CN111626312A - Wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning - Google Patents

Wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning Download PDF

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CN111626312A
CN111626312A CN201910150310.4A CN201910150310A CN111626312A CN 111626312 A CN111626312 A CN 111626312A CN 201910150310 A CN201910150310 A CN 201910150310A CN 111626312 A CN111626312 A CN 111626312A
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dictionary
wind turbine
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王森林
吕勇
易灿灿
周明乐
李小彪
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Wuhan University of Science and Engineering WUSE
Wuhan University of Science and Technology WHUST
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Abstract

The invention discloses a wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning, which comprises the following steps of: acquiring a bearing signal of a wind turbine, reconstructing a fault signal of the one-dimensional wind turbine to a high-dimensional phase space by utilizing phase space reconstruction, and acquiring a matrix of a reconstructed signal to form a bearing fault diagnosis original feature set Y; partitioning the sample matrix, and dividing the sample matrix into L types according to different categories through a K _ means classifier; the ith matrix signal is optimized and updated through separable dictionary learning, and sparse coefficients are output
Figure DDA0001981339690000011
Separable dictionary Ai，Bi(ii) a Repeating the steps, obtaining a set of all sparse coefficients and dictionary matrixes, and reconstructing through a 2D _ OMP algorithm; for signal YiPerforming integrated treatment to obtain Y' and outputA signal Y' reflecting fault characteristics is obtained, so that non-stationary fault information of the wind turbine bearing is obtained; the invention not only keeps the local spatial correlation in the high-dimensional signal, but also greatly improves the reconstruction efficiency.

Description

Wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning
Technical Field
The invention relates to the field of fault diagnosis of bearings, in particular to a wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning.
Background
At present, rolling bearings have penetrated the aspects of mechanized production, and once a fault occurs, the fault is not found in time in the early stage, so that not only can a new fault be caused, but also equipment can be damaged, and huge economic loss is caused. Therefore, the bearing-oriented early fault diagnosis method has great significance for guaranteeing the safe operation of equipment.
The traditional bearing fault diagnosis technology carries out fault identification by extracting characteristic quantity aiming at vibration signal time domain or frequency domain characteristics, and the effective extraction of the fault characteristics directly influences the fault diagnosis precision. Especially, when the bearing hides the early weak fault and the fault information is submerged by the vibration signals and random noise of other parts, the extraction is difficult by using the traditional time-frequency domain method. In fact, the rolling bearing presents strong non-steady and non-linear characteristics under different fault states due to the influence of factors such as rigidity, friction force, clearance, external load and the like, and the traditional bearing fault diagnosis technology does not consider the non-linear factors of the bearing. Therefore, bearing fault diagnosis technology based on nonlinear time series analysis becomes a research hotspot. The phase space reconstruction is a main method for solving the nonlinear problem, a one-dimensional signal is expanded to a high-dimensional phase space, implicit dynamic characteristics of the signal are obtained from the signal, and deep information is mined.
