Motor bearing fault diagnosis method based on NRBO-DHKELM

Abstract

The invention aims to provide a motor bearing fault diagnosis method based on NRBO-DHKELM, and the method comprises the following steps: A, collecting a plurality of groups of original vibration signals of a normal motor bearing and a fault motor bearing, carrying out the decomposition through employing an EEMD algorithm, and constructing a training set; b, optimizing a hidden layer node number, a regularization coefficient, a penalty coefficient of a top layer HKELM, a kernel parameter and a weight parameter of the DHKELM model by adopting an NRBO algorithm, inputting the parameters into a training set for training to obtain an optimal solution of the parameters, and substituting the optimal solution into the DHKELM model to obtain an optimized DHKELM model; c, decomposing the original vibration signal of the motor bearing to be detected by using an EEMD algorithm to construct a feature set; and E, inputting the feature set into the trained NRBO-DHKELM model for processing so as to identify the fault type. The method is scientific and reasonable in design, can effectively improve the accuracy of motor bearing fault diagnosis, and has higher reliability.

Description

Technical Field

[0001] The invention relates to the technical field of motor bearing fault diagnosis, and in particular to a motor bearing fault diagnosis method based on NRBO-DHKELM. Background Art

[0002] With the continuous development of industrial production and the advancement of intelligent manufacturing, the stability of the motor's operating state, as a key driving device, directly affects the efficiency and safety of the entire production system. As one of the core components of the motor, the health of the motor bearing is crucial to the normal operation of the equipment. Bearing failure may not only cause equipment damage, but also cause serious production accidents and cause huge economic losses. Therefore, achieving accurate diagnosis of motor bearing failure has become the focus of current industrial research.

[0003] Motor bearing fault diagnosis methods can be mainly divided into three categories: signal processing-based methods, model-based methods, and data-driven methods. Signal processing-based methods, such as Fourier transform (FT) and wavelet transform (WT), can analyze signals intuitively, but they rely too much on manual feature extraction and have poor robustness to noise, which limits their application in complex industrial environments. Model-based methods require the establishment of accurate physical models, but due to the complexity of the bearing system and the diversity of operating conditions, this modeling process faces many challenges in practical applications, such as the difficulty in accurately obtaining model parameters and the difficulty of the model covering all possible operating conditions.

[0004] In contrast, data-driven diagnostic methods can automatically learn features from data, reduce reliance on manual feature extraction, and show stronger adaptability and diagnostic accuracy. Data-driven bearing diagnostic methods mainly include deep belief networks (DBNs), convolutional neural networks (CNNs), support vector machines (SVMs), extreme learning machines (ELMs), and other technologies. These technologies can achieve efficient fault diagnosis and classification under complex working conditions through automatic feature extraction and optimization model construction.

[0005] Although the above methods have played an important role in motor bearing fault diagnosis, the diagnostic accuracy, robustness and reliability need to be further improved. Therefore, it is necessary to further develop the motor bearing fault diagnosis method. Summary of the invention

[0006] The present invention aims to provide a motor bearing fault diagnosis method based on NRBO-DHKELM. The method is scientifically and reasonably designed, can effectively improve the accuracy of motor bearing fault diagnosis, and has higher reliability.

[0007] The technical solution of the present invention is as follows:

[0008] The motor bearing fault diagnosis method based on NRBO-DHKELM comprises the following steps:

[0009] A. Collect multiple groups of original vibration signals of normal motor bearings and faulty motor bearings respectively, decompose them using the EEMD algorithm, reconstruct the IMF components with a correlation coefficient greater than 0.5 after decomposition, calculate the time domain and frequency domain features of each reconstructed signal, and then unify the dimensions of these two features of each reconstructed signal to form a training set;

[0010] B. Use the NRBO algorithm to optimize the number of hidden layer nodes, regularization coefficient, penalty coefficient of top HKELM, kernel parameter and weight parameter of the DHKELM model, input the training set for training, and obtain the optimal solution of the number of hidden layer nodes, regularization coefficient, penalty coefficient of top HKELM, kernel parameter and weight parameter, and bring it into the DHKELM model to obtain the optimized DHKELM model;

[0011] C. The original vibration signal of the motor bearing to be tested is decomposed using the EEMD algorithm, and the IMF components with a correlation coefficient greater than 0.5 after decomposition are reconstructed. The time domain and frequency domain features of the reconstructed signal are calculated, and then the image dimensions are constructed and unified to form a feature set;

[0012] E. Input the feature set into the trained NRBO-DHKELM model to process and identify the fault type.

