to the global survey exploration. The mathematical model of this stage is as follows:(3)xi,jc_t+1=bestxj÷MOPc_t+ε×D,r2<0.5,bestxj×MOPc_t×D,r2≥0.5,(4)D=μUBj−LBj+LBj,MOPc_t=1−ct1/αct1/α,where xi,jc_t+1 is the i-th solution of the c_t+1 iterations; bestxj is the position of the best solution in the j-th dimension during the iteration; UBj,DBj denote the upper and lower bounds of the optimal value in the j-th dimension, respectively; ε is the minimum constant; μ is the control parameter to adjust the exploration process; math optimizer probability (MOP) is a coefficient number; and r2∈0,1 is a random number.(3) Exploitation Phase. In this phase, AOA uses addition (A) and subtraction (S). A and S have significantly low dispersion and can easily approach the goal. Therefore, strengthening the connection between S and A to support the exploitation phase is faster. The mathematical model of this phase is as follows:(5)xi,jc_t+1=bestxj−MOPct+ε+D,r3<0.5,bestxj+MOPc_t+D,r3≥0.5,where r3∈0,1 is a random number. This phase utilizes the search space by performing a deep search.(4) Modification. Similar to other algorithms, AOA encounters the problem of global search and local search imbalance in the process of finding the best. MOA is linearly growing, which determines the exploration phase or exploitation phase of the algorithm, the larger the MOA, the stronger the local search capability, and the smaller the MOA, the stronger the global search capability. As shown in Figure 5, the optimization search process of AOA is nonlinear, and the linearly growing MOA cannot accurately express the actual iterative process of AOA. For exploration and exploitation, the MOA growth interval defined by AOA is [0.2, 1], and the MOA with the introduction of cosine factor is smaller and increases slowly to fully perform a global search in the early stage of AOA iteration and increases rapidly to perform a local search in the late stage of iteration.The balance of global search and local search affects the performance of AOA. The MOA formula is reconstructed according to the characteristics of Figure5, and the cosine factor is introduced to dynamically adjust the balance of the global and local search to improve the algorithm’s search accuracy and stability, and the MOA value changes as shown in Figure 6.(6)MOAc_t=Min+Max−Mincosc_tm_t·π2+π+1.Figure 6
Change of MOA.


## 3.3.2. SVM Parameter Optimization

SVM adopts the principle of structural risk minimization, has good generalization ability, and can better solve small sample and nonlinear problems. The selection of SVM parameters including penalty factor and kernel function parameters is sensitive, and finding the best parameters is a key step to improving the classification ability of SVM models. The traditional method uses the grid-search, but due to many combinations of parameters, this method is very slow and cannot achieve satisfactory results [39], and more metaheuristic algorithms are currently used to find the parameters of SVM. For example, Tao et al. [40] used a genetic algorithm (GA) combined with SVM to solve the multi-classification problem; Zhu et al. [19] used improved particle swarm optimization (PSO) to select the parameters of SVM to get better results. To solve the problem of accurate identification of tool wear status in titanium machining, Kong et al. [41] optimized SVM using the whale optimization algorithm (WOA). Eswaramoorthy et al. [42] used gray wolf optimization (GWO) to find a better combination of internal parameters of SVM. Houssein et al. [43] combine Harris Hawks optimization (HHO) metaheuristics with SVM and used it for chemical description and compound activity. Although scholars have conducted a lot of research on SVM parameter selection, different data sets affect the classification accuracy of SVM, and different optimization algorithms are used to search the parameters of SVM for different data sets. Therefore, we try to use modified AOA to select the parameters of SVM based on the urban rail bogie traction seat data set.We assume that the training samples arexi,yi, where i=1,2,...,n,x∈Rd,y is the class label. SVM realizes the optimization of the problem under limited conditions. Let the optimal classification function and constraints be as follows:(7)fx=sgn∑i=1naiyikxi,x+b,ai≠0,min12ω+C∑i=1nξi,where xi is the support vector, x is the classification vector, k· is the kernel function, a and b are the coefficients to determine the optimal hyperplane, C is the penalty coefficient, and ξi is the relaxation coefficient. Through the Lagrange functional algorithm, this problem is transformed into a quadratic optimization problem as follows:(8)max∑i=1nai−12∑i,j=1naiajyiyjkxi,x,s.t.∑i=1nyiai=0,0≤aj≤C,i=1,2,...,n,b is obtained by equation (9)(9)yi∑i=1naiyikxi,x+b−1=0.A Gaussian function represents the kernel function as follows:(10)kx,y=exp−xi−xj2σ2.Obviously, in the SVM parameter selection, the penalty factorC and the kernel function parameter σ are more critical for constructing the optimal classifier. We use C,σ as the optimized combination optimized by modified AOA, and the classification accuracy of the training set is selected as the evaluation basis to evaluate the best . The classification model is built, and its flowchart is shown in Figure 7.Figure 7
The flow chart of modified AOA-SVM.


