Fault diagnosis method for aircraft engine bearings based on spectral wavelet transform and multi-scale permutation entropy

Abstract

The present invention discloses an aero-engine bearing fault diagnosis method based on spectral wavelet transform and multi-scale permutation entropy, which converts the collected original vibration signal of the test piece into a horizontal visible graph; decomposes the horizontal visible graph into scale coefficients and spectral wavelet coefficients by using spectral wavelet transform, and performs denoising; calculates the multi-scale permutation entropy of the test piece based on the denoised signal, and uses it as the health status index of the test piece; calculates the Mahalanobis distance of the test piece under different health states based on the health status index set under different health states, and diagnoses the aero-engine bearing fault according to the Mahalanobis distance. The present invention can effectively diagnose different health states and different fault levels of the bearing, and the method has good noise resistance and high robustness, provides a higher accuracy rate for the fault diagnosis result of the bearing, realizes the accurate diagnosis of the fault type of the aero-engine bearing, and can effectively monitor the engine rotor bearing fault.

Description

Technical Field

[0001] The invention belongs to the field of aircraft engine fault detection, relates to aircraft engine fault detection technology, and in particular to an aircraft engine bearing fault diagnosis method based on spectral wavelet transform and multi-scale permutation entropy. Background Art

[0002] Bearings are a key component in rotating machinery, playing an important role in transmitting speed and load. Their health directly affects the safe operation of the entire mechanical equipment. Modern aerospace turbine engine rotor systems usually use intermediate main bearings, which work in high-speed, high-load, and high-temperature environments for a long time, and the working load varies greatly. During operation, they are prone to fatigue peeling, pitting, wear and other failures. When a bearing fails, the damaged point and other parts in contact with it collide repeatedly, which will produce impact vibration. Once the situation is serious, it will cause functional failure of the rotating machinery, economic losses or casualties.

[0003] As one of the core components of an aircraft, the stable operation and high-efficiency performance of an aircraft engine are important guarantees for flight safety. Due to the long-term operation of aircraft engines, the bearings therein will be subject to various forms of wear and damage, which will have a serious impact on the operation of the aircraft and endanger flight safety. At present, the industry needs a highly efficient aircraft engine bearing fault detection technology to monitor the working status of the aircraft engine in real time, diagnose faults in a timely manner, and prevent and avoid potential problems. At the same time, the application of high-efficiency bearing fault detection technology can also effectively improve the maintenance efficiency of aircraft engines, shorten the maintenance cycle, and improve the efficiency and safety of aircraft use. Therefore, aircraft engine bearing fault detection technology plays an important role and significance in ensuring aviation safety, improving aircraft performance, and reducing maintenance costs.

[0004] The bearings in aircraft engines are installed on the internal shaft of the rotor system, and the vibration signals need to be collected through the vibration sensor array on the outer duct casing. However, due to the complex assembly structure and the long transmission path between the bearing seat and the vibration sensor, the vibration signal will be greatly attenuated during the collection process. At the same time, there are complex structures such as elastic supports with oil film damping and thin-walled casings inside the aircraft engine, which will have a strong shock-absorbing effect on the vibration signal.

[0005] Therefore, it is difficult for existing bearing vibration fault detection methods to accurately diagnose aircraft engine bearing faults. Summary of the invention

[0006] In view of this, the purpose of the present invention is to address the problem in the prior art that the vibration signal attenuation is large and has a great impact on the detection of aircraft engine bearing faults. An aircraft engine bearing fault diagnosis method based on spectral wavelet transform and multi-scale permutation entropy is provided. By performing graph signal processing and threshold denoising on the fault signal and obtaining the health status index of the bearing, effective diagnosis of aircraft engine faults can be achieved.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions to achieve it.

[0008] The invention provides an aero-engine bearing fault diagnosis method based on spectral wavelet transform and multi-scale permutation entropy, comprising the following steps:

[0009] S1 converts the collected original vibration signal of the test piece into a horizontal visible graph;

[0010] S2 uses spectral wavelet transform to decompose the horizontal visible graph into scale coefficients and spectral wavelet coefficients, and performs denoising; specifically, it includes the following sub-steps:

[0011] S21 uses spectral wavelet transform to decompose the horizontal visible graph and obtain scale coefficients and spectral wavelet coefficients;

[0012] S22 performs filtering on the spectrum wavelet coefficients based on the adaptive threshold method of wavelet coefficients;

[0013] S23 performs inverse spectral wavelet transform using the scale coefficient and the filtered spectral wavelet coefficient to obtain a denoised signal;

[0014] S3 calculates the multi-scale permutation entropy of the device under test based on the denoised signal in step S2, and uses it as a health status indicator of the device under test;

[0015] S4 calculates the Mahalanobis distance of the test piece under different health states based on the health state indicator set under different health states, and diagnoses the aircraft engine bearing fault according to the Mahalanobis distance.

