A rolling bearing fault diagnosis method based on DS evidence theory

Abstract

The present invention discloses a rolling bearing fault diagnosis method based on DS evidence theory, firstly, the life cycle vibration signal of the rolling bearing is imported; the vibration signal is decomposed into multiple intrinsic mode function IMF components by using the empirical mode decomposition EMD method, and the sample entropy of each IMF component is calculated; the sample entropy of the IMF component is used as a feature vector for training to obtain the basic probability distribution BPA by using a random forest model, and three diagnostic units are used to obtain three groups of evidence bodies; the distance between each evidence body is calculated, and the support matrix between the evidences is determined by the distance size, and the feature vector corresponding to the maximum eigenvalue in the evidence support matrix is ​​used as the weight vector of the evidence, and the relative discount factor of each piece of evidence is determined to correct the evidence, and the fused BPA is calculated by using the DS fusion rule, and finally the classification result of the fault is obtained. The present invention solves the problem of low accuracy of the rolling bearing fault diagnosis method existing in the prior art.

Description

Technical Field

[0001] The invention belongs to the technical field of fault diagnosis, and in particular relates to a rolling bearing fault diagnosis method based on DS evidence theory. Background Art

[0002] Mechanical equipment in modern production processes is constantly developing towards large-scale, complex, high-speed and intelligent. If these mechanical equipment cannot be promptly and effectively detected and diagnosed at the initial stage of a fault, the fault will be aggravated, and the consequences may cause downtime, and in more serious cases, huge economic losses or even personal injury. Therefore, intelligent, fast and accurate diagnosis of mechanical equipment failures is an important guarantee for safe production and improving economic benefits, and has important practical significance.

[0003] Conventional fault diagnosis methods for rolling bearings mostly focus on feature analysis and extraction of fault information obtained by a single sensor, and then determine the presence and type of fault. This type of method has the advantages of simple structure, small amount of calculation, and easy implementation. However, the biggest disadvantage of this type of method is the low accuracy of fault diagnosis. By fusing information from multiple sensors, the system can effectively avoid many inherent defects of a single sensor. The application of DS evidence theory makes up for the shortcomings of single sensor diagnosis, gives play to the advantages of multi-sensor diagnosis, and helps the entire system meet the actual needs of engineering practice. Summary of the invention

[0004] The purpose of the present invention is to provide a rolling bearing fault diagnosis method based on DS evidence theory, which solves the problem of low accuracy of rolling bearing fault diagnosis methods in the prior art.

[0005] The technical solution adopted by the present invention is a rolling bearing fault diagnosis method based on DS evidence theory, which is specifically implemented according to the following steps:

[0006] Step 1: Import the vibration signal of the rolling bearing throughout its life cycle from normal state to failure and finally complete failure;

[0007] Step 2: Using EMD to decompose the vibration signals from multiple homogeneous sensors on the rolling bearing into multiple intrinsic mode function (IMF) components, further calculating the sample entropy of each IMF component and using it as the feature vector of the vibration signal;

[0008] Step 3: Select the feature vector composed of IMF component sample entropy and input it into the random forest model for training and classification. Convert the voting results of the random forest into evidence, use the proportion of the number of votes to the total number of decision trees as the basic probability distribution BPA, and use three diagnostic units to obtain three groups of evidence.

[0009] Step 4: Fusion of multi-source evidence information. First, based on the three groups of evidence obtained, calculate the distance between each two groups of evidence, and determine the mutual support matrix between the evidences based on the distance. Use the eigenvector corresponding to the maximum eigenvalue in the evidence support matrix as the weight vector of the evidence. Then determine the relative discount factor of each piece of evidence, correct the evidence information, fuse it using the DS rule, calculate the fused BPA, and finally make a decision to obtain the fault classification result.