## 4. Experimental Verification

### 4.1. Signal Analysis of Traction Seat

Each of the three health states has6000×1200 vibration signals, and each of the three states has 6000×400 vibration signals. The number of sampling points N is chosen to 1024, 2048, and 4096 to provide an experimental data set that is adequate in terms of data correctness and experimental prediction speed. Figures 8–10 display the results of time domain and frequency domain analysis performed on the original vibration signals for the traction seat of its three health states when N = 1024, 2048, and 4096.Figures8–10 show the three traction seat states of exhibit distinct differences in the time domain and frequency domain waveform plots. In the time domain, the amplitude of the normal state ranges from −100 to 100, the amplitude of the small crack ranges from −1000 to 1000, and the amplitude of the large crack ranges from −10 to 10. In the frequency domain, the amplitude of the normal state ranges from 0 to 40, the amplitude of the small crack ranges from 0 to 400, and the amplitude of the large crack ranges from 0 to 1.2. This demonstrates that the vibration signal-based method can identify the traction seat state, and the difference in traction seat state can be seen by the vibration signal in the time domain and frequency domain, but there is uncertainty and inaccuracy. As the experimental data set is more suited for data accuracy and experimental prediction speed, N is set to 1024.Figure 8
Analysis of three traction seat states in the time domain and frequency domain withN = 1024.Figure 9
Analysis of three traction seat states in the time domain and frequency domain withN = 2048.Figure 10
Analysis of three traction seat states in the time domain and frequency domain withN = 4096.Figure 11
The original signal of the large crack state of the traction seat and IMFs component diagram of VMD decomposition.


#### 4.1.1. Time Domain Analysis

To quantitatively observe the traction seat stat, the characteristic parameters in the time domain and frequency domain were further extracted for the traction seat, so that the vibration data could be quantitatively analyzed. Due to the limited space, the time domain characteristic parameter values of some samples were selected for observation, as shown in Table3.Table 3
The time domain characteristic parameter values of some samples.
StateNormalSmall crackLarge crackSample groupN1N2N3S1S2S3L1L2L3Mean−2.111−2.108−2.022−2.022−2.449−2.336−0.095−0.079−0.114MSE56.02256.17556.035584.316583.275583.4323.8343.8393.837Energy1.882e + 061.892e + 061.883e + 062.045e + 082.037e + 082.038e + 088.814e + 038.835e + 038.827e + 03Crest factor1.4901.4751.4781.4871131.4881.4882.7862.5842.546Kurtosis1.4751.4741.4771.6031.6041.6023.5663.5663.103Partial degrees−0.066−0.070−0.0700.2750.2760.2780.4630.0650.294Peak90.53988.70886.877960.462958.936958.93611.14810.53810.538Vp−p166.931165.710165.7101736.4501735.5341735.84021.36219.83619.531RMS65.80265.98965.818753.251751.858752.0674.0444.0494.047Peak factor1.3751.3441.3191.2751.2751.2752.6202.6202.756Pulse factor−42.872−42.076−41.367−474.941−391.560−410.747−130.802−121.590−116.343Margin factor1.9451.9091.8761.9982.0132.0084.0364.0554.477Waveform factor−31.159−31.300−31.340−474.941−307.004−321.933−49.919−46.407−42.201In Table3, the differences between the characteristic parameters of the normal and faulty states of the traction seat can be identified, but the degree of cracking in the faulty state cannot be accurately distinguished by the time-domain characteristic parameters alone.


#### 4.1.2. Frequency Domain Analysis

Theoretically, compared with the original signal data in the time domain, the data in the frequency domain has strong regularity and contains more useful information about the original signal, which is helpful for the quantitative analysis of vibration signals. Therefore, the time domain signals of the traction seat are converted into frequency domain signals by FFT. Tables4–6 shows the frequency domain characteristic values of some samples.As can be seen from the frequency domain characteristic parameters listed in Tables4–6, the traction seat three states can be well distinguished by combining with the frequency domain characteristic parameters, but there is uncertainty and low efficiency. The actual operating conditions of vehicles will be affected by a variety of uncertainties, to make a further accurate judgment, it is necessary to extract and quantify the characteristics of the traction seat. Then, the traction seat’s vibration signal is time-frequency analyzed and its vibration signal is decomposed using VMD.Table 4
Frequency domain characteristic parameter values of the part of some normal state samples.
The normal stateSample groupN1N2N3Maximum value frequency251.000249.000250.000The power spectrum and1848944.6461849363.8661881778.828Root mean square spectrum5603.8985773.9675785.471Mean power spectrum3081.5743080.6633023.802Variance of power spectrum3129.8453016.8103016.651Power spectrum skewness−4.675e − 09−4.676e − 09−4.676e − 09Power spectrum kurtosis0.0000150.0000120.000012Relative peak of power spectrum6.6586.6695.231Table 5
Frequency domain characteristic parameter values of the part of some small crack state samples.
The small crack stateSample groupS1S2S3Maximum value frequency250.000250.000250.000The power spectrum and203469054.902205739152.481205720098.156Root mean square spectrum62595.38966442.62360399.422Mean power spectrum343454.929352560.766349299.300Variance of power spectrum345356.266340903.784338663.515Power spectrum skewness−4.660e − 09−4.660e − 09−4.659e − 09Power spectrum kurtosis0.0001270.0001360.000143Relative peak of power spectrum0.6940.6890.685