[0016] In the above step S1, the specific implementation method is: map the collected one-dimensional original vibration signal into a two-dimensional matrix, and then use each element of the two-dimensional matrix clock as a node in the graph, and use the Euclidean distance between two nodes as the weight of the edge between the corresponding two nodes, so as to obtain an undirected weighted graph, that is, a horizontal visible graph; through this method, the information in the one-dimensional time series is stored in the matrix form of the graph, and the time series signal is analyzed in the form of a horizontal visible graph. Then, based on the graph theory, the graph matrix representation is obtained, including the adjacency matrix, the degree diagonal matrix and the Laplace matrix, and the eigenvalues ​​and eigenvectors of the Laplace matrix are obtained.

[0017] In the above step S2, the horizontal visibility graph obtained in S1 is denoised using the time series signal threshold denoising method of spectral wavelet transform.

[0018] In the above step S21, the present invention uses the conventional spectral wavelet transform method disclosed in the art to decompose the horizontal visible graph into scale coefficients and spectral wavelet coefficients; first, the spectral wavelet kernel function, scale function kernel, scale parameter, decomposition level and spectral wavelet operator corresponding to the scale parameter used in the spectral wavelet transform are set. The spectral wavelet kernel function, scale function kernel, scale parameter and spectral wavelet operator corresponding to the scale parameter are defined according to the eigenvalues ​​of the Laplace matrix. The decomposition level can be determined according to the signal-to-noise ratio.

[0019] The horizontal visualization image is decomposed into several sub-bands using spectral wavelet transform to obtain the scale coefficient and spectral wavelet coefficient of the image signal (the first sub-band is the scale coefficient, and the remaining sub-bands are the spectral wavelet coefficients corresponding to the scale parameters).

[0020] In the above step S22, based on the adaptive threshold method of wavelet coefficients, the wavelet coefficients of the spectrum are filtered, mainly including nonlinear trend removal and shrinkage; the specific process is as follows:

[0021] (1) The wavelet coefficient W at the jth scale j Identify all local extreme values ​​in , j = 1, 2, ..., J, J is the total number of selected scales;

[0022] (2) Obtain the wavelet coefficient vector W at the jth scale j The upper envelope of En u and the lower envelope En l ;

[0023] (3) Eliminate W j The nonlinear trend in the free nonlinear wavelet coefficients

[0024] (4) The four thresholds are calculated by the following formula The wavelet coefficients are divided into five regions

[0025]

[0026] in, and Respectively The positive and negative wavelet coefficients in; med(·) represents the median operation; erfc -1 (·) represents the inverse complementary error function; std(·) is the standard deviation;

[0027] (5) Calculate the wavelet coefficient W of the shrunken spectrum according to the following formulaj ′:

[0028]

[0029] Where W′ j，k W′ j The kth wavelet coefficient in; exp(·) represents the exponential operation; θ represents the parameter for identifying the rate of change of the transition zone coefficient ( and ), θ is set to 5.

[0030] In the above step S3, the calculation method of the multi-scale permutation entropy is implemented by a conventional method disclosed in the art. The optimal multi-scale permutation entropy parameter used in the present invention is obtained by optimizing the differential evolution algorithm.

[0031] In the above step S4, the Mahalanobis distance of the test piece in different health states is:

[0032]

[0033] Where D is the health status indicator of the device under test, D t is the health status indicator set under the t-th health status, t = 1, 2, ..., T, T represents the number of health status, mean (D t ) and var(D t ) means D t The mean and variance of .

[0034] D t It is obtained by calculating the multi-scale permutation entropy of several samples in the tth health state.

[0035] Compared with the prior art, the aircraft engine bearing fault diagnosis method based on spectral wavelet transform and multi-scale permutation entropy provided by the present invention has the following beneficial effects:

[0036] (1) The present invention utilizes the mapping relationship between one-dimensional time series signals and horizontal visibility graphs, and combines the spectral wavelet transform to perform denoising. The spectral wavelet threshold denoising method used provides a new approach for multi-scale analysis and denoising of one-dimensional time series signals.