[0010] The present invention is also characterized in that:

[0011] Step 2 is implemented as follows:

[0012] Step 2.1: Use EMD to decompose the original vibration signal into multiple IMF components. Sample an IMF component with N points. The time series formed after sampling is:

[0013] X(k)={x(1),x(2),…,x(k),…,x(N)}, where k=1,2,…,N, select n consecutive data points in X(k) to form a window subsequence X n (i) = {x(i), x(i+1), ..., x(i+n-1)}, and get the window subsequence X n The number of (i) is N-n+1, ​​i.e., i=1,2,…,N-n+1;

[0014] Step 2.2: Define two window subsequences X n (i) With X n (j) The distance d[X n (i),X n (j)] is X n (i) With X n (j) corresponds to the absolute value of the maximum difference of the data points, that is:

[0015] d[X n (i),X n (j)] = max[X n (i+b)-X n (j+b)] (1)

[0016] Where b = 0, 1, 2, ... n-1;

[0017] Step 2.3: Given a threshold r, calculate each window subsequence X n (i) The distances with other window subsequences, a total of Nn, count the number of distances less than the threshold r and calculate their proportion in the total number of Nn distances for:

[0018]

[0019] In the formula, count{*} represents the number of statistics that meet the conditions; j = 1, 2, ... N-n+1 and j≠i, that is, the values ​​of j and i cannot be the same in the same value range;

[0020] Step 2.4: For each window subsequence X n (i) All calculated And find the average value B n (r) is:

[0021]

[0022] Step 2.5: Increase the length of the window subsequence from n to n+1, repeat step 2.4, and calculate the average value B when the sequence length is n+1 n+1 (r) is:

[0023]

[0024] Step 2.6: Calculate the sample entropy SampEn(n,r,N) of an IMF component as:

[0025]

[0026] Step 2.7: Repeat steps 2.1 to 2.6 to calculate the sample entropy of the remaining multiple IMF components.

[0027] Step 3 is implemented as follows:

[0028] Step 3.1, select the sample entropy of the first three IMF components in step 2 to form a feature vector, input the feature vector into the trained random forest classifier and obtain the voting results of various faults;

[0029] Step 3.2: Assume that there are l types of faults that need to be classified and identified, and the total number of decision trees of the random forest classifier is N. t , let θ g represents the g-th fault, g = 1, 2, ..., l, and the fault identification framework is expressed as θ = (θ1, θ2, ..., θ g ), use v g Indicates the fault θ when random forest is used for classification g The number of votes is expressed as m(θ g ) indicates fault θ g The basic probability allocation BPA of the random forest is that all decision trees vote for each fault, so we get:

[0030]

[0031] in To identify the empty set in the frame, if we set:

[0032]

[0033] Can launch:

[0034]

[0035] Combining equations (6) and (8), we can get m(θ g ) is the fault θ g BPA, of which is the proportion of the number of votes for the fault type to the total number of decision trees;

[0036] Step 3.3: Combine EMD and sample entropy with random forest as a diagnostic unit. Each diagnostic unit performs independent diagnosis. Use three diagnostic units to diagnose the fault. The first diagnostic unit obtains the fault θ g The BPA is m1(θ g ), the fault θ is obtained by the second diagnosis unit g The BPA is m2(θ g ), the fault θ is obtained by the third diagnostic unit g The BPA is m3(θ g ), and finally m1(θ g )、m2(θ g )、m3(θ g ) are three groups of evidence integrated into the DS evidence theory.

[0037] Step 4 is as follows:

[0038] Step 4.1: Based on the three sets of evidence m1(θ obtained in step 3 g )、m2(θ g )、m3(θ g ), first calculate the distance between the three groups of evidence, the calculation formula is as follows:

[0039]

[0040]

[0041]

[0042] In the formula <m1(θ g ),m2(θ g )> is m1(θ g ) and m2(θ g ), <m1(θ g ),m3(θ g )> is m1(θ g) and m3(θ g ), <m2(θ g ),m3(θ g )> is m2(θ g ) and m3(θ g ), ||m1(θ g )|| 2 = <m1(θ g ),m1(θ g )>,||m2(θ g )|| 2 = <m2(θ g ),m2(θ g )>,||m3(θ g )|| 2 = <m3(θ g ),m3(θ g )>;

[0043] Step 4.2: Determine the consistency between the evidences based on the distance between the two pieces of evidence, also known as mutual support, which is:

[0044] [sup] a,b =1-d(m a (θ g ),m b (θ g )) (12)

[0045] Where a, b = 1, 2, 3, so the 3×3 dimensional mutual support matrix S of the evidence is:

[0046]

[0047] Where S a,b Indicates evidence m a (θ g ) and evidence m b (θ g ) is similar to S a,b =S b,a , so S is a symmetric matrix;