#### 4.1.3. Time-Frequency Analysis

VMD is an adaptive and completely nonrecursive method for modal variation and signal processing [44]. The number of its modal decompositions can be determined according to the actual situation, and it can adaptively match the optimal center frequency and finite bandwidth of each mode. In time-frequency analysis, the VMD method is used to analyze the signal by decomposing the complex high-frequency signal into several subsignals, each with a central frequency, and then reproducing the complex vibration signal together. Due to the experiment’s limited space, the traction seat’s large crack fault is taken as an example in the experiment. The key is to find the modal number K of the VMD algorithm. The VMD decomposition of the traction seat large crack state data was carried out, and K was set to 2, 3, 4, 5, and 6. The modal center frequencies corresponding to different K values are shown in Table 6, and Figure 11 for the decomposed IMFs component diagram.Combined with the center frequency value (Table7) and IMFs component diagram (Figure 11), it can be determined that when K is 4, the vibration signal of the traction seat can be better represented in the experiment. Now, the key parameter K in the experimental VMD is set to 4, and VMD decomposition is carried out for the small crack state of the traction seat. Figure 12 displays the IMFs component that was produced by the decomposition of the signal data for the small crack traction seat.Table 6
Frequency domain characteristic parameter values of the part of some large crack state samples.
The large crack stateSample groupL1L2L3Maximum value frequency99.000100.000151.000The power spectrum and4731.5935533.8655384.857Root mean square spectrum739.136742.950742.958Mean power spectrum8.28813.66010.599Variance of power spectrum8.2888.2167.885Power spectrum skewness−6.375e − 09−6.513e − 09−6.501e − 09Power spectrum kurtosis0.0000030.0000050.000004Relative peak of power spectrum92.290591.31780.250Table 7
Modal center frequencies correspond to differentK values.
KCenter frequency (Hz)259173————359173407———458116174408——558116174290408—658116174229348408Figure 12
The original signal of the small crack state of the traction seat and IMFs component diagram of VMD decomposition.In Figure12, each IMFs center frequency is distinct from the others, the mode aliasing issue may be successfully avoided. This method can be used to obtain relatively simple modal components quickly. The energy characteristic values of IMFs components of some samples in the three traction seat states are in Table 8.Table 8
Energy eigenvalues of IMFs components for some samples.
StateNormalSmall crackLarge crackSample groupN1N2N3S1S2S3L1L2L3IMF_1 energy2810.0512807.1772724.432326216.846274433.601269368.32231.52122.84923.580IMF_2 energy3620.0013867.7303779.950517319.8351734221.1721803900.6483368.6943336.2363710.523IMF_3 energy2892.1492751.0882168.1786763948.3872766758.1194457329.6101526.0981588.3311545.651IMF_4 energy86579.959180216.833153785.2023166609.2942766758.1195846717.0771221.9161223.6531273.770


### 4.2. Feature Extraction and Fusion Based on PCA-OVO

At the beginning of the experiment, the characteristic parameters related to classification were extracted from the time domain, frequency domain, and time-frequency analysis as much as possible. However, too many characteristic parameters can not only provide abundant information, but also lead to information redundancy, increasing the computational effort. The high-dimensional feature sets are downscaled using PCA, where the time domain feature set is 13-dimensional with 13 components, the frequency domain feature set is 8-dimensional with 8 components, and the time-frequency feature set is 4-dimensional with 4 components. In the experiment, the PCA function of the Sklearn dimension reduction module in Python is used to achieve dimension reduction. The components are set to 6, 5, and 3, which is dimension reduction. Time domain features are reduced from 13 to 6 dimensions; frequency domain features are reduced from 8 to 5 dimensions; and time-frequency characteristics are reduced from 4 to 3 dimensions. Feature dimension reduction can remove redundant features of repeated attributes, reduce computation, and accelerate model convergence.After PCA treatment, the cumulative contribution can be calculated based on the contribution of each principal component. The processed principal elements are arranged in descending order according to the contribution rate. The more the principal elements are arranged in the front, the more original information they retain. When the cumulative contribution rate reaches 99%, the selected principal elements can better represent the original information. As can be obtained from Table9, the first four components in the time domain features are selected, the first three components in the frequency domain features are selected, and the first two components in the time-frequency domain features are selected. To visualize the results, plot them as a histogram, as shown in Figure 13. In the experiment, the main four components in the time domain were obtained, which were set as the principal components P-T1, P-T2, P-T3, and P-T4. Similarly, the principal components P-F1, P-F2, and P-F3 are in the frequency domain; time-frequency principal components: P-TF1, P-TF2, and P-TF3. The set after dimensionality reduction {P-T1, P-T2, P-T3, P-T4, P-F1, P-F2, P-F3, P-TF1, P-TF2, P-TF3} was obtained, and then the OVO algorithm was applied to obtain the sensitive feature set of traction seat, which was used as the input of modified AOA-SVM.Figure 13
Component proportions after PCA dimension reduction.Table 9
Contribution rate of the principal component.
The principal componentsContribution rate (%)Cumulative contribution rate (%)Time domain157.74257.742222.85380.599316.37196.96942.76699.73450.15699.89060.06299.952Frequency domain176.87576.875218.28295.15734.48099.63840.18899.82650.17499.999Time-frequency domain176.87576.876222.34896.34833.652100.000