[0013] In step A, the faulty motor bearings include outer ring cracked bearings, inner ring cracked bearings, cage fractured bearings, and composite pitting fault bearings.

[0014] In the steps A and C, the dimensions of the time domain and frequency domain features of each reconstructed signal are uniformly constructed as 1000×7.

[0015] In step B, the output formula of the DHKELM model is as follows:

[0016]

[0017] Where C is the regularization coefficient, T is the target matrix, I is the identity matrix, and ΩKELM is the kernel matrix;

[0018] The ΩKELM kernel matrix expression is:

[0019]

[0020] Where H is the output matrix of the output layer, h(x i )、h(x j ) is the output function of the hidden layer, k(xi ,x j ) is the kernel function, K H (x i , x j ) is the mixed kernel function;

[0021] Mixed kernel function K H (x i , x j )The formula is:

[0022] K H (x i ,x j )=θ·K Poly +(1-θ)·K RBF (3)

[0023] In the formula, θ is the weight parameter of the mixed kernel function, K poly is the polynomial kernel function, K RBF is the Gaussian radial basis kernel function;

[0024] Polynomial kernel function K poly The formula is:

[0025] K Poly (x i ,x j )=(x i T x j +b) d (4)

[0026] In the formula, b is a constant term and d is the degree of the polynomial;

[0027] The Gaussian radial basis kernel function K mentioned RBF The expression is:

[0028]

[0029] Where γ is the exponential parameter of the Gaussian radial basis kernel parameter.

[0030] In step B, the calculation process of NRBO algorithm optimization is as follows:

[0031] a. Population initialization: For a given number of individuals N p Assume that the parameter to be optimized has dim dimensions. The position of the initial solution of the randomly generated population is:

[0032]

[0033] In the formula, is the position of the nth individual in the jth dimension; j∈[1,dim], n∈[1,Νp ]; lb and ub are the lower and upper bounds of the parameters to be optimized; rand is a random number between (0,1);

[0034] b. Calculate the initial fitness value: According to the set fitness function, calculate the fitness value of each individual, and select the best fitness value and the worst fitness value and their corresponding position X q and X p ;

[0035] c. Apply the NRSR rule to explore new solutions, and the updated root position is as follows:

[0036] x n+1 =x n -NRSR (7)

[0037] d. Trap avoidance operation TAO: By introducing a random number rand in the interval (0,1) and comparing it with the DF value, the new value generated is:

[0038]

[0039] In the formula, represents the nth individual in the tth iteration, rand represents a random number between (0, 1), DF represents an important factor controlling the performance of NRBO, and usually DF = 0.6, θ 1 and θ 2 are random numbers between (-1,1) and (-0.5,0.5), μ 1 and μ 2 is a random number. A random number Δ between (0,1) is compared with 0.5. If Δ≥0.5, then μ 1 and μ 2 The value is 1, otherwise, according to μ 1 =3rand,μ 2 =rand for calculation.

[0040] The fitness function for calculating the initial fitness value in step b is as follows:

[0041]

[0042] In the formula, f(x i ) represents the result predicted by the model, y i Indicates the actual result; ∏(f(x i )=y i ) means that if f(x i )=y i is equal to 1, otherwise it is 0.

[0043] In the step C, the calculation formula of NRSR is as follows:

[0044]

[0045] y p =r 1 ×(Mean(Z n+1 +x n )+r 1 ×Vx) (12)

[0046] y q =r 1 ×(Mean(Z n+1 +x n )-r 1 ×Vx) (13)

[0047]

[0048] Where randn is a random number between (0,1); y p and q Is to use Z n+1 and x n The positions of the two generated vectors, r 1 Represents a random number between (0,1), X q is the current optimal solution, rand(1,dim) is a random number, represents the nth individual in the tth iteration.

[0049] In NRSR, the new position vector formula during the next iteration is as follows:

[0050]

[0051] In the formula, r 2 Represents a random number between (0,1).

[0052] In the steps A and C, the calculation formula for reconstruction using the IMF component is as follows:

[0053]

[0054] Where s(n) is the reconstructed signal, Cov is the covariance between IMFp(n) and x(n), and Var is the variance of the corresponding sequence.

[0055] The algorithm names corresponding to the English abbreviations in this invention are as follows:

[0056] NRBO: Newton-Raphson-based optimizer;

[0057] DHKELM: Optimizing deep hybrid kernel extreme learning machine;

[0058] EEMD: ensemble empirical mode decomposition.

