Rolling bearing fault diagnosis method based on SSA-mRVM

In order to accurately diagnose the faults of rolling bearings, in this paper, a fault diagnosis method is proposed based on multiclass relevance vector machines (mRVM) optimized by the sparrow search algorithm (SSA). Complete ensemble empirical mode decomposition (CEEMD) is applied to feature extraction of vibration signals. Optimizing the parameters of multiclass relevance vector machines involves the use of the sparrow search algorithm. The optimized multiclass relevance vector machines model is applied for fault diagnosis to obtain accurate diagnostic results.


Introduction
With the rapid development of science and technology and modern industry, modern mechanical equipment has become increasingly large and complex, and the degree of automation of mechanical equipment has become higher.There are still close relationships between different equipment, forming a whole system in the production process.In the production of factories, mechanical equipment also plays an irreplaceable role.The use of mechanical equipment can not only improve industrial productivity but also reduce production costs.Most modern mechanical equipment includes rotating machinery, which is widely used in important engineering fields such as mechanical manufacturing, power, chemical, metallurgy, and power.Common rotating machinery includes generators, electric motors, steam turbines, blowers, and so on.In the production process, mechanical equipment is affected by various factors and causes varying degrees of damage to the equipment, leading to mechanical equipment failures.This not only damages the mechanical equipment itself, but also affects the quality of production products, and also causes varying degrees of physical harm to production personnel.The normal operation of mechanical equipment is closely related to the normal production in the factory; therefore, the normal operation of mechanical equipment is very important.Fault diagnosis of mechanical equipment is an important measure to ensure the normal operation of mechanical equipment.
Rolling bearings are a basic component widely used in mechanical equipment, and their stability is crucial for mechanical equipment.In the event of high-strength and long-term working conditions, rolling bearings may inevitably fail.The failure of rolling bearings affects the stability of mechanical equipment, thereby affecting product quality and even causing safety accidents.By diagnosing the faults of rolling bearings and repairing them promptly, the mechanical equipment can operate normally.
Rolling bearing fault diagnosis is a hot research topic.There are many researchers conducting research on rolling fault diagnosis.In [1], a rolling bearing fault diagnosis algorithm based on sample screening and deep belief neural network is proposed.This algorithm screens the signal components obtained from VMD based on energy fluctuations, and uses deep confidence neural networks for fault identification.In [2], a fault classification method for wind turbine rolling bearings based on optimized VMD and ensemble learning is proposed.This algorithm takes the minimum envelope entropy of the decomposed signal as the fitness function, optimizes the number of component signals and penalty factors, screens the decomposed component signals, and finally uses XGBoost for fault identification.Considering the difficulty in obtaining a large number of typical fault samples, a rolling bearing fault diagnosis method based on the combination of CEEMD and ELM is proposed.The CEEMD is used to decompose the non-stationary original acceleration vibration signal of rolling bearings, obtain the decomposed IMF components, calculate their energy entropy, and extract energy features.Extreme learning machines are used to determine the working state and fault type of rolling bearings [3].In [4], an End-to-End rolling bearing fault diagnosis method based on multi attention mechanism is proposed.First, by integrating the vibration acceleration signal, velocity and displacement signals can be obtained.The acceleration, velocity, and displacement signals are combined to form an image with feature enhancement.Then, a deep residual network that combines channel attention and spatial attention mechanisms is used to achieve feature extraction of vibration signals.Finally, multiple classification functions are used to complete the fault diagnosis of rolling bearings.
Relevance vector machines (RVM) are a learning algorithm proposed by Tipping, which is based on Bayesian theory and statistical learning theory.The performance of RVM is basically the same as that of support vector machines.RVM has good performance in handling small-sample problems, strong generalization ability, and better sparsity.Psorakis et al. proposed the mRVM algorithm, which is based on binary classification correlation vector machines, which can be directly used to solve multiclassification problems [5].SSA is an intelligent optimization algorithm [6].In this article, the relevance vector machines model combined with the sparrow search algorithm will be adopted for rolling bearing fault diagnosis.