### 4.3. Pattern Recognition Experiment

According to the different fault states of the sample, 280 sets of data were randomly selected for each group of states as the training set and 120 sets of data as the test set. To evaluate the effectiveness of the classifier, the bogie traction seat feature set of urban rail vehicles extracted by PCA-OVO is used as input, and the SVM optimized by the modified AOA (named CAOA-SVM) is compared with various metaheuristic optimization algorithms such as PSO, GA, WOA, GWO, HHO, AOA to optimize the SVM parameters for the experimental simulation. Let the population size of the optimization algorithm be 30 and the maximum number of iterations be 200. Let the penalty factor seeking range be [0, 200] and the kernel function parameter seeking range be [0, 200]. The accuracy of the optimization algorithm optimizes the SVM diagnostic model as shown in Figure14. The optimal combination of penalty factor C and kernel function parameters σ after optimization and the diagnostic model accuracy are recorded in Table 10.Figure 14
Accuracy of models.Table 10
Comparison of the experimental analysis of diagnostic models.
Diagnostic modelCσAccuracy (%)PSO-SVM0.01181.244100GA-SVM0.97535.01096.991WOA-SVM1.05151.54697.452GWO-SVM0.84956.07196.873HHO-SVM0.11768.45799.218AOA-SVM0.004141.31198.823CAOA-SVM0.01582.374100The data in Table10 show that the accuracy of all diagnostic models can reach more than 95%, which indicates that the PCA-OVO special diagnosis extraction fusion method used in this paper can be feasible, and it can extract relatively complete traction seat feature information. The diagnostic accuracy of PSO-SVM, HHO-SVM, and CAOA-SVM in Table 10 is the highest, and it has obvious advantages compared with other diagnostic models. From Figure 14, it shows that CAOA-SVM is less effective at the beginning of the iteration, which is because AOA focuses on global search in the early stage that can avoid getting into local better values, and compared with PSO-SVM and HHO-SVM models, CAOA-SVM can reach the goal with fewer iterations while maintaining high accuracy diagnostic classification. In conclusion, the intelligent diagnostic model of traction seat of the urban rail vehicle based on CAOA-SVM can better identify faults and obtain accurate diagnostic results.


## 4.1. Signal Analysis of Traction Seat

Each of the three health states has6000×1200 vibration signals, and each of the three states has 6000×400 vibration signals. The number of sampling points N is chosen to 1024, 2048, and 4096 to provide an experimental data set that is adequate in terms of data correctness and experimental prediction speed. Figures 8–10 display the results of time domain and frequency domain analysis performed on the original vibration signals for the traction seat of its three health states when N = 1024, 2048, and 4096.Figures8–10 show the three traction seat states of exhibit distinct differences in the time domain and frequency domain waveform plots. In the time domain, the amplitude of the normal state ranges from −100 to 100, the amplitude of the small crack ranges from −1000 to 1000, and the amplitude of the large crack ranges from −10 to 10. In the frequency domain, the amplitude of the normal state ranges from 0 to 40, the amplitude of the small crack ranges from 0 to 400, and the amplitude of the large crack ranges from 0 to 1.2. This demonstrates that the vibration signal-based method can identify the traction seat state, and the difference in traction seat state can be seen by the vibration signal in the time domain and frequency domain, but there is uncertainty and inaccuracy. As the experimental data set is more suited for data accuracy and experimental prediction speed, N is set to 1024.Figure 8
Analysis of three traction seat states in the time domain and frequency domain withN = 1024.Figure 9
Analysis of three traction seat states in the time domain and frequency domain withN = 2048.Figure 10
Analysis of three traction seat states in the time domain and frequency domain withN = 4096.Figure 11
The original signal of the large crack state of the traction seat and IMFs component diagram of VMD decomposition.