[0037] (2) The present invention aims at the problem that the wavelet coefficients of the spectrum have nonlinear trends, especially in the case of strong background noise. In the wavelet threshold denoising method of the spectrum, free nonlinear wavelet coefficients are used to replace the wavelet coefficients to achieve nonlinear trend removal.

[0038] (3) In order to solve the problem of excessive dependence of multi-scale permutation entropy on its parameters, the present invention introduces a differential evolution algorithm to iteratively optimize its key parameters, which provides a new idea for the application of multi-scale permutation entropy in the field of bearing fault diagnosis.

[0039] (4) The present invention can effectively diagnose different health states and different fault levels of bearings, and the method has good noise resistance and high robustness, providing a higher accuracy rate for the bearing fault diagnosis results, and realizing accurate diagnosis of aircraft engine bearing fault types. It can effectively monitor engine rotor bearing faults, thereby avoiding major accidents, and has important theoretical reference and military application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The present invention provides a flow chart of an aircraft engine bearing fault diagnosis method based on spectral wavelet transform and optimal multi-scale permutation entropy.

[0041] Figure 2 This is a flowchart of using spectral wavelet threshold denoising in an embodiment of the present invention.

[0042] Figure 3 1 is a vibration signal before and after the spectral wavelet threshold denoising method is used in an embodiment of the present invention; wherein (a) corresponds to the original vibration signal, and (b) corresponds to the vibration signal after the spectral wavelet threshold denoising method is used.

[0043] Figure 4 Result diagram of the noise robustness verification experiment in the embodiment of the present invention. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions of various embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0045] Example

[0046] The present embodiment provides an aero-engine bearing fault diagnosis method based on spectral wavelet transform and multi-scale permutation entropy, such as Figure 1 and Figure 2 As shown, the following steps are included:

[0047] S1 converts the collected original vibration signal of the test piece into a horizontal visual graph.

[0048] S2 uses spectral wavelet transform to decompose the horizontal visibility graph into scale coefficients and spectral wavelet coefficients, and performs denoising;

[0049] S3 calculates the multi-scale permutation entropy of the device under test based on the denoised signal in step S2, and uses it as a health status indicator of the device under test;

[0050] S4 calculates the Mahalanobis distance of the test piece under different health states based on the health state indicator set under different health states, and diagnoses the aircraft engine bearing fault according to the Mahalanobis distance.

[0051] In the above step S1, during the data collection process, the vibration acceleration sensor is installed on the surface of the engine, and the vibration sensor array located at the engine surface casing obtains the aircraft engine bearing fault signal, and the vibration signal is used as the original signal for fault diagnosis. The collected original vibration signal sample data is divided into training data and test data for use in subsequent steps.

[0052] This embodiment uses the bearing vibration signal collected by the Railway Research and Education Center of the University of Birmingham for example verification.

[0053] The collected one-dimensional original vibration signal is mapped into a two-dimensional matrix. For example, a one-dimensional time series consisting of 1024 sampling points is mapped into a 32×32 matrix, and each 32 sample points form a row of the matrix in sequence. Then, each element of the two-dimensional matrix clock is used as a node in the graph to construct an undirected weighted graph. The weight of the edge connecting each node of the undirected weighted graph is calculated by using the Euclidean distance between the two nodes as the weight of the edge between the corresponding two nodes. The calculation formula is as follows:

[0054] a ij =||x i -x j ||;

[0055] In the formula, x i and x j are the values ​​of node i and node j respectively. The defined weight is the Euclidean distance between the two nodes, which truly reflects the difference between the vertices.

[0056] Based on graph theory, we get the graph matrix representation, including the adjacency matrix A, the degree diagonal matrix D and the Laplace matrix L, L = DA. Then we perform standard orthogonal decomposition on L to obtain the eigenvalues ​​{λ l} and the eigenvector u l ,,l=0,1,…,N-1, N is the number of sampling points.

[0057] The above step S2 uses the time series signal threshold denoising method of spectral wavelet transform to denoise the horizontal visibility graph obtained in S1, which specifically includes the following sub-steps:

[0058] S21 uses spectral wavelet transform to decompose the horizontal visibility graph and obtain scale coefficients and spectral wavelet coefficients.

