Bearing fault diagnosis method based on interpolation multi-scale extension permutation entropy

Abstract

The invention discloses a bearing fault diagnosis method based on interpolation multi-scale extension permutation entropy, and relates to the technical field of bearing fault diagnosis, and the method comprises the following steps: 1, collecting time domain vibration signals of a bearing under different working conditions through a sensor; step 2, interpolating multiple scales, carrying out coarse graining on each sample according to a scale factor s to obtain s sub-signals, and carrying out interpolation on each sub-signal in an interpolation interval by utilizing radial basis function interpolation; 3, calculating extended permutation entropies of all sub-signals after each sample is interpolated into multiple scales, wherein the extended permutation entropies of all sub-sequences form a feature vector; 4, designing an extreme learning machine classifier; and 5, classifying test set samples by using the trained extreme learning machine classifier to obtain a fault diagnosis result. According to the bearing fault diagnosis method based on the interpolation multi-scale extension permutation entropy, the bearing fault information can be extracted more comprehensively, and the accuracy of bearing fault diagnosis can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of bearing fault diagnosis, and in particular to a bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy. Background Art

[0002] As a key component in mechanical systems, bearings play a crucial role in supporting rotating components and transmitting loads, and are indispensable in many core fields such as wind power generation and transportation. However, in actual applications, bearings need to work continuously for a long time, and in this process, wear, corrosion, cracks, and even spalling are inevitable, resulting in bearing failures. Especially for key parts such as the inner ring, outer ring, and rolling elements of bearings, once damaged, it will seriously threaten the reliability and stability of the entire equipment. Therefore, it is of great importance to take scientific and efficient means to diagnose bearing faults in a timely and accurate manner. This not only concerns the safe and stable operation of the equipment, but also directly affects the stability and efficiency of the entire production process.

[0003] With the continuous innovation of fault diagnosis technology, bearing fault diagnosis has entered a new stage of development. At present, the main technical means of bearing fault diagnosis include machine learning, time-domain analysis, frequency-domain analysis, and modern signal processing methods. Machine learning methods need to comprehensively consider various operating parameters and build accurate mathematical models in the absence of sufficient experience and data support. However, with the increasing complexity of the model and the expansion of the number of parameters, the model may encounter the challenge of overfitting, thus weakening its prediction and generalization ability on new data. Bearing fault signals often exhibit complex non-linear characteristics, which makes it difficult for traditional linear fault diagnosis techniques to accurately identify fault types. Therefore, a variety of non-linear dynamic characteristic quantities are introduced to improve the accuracy of diagnosis, including correlation dimension, approximate entropy, maximum Lyapunov exponent, and permutation entropy. Among these characteristic quantities, permutation entropy not only has a fast calculation speed, but also shows higher efficiency in distinguishing different fault modes.

[0004] As a classical non-linear dynamic measure, permutation entropy is often used to detect the dynamic changes of signals. However, it ignores the differences within the permutation patterns, resulting in inaccurate estimation of complexity dynamics. To address this problem, cosine similarity is used to expand the permutation patterns, and extended permutation entropy is proposed to enhance the accuracy of permutation entropy. In addition, in this study, interpolation multi-scale is introduced into the extended permutation entropy, and interpolation multi-scale extended permutation entropy is proposed to extract the characteristics of bearing signals at different time scales and comprehensively characterize their fault characteristics. Summary of the Invention

[0005] The object of the present invention is to provide a bearing fault diagnosis method based on interpolated multi-scale extended permutation entropy, which can extract bearing fault information more comprehensively and effectively improve the accuracy of bearing fault diagnosis.

[0006] To achieve the above object, the present invention provides a bearing fault diagnosis method based on interpolated multi-scale extended permutation entropy, including the following steps:

[0007] Step 1: Use a sensor to collect the time-domain vibration signals of the bearing under different working conditions. Divide each signal into M samples, each sample has a length of N, and there are a total of 5M samples;

[0008] Step 2: Interpolated multi-scale. Coarsen each sample according to the scale factor s to obtain s sub-signals. Use radial basis function interpolation to interpolate each sub-signal with the interpolation interval;

[0009] Step 3: Calculate the extended permutation entropy of all sub-signals after interpolated multi-scale for each sample. The extended permutation entropy values of all subsequences form a feature vector;

[0010] Step 4: Design of an extreme learning machine classifier. Randomly select the feature vectors of some samples as the training set samples of the extreme learning machine classifier, and the remaining samples as the test set samples of the classifier;

[0011] Step 5: Bearing fault diagnosis. Use the trained extreme learning machine classifier to classify the test set samples to obtain the fault diagnosis result.