The noise in the fault vibration signal has a great influence on the matrix effect obtained by phase space reconstruction, so that effective denoising of the signal is important. In recent years, classification techniques based on sparse representation have been successfully applied to the fields of image denoising, target identification, image super-resolution reconstruction, image retrieval, defect detection, and the like. The goal of sparse representation is that the signal can be linearly represented by several atoms of a dictionary. Since the analysis dictionary cannot sparsely represent detailed parts of the fault signal, the adaptive dictionary receives much attention. At present, from MicThe K _ SVD algorithm proposed by hale Aharon, et al, 2006 is of most interest. K _ SVD is an iterative replacement algorithm that alternates between a sparse coding process based on current dictionary training samples and an optimization process of atoms to better fit the training samples. However, the dictionary update object in the K _ SVD algorithm is an atom, each dictionary update needs to update the atoms in the dictionary one by one, and each atom update needs to perform SVD (singular value decomposition) decomposition on the training sample represented by the atom, which not only easily causes the problem to fall into a local optimal solution, but also causes the efficiency of dictionary update to be low. To overcome this drawback, r.rubinstein et al proposed a K _ SVD analysis algorithm in 2013 from the view of dual analysis of sparse representation. All the dictionary learning algorithms mentioned above optimize atoms one by one in the dictionary optimization process. In 2013, s.hawe et al proposed a new separable dictionary learning algorithm (SeDiL) that projects a small dictionary onto a diagonal manifold and optimizes it using the CG method, reducing the amount of computation by introducing separability, O (m)2) To O (m). In the field of mechanical fault diagnosis, the method combines K _ SVD with a wavelet denoising method by the method of Zhong, so that the accuracy of fault diagnosis is improved. However, the algorithm has obvious defects in application, when the signal is long, the atomic weight of the over-complete dictionary is extremely large, a large amount of redundant information is contained, and the operation speed is low; when the signal noise is large, the K _ SVD is greatly influenced by the signal phase, the signal characteristics cannot be well extracted, and the reconstruction accuracy and efficiency are reduced.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning, firstly, reconstructing a one-dimensional wind turbine fault signal to a high-dimensional phase space by utilizing phase space reconstruction to obtain a matrix of the reconstructed signal so as to form a bearing fault diagnosis original characteristic set; then, the matrix is processed in a blocking mode, a separable dictionary of each category matrix signal is optimized through QR decomposition, and the separated signals are reconstructed, so that non-stationary fault information of the wind turbine bearing is obtained; the invention divides the signal matrix into blocks and then performs multi-separation dictionary learning (MSeDiL) on each class matrix block, and greatly improves the reconstruction efficiency because the signals expressed by the underdetermined dictionary in each matrix block are single.
The purpose of the invention is realized by the following technical scheme: a wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning comprises the following specific steps:
s1, collecting a bearing signal of the wind turbine, and constructing a training sample matrix through phase space reconstruction;
step S2, the sample matrix is partitioned, and the sample matrix is divided into L types according to different types through a K _ means classifier;
step S3, the ith matrix signal is optimized and updated through separable dictionary learning, and sparse coefficient is output
Figure BDA0001981339670000021
Separable dictionary Ai，Bi；
Step S4, repeating the step S3, obtaining all sparse coefficient and dictionary matrix sets, and reconstructing through a 2D _ OMP algorithm;
step S5, for signal YiAnd performing integrated processing to obtain Y ', and outputting a signal Y' reflecting fault characteristics.
In an embodiment of the invention, the signal in the step S1 is denoted as yiWherein i ═ 1,2,3, …, N; introducing phase space reconstruction, reconstructing the signal to a phase space of l dimension, and the sequence expression after reconstruction is yi＝(yi+(l-1)τ,…,yi+τ,yi). Line vector yiIndividual position information representing the phase space reconstruction. The nonlinear dynamical system definition indicates that these vectors are connected in columns to form a trajectory matrix, thereby creating the following phase-space reconstruction matrix: y ═ Y1+(l-1)τY2+(l-2)τ… YN)T. In the formula: y isiIs the ith phase point; l is the embedding dimension; τ is the delay time.
In an embodiment of the invention, in the step S2, the signal matrix is classified by a K _ means classifier, and L is the number of the divided small matrices, which depends on the size of the signal matrix.
In an embodiment of the present invention, in step S3, the 2D _ OMP algorithm and the separable dictionary are introduced to update the coefficient matrix and the dictionary matrix of each class of matrix respectively, and there are three unknowns in the optimization process of the separated dictionary of each class, which are the separated dictionary a respectivelyiAnd BiAnd a sparse coefficient matrix
Figure BDA0001981339670000022
In the known optimization theory, because0The norm is non-convex and cannot be solved by a convex optimization algorithm, so that l is often taken as a sparse measurement function0Norm relaxation of l1And solving the norm. If the sample signal matrix Y is divided into L blocks in step S1, the number of signal matrices of the ith block is Ni，A＝{A1,A2,…,ALB ═ B1,B2,…,BLThe dictionary sequences composed of separate dictionaries are respectively represented, so the objective function of a multi-separate dictionary can be represented as:
Figure BDA0001981339670000023
because the signal sample matrixes are independent from each other, the formula (1) can be divided into the sum of a plurality of independent objective functions, wherein the ith objective function comprises:
Figure BDA0001981339670000024
introducing a new sequence of Lambertian operators
Figure BDA0001981339670000031
Solving by taking the above constraint conditions as a regular term in the objective function, the formula (2) can be converted into:
Figure BDA0001981339670000032
wherein liThe most common solving algorithm for the problem is an Alternating Direction Multiplier (ADM), and aiming at different variable constraint conditions, the whole objective function is divided into a plurality of independent solving problems to realize the optimization of the whole objective.