### 4.1.1. Time Domain Analysis

To quantitatively observe the traction seat stat, the characteristic parameters in the time domain and frequency domain were further extracted for the traction seat, so that the vibration data could be quantitatively analyzed. Due to the limited space, the time domain characteristic parameter values of some samples were selected for observation, as shown in Table3.Table 3
The time domain characteristic parameter values of some samples.
StateNormalSmall crackLarge crackSample groupN1N2N3S1S2S3L1L2L3Mean−2.111−2.108−2.022−2.022−2.449−2.336−0.095−0.079−0.114MSE56.02256.17556.035584.316583.275583.4323.8343.8393.837Energy1.882e + 061.892e + 061.883e + 062.045e + 082.037e + 082.038e + 088.814e + 038.835e + 038.827e + 03Crest factor1.4901.4751.4781.4871131.4881.4882.7862.5842.546Kurtosis1.4751.4741.4771.6031.6041.6023.5663.5663.103Partial degrees−0.066−0.070−0.0700.2750.2760.2780.4630.0650.294Peak90.53988.70886.877960.462958.936958.93611.14810.53810.538Vp−p166.931165.710165.7101736.4501735.5341735.84021.36219.83619.531RMS65.80265.98965.818753.251751.858752.0674.0444.0494.047Peak factor1.3751.3441.3191.2751.2751.2752.6202.6202.756Pulse factor−42.872−42.076−41.367−474.941−391.560−410.747−130.802−121.590−116.343Margin factor1.9451.9091.8761.9982.0132.0084.0364.0554.477Waveform factor−31.159−31.300−31.340−474.941−307.004−321.933−49.919−46.407−42.201In Table3, the differences between the characteristic parameters of the normal and faulty states of the traction seat can be identified, but the degree of cracking in the faulty state cannot be accurately distinguished by the time-domain characteristic parameters alone.


### 4.1.2. Frequency Domain Analysis

Theoretically, compared with the original signal data in the time domain, the data in the frequency domain has strong regularity and contains more useful information about the original signal, which is helpful for the quantitative analysis of vibration signals. Therefore, the time domain signals of the traction seat are converted into frequency domain signals by FFT. Tables4–6 shows the frequency domain characteristic values of some samples.As can be seen from the frequency domain characteristic parameters listed in Tables4–6, the traction seat three states can be well distinguished by combining with the frequency domain characteristic parameters, but there is uncertainty and low efficiency. The actual operating conditions of vehicles will be affected by a variety of uncertainties, to make a further accurate judgment, it is necessary to extract and quantify the characteristics of the traction seat. Then, the traction seat’s vibration signal is time-frequency analyzed and its vibration signal is decomposed using VMD.Table 4
Frequency domain characteristic parameter values of the part of some normal state samples.
The normal stateSample groupN1N2N3Maximum value frequency251.000249.000250.000The power spectrum and1848944.6461849363.8661881778.828Root mean square spectrum5603.8985773.9675785.471Mean power spectrum3081.5743080.6633023.802Variance of power spectrum3129.8453016.8103016.651Power spectrum skewness−4.675e − 09−4.676e − 09−4.676e − 09Power spectrum kurtosis0.0000150.0000120.000012Relative peak of power spectrum6.6586.6695.231Table 5
Frequency domain characteristic parameter values of the part of some small crack state samples.
The small crack stateSample groupS1S2S3Maximum value frequency250.000250.000250.000The power spectrum and203469054.902205739152.481205720098.156Root mean square spectrum62595.38966442.62360399.422Mean power spectrum343454.929352560.766349299.300Variance of power spectrum345356.266340903.784338663.515Power spectrum skewness−4.660e − 09−4.660e − 09−4.659e − 09Power spectrum kurtosis0.0001270.0001360.000143Relative peak of power spectrum0.6940.6890.685