[0012] Preferably, the interpolated multi-scale extended permutation entropy in step 2 includes the following steps:

[0013] S1. For a signal x = {x(i), i = 1, 2,..., N} with a length of N, the sub-signal obtained by coarsening at scale s is defined as:

[0014]

[0015] In the formula, represents rounding down, and s represents the scale factor;

[0016] S2. Divide into n subsequences according to the interpolation interval R

[0017] The nth subsequence The position index I of the interpolation points n , is as follows:

[0018]

[0019] S3. According to the nth subsequence and the position index I of its interpolation points j,n , obtain the radial basis function interpolation subsequence which is defined as follows:

[0020]

[0021] The interpolated multiscale signal at scale s. The interpolated multiscale signal consists of all and is defined as follows:

[0022]

[0023] S4. Calculate the extended permutation entropy value of Y s to obtain the interpolated multiscale extended permutation entropy value at this scale, which is defined as follows:

[0024] IMEPE(x, m, τ, s, R) = EPE(Y s , m, τ).

[0025] Preferably, the radial basis function interpolation function corresponding to the nth subsequence is as follows:

[0026]

[0027] where: λ i is the coefficient to be determined, and φ(x) is the Gaussian kernel function, which is as follows:

[0028]

[0029] Preferably, the extended permutation entropy described in step three is an improvement of the permutation entropy, and the specific steps are as follows:

[0030] S31. Perform phase space reconstruction on the signal x to obtain its phase space reconstruction matrix X. The reconstruction formula of X is as follows:

[0031]

[0032] where x = {x(i), i = 1, 2,..., N}; m is the embedding dimension, τ is the delay time constant, and k is the number of row vectors of the reconstruction matrix X, k = N - (m - 1)τ;

[0033] S32. Sort the elements of each row of the matrix X in ascending order as follows:

[0034] x(i + (j1 - 1)τ) < x(i + (j2 - 1)τ) < … < x(i + (j m - 1)τ);

[0035] where \(i\in(1,k)\), \(j_1,j_2,j_3,\cdots,j\) m is the index of the column where the element is located;

[0036] The symbol sequence of the \(k\)-th row of matrix \(X\) is as follows:

[0037] \(y(k)=[j_1,j_2,\cdots,j\) m ;

[0038] S33. Convert \(y(k)\) into a specific permutation pattern \(s(k)\), and there are \(m!\) patterns;

[0039] S34. The patterns corresponding to each \(y(k)\) will be arranged row by row to obtain a pattern matrix \(S\) of length \(k\),

[0040] \(S = [s(1),s(2),\cdots,s(k)]\);

[0041] S35. Calculate the cosine similarity matrix \(D = [d_1,d_2,\cdots,d\) u between adjacent row vectors in the phase space reconstruction matrix \(X\), and its specific expression is:

[0042]

[0043] where \(X\) u \cdot X u+1 represents the inner product of \(X\) u and \(X\) u+1 ;

[0044] S36. Convert the sequence \(D\) into a matrix \(\Delta = [g_1,g_1,\cdots,g\) u through the rounding function, and then supplement \(\Delta\) to \(S\) as an extended pattern to generate the pattern matrix \(P\);

[0045] S37. Count the probability of each pattern appearing in \(P\), and the normalized EPE is defined as follows:

[0046]

[0047] where \(x\) is the input signal, \(m\) represents the embedding dimension, \(\tau\) represents the delay time constant, and \(Probability(P = i)\) represents the probability of pattern \(i\) appearing in the pattern matrix \(P\).

[0048] Preferably, if two elements in the same row of matrix \(X\) in S32 have equal values, they are sorted according to their indices as follows:

[0049] \(x(i+(j_1 - 1)\tau)\leq x(i+(j_2 - 1)\tau)\).

[0050] Preferably, the extended pattern \(g\) u and the pattern matrix \(P\) are defined as:

[0051] g u = round(m!d u + 0.5);

[0052] P = {S, Δ};

[0053] In the formula, round() represents the rounding function, and {S, Δ} represents the row-wise concatenation of matrix S and matrix Δ.

[0054] Preferably, the extended permutation entropy values of all subsequences form a feature vector:

[0055] EPE = [EPE1, EPE2, …, EPE s ;

[0056] In the formula, EPE s is the EPE value of the sth sub-signal. Repeat steps 1 to 3 to obtain the feature vectors of all samples and form a feature set of 5M × s.

