The Application and Research of Particle Swarm Optimization Radial Basis Function Network Driven by Edge Computing in Bogie Fault Diagnosis

The bogie system is a key system that affects the safety and quality of high-speed train operation. Constructing a fault diagnosis model for the bogie system can effectively improve the safety and comfort of high-speed train operation. The traditional modeling method uses the BP neural network to fit the temperature and other parameters of the bogie system. However, because the BP neural network is prone to fall into local minima, slow convergence and poor diagnostic accuracy, this paper proposes a radial basis function network bogie fault diagnosis model based on particle swarm optimization based on edge computing. The model combines edge computing and particle swarm optimization algorithm to improve the accuracy and real-time of bogie fault diagnosis. By implementing model training and inference on edge devices, data transmission latency has been reduced and diagnostic efficiency has been improved. A particle radial basis neural network (PSRB) was designed using a highly convergent particle swarm optimization algorithm, and the parameters of the radial basis neural network (RBF Neural Networks) were optimized using the Particle Swarm Optimization algorithm. Based on the complexity of the input parameters of the bogie system, determine the input and output parameters of the model, and use particle swarm optimization algorithm to search for the optimal values of the basis function center, width, and output layer weight threshold of the RBF neural network. The composite algorithm was applied to the fault diagnosis of the bogie system, and a particle radial basis neural network bogie fault diagnosis model was designed. The simulation and experimental results of the model show that the diagnostic model can effectively improve the identification accuracy of fault diagnosis, with a minimum error accuracy of 0.0255, saving computation time. The computation time is reduced to 2.9 seconds, eliminating the influence of non target parameters on the inversion results. This model can also be used in other systems of high-speed trains and has practical application value.


Introduction
As a key component of railway train operation, the stability and reliability of bogie performance have a significant impact on the safety and stability of train operation.However, due to factors such as longterm service, harsh environments, and complex loads, bogies are prone to various failures, such as cracks, wear, and loosening.These failures not only affect the safety of train operation, but may also cause major accidents.Therefore, accurate fault diagnosis of bogies is an important means to ensure the safety of railway transportation.
Traditional bogie fault diagnosis methods mainly rely on manual inspection and empirical judgment, and there are issues such as low diagnosis efficiency and poor precision.Currently, wavelet filtering algorithms are widely used for noise reduction and feature extraction, and empirical mode decomposition (EMD) is used for feature extraction.Then linear fitting is performed on the fault features.Traditional linear diagnosis methods linearize nonlinear problems near the initial model, which will necessarily lead to problems such as dependence on the initial model, poor diagnosis accuracy, and difficulty in solving partial derivative matrices.BP neural networks have gradually become widely used in fault diagnosis problems due to their unique memory learning ability and nonlinear approximation ability [1].Jiang Chen was the first to introduce neural network algorithms into the fault diagnosis of EMUs [2].MYRADOV GUVANCH proposed a study on fault diagnosis of train components based on BP neural networks [3].However, when training weights and thresholds using BP neural networks, most commonly used is the gradient descent method, which can easily cause the weights and thresholds to fall into local minima during training, leading to poorer inversion accuracy and longer time.To address this issue, Singh compared and validated the experimental results of radial basis function (RBF) neural networks with BP neural networks, and the results showed that RBF neural networks have better inversion prediction capabilities [4].However, RBF neural networks also have disadvantages: the results of K-means clustering algorithm are sensitive to initial parameters, often leading to incomplete learning of some nodes and poor convergence performance; it is difficult to determine the number of hidden layer neurons, and there is currently no theoretical basis.In recent years, with the continuous development of artificial intelligence technology, algorithms such as deep learning and neural networks have been widely used in the field of fault diagnosis.Among them, the radial basis function (RBF) network, as a neural network with good nonlinear approximation capabilities, has performed well in fault diagnosis.However, how to optimize the parameters of the RBF network to improve its generalization performance and diagnosis accuracy is an important issue in this field [5][6][7][8][9][10].
To address the above issues, this paper proposes a particle swarm optimization RBF network bogie fault diagnosis model based on edge computing.This model utilizes particle swarm optimization algorithm to optimize parameters such as the centers, widths, and thresholds of the RBF network, aiming to improve diagnosis accuracy and generalization performance.At the same time, by using edge computing technology, the model is deployed on edge devices to achieve real-time fault diagnosis and early warning, reducing data transmission latency and improving diagnosis efficiency.