### 4.1.3. Time-Frequency Analysis

VMD is an adaptive and completely nonrecursive method for modal variation and signal processing [44]. The number of its modal decompositions can be determined according to the actual situation, and it can adaptively match the optimal center frequency and finite bandwidth of each mode. In time-frequency analysis, the VMD method is used to analyze the signal by decomposing the complex high-frequency signal into several subsignals, each with a central frequency, and then reproducing the complex vibration signal together. Due to the experiment’s limited space, the traction seat’s large crack fault is taken as an example in the experiment. The key is to find the modal number K of the VMD algorithm. The VMD decomposition of the traction seat large crack state data was carried out, and K was set to 2, 3, 4, 5, and 6. The modal center frequencies corresponding to different K values are shown in Table 6, and Figure 11 for the decomposed IMFs component diagram.Combined with the center frequency value (Table7) and IMFs component diagram (Figure 11), it can be determined that when K is 4, the vibration signal of the traction seat can be better represented in the experiment. Now, the key parameter K in the experimental VMD is set to 4, and VMD decomposition is carried out for the small crack state of the traction seat. Figure 12 displays the IMFs component that was produced by the decomposition of the signal data for the small crack traction seat.Table 6
Frequency domain characteristic parameter values of the part of some large crack state samples.
The large crack stateSample groupL1L2L3Maximum value frequency99.000100.000151.000The power spectrum and4731.5935533.8655384.857Root mean square spectrum739.136742.950742.958Mean power spectrum8.28813.66010.599Variance of power spectrum8.2888.2167.885Power spectrum skewness−6.375e − 09−6.513e − 09−6.501e − 09Power spectrum kurtosis0.0000030.0000050.000004Relative peak of power spectrum92.290591.31780.250Table 7
Modal center frequencies correspond to differentK values.
KCenter frequency (Hz)259173————359173407———458116174408——558116174290408—658116174229348408Figure 12
The original signal of the small crack state of the traction seat and IMFs component diagram of VMD decomposition.In Figure12, each IMFs center frequency is distinct from the others, the mode aliasing issue may be successfully avoided. This method can be used to obtain relatively simple modal components quickly. The energy characteristic values of IMFs components of some samples in the three traction seat states are in Table 8.Table 8
Energy eigenvalues of IMFs components for some samples.
StateNormalSmall crackLarge crackSample groupN1N2N3S1S2S3L1L2L3IMF_1 energy2810.0512807.1772724.432326216.846274433.601269368.32231.52122.84923.580IMF_2 energy3620.0013867.7303779.950517319.8351734221.1721803900.6483368.6943336.2363710.523IMF_3 energy2892.1492751.0882168.1786763948.3872766758.1194457329.6101526.0981588.3311545.651IMF_4 energy86579.959180216.833153785.2023166609.2942766758.1195846717.0771221.9161223.6531273.770


## 4.1.1. Time Domain Analysis

To quantitatively observe the traction seat stat, the characteristic parameters in the time domain and frequency domain were further extracted for the traction seat, so that the vibration data could be quantitatively analyzed. Due to the limited space, the time domain characteristic parameter values of some samples were selected for observation, as shown in Table3.Table 3
The time domain characteristic parameter values of some samples.
StateNormalSmall crackLarge crackSample groupN1N2N3S1S2S3L1L2L3Mean−2.111−2.108−2.022−2.022−2.449−2.336−0.095−0.079−0.114MSE56.02256.17556.035584.316583.275583.4323.8343.8393.837Energy1.882e + 061.892e + 061.883e + 062.045e + 082.037e + 082.038e + 088.814e + 038.835e + 038.827e + 03Crest factor1.4901.4751.4781.4871131.4881.4882.7862.5842.546Kurtosis1.4751.4741.4771.6031.6041.6023.5663.5663.103Partial degrees−0.066−0.070−0.0700.2750.2760.2780.4630.0650.294Peak90.53988.70886.877960.462958.936958.93611.14810.53810.538Vp−p166.931165.710165.7101736.4501735.5341735.84021.36219.83619.531RMS65.80265.98965.818753.251751.858752.0674.0444.0494.047Peak factor1.3751.3441.3191.2751.2751.2752.6202.6202.756Pulse factor−42.872−42.076−41.367−474.941−391.560−410.747−130.802−121.590−116.343Margin factor1.9451.9091.8761.9982.0132.0084.0364.0554.477Waveform factor−31.159−31.300−31.340−474.941−307.004−321.933−49.919−46.407−42.201In Table3, the differences between the characteristic parameters of the normal and faulty states of the traction seat can be identified, but the degree of cracking in the faulty state cannot be accurately distinguished by the time-domain characteristic parameters alone.


## 4.1.2. Frequency Domain Analysis

Theoretically, compared with the original signal data in the time domain, the data in the frequency domain has strong regularity and contains more useful information about the original signal, which is helpful for the quantitative analysis of vibration signals. Therefore, the time domain signals of the traction seat are converted into frequency domain signals by FFT. Tables4–6 shows the frequency domain characteristic values of some samples.As can be seen from the frequency domain characteristic parameters listed in Tables4–6, the traction seat three states can be well distinguished by combining with the frequency domain characteristic parameters, but there is uncertainty and low efficiency. The actual operating conditions of vehicles will be affected by a variety of uncertainties, to make a further accurate judgment, it is necessary to extract and quantify the characteristics of the traction seat. Then, the traction seat’s vibration signal is time-frequency analyzed and its vibration signal is decomposed using VMD.Table 4
Frequency domain characteristic parameter values of the part of some normal state samples.
The normal stateSample groupN1N2N3Maximum value frequency251.000249.000250.000The power spectrum and1848944.6461849363.8661881778.828Root mean square spectrum5603.8985773.9675785.471Mean power spectrum3081.5743080.6633023.802Variance of power spectrum3129.8453016.8103016.651Power spectrum skewness−4.675e − 09−4.676e − 09−4.676e − 09Power spectrum kurtosis0.0000150.0000120.000012Relative peak of power spectrum6.6586.6695.231Table 5
Frequency domain characteristic parameter values of the part of some small crack state samples.
The small crack stateSample groupS1S2S3Maximum value frequency250.000250.000250.000The power spectrum and203469054.902205739152.481205720098.156Root mean square spectrum62595.38966442.62360399.422Mean power spectrum343454.929352560.766349299.300Variance of power spectrum345356.266340903.784338663.515Power spectrum skewness−4.660e − 09−4.660e − 09−4.659e − 09Power spectrum kurtosis0.0001270.0001360.000143Relative peak of power spectrum0.6940.6890.685