[0057] Therefore, the present invention adopts the above-mentioned bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy. Based on permutation entropy, combined with cosine similarity and interpolation multi-scale, a bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy is proposed. The identification of different bearing fault modes is realized, and fault feature information is obtained more comprehensively from multiple scales, improving the identification accuracy of traditional permutation entropy for bearing faults.

[0058] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a flowchart of a bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy of the present invention;

[0060] Figure 2 are five bearing signal diagrams of the present invention. (a) is a rolling element fault, (b) is an inner raceway fault, (c) is an outer raceway fault, (d) is a combined inner and outer raceway fault, and (e) is healthy;

[0061] Figure 3 is a bearing fault feature distribution diagram of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0062] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0063] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings as understood by those of ordinary skill in the field to which the present invention pertains. The "first", "second" and similar terms used in the present invention do not denote any order, quantity or importance, but are only used to distinguish different components. Words such as "comprising" or "including" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Upper", "lower", "left", "right", etc. are only used to represent relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0064] Embodiment

[0065] Please refer to Figures 1-3 , the present invention provides a bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy, including the following steps:

[0066] Step 1: Collect the time-domain vibration signals of the bearing under different working conditions, use sensors to collect the time-domain vibration signals of rolling element faults, inner raceway faults, outer raceway faults, combined inner and outer raceway faults, and healthy conditions, and intercept the data of the first ks duration of each signal as the original signal, and divide the signal into n samples, and the signal duration of each sample Divide each type of signal into M samples, each sample has a length of N, for a total of 5M samples.

[0067] Step 2: Interpolation multi-scale, coarsen each sample according to the scale factor s to obtain s sub-signals, and use radial basis function interpolation to interpolate each sub-signal with the interpolation interval.

[0068] S1. For a signal x = {x(i), i = 1, 2,..., N} with a length of N, the sub-signal obtained by coarsening at scale s is defined as:

[0069]

[0070] In the formula, represents rounding down, and s represents the scale factor.

[0071] S2. According to the interpolation interval R, is divided into n sub-sequences

[0072] The radial basis function interpolation function corresponding to the nth sub-sequence is as follows:

[0073]

[0074] Where: λ i is the coefficient to be determined, and φ(x) is the Gaussian kernel function, as follows:

[0075]

[0076] The nth subsequence The position index I of the interpolation point n , as follows:

[0077]

[0078] S3. According to the nth subsequence and its position index I of the interpolation point j,n , obtain the radial basis function interpolation subsequence Defined as follows:

[0079]

[0080] The interpolation multi-scale signal at scale s The interpolation multi-scale signal consists of all and is defined as follows:

[0081]

[0082] S4. Calculate the extended permutation entropy value of Y s to obtain the interpolation multi-scale extended permutation entropy value at this scale, defined as follows:

[0083] IMEPE(x,m,τ,s,R) = EPE(Y s ,m,τ);

[0084] Step 3. Calculate the extended permutation entropy of all sub-signals after interpolation multi-scale for each sample. The extended permutation entropy values of all subsequences form a feature vector:

[0085] EPE = [EPE1, EPE2,..., EPE s ;

[0086] Where, EPE s is the EPE value of the sth sub-signal. Repeat steps 1 to 3 to obtain the feature vectors of all samples and form a 5M×s feature set.

[0087] S1. For a signal x = {x(i), i = 1, 2,..., N} with length N, perform phase space reconstruction to obtain its phase space reconstruction matrix X. The reconstruction formula of X is as follows:

[0088]

[0089] Wherein, m is the embedding dimension, τ is the delay time constant, k is the number of row vectors of the reconstruction matrix X, and k = N - (m - 1)τ.

[0090] S2. Sort the elements of each row of the matrix X in ascending order as follows:

[0091] x(i + (j1 - 1)τ) < x(i + (j2 - 1)τ) < … < x(i + (j m - 1)τ);

[0092] Wherein, i ∈ (1, k), and j1, j2, j3, …, j m are the indices of the columns where the elements are located. If the values of two elements in the same row are equal, for example:

[0093] x(i + (j1 - 1)τ) = x(i + (j2 - 1)τ), j1 < j2;

[0094] then they are sorted according to their indices as follows:

[0095] x(i + (j1 - 1)τ) ≤ x(i + (j2 - 1)τ);

[0096] The symbol sequence of the k-th row of the matrix X is as follows:

[0097] y(k) = [j1, j2, …, j m ;

[0098] The symbol matrix Y composed of all y(k) is defined as:

[0099]

[0100] S3. Convert y(k) into a specific permutation pattern s(k), and there are m! patterns. For example, when the embedding dimension m is 3, the types of permutation patterns do not exceed 3! = 6. Among them, the symbol sequence [1, 2, 3] corresponds to the permutation pattern 1, the symbol sequence [1, 3, 2] corresponds to the permutation pattern 2, the symbol sequence [2, 1, 3] corresponds to the permutation pattern 3, the symbol sequence [2, 3, 1] corresponds to the permutation pattern 4, the symbol sequence [3, 1, 2] corresponds to the permutation pattern 5, and the symbol sequence [3, 2, 1] corresponds to the permutation pattern 6. When the embedding dimension m is set to other values, the corresponding relationship of the permutation patterns is similar.