In an embodiment of the present invention, the specific solving process of the multi-separation underdetermined dictionary learning algorithm in the steps S3 and S4 is as follows:
a) inputting a clustering number L, a positive sparsity parameter lambda, a mean value mu and a maximum mean value mumaxCoefficient ρ, i-th matrix
Figure BDA0001981339670000033
A＝{A1,A2,…,AL}、Ai∈Rm×a(a＜m)、B＝{B1,B2,…,BL}、Bi∈Rm×b(b＜m)；
b) Dividing the matrix samples into L clusters, and selecting the ith sample
Figure BDA0001981339670000034
Optimizing;
c) setting the number of samples i to 1(i is less than or equal to L);
d) initializing residual error kappa, iteration number Iter 1, introducing new Lagrange multiplier, and forming Lagrange multiplier matrix
Figure BDA0001981339670000035
Updating orthogonal matrix A by QR decompositioniNamely:
Figure BDA0001981339670000036
e) if j is 1, combined with T(w)i＝(|wi|-)+sgn(wi) This soft threshold operator updates the independent sparse coefficient matrix
Figure BDA0001981339670000037
The method can obtain the product with the advantages of high yield,
Figure BDA0001981339670000038
f) if j is equal to NiThen stop
Figure BDA0001981339670000039
Otherwise, j is j +1, returning to the step e), and continuing the iteration;
g) updating orthogonal matrix BiAnalogously to A in step d)iThe update of (a), namely:
Figure BDA00019813396700000310
h) if j is equal to 1, updating the independent matrix
Figure BDA00019813396700000311
Then there are:
Figure BDA0001981339670000041
i) if j is equal to NiThen stop
Figure BDA0001981339670000042
Iteration of (2); otherwise, j equals j +1, and returns to the step h) and continues the iteration.
j) Updating lagrange multiplier matrices
Figure BDA0001981339670000043
The following can be obtained:
Figure BDA0001981339670000044
k) if it is
Figure BDA0001981339670000045
Or if the iteration time Iter is maxIter, stopping the iteration; otherwiseAnd Iter +1, returning to the step d), and continuing the iteration.
L) if i ═ L, stopping the iteration; otherwise, returning to the step c) and continuing the iteration, wherein i is equal to i + 1.
m) output
Figure BDA0001981339670000046
A，B。
In an embodiment of the invention, in the step S5, the signal of block reconstruction is integrally learned ∑ Yi＝Y'。
In one embodiment of the present invention, dictionary Ai∈Rm×n，Bi∈Rm×nIs a dictionary DiI.e. by
Figure BDA0001981339670000047
Compared with the prior art, the invention has the following characteristics and beneficial effects:
(1) in the invention, a Lagrange multiplier is introduced in the process of optimizing the dictionary, the problem with constraint is converted into the problem without constraint, and because the objective function has a plurality of independent variables, the ADM algorithm is utilized to realize the idea of optimizing the whole objective by optimizing the problem of decomposition, and the optimization of the whole objective is finally realized by performing iterative optimization on the problem of decomposition only containing one variable.
(2) After the signal matrix is partitioned, each matrix block separation dictionary only performs sparse representation on the signal blocks belonging to the matrix, and the represented signal types are more single, so that the separation dictionaries belonging to each class are incomplete, namely columns in the dictionary are smaller than rows. Considering the constraint conditions of standardization and column independence of dictionary atoms, QR decomposition is adopted to obtain an optimal separation dictionary.
(3) For the invention1The norm is used as a sparsity measurement function, a target function of sparse coding is converted into a convex linear programming problem, and then a soft threshold operator is used for updating a sparse coefficient.