## 4.1.3. Time-Frequency Analysis

VMD is an adaptive and completely nonrecursive method for modal variation and signal processing [44]. The number of its modal decompositions can be determined according to the actual situation, and it can adaptively match the optimal center frequency and finite bandwidth of each mode. In time-frequency analysis, the VMD method is used to analyze the signal by decomposing the complex high-frequency signal into several subsignals, each with a central frequency, and then reproducing the complex vibration signal together. Due to the experiment’s limited space, the traction seat’s large crack fault is taken as an example in the experiment. The key is to find the modal number K of the VMD algorithm. The VMD decomposition of the traction seat large crack state data was carried out, and K was set to 2, 3, 4, 5, and 6. The modal center frequencies corresponding to different K values are shown in Table 6, and Figure 11 for the decomposed IMFs component diagram.Combined with the center frequency value (Table7) and IMFs component diagram (Figure 11), it can be determined that when K is 4, the vibration signal of the traction seat can be better represented in the experiment. Now, the key parameter K in the experimental VMD is set to 4, and VMD decomposition is carried out for the small crack state of the traction seat. Figure 12 displays the IMFs component that was produced by the decomposition of the signal data for the small crack traction seat.Table 6
Frequency domain characteristic parameter values of the part of some large crack state samples.
The large crack stateSample groupL1L2L3Maximum value frequency99.000100.000151.000The power spectrum and4731.5935533.8655384.857Root mean square spectrum739.136742.950742.958Mean power spectrum8.28813.66010.599Variance of power spectrum8.2888.2167.885Power spectrum skewness−6.375e − 09−6.513e − 09−6.501e − 09Power spectrum kurtosis0.0000030.0000050.000004Relative peak of power spectrum92.290591.31780.250Table 7
Modal center frequencies correspond to differentK values.
KCenter frequency (Hz)259173————359173407———458116174408——558116174290408—658116174229348408Figure 12
The original signal of the small crack state of the traction seat and IMFs component diagram of VMD decomposition.In Figure12, each IMFs center frequency is distinct from the others, the mode aliasing issue may be successfully avoided. This method can be used to obtain relatively simple modal components quickly. The energy characteristic values of IMFs components of some samples in the three traction seat states are in Table 8.Table 8
Energy eigenvalues of IMFs components for some samples.
StateNormalSmall crackLarge crackSample groupN1N2N3S1S2S3L1L2L3IMF_1 energy2810.0512807.1772724.432326216.846274433.601269368.32231.52122.84923.580IMF_2 energy3620.0013867.7303779.950517319.8351734221.1721803900.6483368.6943336.2363710.523IMF_3 energy2892.1492751.0882168.1786763948.3872766758.1194457329.6101526.0981588.3311545.651IMF_4 energy86579.959180216.833153785.2023166609.2942766758.1195846717.0771221.9161223.6531273.770