[0059] First, we need to set the spectral wavelet kernel function, scale function kernel, scale parameter, decomposition level and spectral wavelet operator corresponding to the scale parameter used by the spectral wavelet transform.

[0060] (1) Spectral wavelet kernel function g(x)

[0061] g(x)=xe -x ;

[0062] Where x represents the eigenvalue of the Laplace matrix.

[0063] (2) Scale parameter t

[0064] The scale parameter t is given by the upper limit of the Laplace eigenvalue λ max , design parameter K and decomposition layer number J;

[0065] Minimum scale parameter t 1 =1 / λ max , the maximum scale parameter is t J =2 / λ min ,λ min =λ max / K. K ranges from 20 to 30, and in this embodiment, it is 20. J ranges from 5 to 7, and in this embodiment, it is 5.

[0066] Each t satisfies uniform distribution.

[0067] (3) The spectral wavelet operator corresponding to the scale parameter is g(tx).

[0068] (4) Scaling function kernel h(x)

[0069] The scaling function kernel h(x) behaves like a low-pass filter, satisfying h(x)>0 and

[0070]

[0071] In the formula, γ=h(0)=g max .

[0072] Based on the spectral wavelet operator corresponding to the above-mentioned scaling function kernel and scaling parameter, the horizontal visibility graph is subjected to spectral wavelet transform and decomposed into J+1 subbands: the first subband is the scaling coefficient S(n), and the remaining subbands are the spectral wavelet coefficients W(t j , n), as follows:

[0073]

[0074]

[0075] Where n represents the nth node in the horizontal visibility graph; The Fourier transform of the graph representing the horizontal visibility graph, x(n) represents the nth node signal; u l (n) represents the eigenvector u l The nth component, is the eigenvector μ l The complex conjugate of (·).

[0076] S22 uses the adaptive threshold method based on wavelet coefficients to filter the spectrum wavelet coefficients. The specific process is as follows:

[0077] (1) The wavelet coefficient W at the jth scale j Identify all local extreme values ​​in , j = 1, 2, ..., J, J is the total number of selected scales;

[0078] (2) Obtain the wavelet coefficient vector W at the jth scale j The upper envelope of En u and the lower envelope En l ;

[0079] (3) Eliminate W j The nonlinear trend in the free nonlinear wavelet coefficients

[0080] (4) The four thresholds are calculated by the following formula The wavelet coefficients are divided into five regions

[0081]

[0082] in, and Respectively The positive and negative wavelet coefficients in; med(·) represents the median operation; erfc -1 (·) represents the inverse complementary error function; std(·) is the standard deviation;

[0083] (5) Calculate the wavelet coefficient W of the shrunken spectrum according to the following formula j ′:

[0084]

[0085] Where W′ j，k W′ j The kth wavelet coefficient in; exp(·) represents the exponential operation; θ represents the parameter for identifying the rate of change of the transition zone coefficient ( and ), θ is set to 5, J=5.

[0086] S23 performs inverse spectral wavelet transform using the scale coefficient and the filtered spectral wavelet coefficient to obtain a denoised signal. The nodes in the denoised signal are represented by x′(n).

[0087] Figure 3 The original vibration signal (a) and the vibration signal after denoising using the spectrum wavelet threshold method (b) are given. It can be seen from the figure that the noise in the original vibration signal can be effectively removed.

[0088] S3 calculates the multi-scale permutation entropy of the device under test based on the denoised signal in step S2, and uses it as a health status indicator of the device under test.

[0089] The multi-scale permutation entropy is calculated by the following steps:

[0090] S31 performs coarse-graining processing on the denoised signal to obtain a coarse-grained time series

[0091]

[0092] In the formula, s represents the scale factor, N represents the length of the time series, that is, the number of sampling points, and [N / s] represents rounding.

[0093] S32 performs spatial reconstruction on the coarse-grained time series to obtain the qth reconstruction component

[0094]

[0095] Where τ represents the time delay and m represents the embedding dimension.

[0096] S33 takes the qth reconstruction component Each element in is associated with an integer from 1 to m, and arranged in ascending order, we can get m! symbol sequences, among which there are R non-repeating symbol sequences.

[0097] S r =(k 1 , k 2 , ..., k m ), r=1, 2,..., R, R≤m!

[0098] In the formula, k 1 , k 2 , ..., k m The index symbol of the element.

[0099] S34 The probability of each symbol sequence appearing is P r , define the multi-scale permutation entropy Q in the form of Shannon entropype for:

[0100]

[0101] S35 normalizes the multi-scale permutation entropy.