The Edge Computing Driven Particle Swarm Optimization Radial Basis Function Network Bogie Fault Diagnosis Model
This section will introduce in detail the construction process of the edge computing based particle swarm optimization radial basis function network bogie fault diagnosis model.The model combines edge computing and particle swarm optimization algorithm to improve the accuracy and real-time of bogie fault diagnosis.

Overall Architecture and Design Idea of the Model
The bogie fault diagnosis model based on edge computing particle swarm optimization radial basis function network is mainly composed of three modules: data acquisition, data processing and fault diagnosis.The data acquisition module is responsible for collecting real-time data from the relevant sensors of the bogie; The data processing module pre-processes the collected raw data and extracts features related to the fault; The fault diagnosis module is the core part of this model, using the particle swarm optimization algorithm to optimize the parameters of the radial basis function network model to achieve high accuracy fault diagnosis.
The design idea is mainly based on the following points: First, use edge computing technology to deploy the model on edge devices near the data source to reduce data transmission delay and improve diagnostic efficiency; Secondly, the parameters of the radial basis function network, such as the center, width, and threshold, are optimized using the particle swarm optimization algorithm to improve the generalization performance and diagnostic accuracy of the model.Finally, the effectiveness and superiority of the model are verified through experiments.

Structure and Parameters of Radial Basis Function Neural Network
The structure of RBF neural network is similar to that of multilayer forward network, which is a threelayer forward network.The input layer consists of signal source nodes; the second layer is the hidden layer, the number of hidden units depends on the needs of the problem described, and the transformation function of hidden units RBF is a radial symmetric and decaying non-negative nonlinear function of the center point; the third layer is the output layer, which responds to the input pattern.The transformation from input space to hidden layer space is nonlinear, while the transformation from hidden layer space to output layer space is linear.The structure of RBF neural network is shown in figure 1, where the nodes in each layer are m, o, and p.  = [ 1 ,  2 ,  3 ,⋅⋅⋅⋅⋅⋅   ]  As an input layer node, [ 1 ,  2 ,  3 ,⋅⋅⋅⋅⋅⋅   ]  represents the data center point of the ith node,  = [ 1 ,  2 ,  3 ,⋅⋅⋅⋅⋅⋅   ]  represents the output layer unit threshold, Σ represents the output layer neurons using a linear activation function,   represents the output layer weights, and  = [ 1 ,  2 ,  3 ,⋅⋅⋅⋅⋅⋅   ]  represents the network output.
The commonly used radial basis function in radial basis neural networks is the Gaussian function, so the activation function of radial basis neural networks can be represented as In the formula, represents the width of the radial basis function, and ||.|| represents the Euclidean norm.
The output of the neural network can be obtained from the structure of the radial basis neural network given by Equation 1.
Currently, the commonly used training algorithm for radial basis function neural networks is based on gradient optimization algorithm, which can be expressed as:   = {  ,   },   are model training samples, where k=1~M, and  = (  ,   ,   ) is searched to minimize the following formula: Before applying the RBF neural network, it is important to determine the number of input and output layer nodes and the number of hidden layer neurons of the neural network.After determining the basic parameters of the neural network, the PSO algorithm is applied to search for the optimal parameters of the RBF neural network: (1) basis function center  , (2) basis function width,   and (3) output layer weight threshold  .[5][6][7][8][9].In the foraging process of birds, initially, different birds are in random positions and flying in different directions.However, over time, birds initially located at random positions will gradually converge into small groups and fly in the same direction towards a common goal, which is the "food source," through their own exploration and learning from their peers' flight trajectories.In PSO, each feasible solution is regarded as a bird in the search space, also known as a "particle."A collection of multiple feasible solutions is considered as a population.Each particle has characteristics such as velocity and position.The fitness function is used to evaluate the goodness of a particle (i.e., how close it is to the food source).The optimal position of each particle during the flight process,, which is the optimal solution found by the particle itself, is called individual extreme value, while the optimal solution found by the entire population is called global extreme value.PSO is a method that continuously updates itself based on individual and global extreme values during each iteration to find the optimal solution.
Suppose that in a D-dimensional search space, a population consisting of N particles = [ 1 ,  2 ,  3 ,⋅ ⋅⋅⋅⋅⋅   ] , the ith particle represents a D-dimensional vector, that is   = [ 1 ,  2 ,  3 ,⋅⋅⋅⋅⋅⋅   ], the position of the ith particle in the D-dimensional search space.The position of each particle is a potential solution.The velocity of the ith particle is also a D-dimensional vector, that is  = [ 1 ,  2 ,  3 ,⋅⋅⋅⋅⋅ ⋅   ], let the individual extreme value corresponding to the optimal position searched by the ith particle after h iterations be  = [ 1 ,  2 ,  3 ,⋅⋅⋅⋅⋅⋅   ], the optimal position searched by the entire particle population after h iterations be   = [ 1 ,  2 ,  3 ,⋅⋅⋅⋅⋅⋅   ].The update formula for the position and velocity of particles is as follows: Where: i=1, 2, …, n; d=1, 2, …, D;  is the current iteration number;  is the inertia factor;  1 and  2 are the acceleration coefficients;  1 and  2 are random numbers distributed according to the [0,1] distribution.In addition, in the update calculation, in order to prevent blind search, the position and velocity are generally limited to the ranges of [