## 4.2. Feature Extraction and Fusion Based on PCA-OVO

At the beginning of the experiment, the characteristic parameters related to classification were extracted from the time domain, frequency domain, and time-frequency analysis as much as possible. However, too many characteristic parameters can not only provide abundant information, but also lead to information redundancy, increasing the computational effort. The high-dimensional feature sets are downscaled using PCA, where the time domain feature set is 13-dimensional with 13 components, the frequency domain feature set is 8-dimensional with 8 components, and the time-frequency feature set is 4-dimensional with 4 components. In the experiment, the PCA function of the Sklearn dimension reduction module in Python is used to achieve dimension reduction. The components are set to 6, 5, and 3, which is dimension reduction. Time domain features are reduced from 13 to 6 dimensions; frequency domain features are reduced from 8 to 5 dimensions; and time-frequency characteristics are reduced from 4 to 3 dimensions. Feature dimension reduction can remove redundant features of repeated attributes, reduce computation, and accelerate model convergence.After PCA treatment, the cumulative contribution can be calculated based on the contribution of each principal component. The processed principal elements are arranged in descending order according to the contribution rate. The more the principal elements are arranged in the front, the more original information they retain. When the cumulative contribution rate reaches 99%, the selected principal elements can better represent the original information. As can be obtained from Table9, the first four components in the time domain features are selected, the first three components in the frequency domain features are selected, and the first two components in the time-frequency domain features are selected. To visualize the results, plot them as a histogram, as shown in Figure 13. In the experiment, the main four components in the time domain were obtained, which were set as the principal components P-T1, P-T2, P-T3, and P-T4. Similarly, the principal components P-F1, P-F2, and P-F3 are in the frequency domain; time-frequency principal components: P-TF1, P-TF2, and P-TF3. The set after dimensionality reduction {P-T1, P-T2, P-T3, P-T4, P-F1, P-F2, P-F3, P-TF1, P-TF2, P-TF3} was obtained, and then the OVO algorithm was applied to obtain the sensitive feature set of traction seat, which was used as the input of modified AOA-SVM.Figure 13
Component proportions after PCA dimension reduction.Table 9
Contribution rate of the principal component.
The principal componentsContribution rate (%)Cumulative contribution rate (%)Time domain157.74257.742222.85380.599316.37196.96942.76699.73450.15699.89060.06299.952Frequency domain176.87576.875218.28295.15734.48099.63840.18899.82650.17499.999Time-frequency domain176.87576.876222.34896.34833.652100.000


## 4.3. Pattern Recognition Experiment

According to the different fault states of the sample, 280 sets of data were randomly selected for each group of states as the training set and 120 sets of data as the test set. To evaluate the effectiveness of the classifier, the bogie traction seat feature set of urban rail vehicles extracted by PCA-OVO is used as input, and the SVM optimized by the modified AOA (named CAOA-SVM) is compared with various metaheuristic optimization algorithms such as PSO, GA, WOA, GWO, HHO, AOA to optimize the SVM parameters for the experimental simulation. Let the population size of the optimization algorithm be 30 and the maximum number of iterations be 200. Let the penalty factor seeking range be [0, 200] and the kernel function parameter seeking range be [0, 200]. The accuracy of the optimization algorithm optimizes the SVM diagnostic model as shown in Figure14. The optimal combination of penalty factor C and kernel function parameters σ after optimization and the diagnostic model accuracy are recorded in Table 10.Figure 14
Accuracy of models.Table 10
Comparison of the experimental analysis of diagnostic models.
Diagnostic modelCσAccuracy (%)PSO-SVM0.01181.244100GA-SVM0.97535.01096.991WOA-SVM1.05151.54697.452GWO-SVM0.84956.07196.873HHO-SVM0.11768.45799.218AOA-SVM0.004141.31198.823CAOA-SVM0.01582.374100The data in Table10 show that the accuracy of all diagnostic models can reach more than 95%, which indicates that the PCA-OVO special diagnosis extraction fusion method used in this paper can be feasible, and it can extract relatively complete traction seat feature information. The diagnostic accuracy of PSO-SVM, HHO-SVM, and CAOA-SVM in Table 10 is the highest, and it has obvious advantages compared with other diagnostic models. From Figure 14, it shows that CAOA-SVM is less effective at the beginning of the iteration, which is because AOA focuses on global search in the early stage that can avoid getting into local better values, and compared with PSO-SVM and HHO-SVM models, CAOA-SVM can reach the goal with fewer iterations while maintaining high accuracy diagnostic classification. In conclusion, the intelligent diagnostic model of traction seat of the urban rail vehicle based on CAOA-SVM can better identify faults and obtain accurate diagnostic results.


## 5. Conclusion

To solve the problem of low efficiency of the traditional traction seat fault signal analysis method, this study combines the PCA-OVO multifeature extraction and fusion algorithm and proposes a bogie traction seat intelligent diagnosis model based on a modified arithmetic optimization algorithm to optimize the SVM parameters. The experiments are based on the data collected from the urban rail bogie traction seat simulation experimental platform, and the PCA-OVO algorithm is used to extract sensitive feature sets for training and testing the CAOA-SVM intelligent diagnostic model. The experimental results show that the SVM intelligent diagnostic model with the PCA-OVO extracted feature set as input and the parameters optimized by the modified arithmetic optimization algorithm has excellent diagnostic accuracy. The model can successfully diagnose the fault status and improve the accuracy of traction seat status diagnosis, which can provide a more dependable method for diagnosing traction seat fault status. The combination of VMD and improved SVM model has yielded better recognition results. In the subsequent research, we can consider combining other advanced mode recognition methods to identify the status of traction seat to improve the recognition accuracy while increasing the credibility and reliability of the results. According to the current maintenance standards, the traction seat crack state is divided into three categories: normal, small crack, and large crack, how to refine the state more, so as to provide new ideas on traction seat crack extension, fault evolution, and service life evaluation is the next research focus.



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*Source: 1221186-2022-12-16.xml*