[0102] When P r =1 / m!, the probability of each symbol sequence appearing is equal. At this time, the complexity of the time series is the highest and the entropy is the largest, which is ln(m!). For the convenience of representation, Q is usually pe Normalize it, that is:

[0103]

[0104] Normalized multi-scale permutation entropy Q npe The value range of Q is [0,1], and its size reflects the complexity and randomness of the time series. npe The larger it is, the more random the time series is; conversely, the smaller it is, the more regular the time series is.

[0105] In the process of calculating multi-scale permutation entropy, the selection of parameters is particularly important, including the scale factor s, the embedding dimension m, and the time delay τ. In order to optimize these parameters, the initial value range of these parameters is first given, and then the differential evolution algorithm DE is used to optimize these parameters to obtain the optimal entropy value. For the specific operation of the differential evolution algorithm, see Storn R, Price K. Differential Evolution-A Simple and Efficient Heuristic for global optimization over continuous spaces [J]. Journal of global optimization, 1997, 11 (4): 341.

[0106] The above parameters are optimized by the differential evolution algorithm. Then, according to the optimized parameters, the multi-scale permutation entropy of the test object is determined through steps S31-S35, and used as the health status indicator of the test object.

[0107] S4 calculates the Mahalanobis distance of the test piece under different health states based on the health state indicator set under different health states, and diagnoses the aircraft engine bearing fault according to the Mahalanobis distance.

[0108] Several samples in different health states are obtained; five different health states are given here, as shown in Table 1. Then, the multi-scale permutation entropy of each sample in each health state is calculated according to the steps S31-S35 given above, so as to obtain the corresponding health state indicator set.

[0109] Then, the Mahalanobis distance of the test piece in different health states is calculated according to the following formula:

[0110]

[0111] Where D is the health status indicator of the device under test, D t is the health status indicator set under the tth health state, t=1,2,…,T, T represents the number of health states, mean(D t ) and var(D t ) means D t The mean and variance of .

[0112] The healthy state with the smallest MD value is taken as the healthy state of the DUT.

[0113] The faulty bearing samples used in the test have five health states as described in the following table. 20 vibration signal samples are collected for each health state, with a total of 100 sample data. For each health state, 5 samples are randomly selected for training and the remaining samples are tested. A total of 25 training samples and 75 test samples are divided.

[0114] Table 1 Classification of aircraft engine bearing health status

[0115]

[0116] The multi-scale permutation entropy parameters are optimized by differential evolution algorithm for the above 25 training samples; and the health status indicator set of different health status is determined at the same time.

[0117] Then, according to the steps S1-S4 given above, the health status of the test samples is tested, and the results are shown in Table 2. The Mahalanobis distance values ​​between the test samples and the training samples in various health states are calculated. The results show that this method can effectively and accurately diagnose different health states of bearings with different fault levels.

[0118] Table 2 Health status classification results of test samples

[0119]

[0120]

[0121]

[0122] At the same time, in order to verify the robustness of the method proposed in the present invention under the influence of different noises, the performance of the proposed method is tested using signals with different noise levels. Gaussian white noise is added to the test signal with a signal-to-noise ratio range of -15 dB to 35 dB. The classification accuracy of the signal with different signal-to-noise ratios using the method proposed in the present invention is shown in Figure 2. Figure 4 As shown in the figure, when the signal-to-noise ratio is less than 0 dB, the classification accuracy of this method can reach 82%. When the signal-to-noise ratio is greater than 0 dB, the classification accuracy can reach 99.5%. The results show that this method has good noise tolerance.

[0123] Those skilled in the art will appreciate that the embodiments herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for diagnosing aircraft engine bearing faults based on spectral wavelet transform and multi-scale permutation entropy, characterized in that: The following steps are involved: S1 converts the collected original vibration signal of the test piece into a horizontal visible graph; S2 uses spectral wavelet transform to decompose the horizontal visible graph into scale coefficients and spectral wavelet coefficients, and performs denoising. The following steps are included: S21 uses spectral wavelet transform to decompose the horizontal visible graph and obtain scale coefficients and spectral wavelet coefficients; S22 performs filtering on the spectrum wavelet coefficients based on the adaptive threshold method of wavelet coefficients; S23 performs inverse spectral wavelet transform using the scale coefficient and the filtered spectral wavelet coefficient to obtain a denoised signal; S3 calculates the multi-scale permutation entropy of the device under test based on the denoised signal in step S2, and uses it as a health status indicator of the device under test; S4 calculates the Mahalanobis distance of the test piece under different health states based on the health state indicator set under different health states, and diagnoses the aircraft engine bearing fault according to the Mahalanobis distance.