Neural Network Inversion Model Based on PSRB
The neural network prediction model based on PSRB is divided into three parts: the determination of the RBF neural network structure, PSO optimization, and neural network inversion.The structure of the RBF neural network needs to be determined based on the number of input and output parameters of the inverse problem, and the dimension of the individual particles in the particle swarm is then obtained.
The hybrid fault diagnosis model established in this article has 3 input layer nodes, 22 hidden layer nodes, and 1 output layer node.The number of training iterations is set to 1000, and the training target is 0.01.The model algorithm flow is shown in figure 2. The specific steps are as follows: 1) First, establish the neural network structure based on the research object, determine the input variables, output variables, and initialize the number of neurons in the input layer, hidden layer, and output layer of the neural network.
2) The weight threshold between neurons in different layers of the neural network, the center of the basis function, and the width of the basis function are used as parameters for real-number encoding.
3) Initialize the initial velocity, position, and randomly generated population of particles.4) Calculate the fitness function value of each particle, update the velocity and position of each particle using equations ( 4) and ( 5), and generate the next generation of particles.Determine the individual and global extrema of each particle; if the current position of the particle meets the error requirement or reaches the maximum number of iterations, stop the iteration.The parameters corresponding to the global extremum of the particle swarm are the optimal parameters for the neural network.
5) Use the optimal parameters optimized by PSO as the initial values of the RBF neural network to initialize the parameters of the neural network.

Simulation Testing and Verification
In this analysis, 11 sets of temperature data of the EMUs with failures were selected to verify the bogie fault diagnosis and early warning model using the temperature data of 32 bearing measurement points of these 11 vehicles.The distribution of temperature measurement points on the whole vehicle is shown in figures 3. The passenger compartment layer: there are 16 passenger compartments in total, composed of 8 EMUs and 8 trailing cars; each vehicle is equipped with a temperature sensor.The bogie layer: on each EMU bogie, temperature sensors are installed on the bearing of the axle box, gearbox, and motor; on each trailing bogie, a temperature sensor is installed on the bearing of the axle box.Each EMU bogie is equipped with 4 bearing temperature measurement points for the axle box, 2 measurement points for each wheel set unit, located at the axle box of each wheel; there are 6 motor temperature measurement points, 3 measurement points for each motor, distributed at the bearing temperature measurement point at the motor drive end, the bearing temperature measurement point at the non-drive end of the motor, and the rotor temperature measurement point of the motor; there are 4 large gear temperature measurement points, 2 for each gearbox, located at the wheel side and motor side; there are 4 small gear temperature measurement points, 2 for each small gearbox, located at the wheel side and motor side.In this article, a sample dataset was created using temperature, vibration, and speed data of a certain bogie of a certain EMU model in 2016.There were 120 training data samples and 5 test sets.The test set data did not participate in network training.