(4) According to the invention, the phase space reconstruction theory is applied to the one-dimensional vibration signal, so that the information in the vibration signal can be fully displayed; the multi-separation underdetermined dictionary learning method respectively updates the sparse coefficient and the dictionary of each classified signal matrix to obtain the signal components reflecting the fault characteristics, not only maintains the local spatial correlation in the high-dimensional signals, but also improves the reconstruction efficiency.
Drawings
FIG. 1 is a structural diagram of a direct-drive permanent magnet wind generating set and a sensor measuring point layout diagram in the embodiment;
in the figure: 1-impeller blade 2-generator stator 3-anemometry system 4-base 5-yaw drive 6-generator rotor 7-tower 8-wheel rim 9-variable pitch system
FIG. 2 is a flow chart of a wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning in the embodiment;
FIG. 3 is a diagram illustrating the reconstruction effect of different L sizes of signal matrices in an embodiment;
FIG. 4 is a graph showing the effect of the number of A.multidot.B atoms on the reconstruction results in examples;
FIG. 5 is a flow chart of a multi-separation dictionary learning algorithm in an embodiment;
FIG. 6 is a time domain diagram of a horizontal vibration (1H) signal of a rear bearing of a wind turbine in the embodiment;
FIG. 7 is a frequency domain diagram of a horizontal vibration (1H) signal of a rear bearing of a wind turbine in an embodiment;
FIG. 8 is a frequency domain diagram of a SeDiL reconstructed signal of a wind turbine rear bearing horizontal vibration (1H) signal in an embodiment;
FIG. 9 is a frequency domain diagram of a horizontal vibration (1H) signal of a rear bearing of a wind turbine in an embodiment after an FMSeDiL reconstruction signal.
Detailed Description
In order to more clearly illustrate the present invention and/or the technical solutions in the prior art, the following will describe embodiments of the present invention with reference to the accompanying drawings. It is obvious that the drawings in the following description are only some examples of the invention, and that for a person skilled in the art, other drawings and embodiments can be derived from them without inventive effort.
Examples
In the embodiment, fault data of the rolling bearing of the direct-drive permanent magnet wind driven generator are analyzed. The structure of the wind generating set is shown in fig. 1, wherein 1H is the horizontal direction of a main bearing, 1V is the vertical direction of the main bearing, and 1A is the axial direction of the main bearing. The mechanical characteristic frequencies of the wind turbine at rated power are shown in table 1.
TABLE 1 mechanical characteristic frequency of rear bearing of wind turbine
Figure BDA0001981339670000051
A horizontal vibration (1H) signal of a rear bearing of the wind turbine is selected as a processing object, and the time domain and the frequency domain of the actually measured signal are shown in figures 6 and 7. It is difficult to see the failure information from the figure. The embodiment provides a wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning, and a flow chart is shown in FIG. 2.
S1, collecting a bearing signal of the wind turbine, and constructing a training sample matrix through phase space reconstruction;
step S2, the sample matrix is partitioned, and the sample matrix is divided into L types according to different types through a K _ means classifier;
step S3, the ith matrix signal is optimized and updated through separable dictionary learning, and sparse coefficient is output
Figure BDA0001981339670000052
Separable dictionary Ai，Bi；
Step S4, repeating the step S3, obtaining all sparse coefficient and dictionary matrix sets, and reconstructing through a 2D _ OMP algorithm;
step S5, for signal YiAnd performing integrated processing to obtain Y ', and outputting a signal Y' reflecting fault characteristics.
In an embodiment of the invention, the signal in the step S1 is denoted as yiWherein i ═ 1,2,3, …, N; introducing phase space reconstruction, reconstructing the signal to a phase space of l dimension, and the sequence expression after reconstruction is yi＝(yi+(l-1)τ,…,yi+τ,yi). Line vector yiIndividual position information representing the phase space reconstruction. The nonlinear dynamical system definition indicates that these vectors are connected in columns to form a trajectory matrix, thereby creating the following phase-space reconstruction matrix: y ═ Y1+(l-1)τY2+(l-2)τ… YN)T. In the formula: y isiIs the ith phase point; l is the embedding dimension; τ is the delay time.