[0059] Compared with the prior art, the present invention has the following advantages:

[0060] The method of the present invention uses the ensemble empirical mode decomposition (EEMD) method to successfully extract the time domain and frequency domain indicators of the effective vibration signal components of the motor bearing, and constructs a feature data set to prepare for subsequent fault detection and classification. The DHKELM model parameters are optimized by the NRBO algorithm, and the NRBO-DHKELM model is established. After testing and verification, the DHKELM model can effectively improve the accuracy of motor bearing fault diagnosis, and has higher reliability, and the effect is better than other models in the prior art.

[0061] The DHKELM model constructed in the present invention combines the advantages of deep learning and ELM, automatically extracts features through deep learning, and utilizes the fast learning ability of ELM to achieve efficient fault diagnosis.

[0062] The present invention also optimizes the key parameters of the DHKELM model through NRBO to further improve the convergence speed and accuracy of the model.

[0063] The method of the present invention not only excels in diagnostic accuracy, but also has high robustness and reliability, and can effectively cope with complex industrial site requirements and meet the actual application scenarios of modern intelligent manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 This is a network structure diagram of the DHKELM of Example 1;

[0065] Figure 2 The DHKELM model test result diagram before and after NRBO optimization of Example 2; Figure 2 (a) is the test result diagram of the unoptimized DHKELM model; Figure 2 (b) is the test result diagram of the NRBO-DHKELM model obtained after optimization;

[0066] Figure 3 This is a comparison chart of the diagnostic performance of different machine learning models and DHKELM in Example 2;

[0067] Figure 4 This is a comparison chart of the diagnostic performance of DHKELM optimized by different heuristic algorithms in Example 2; DETAILED DESCRIPTION

[0068] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0069] Example 1

[0070] The motor bearing fault diagnosis method based on NRBO-DHKELM includes the following steps:

[0071] A. Collect multiple groups of original vibration signals of normal motor bearings and faulty motor bearings respectively, decompose them using the EEMD algorithm, reconstruct the IMF components with a correlation coefficient greater than 0.5 after decomposition, calculate the time domain and frequency domain features of each reconstructed signal, and then unify the dimensions of these two features of each reconstructed signal into 1000×7 to construct a training set;

[0072] The faulty motor bearings include outer ring cracked bearings, inner ring cracked bearings, cage fractured bearings, and composite pitting fault bearings.

[0073] B. Use the NRBO algorithm to optimize the number of hidden layer nodes, regularization coefficient, penalty coefficient of top HKELM, kernel parameter and weight parameter of the DHKELM model, input the training set for training, and obtain the optimal solution of the number of hidden layer nodes, regularization coefficient, penalty coefficient of top HKELM, kernel parameter and weight parameter, and bring it into the DHKELM model to obtain the optimized DHKELM model;

[0074] like Figure 1 As shown in Figure 1, the DHKELM model combines the autoencoder (AE) with the ELM to form an ELM-AE structure. Multiple ELM-AE units are stacked to form a deep learning network. The DHKELM model is then constructed by using a hybrid kernel mapping instead of a random mapping.

[0075] The output formula of the DHKELM model is as follows:

[0076]

[0077] Where C is the regularization coefficient, T is the target matrix, I is the identity matrix, and ΩKELM is the kernel matrix;

[0078] The ΩKELM kernel matrix expression is:

[0079]

[0080] Where H is the output matrix of the output layer, h(x i )、h(x j ) is the output function of the hidden layer, k(x i ,x j ) is the kernel function, KH (x i , x j ) is the mixed kernel function;

[0081] Mixed kernel function K H (x i , x j )The formula is:

[0082] K H (x i ,x j )=θ·K Poly +(1-θ)·K RBF (3)

[0083] In the formula, θ is the weight parameter of the mixed kernel function, K poly is the polynomial kernel function, K RBF is the Gaussian radial basis kernel function;

[0084] Polynomial kernel function K poly The formula is:

[0085] K Poly (x i ,x j )=(x i T x j +b) d (4)

[0086] In the formula, b is a constant term and d is the degree of the polynomial;

[0087] The Gaussian radial basis kernel function K mentioned RBF The expression is:

[0088]

[0089] Where γ is the exponential parameter of the Gaussian radial basis kernel parameter.