Comparison of PSRB Neural Network Inversion with other Inversion Methods
In 2017, 17 faults occurred in 11 groups of vehicles.The fault diagnosis and early warning models for the bogie system were constructed based on BP neural network, RBF neural network, and PSRB hybrid neural network, respectively.The BP fault diagnosis model: 6 early warnings, 5 accurate alarms, 3 false alarms, 3 missed alarms.RBF neural network: 7 early warnings, 5 accurate alarms, 3 false alarms, 2 missed alarms.PSRB hybrid neural network: 9 early warnings, 5 accurate alarms, 3 false alarms, 1 missed alarm.For details, see table From the model comparison diagrams in tables 1 and 2, we can clearly reflect the superiority of the PSRB algorithm, with high accuracy in fault diagnosis, long lead time for prediction, good prediction effect, and fewer missed reports.Tables 1 and 2 are the comparison tables of model validation and model performance results for fault diagnosis using BP neural network, RBF neural network method, and PSRB method, respectively.The following conclusions are drawn: (1) In view of the problem that neural networks are prone to falling into local minima and have relatively poor convergence, we apply PSO algorithm to optimize the parameters of neural networks.The PSRB neural network algorithm is significantly better than the BP neural network, and the number of iterations is significantly smaller than the RBF neural network, greatly saving computation time.
(2) When using the RBF neural network method for inversion, it is necessary to adjust the number of hidden layer nodes multiple times, resulting in a large number of iterations and a long time consumption.
When using the PSRB method for inversion, because the initial parameters of the RBF neural network are optimized first, better results can be obtained during the inversion process, and the time is also relatively fast.
(3) The prediction error is a parameter that indicates the stability of the data.From the prediction error values of the three neural network methods, PSRB is superior to RBF and BP neural network models.In the fault diagnosis model 1, the maximum absolute error of the former is only 26.31, while the latter two are as high as 49.65 and 78.36.

Conclusion
This article combines the PSO algorithm and RBF neural network algorithm to achieve a nonlinear hybrid fault diagnosis model, overcoming the shortcomings of neural networks that are prone to falling into local minima, relying on initial weight selection, and having long inversion time and slow convergence speed when used alone.The article proposes to jointly invert the particle swarm algorithm and RBF neural network.Through the verification of the actual operation data of the EMU bogie, and compared with the RBF neural network inversion and BP neural network, the algorithm has good application prospects.The innovation of this paper is mainly reflected in the following aspects: for the first time, edge computing and particle swarm optimization algorithm are combined to apply to the field of bogie fault diagnosis, which improves the real-time and accuracy of diagnosis; A radial basis function

2. 3 .
Particle Swarm Optimization (PSO) 2.3.1.PSO Algorithm.Particle Swarm Optimization (PSO) is a random optimization algorithm that mimics the foraging behavior of birds.It was introduced by Dr. Eberhart and Dr. Kennedy in 1995

6 )
Use the RBF neural network algorithm for further training until the target error converges to the set accuracy and reaches the expected standard, and the training is complete.

Figure 2 .
Figure 2. Flow diagram of the PSRB algorithm.

Figure 3 .
Figure 3. Sensor acquisition points of the bogie of the EMU.
for bogie fault diagnosis is designed, which can effectively learn and represent fault characteristics; The effectiveness and superiority of the model were verified through experiments, providing new technical support for railway transportation safety.The research results of this article not only have important theoretical significance for bogie fault diagnosis, but also have extensive practical application value.In the future, we will further optimize the model structure and improve the diagnostic performance to ensure the safety of railway transportation.

Table 1 .
1. Verification of the fault diagnosis and early warning model.

Table 2 .
Comparison of the three inverse algorithm test result.