[0048] Step 4.3: Assume the weight coefficient of the evidence of group a is β a , a=1,2,3, then

[0049] λβ a =β1S 1,a +β2S 2,a +β3S 3,a (14)

[0050] Where λ is the proportionality coefficient, let β = (β1, β2, β3) T, then from formula (14) we can get:

[0051] λβ=S T β (15)

[0052] Since S is a symmetric matrix, that is, S T =S, so λ is the eigenvalue of the S matrix, and β is its corresponding eigenvector;

[0053] Step 4.4: Select the evidence with the largest weight coefficient, i.e. the most credible evidence, as the key evidence. Its weight coefficient β max for:

[0054] β max =max(β1,β2,β3) (16)

[0055] Where β1, β2 and β3 are the weight coefficients of the first, second and third groups of evidence respectively, and then the relative weight vector β of each evidence is obtained * for:

[0056] β * =[β1,β1,β3] / β max (17)

[0057] The discount factor α is thus determined for the basic probability distribution of the evidence group a. a for:

[0058]

[0059] The basic probability distribution value of the evidence is modified according to the discount factor. The basic probability distribution value of the evidence in group a after modification is for:

[0060]

[0061] Where m a (θ g ) assigns a value to the basic probability of the a-th group of evidence;

[0062] Step 4.5, there are l types of faults, namely θ1, θ2, ..., θ l According to the DS fusion rule, the corrected first set of evidence and the corrected second set of evidence are first fused to obtain the first fusion result. for:

[0063]

[0064] Where p,q=1,2,...,l, Assign values ​​to the basic probabilities of the first set of evidence after correction, is the basic probability distribution value of the second group of evidence after correction. Then the first fusion result and the basic probability distribution value of the third group of evidence after correction are fused to obtain the second fusion result. for:

[0065]

[0066] Where p,q=1,2,...,l, Assign values ​​to the base probabilities of the first fusion of evidence, Assign values ​​to the base probabilities of the revised third set of evidence;

[0067] Make a decision based on the result of the second fusion. where g=1,2,...,l, so They represent the probabilities of type 1, type 2, …, and type l faults respectively. The size of each probability is compared, and the fault type with the highest probability is taken as the final diagnosis result.

[0068] The beneficial effect of the present invention is that the rolling bearing fault diagnosis method based on DS evidence theory, aimed at the limitations of a single sensor fault diagnosis information source being single and incomplete, converts the voting results of the random forest into evidence on the basis of empirical mode decomposition and random forest as core algorithms, realizes the combination of random forest and DS evidence theory, overcomes the problem of incomplete information of a single sensor, and has strong robustness. At the same time, this fault diagnosis method can easily introduce more sensors, truly achieve complementary advantages between sensors, realize comprehensive collection of fault information, and provide guarantee for accurate diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is an overall algorithm block diagram of a rolling bearing fault diagnosis method based on DS evidence theory of the present invention;

[0070] Figure 2 It is a diagnostic unit block diagram of a rolling bearing fault diagnosis method based on DS evidence theory of the present invention. DETAILED DESCRIPTION

[0071] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0072] The present invention provides a rolling bearing fault diagnosis method based on DS evidence theory, the flow chart is as follows: Figure 1 As shown, the specific implementation steps are as follows:

[0073] Step 1: Import the vibration signals of the rolling bearing throughout its life cycle from normal state to failure and finally complete failure, such as the rolling bearing failure test data obtained from the official website of the Bearing Research Center of the University of the Western Reserve in the United States;

[0074] Step 2: Use Empirical Mode Decomposition (EMD) to decompose the vibration signals from multiple homogeneous sensors on the rolling bearing into multiple intrinsic mode function (IMF) components, and further calculate the sample entropy of each IMF component and use it as the feature vector of the vibration signal.