[0090] In step B, the calculation process of NRBO algorithm optimization is as follows:

[0091] a. Population initialization: For a given number of individuals N p Assume that the parameter to be optimized has dim dimensions. The position of the initial solution of the randomly generated population is:

[0092]

[0093] In the formula, is the position of the nth individual in the jth dimension; j∈[1,dim], n∈[1,Ν p]; lb and ub are the lower and upper bounds of the parameters to be optimized; rand is a random number between (0,1);

[0094] b. Calculate the initial fitness value: According to the set fitness function, calculate the fitness value of each individual, and select the best fitness value and the worst fitness value and their corresponding position X q and X p ;

[0095] c. Apply the NRSR rule to explore new solutions, and the updated root position is as follows:

[0096] x n+1 =x n -NRSR (7)

[0097] d. Trap avoidance operation TAO: By introducing a random number rand in the interval (0,1) and comparing it with the DF value, the new value generated is:

[0098]

[0099] In the formula, represents the nth individual in the tth iteration, rand represents a random number between (0, 1), DF represents an important factor controlling the performance of NRBO, and usually DF = 0.6, θ 1 and θ 2 are random numbers between (-1,1) and (-0.5,0.5), μ 1 and μ 2 is a random number. A random number Δ between (0,1) is compared with 0.5. If Δ≥0.5, then μ 1 and μ 2 The value is 1, otherwise, according to μ 1 =3rand,μ 2 =rand for calculation.

[0100] The fitness function for calculating the initial fitness value in step b is as follows:

[0101]

[0102] In the formula, f(x i ) represents the result predicted by the model, y i Indicates the actual result; ∏(f(x i )=y i ) means that if f(x i )=y i is equal to 1, otherwise it is 0.

[0103] In the step C, the calculation formula of NRSR is as follows:

[0104]

[0105] y p =r 1 ×(Mean(Z n+1 +x n )+r 1 ×Vx) (12)

[0106] y q =r 1 ×(Mean(Z n+1 +x n )-r 1 ×Vx) (13)

[0107]

[0108] Where randn is a random number between (0,1); y p and q Is to use Z n+1 and x n The positions of the two generated vectors, r 1 Represents a random number between (0,1), X q is the current optimal solution, rand(1,dim) is a random number, represents the nth individual in the tth iteration.

[0109] In NRSR, the new position vector formula during the next iteration is as follows:

[0110]

[0111]

[0112] In the formula, r 2 Represents a random number between (0,1).

[0113] C. The original vibration signal of the motor bearing to be tested is decomposed using the EEMD algorithm, and the IMF components with a correlation coefficient greater than 0.5 after decomposition are reconstructed. The time domain and frequency domain features of the reconstructed signal are calculated, and then the image dimensions are unified into 1000×7 to construct a feature set;

[0114] E. Input the feature set into the trained NRBO-DHKELM model to process and identify the fault type.

[0115] In the steps A and C, the calculation formula for reconstruction using the IMF component is as follows:

[0116]

[0117] Where s(n) is the reconstructed signal, Cov is the covariance between IMFp(n) and x(n), and Var is the variance of the corresponding sequence.

[0118] Example 2

[0119] 1. Motor bearing fault diagnosis test

[0120] 1. On the outer raceway, inner raceway and cage of the bearing, the raceways are damaged by wire cutting, and the outer ring crack, inner ring crack and cage crack faults are artificially simulated. A pit is machined on the outer raceway, inner raceway and rolling element of the bearing by electric spark, and the composite pitting fault of the inner and outer rings and rolling element is artificially simulated.

[0121] Repeated tests were performed on this normal motor bearing and four faulty motor bearings with outer ring cracks, inner ring cracks, cage cracks, and pitting of outer and inner ring rolling elements. 200 samples were selected for each bearing, and there were 1024 data points in the samples. The training set and the test set were divided into a 7:3 ratio, that is, the training set contained 560 faulty bearing samples and 140 normal bearing samples, and the test set contained 240 faulty bearing samples and 60 normal bearing samples.