Application of multiclass relevance vector machines and sparrow search algorithm
The concept of using the sparrow search algorithm is to optimize multiclass relevance vector machines based on the rolling bearing fault diagnosis method.Therefore, the basic principle of this algorithm is introduced.Subsequently, a set of experimental data will be proposed to use optimization models for fault diagnosis and find the best results.

Multiclass relevance vector machines
Multiclass relevance vector machines (mRVM) are a machine learning algorithm based on a hierarchical Bayesian model, which utilizes auxiliary regression variables and weight parameters to extend RVM to solve multi-classification problems and output category probabilities.
The training sample set is X = {x i , t i } N i=1 , where there is the input feature vector x i ∈R D , D is the dimension of a vector, and the category label t i ∈{1, ..., C}.The basis kernel function is represented as K(x i , x j ) = <Φ(x i ), Φ(x j )>, K∈R N×N , k ij is a row in K.The ability of mRVM to achieve multi-classification is achieved through auxiliary variables.The auxiliary variable is Y∈R C×N , following the standard noise model as y cn |w c , k n ~NY cn (w c T k n , 1), t i ∈{1, ..., C} [7].Regression targets are transformed into category labels using polynomial probability linking functions: t n = i, y ni > y nj , Ɐi ≠ j.By introducing a multinomial probability likelihood function, the class member probability output is obtained by:

P t i w k P t i y P y w k w w k
where μ follows a standard normal distribution: μ~N(0, 1), and Φ is the Gaussian cumulative distribution function.

Sparrow search algorithm for optimizing kernel function parameters
The parameter values of the mRVM are crucial for its generalization ability and performance.In order to obtain the optimal kernel function parameter values, the SSA is used to optimize the kernel function parameters.The position of the sparrow represents the kernel function parameters, and the fitness function is mRVM for fault diagnosis error rate.The global best position is the optimal parameter value of the kernel function.Figure 1 shows the flowchart of optimizing mRVM parameters using SSA [6].exp( ) The flowchart of optimizing mRVM parameters using SSA.

Experiment and implementation
In this experiment, rolling bearing data from CWRU is used.The experimental data includes vibration signal data of rolling bearings under 4 types of working conditions.Bearing vibration data with loads of 0 HP and 1 HP is adopted.In this experiment, CEEMD was used to decompose the vibration signal and obtain multiple component signals, and the calculated fuzzy entropy of the obtained component signal was used as the fault feature vector.Figure 3 shows the time-domain waveforms of each sample data for four types of faults with loads of 0 HP, respectively.Each sample data consists of 2048 sets of vibration signal data.
Here, a vibration signal data sample is used as an example to describe the process of feature extraction.By using CEEMD to decompose the vibration signal of the rolling ball fault in Figure 3, multiple IMF component signals were obtained, and the time-domain waveform of the first 6 signal components is shown in Figure 4.The fuzzy entropy value is calculated for the 8 signal components obtained above, which are {0.5265,0.7370, 0.3051, 0.5916, 0.4983, 0.3609, 0.2093, 0.0943}.Table 1 shows the fuzzy entropy of some test samples.

Conclusion
In this article, SSA is used to optimize the parameters of mRVM, which can quickly obtain the optimal kernel function parameter values, making mRVM maintain good generalization ability, and improving the accuracy of fault diagnosis.Through experimental verification, the results indicate that the proposed method is feasible and effective.Next, online testing will be conducted on the fault effectiveness of this method in the mechanical equipment of the factory.

Figure 2
shows the workflow diagram of a fault diagnosis method based on SSA-mRVM.

Figure 4 .
Figure 4. Signal components obtained from CEEMD decomposition of rolling ball fault samples.

Table 1 .
Fuzzy Entropy of Partial Test Samples.

Table 2 .
Fault accuracy results of three methods.