[0075] Step 2 is implemented as follows:

[0076] Step 2.1: Use EMD to decompose the original vibration signal into multiple IMF components. Sample an IMF component with N points. The time series formed after sampling is:

[0077] X(k)={x(1),x(2),…,x(k),…,x(N)}, where k=1,2,…,N, select n consecutive data points in X(k) to form a window subsequence X n (i) = {x(i), x(i+1), ..., x(i+n-1)}, and get the window subsequence X n The number of (i) is N-n+1, ​​i.e., i=1,2,…,N-n+1;

[0078] Step 2.2: Define two window subsequences X n (i) With X n (j) The distance d[X n (i),X n (j)] is X n (i) With X n (j) corresponds to the absolute value of the maximum difference of the data points, that is:

[0079] d[X n (i),X n (j)] = max[X n (i+b)-X n (j+b)] (1)

[0080] Where b = 0, 1, 2, ... n-1;

[0081] Step 2.3: Given a threshold r, calculate each window subsequence X n (i) The distances with other window subsequences, a total of Nn, count the number of distances less than the threshold r and calculate their proportion in the total number of Nn distances for:

[0082]

[0083] In the formula, count{*} represents the number of statistics that meet the conditions; j = 1, 2, ... N-n+1 and j≠i, that is, the values ​​of j and i cannot be the same in the same value range;

[0084] Step 2.4: For each window subsequence X n (i) All calculated And find the average value B n (r) is:

[0085]

[0086] Step 2.5: Increase the length of the window subsequence from n to n+1, repeat step 2.4, and calculate the average value B when the sequence length is n+1 n+1 (r) is:

[0087]

[0088] Step 2.6: Calculate the sample entropy SampEn(n,r,N) of an IMF component as:

[0089]

[0090] Step 2.7: Repeat steps 2.1 to 2.6 to calculate the sample entropy of the remaining multiple IMF components.

[0091] Step 3: Select the feature vector composed of IMF component sample entropy and input it into the random forest model for training and classification. Convert the voting results of the random forest into evidence. Take the proportion of the number of votes to the total number of decision trees as the basic probability assignment (BPA). Use three diagnostic units to obtain three groups of evidence. This effectively solves the problem of obtaining BPA in the process of information fusion using DS evidence theory.

[0092] Combination Figure 2 ,Step 3 selects the feature vector composed of EMD dimensionless indicators and inputs it into the random forest model for training and classification. ,The voting results of the random forest are converted into evidence. The proportion of the number of votes to the total number of decision trees is used as BPA. ,Three diagnostic units are used to obtain three groups of evidence bodies, which effectively solves the problem of obtaining BPA in the process of applying DS evidence theory for information fusion.

[0093] Follow the steps below to implement it:

[0094] Step 3.1, select the sample entropy of the first three IMF components in step 2 to form a feature vector, input the feature vector into the trained random forest classifier and obtain the voting results of various faults;

[0095] Step 3.2: Assume that there are l types of faults that need to be classified and identified, and the total number of decision trees of the random forest classifier is N. t , let θ g represents the g-th fault, g = 1, 2, ..., l, and the fault identification framework is expressed as θ = (θ1, θ2, ..., θ g ), use v g Indicates the fault θ when random forest is used for classification g The number of votes is expressed as m(θ g ) indicates fault θ g The basic probability allocation BPA of the random forest is that all decision trees vote for each fault, so we get:

[0096]

[0097] in To identify the empty set in the frame, if we set:

[0098]

[0099] Can launch:

[0100]

[0101] Combining equations (6) and (8), we can get m(θ g ) is the fault θ g BPA, of which is the proportion of the number of votes for the fault type to the total number of decision trees;

[0102] Step 3.3: Combine EMD and sample entropy with random forest as a diagnostic unit. Each diagnostic unit performs independent diagnosis. Use three diagnostic units to diagnose the fault. The first diagnostic unit obtains the fault θ g The BPA is m1(θ g ), the fault θ is obtained by the second diagnosis unit g The BPA is m2(θ g ), the fault θ is obtained by the third diagnostic unit g The BPA is m3(θ g ), and finally m1(θ g )、m2(θ g )、m3(θ g ) are three groups of evidence integrated into the DS evidence theory.

[0103] Step 4: Fusion of multi-source evidence information. First, based on the three groups of evidence obtained, calculate the distance between each two groups of evidence, and determine the mutual support matrix between the evidences based on the distance. Use the eigenvector corresponding to the maximum eigenvalue in the evidence support matrix as the weight vector of the evidence. Then determine the relative discount factor of each piece of evidence, correct the evidence information, fuse it using the DS rule, calculate the fused BPA, and finally make a decision to obtain the fault classification result.