[0122] 2. Perform diagnostic tests based on the method of Example 1, use 240 faulty bearing samples as training sets, input them into step B of Example 1, and use the NRBO algorithm to optimize the number of hidden layer nodes, regularization coefficient, penalty coefficient of the top HKELM, kernel parameters and weight parameters of the DHKELM model. The number of hidden layer nodes set by the NRBO algorithm ranges from [1,300], and the result is an integer. The NRBO population size is 10, and the maximum number of iterations is 20. The optimized model has 3 hidden layers, with the number of nodes being 69, 96, and 88, respectively. The regularization coefficient of the ELM-AE model is 109.889, and the penalty parameter of the top DHKELM model is 501.388. The kernel function selects K RBF and K poly . The optimal parameters of kernel function 1 are 3.258, and the optimal parameters of kernel function 2 are [8.768,7]. The optimal weight of kernel function 1 is 0.308, and the optimal weight of kernel function 2 is 0.692. The fitness value is 0.0067 at the beginning of the iteration process. After the fourth iteration, the global optimal solution is obtained. The fitness function value drops to 0 and remains unchanged in subsequent iterations, which shows that the NRBO algorithm can quickly converge to the optimal solution and has strong optimization ability. The optimal model can be obtained by using the optimal solution as the parameter in the DHKELM model.

[0123] 3. Model testing. The test set data was input into the DHKELM model before and after optimization for testing and comparison. The results are as follows: Figure 2 As shown. Figure 2 (a) shows that the accuracy of the unoptimized DHKELM model is 92%, which indicates that the model's fitting ability is weak. Figure 2 (b) It can be seen that the test set accuracy of the optimized NRBO-DHKELM model reached 100%, which is higher than the accuracy of the model before optimization. This shows that the model fitting ability has been enhanced after parameter optimization, and the classification performance has been improved.

[0124] 2. Comparison of diagnostic performance of different machine learning models and algorithm optimization

[0125] 1. Comparison of diagnostic performance between different machine learning models and DHKELM

[0126] In order to verify the effectiveness and superiority of the DHKELM model, this example compares the model with four common models: BP, SVM, ELM, and KELM. The constructed feature data sets are input into different models for training and classification, and different models are run 10 times. The results are as follows: Figure 3 shown.

[0127] Depend on Figure 3 It can be seen that in the diagnosis of 5 different types of motor bearings, the accuracy of the DHKELM model is significantly higher than that of other models; the DHKELM model has the highest average accuracy of 92.27%, and the accuracy of the SVM, BP, ELM, and KELM models are 86.83%, 88.87%, 76.37%, and 84.56%, respectively, which are all lower than the DHKELM model. This shows that the diagnostic performance of the DHKELM model is significantly better than other machine learning models.

[0128] 2. Comparison of diagnostic performance of DHKELM optimized by different heuristic algorithms

[0129] In order to verify the superiority of the NRBO optimized DHKELM diagnostic model, the NRBO-DHKELM model of the present invention was compared with the WOA-DHKELM, GWO-DHKELM, and SSA-DHKELM models. The different models were run 10 times respectively. The results are shown in Figure 2. Figure 4 shown.

[0130] Depend on Figure 4It can be seen that NRBO-DHKELM has the highest fault accuracy, and its average accuracy of 10 repeatable tests is as high as 99.67%. In addition, the average accuracy of WOA-DHKELM, GWO-DHKELM, and SSA-DHKELM models are 93.47%, 95.33%, and 97.33%, respectively. Compared with the above three methods, the accuracy of NRBO-DHKELM is improved by 6.20%, 4.34%, and 2.34%, respectively. The results show that after EEMD processing, the NRBO-DHKELM model of the present invention has higher accuracy and reliability.

Claims

1. A motor bearing fault diagnosis method based on NRBO-DHKELM, characterized in that: The following steps are involved: A. Collect multiple groups of original vibration signals of normal motor bearings and faulty motor bearings respectively, decompose them using the EEMD algorithm, reconstruct the IMF components with a correlation coefficient greater than 0.5 after decomposition, calculate the time domain and frequency domain features of each reconstructed signal, and then unify the dimensions of these two features of each reconstructed signal to form a training set; B. Use the NRBO algorithm to optimize the number of hidden layer nodes, regularization coefficient, penalty coefficient of top HKELM, kernel parameter and weight parameter of the DHKELM model, input the training set for training, and obtain the optimal solution of the number of hidden layer nodes, regularization coefficient, penalty coefficient of top HKELM, kernel parameter and weight parameter, and bring it into the DHKELM model to obtain the optimized DHKELM model; C. The original vibration signal of the motor bearing to be tested is decomposed using the EEMD algorithm, and the IMF components with a correlation coefficient greater than 0.5 after decomposition are reconstructed. The time domain and frequency domain features of the reconstructed signal are calculated, and then the image dimensions are constructed and unified to form a feature set; E. Input the feature set into the trained NRBO-DHKELM model to process and identify the fault type.