2. The method for diagnosing aircraft engine bearing faults based on spectral wavelet transform and multi-scale permutation entropy according to claim 1, characterized in that: In step S1, the collected one-dimensional original vibration signal is mapped into a two-dimensional matrix, and then each element of the two-dimensional matrix is ​​used as a node in the graph, and the Euclidean distance between two nodes is used as the weight of the edge between the corresponding two nodes, thereby obtaining an undirected weighted graph, that is, a horizontal visible graph.

3. The method for diagnosing aircraft engine bearing faults based on spectral wavelet transform and multi-scale permutation entropy according to claim 1, characterized in that: In step S21, firstly, the spectral wavelet kernel function, scale function kernel, scale parameter, number of decomposition layers and spectral wavelet operator corresponding to the scale parameter used by the spectral wavelet transform are set; then the spectral wavelet transform is used to decompose the horizontal visualization image into several sub-bands, the first sub-band is the scale coefficient, and the remaining sub-bands are the spectral wavelet coefficients corresponding to the scale parameters.

4. The method for diagnosing aircraft engine bearing faults based on spectral wavelet transform and multi-scale permutation entropy according to claim 1 or 3, characterized in that: In step S22, based on the adaptive threshold method of wavelet coefficients, the wavelet coefficients of the spectrum are filtered, including nonlinear trend removal and shrinkage; the specific process is as follows: (1) The wavelet coefficient W at the jth scale j Identify all local extreme values ​​in , j = 1, 2, ..., J, J is the total number of selected scales; (2) Obtain the wavelet coefficient vector W at the jth scale j The upper envelope of En u and the lower envelope En l ; (3) Eliminate W j The nonlinear trend in the free nonlinear wavelet coefficients (4) The four thresholds are calculated by the following formula The wavelet coefficients are divided into five regions in, and Respectively The positive and negative wavelet coefficients in; med(·) represents the median operation; erfc -1 (·) represents the inverse complementary error function; std(·) is the standard deviation; (5) Calculate the wavelet coefficient W of the shrunken spectrum according to the following formula j ′: Among them, W′ j,k W′ j The kth wavelet coefficient in ; exp(·) represents the exponential operation; θ represents the parameter for identifying the rate of change of the coefficient in the transition zone.

5. The method for diagnosing aircraft engine bearing faults based on spectral wavelet transform and multi-scale permutation entropy according to claim 1, characterized in that: In step S3, the multi-scale permutation entropy is calculated by the following steps: S31 performs coarse-graining processing on the denoised signal to obtain a coarse-grained time series Where s represents the scale factor; S32 performs spatial reconstruction on the coarse-grained time series to obtain the qth reconstruction component In the formula, τ represents the time delay, and m represents the embedding dimension; S33 takes the qth reconstruction component Each element in is associated with an integer from 1 to m, and arranged in ascending order, we can get m! symbol sequences, among which there are R non-repeating symbol sequences; S r =(k1,k2,...,k m ),r=1,2,...,R,R≤m! Where k1, k2, ..., k m is the index symbol of the element; S34 The probability of each symbol sequence appearing is P r , define the multi-scale permutation entropy Q in the form of Shannon entropy pe for: S35 normalizes the multi-scale permutation entropy:

6. The method for diagnosing aircraft engine bearing faults based on spectral wavelet transform and multi-scale permutation entropy according to claim 5, characterized in that: The multi-scale permutation entropy parameters used were optimized by the differential evolution algorithm.

7. The method for diagnosing aircraft engine bearing faults based on spectral wavelet transform and multi-scale permutation entropy according to claim 1, 5 or 6, characterized in that: In step S4, the Mahalanobis distance of the test piece in different health states is: Where D is the health status indicator of the device under test, D t is the health status indicator set under the tth health state, t=1,2,…,T, T represents the number of health states, mean(D t ) and var(D t ) means D t The mean and variance of .

8. The method for diagnosing aircraft engine bearing faults based on spectral wavelet transform and multi-scale permutation entropy according to claim 7, characterized in that: D t It is obtained by calculating the multi-scale permutation entropy of several samples in the tth health state.

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