[0104] Step 4: When fusing multi-source evidence information, first determine the mutual support between the evidences based on the distance between the two pieces of evidence, use the eigenvector corresponding to the maximum eigenvalue of the evidence support matrix as the weight vector of the evidence, then determine the relative discount factor of each piece of evidence, and correct the evidence information, and finally fuse them using the DS rule.

[0105] The details are as follows:

[0106] Step 4.1: Based on the three sets of evidence m1(θ obtained in step 3 g )、m2(θ g )、m3(θ g ), first calculate the distance between the three groups of evidence, the calculation formula is as follows:

[0107]

[0108]

[0109]

[0110] In the formula <m1(θ g ),m2(θ g )> is m1(θ g ) and m2(θ g ), <m1(θ g ),m3(θ g )> is m1(θ g ) and m3(θ g ), <m2(θ g ),m3(θ g )> is m2(θ g ) and m3(θ g ), ||m1(θ g )|| 2 = <m1(θ g ),m1(θ g )>,||m2(θ g )|| 2 = <m2(θ g ),m2(θ g )>,||m3(θ g)|| 2 = <m3(θ g ),m3(θ g )>;

[0111] Step 4.2: Determine the consistency between the evidences based on the distance between the two pieces of evidence, also known as mutual support, which is:

[0112] [sup] a,b =1-d(m a (θ g ),m b (θ g )) (12)

[0113] Where a, b = 1, 2, 3, so the 3×3 dimensional mutual support matrix S of the evidence is:

[0114]

[0115] Where S a,b Indicates evidence m a (θ g ) and evidence m b (θ g ) is similar to S a,b =S b,a , so S is a symmetric matrix;

[0116] Step 4.3: The basic principle for determining the weight coefficient is: if a piece of evidence is highly consistent with other evidence, that is, it is highly supported by other evidence, then the weight coefficient of the evidence should be larger, otherwise it should be smaller. Then, the weight of each piece of evidence should be proportional to the comprehensive support of other evidence.

[0117] Assume that the weight coefficient of the evidence in group a is β a , a=1,2,3, then

[0118] λβ a =β1S 1,a +β2S 2,a +β3S 3,a (14)

[0119] Where λ is the proportionality coefficient, let β = (β1, β2, β3) T , then from formula (14) we can get:

[0120] λβ=S T β (15)

[0121] Since S is a symmetric matrix, that is, S T =S, so λ is the eigenvalue of the S matrix, and β is its corresponding eigenvector;

[0122] Step 4.4: Since S is a non-negative non-decomposable matrix, the Perron-Frobenius theorem shows that S has a maximum modulus eigenvalue λ>0 and corresponds to a positive eigenvector β, then β is the weight coefficient vector of the three pieces of evidence.

[0123] The evidence with the largest weight coefficient, i.e. the most credible one, is selected as the key evidence, and its weight coefficient β max for:

[0124] β max =max(β1,β2,β3) (16)

[0125] Where β1, β2 and β3 are the weight coefficients of the first, second and third groups of evidence respectively, and then the relative weight vector β of each evidence is obtained * for:

[0126] β * =[β1,β1,β3] / β max (17)

[0127] The discount factor α is thus determined for the basic probability distribution of the evidence group a. a for:

[0128]

[0129] The basic probability distribution value of the evidence is modified according to the discount factor. The basic probability distribution value of the evidence in group a after modification is for:

[0130]

[0131] Where m a (θ g ) assigns a value to the basic probability of the a-th group of evidence;

[0132] Step 4.5, there are l types of faults, namely θ1, θ2, ..., θ l According to the DS fusion rule, the corrected first set of evidence and the corrected second set of evidence are first fused to obtain the first fusion result. for:

[0133]

[0134] Where p,q=1,2,...,l, Assign values ​​to the basic probabilities of the first set of evidence after correction, is the basic probability distribution value of the second group of evidence after correction. Then the first fusion result and the basic probability distribution value of the third group of evidence after correction are fused to obtain the second fusion result. for:

[0135]

[0136] Where p,q=1,2,...,l, Assign values ​​to the base probabilities of the first fusion of evidence, Assign values ​​to the base probabilities of the revised third set of evidence;

[0137] Make a decision based on the result of the second fusion. where g=1,2,...,l, so They represent the probabilities of type 1, type 2, …, and type l faults respectively. The size of each probability is compared, and the fault type with the highest probability is taken as the final diagnosis result.