[0101] S4. After the permutation pattern conversion in step 3, the patterns corresponding to each y(k) will be arranged in rows to obtain a pattern matrix S with a length of k, and all elements are integers between 1 and m!.

[0102] S = [s(1), s(2), …, s(k)];

[0103] S5. Calculate the cosine similarity matrix D = [d1, d2, …, d u between adjacent row vectors in the phase space reconstruction matrix X, which can be specifically expressed as:

[0104]

[0105] where X u ·X u+1 denotes the inner product of X u and X u+1 .

[0106] S6. Convert the sequence D into a matrix Δ = [g1, g1, …, g u through the rounding function, and then supplement Δ as an extended pattern to S to generate the pattern matrix P. The extended pattern g u and the pattern matrix P are defined as:

[0107] g u = round(m!d u + 0.5);

[0108] P = {S, Δ};

[0109] where round() represents the rounding function, and {S, Δ} represents the row-wise concatenation of matrix S and matrix Δ.

[0110] S7. Statistically analyze the probability of each pattern appearing in P. The normalized EPE is defined as follows:

[0111]

[0112] where x is the input signal, m represents the embedding dimension, τ represents the delay time constant, and Probability(P = i) represents the probability of pattern i appearing in the pattern matrix P.

[0113] Step 4. Design of the extreme learning machine classifier. For each type of bearing signal, randomly select the feature vectors of some samples from the feature set in Step 3 as the training set samples of the extreme learning machine classifier, and the remaining samples as the test set samples of the classifier; input the training set samples into the extreme learning machine for training, and use the trained extreme learning machine classifier to test the test set samples.

[0114] Step 5. Bearing fault diagnosis. Use the trained extreme learning machine classifier to classify the test set samples to obtain the fault diagnosis results.

[0115] Example 1

[0116] Step 1. Use the Southeast Bearing Dataset to verify the effectiveness of the proposed method. Select five types of bearing signals with a diameter of 0.1778 mm and a rotational speed - load configuration set to 20 HZ - 0 V, including healthy, rolling element fault, inner raceway fault, outer raceway fault, and combined inner and outer raceway faults. Each type of bearing signal has 100 samples, and each sample contains 1024 sampling points. The rolling bearing signals in the five normalized states are as Figure 1 shown.

[0117] Step 2. Interpolate the multi - scale, and decompose each sample of the five types of bearing signals into 10 sub - signals.

[0118] Step 3. Calculate the extended permutation entropy value of each sub - signal and establish a feature vector. In this embodiment, the embedding dimension is 3, and the time delay constant is 1. After calculating the extended permutation entropy of all scales, they are combined into a feature vector. IMEPE =

[0119] [IMEPE1, IMEPE2, …, IMEPE s forms a vector, where s is the number of scales.

[0120] Step 4. Design the extreme learning machine classifier. Each type of bearing signal has 100 samples. Randomly select the feature vectors of 50 samples as the training samples of the extreme learning machine classifier, and the feature vectors of the remaining 50 samples as the test samples. Input the training set sample features into the multi - fault classifier based on the extreme learning machine for training, and use the trained extreme learning machine classifier to test the test samples.

[0121] Step 5. Fault diagnosis. Input the validation set features, and obtain the fault diagnosis results through the extreme learning machine classification. At this time, the highest recognition rate is 100%. The distribution of the feature vectors with a scale of 1 for all samples of each type of bearing signal is as Figure 2 shown, and the recognition rates of the interpolated multi - scale extended permutation entropy for bearing faults are shown in Table 1.

[0122] Table 1 Recognition rates of the interpolated multi - scale extended permutation entropy for bearing faults

[0123]

[0124] Therefore, the present invention adopts the above - mentioned bearing fault diagnosis method based on interpolated multi - scale extended permutation entropy. On the basis of permutation entropy, combined with cosine similarity and interpolated multi - scale, a bearing fault diagnosis method based on interpolated multi - scale extended permutation entropy is proposed. It realizes the recognition of different bearing fault modes, obtains more comprehensive fault feature information from multiple scales, and improves the recognition accuracy of traditional permutation entropy for bearing faults.