2. The motor bearing fault diagnosis method based on NRBO-DHKELM as claimed in claim 1, characterized in that: In step A, the faulty motor bearings include outer ring cracked bearings, inner ring cracked bearings, cage fractured bearings, and composite pitting fault bearings.

3. The motor bearing fault diagnosis method based on NRBO-DHKELM as claimed in claim 1, characterized in that: In the steps A and C, the dimensions of the time domain and frequency domain features of each reconstructed signal are uniformly constructed as 1000×7.

4. The motor bearing fault diagnosis method based on NRBO-DHKELM as claimed in claim 1, characterized in that: In step B, the output formula of the DHKELM model is as follows: Where C is the regularization coefficient, T is the target matrix, I is the identity matrix, and ΩKELM is the kernel matrix; The ΩKELM kernel matrix expression is: Where H is the output matrix of the output layer, h(x i )、h(x j ) is the output function of the hidden layer, k(x i ,x j ) is the kernel function, K H (x i , x j ) is the mixed kernel function; Mixed kernel function K H (x i , x j )The formula is: K H (x i ,x j )=θ·K Poly +(1-θ)·K RBF (3) In the formula, θ is the weight parameter of the mixed kernel function, K poly is the polynomial kernel function, K RBF is the Gaussian radial basis kernel function; Polynomial kernel function K poly The formula is: In the formula, b is a constant term and d is the degree of the polynomial; The Gaussian radial basis kernel function K mentioned RBF The expression is: Where γ is the exponential parameter of the Gaussian radial basis kernel parameter.

5. The motor bearing fault diagnosis method based on NRBO-DHKELM as claimed in claim 1, characterized in that: In step B, the calculation process of NRBO algorithm optimization is as follows: a. Population initialization: For a given number of individuals N p Assuming that the parameter to be optimized has dim dimensions, the position of the initial solution of the randomly generated population is: In the formula, is the position of the nth individual in the jth dimension; j∈[1,dim], n∈[1,Ν p ]; lb and ub are the lower and upper bounds of the parameters to be optimized; rand is a random number between (0,1); b. Calculate the initial fitness value: According to the set fitness function, calculate the fitness value of each individual, and select the best fitness value and the worst fitness value and their corresponding position X q and X p ; c. Apply the NRSR rule to explore new solutions, and the updated root position is as follows: x n+1 =x n -NRSR (7) d. Trap avoidance operation TAO: By introducing a random number rand in the interval (0,1) and comparing it with the DF value, the new value generated is: In the formula, represents the nth individual in the tth iteration, rand represents a random number between (0, 1), DF represents an important factor controlling the performance of NRBO, and usually DF = 0.6, θ1 and θ2 are random numbers between (-1, 1) and (-0.5, 0.5) respectively, μ1 and μ2 are random numbers, compared with a random number Δ between (0, 1) and 0.5, if Δ ≥ 0.5, then μ1 and μ2 take the value of 1, otherwise, they are calculated according to μ1 = 3rand, μ2 = rand.

6. The motor bearing fault diagnosis method based on NRBO-DHKELM as claimed in claim 5, characterized in that: The fitness function for calculating the initial fitness value in step b is as follows: In the formula, f(x i ) represents the result predicted by the model, y i Indicates the actual result; ∏(f(x i )=y i ) means that if f(x i )=y i is equal to 1, otherwise it is 0.

7. The motor bearing fault diagnosis method based on NRBO-DHKELM as claimed in claim 5, characterized in that: In the step C, the calculation formula of NRSR is as follows: y p =r1×(Mean(Z n+1 +x n )+r1×Vx) (12) y q =r1×(Mean(Z n+1 +x n )-r1×Vx) (13) Where randn is a random number between (0,1); y p and q Is to use Z n+1 and x n The positions of the two generated vectors, r1 represents a random number between (0,1), and X q is the current optimal solution, rand(1,dim) is a random number, represents the nth individual in the tth iteration.

8. The motor bearing fault diagnosis method based on NRBO-DHKELM as claimed in claim 7, characterized in that: In NRSR, the new position vector formula during the next iteration is as follows: In the formula, r2 represents a random number between (0,1).

9. The motor bearing fault diagnosis method based on NRBO-DHKELM as claimed in claim 1, characterized in that: In the steps A and C, the calculation formula for reconstruction using the IMF component is as follows: Where s(n) is the reconstructed signal, Cov is the covariance between IMFp(n) and x(n), and Var is the variance of the corresponding sequence.

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