[0138] The present invention discloses a rolling bearing fault diagnosis method based on DS evidence theory, which uses Empirical Mode Decomposition (EMD) to extract fault features. On the basis of using the EMD dimensionless index of the vibration signal as the characteristic parameter, a decision tree algorithm is used to classify the fault, the voting result of the random forest classifier is used as evidence, and the proportion of the number of votes for distinguishing the fault type to the total number of decision trees is used as the basic probability assignment (BPA) of the DS evidence theory. Then, the intelligent fault diagnosis based on EMD sample entropy and random forest is used as the diagnosis unit, and the improved DS evidence theory is used to fuse the diagnostic information of the diagnostic units from different sensors to form multi-sensor information fusion fault diagnosis.

Claims

1. A rolling bearing fault diagnosis method based on DS evidence theory, characterized in that: Follow the steps below to implement it: Step 1: Import the vibration signal of the rolling bearing throughout its life cycle from normal state to failure and finally complete failure; Step 2: Using EMD to decompose the vibration signals from multiple homogeneous sensors on the rolling bearing into multiple intrinsic mode function (IMF) components, further calculating the sample entropy of each IMF component and using it as the feature vector of the vibration signal; Step 3: Select the feature vector composed of IMF component sample entropy and input it into the random forest model for training and classification. Convert the voting results of the random forest into evidence, use the proportion of the number of votes to the total number of decision trees as the basic probability distribution BPA, and use three diagnostic units to obtain three groups of evidence. The step 3 is specifically implemented according to the following steps: Step 3.1, select the sample entropy of the first three IMF components in step 2 to form a feature vector, input the feature vector into the trained random forest classifier and obtain the voting results of various faults; Step 3.2: Assume that there are l types of faults that need to be classified and identified, and the total number of decision trees of the random forest classifier is N. t , let θ g represents the g-th fault, g = 1, 2, ..., l, and the fault identification framework is expressed as θ = (θ1, θ2, ..., θ g ), use v g Indicates the fault θ when random forest is used for classification g The number of votes is expressed as m(θ g ) indicates fault θ g The basic probability allocation BPA of the random forest is that all decision trees vote for each fault, so we get: in To identify the empty set in the frame, if we set: Can launch: Combining equations (6) and (8), we can get m(θ g ) is the fault θ g BPA, of which is the proportion of the number of votes for the fault type to the total number of decision trees; Step 3.3: Combine EMD and sample entropy with random forest as a diagnostic unit. Each diagnostic unit performs independent diagnosis. Use three diagnostic units to diagnose the fault. The first diagnostic unit obtains the fault θ g The BPA is m1(θ g ), the fault θ is obtained by the second diagnosis unit g The BPA is m2(θ g ), the fault θ is obtained by the third diagnostic unit g The BPA is m3(θ g ), and finally m1(θ g )、m2(θ g )、m3(θ g ) as three groups of evidence integrated by DS evidence theory; Step 4: Fusion of multi-source evidence information. First, based on the three groups of evidence obtained, calculate the distance between each two groups of evidence, and determine the mutual support matrix between the evidences based on the distance. Use the eigenvector corresponding to the maximum eigenvalue in the evidence support matrix as the weight vector of the evidence. Then determine the relative discount factor of each piece of evidence, correct the evidence information, fuse it using the DS rule, calculate the fused BPA, and finally make a decision to obtain the fault classification result.