[0125] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy, characterized in that: The following steps are involved: Step 1: Use sensors to collect time domain vibration signals of bearings under different working conditions, and divide each signal into M samples, each sample length is N, and a total of 5M samples; Step 2: interpolation multi-scale, coarsening each sample according to the scale factor s to obtain s sub-signals, and using radial basis function interpolation to interpolate each sub-signal in the interpolation interval; Step 3: Calculate the extended permutation entropy of all sub-signals after each sample is interpolated and multi-scaled, and the extended permutation entropy values ​​of all sub-sequences constitute a feature vector; Step 4: Design an extreme learning machine classifier. Randomly select the feature vectors of some samples as the training set samples of the extreme learning machine classifier, and the remaining samples as the test set samples of the classifier. Step 5: Bearing fault diagnosis: Use the trained extreme learning machine classifier to classify the test set samples and obtain the fault diagnosis results.

2. A bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy according to claim 1, characterized in that: The interpolation multi-scale extended permutation entropy in step 2 includes the following steps: S1. For a signal x={x(i),i=1,2,...,N} of length N, coarse-graining is performed to obtain a sub-signal of scale s. Defined as: In the formula, represents rounding down, and s represents the scale factor; S2, according to the interpolation interval R Divide into n subsequences The nth subsequence The position index of the interpolation point I n , as shown below: S3, according to the nth subsequence and the position index of its interpolation point I j,n , get the radial basis function interpolation subsequence The definition is as follows: The interpolated multiscale signal at scale s is composed of all Composition, defined as follows: S4. Calculate Y s The extended permutation entropy value of is used to obtain the interpolated multi-scale extended permutation entropy value at this scale, which is defined as follows: IMEPE(x,m,τ,s,R)=EPE(Y s ,m,τ).

3. A bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy according to claim 2, characterized in that: The radial basis function interpolation function corresponding to the nth subsequence As shown below: Where: i is the coefficient to be determined, φ(x) is the Gaussian kernel function, as shown below:

4. A bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy according to claim 3, characterized in that: The extended permutation entropy described in step 3 is an improvement on the permutation entropy. The specific steps are as follows: S31. Reconstruct the phase space of the signal x to obtain its phase space reconstruction matrix X. The reconstruction formula of X is as follows: Where x = {x(i), i = 1, 2, ..., N}; m is the embedding dimension, τ is the delay time constant, k is the number of row vectors of the reconstruction matrix X, k = N-(m-1)τ; S32. Sort the elements of each row of the matrix X in ascending order as follows: x(i+(j1-1)τ) <x(i+(j2-1)τ)<…<x(i+(j m -1)t); Where i∈(1,k), j1,j2,j3,…,j m is the index of the column where the element is located; The symbol sequence of the k-th row of matrix X is as follows: y(k)=[j1,j2,…,j m ]; S33, convert y(k) into a specific arrangement pattern s(k), there are m! patterns; S34. The patterns corresponding to each y(k) will be arranged in rows to obtain a pattern matrix S of length k. S = [s(1), s(2), ..., s(k)]; S35, calculate the cosine similarity matrix D = [d1, d2, ..., d u ], which can be specifically expressed as: Where, X u ·X u+1 Represents X u and X u+1 The inner product of S36, convert the sequence D into a matrix Δ=[g1,g1,…,g u ], and then add Δ to S as an extended pattern to generate the pattern matrix P; S37. Count the probability of each pattern in P. The normalized EPE is defined as follows: Wherein, x is the input signal, m represents the embedding dimension, τ represents the delay time constant, and Probability(P=i) represents the probability of occurrence of pattern i in the pattern matrix P.

5. The bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy according to claim 4 is characterized in that: In S32, if two elements in the same row of matrix X have the same value, they are sorted according to their indexes as follows: x(i+(j1-1)τ)≤x(i+(j2-1)τ).

6. A bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy according to claim 5, characterized in that: S36 Extended Mode g u And the pattern matrix P is defined as: g u =round(m!d u +0.5); P = {S, Δ}; Where round() represents the rounding function, and {S,Δ} represents the concatenation of matrix S and matrix Δ by rows.

7. A bearing fault diagnosis method based on interpolation multi-scale extended permutation entropy according to claim 6, characterized in that: The extended permutation entropy values ​​of all subsequences constitute the feature vector: EPE=[EPE1,EPE2,…,EPE s ]; Where, EPE s is the EPE value of the sth sub-signal, and steps 1 to 3 are repeated to obtain the feature vectors of all samples and form a 5M×s feature set.

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