2. A rolling bearing fault diagnosis method based on DS evidence theory according to claim 1, characterized in that: The step 2 is specifically implemented according to the following steps: Step 2.1: Use EMD to decompose the original vibration signal into multiple IMF components. Sample an IMF component with N points. The time series formed after sampling is: X(k)={x(1),x(2),…,x(k),…,x(N)}, where k=1,2,…,N, select n consecutive data points in X(k) to form a window subsequence X n (i) = {x(i), x(i+1), ..., x(i+n-1)}, and get the window subsequence X n The number of (i) is N-n+1, ​​i.e., i=1,2,...,N-n+1; Step 2.2: Define two window subsequences X n (i) With X n (j) The distance d[X n (i),X n (j)] is X n (i) With X n (j) corresponds to the absolute value of the maximum difference of the data points, that is: d[X n (i),X n (j)]=max[X n (i+b)-X n (j+b)] (1) Where b = 0, 1, 2, ... n-1; Step 2.3: Given a threshold r, calculate each window subsequence X n (i) The distances with other window subsequences, a total of Nn, count the number of distances less than the threshold r and calculate their proportion in the total number of Nn distances for: In the formula, count{*} represents the number of statistics that meet the conditions; j = 1, 2, ... N-n+1 and j≠i, that is, the values ​​of j and i cannot be the same in the same value range; Step 2.4: For each window subsequence X n (i) All calculated And find the average value B n (r) is: Step 2.5: Increase the length of the window subsequence from n to n+1, repeat step 2.4, and calculate the average value B when the sequence length is n+1 n+1 (r) is: Step 2.6: Calculate the sample entropy SampEn(n,r,N) of an IMF component as: Step 2.7: Repeat steps 2.1 to 2.6 to calculate the sample entropy of the remaining multiple IMF components.

3. A rolling bearing fault diagnosis method based on DS evidence theory according to claim 2, characterized in that: The step 4 is specifically as follows: Step 4.1: Based on the three sets of evidence m1(θ obtained in step 3 g )、m2(θ g )、m3(θ g ), first calculate the distance between the three groups of evidence, the calculation formula is as follows: In the formula <m1(θ g ),m2(θ g )> is m1(θ g ) and m2(θ g ), <m1(θ g ),m3(θ g )> is m1(θ g ) and m3(θ g ), <m2(θ g ),m3(θ g )> is m2(θ g ) and m3(θ g ), ||m1(θ g )|| 2 = <m1(θ g ),m1(θ g )>,||m2(θ g )|| 2 = <m2(θ g ),m2(θ g )>,||m3(θ g )|| 2 = <m3(θ g ),m3(θ g )>; Step 4.2: Determine the consistency between the evidences based on the distance between the two pieces of evidence, also known as mutual support, which is: [sup] a,b =1-d(m a (i g ),m b (i g )) (12) Where a, b = 1, 2, 3, so the 3×3 dimensional mutual support matrix S of the evidence is: Where S a,b Indicates evidence m a (θ g ) and evidence m b (θ g ) is similar to S a,b =S b,a , so S is a symmetric matrix; Step 4.3: Assume the weight coefficient of the evidence of group a is β a , a=1,2,3, then lb a =β1S 1,a +β2S 2,a +β3S 3,a (14) Where λ is the proportionality coefficient, let β = (β1, β2, β3) T , then from formula (14) we can get: λβ=S T b (15) Since S is a symmetric matrix, that is, S T =S, so λ is the eigenvalue of the S matrix, and β is its corresponding eigenvector; Step 4.4: Select the evidence with the largest weight coefficient, i.e. the most credible evidence, as the key evidence. Its weight coefficient β max for: b max =max(β1,β2,β3) (16) Where β1, β2 and β3 are the weight coefficients of the first, second and third groups of evidence respectively, and then the relative weight vector β of each evidence is obtained * for: β * ＝[β1,β1,β3] / β max (17) The discount factor α is thus determined for the basic probability distribution of the evidence group a. a for: The basic probability distribution value of the evidence is modified according to the discount factor. The basic probability distribution value of the evidence in group a after modification is for: Where m a (θ g ) assigns a value to the basic probability of the a-th group of evidence; Step 4.5, there are l types of faults, namely θ1, θ2, ..., θ l According to the DS fusion rule, the corrected first set of evidence and the corrected second set of evidence are first fused to obtain the first fusion result. for: Where p,q=1,2,...,l, Assign values ​​to the basic probabilities of the first set of evidence after correction, is the basic probability distribution value of the second group of evidence after correction. Then the first fusion result and the basic probability distribution value of the third group of evidence after correction are fused to obtain the second fusion result. for: Where p,q=1,2,...,l, Assign values ​​to the base probabilities of the first fusion of evidence, Assign values ​​to the base probabilities of the revised third set of evidence; Make a decision based on the result of the second fusion. where g=1,2,...,l, so They represent the probabilities of type 1, type 2, …, and type l faults respectively. The size of each probability is compared, and the fault type with the highest probability is taken as the final diagnosis result.

Images