In an embodiment of the present invention, in the step S2, the signal matrix is classified by a K _ means classifier, where L is the number of the divided small matrices, and depends on the size of the signal matrix, as shown in fig. 3, it can be known through a series of simulation experiments that when L is less than or equal to 16, the effect is better, and L is generally equal to 8.
In an embodiment of the present invention, in step S3, the 2D _ OMP algorithm and the separable dictionary are introduced to update the coefficient matrix and the dictionary matrix of each class of matrix respectively, and there are three unknowns in the optimization process of the separated dictionary of each class, which are the separated dictionary a respectivelyiAnd BiAnd a sparse coefficient matrix
Figure BDA0001981339670000061
The size of the dictionary A, B is selected to influence the reconstruction efficiency, and the denoising effects of different A, B are shown in fig. 4.
In the known optimization theory, because0The norm is non-convex and cannot be solved by a convex optimization algorithm, so that l is often taken as a sparse measurement function0Norm relaxation of l1And solving the norm. If the sample signal matrix Y is divided into L blocks in step S1, the number of signal matrices of the ith block is Ni，A＝{A1,A2,…,ALB ═ B1,B2,…,BLThe dictionary sequences composed of separate dictionaries are respectively represented, so the objective function of a multi-separate dictionary can be represented as:
Figure BDA0001981339670000062
because the signal sample matrixes are independent from each other, the formula (1) can be divided into the sum of a plurality of independent objective functions, wherein the ith objective function comprises:
Figure BDA0001981339670000063
introducing a new sequence of Lambertian operators
Figure BDA0001981339670000064
Solving by taking the above constraint conditions as a regular term in the objective function, the formula (2) can be converted into:
Figure BDA0001981339670000065
wherein liThe most common solving algorithm for the problem is an Alternating Direction Multiplier (ADM), and aiming at different variable constraint conditions, the whole objective function is divided into a plurality of independent solving problems to realize the optimization of the whole objective.
In an embodiment of the present invention, a flowchart of the multi-separation underdetermined dictionary learning algorithm in the steps S3 and S4 is shown in fig. 5, and a specific solving process is as follows:
a) inputting a clustering number L, a positive sparsity parameter lambda, a mean value mu and a maximum mean value mumaxCoefficient ρ, i-th matrix
Figure BDA0001981339670000066
A＝{A1,A2,…,AL}、Ai∈Rm×a(a＜m)、B＝{B1,B2,…,BL}、Bi∈Rm×b(b＜m)；
b) Dividing the matrix samples into L clusters, and selecting the ith sample
Figure BDA0001981339670000067
Optimizing;
c) setting the number of samples i to 1(i is less than or equal to L);
d) initializing residual error kappa, iteration number Iter 1, introducing new Lagrange multiplier, and forming Lagrange multiplier matrix
Figure BDA00019813396700000714
Updating orthogonal matrix A by QR decompositioniNamely:
Figure BDA0001981339670000071
e) if j is 1, combined with T(w)i＝(|wi|-)+sgn(wi) This soft threshold operator updates the independent sparse coefficient matrix
Figure BDA0001981339670000072
The method can obtain the product with the advantages of high yield,
Figure BDA0001981339670000073
f) if j is equal to NiThen stop
Figure BDA0001981339670000074
Otherwise, j is j +1, returning to the step e), and continuing the iteration;
g) updating orthogonal matrix BiAnalogously to A in step d)iThe update of (a), namely:
Figure BDA0001981339670000075
h) if j is equal to 1, updating the independent matrix
Figure BDA0001981339670000076
Then there are:
Figure BDA0001981339670000077
i) if j is equal to NiThen stop
Figure BDA0001981339670000078
Iteration of (2); otherwise, j equals j +1, and returns to the step h) and continues the iteration.
j) Updating lagrange multiplier matrices
Figure BDA0001981339670000079
The following can be obtained:
Figure BDA00019813396700000710
k) if it is
Figure BDA00019813396700000711
Or if the iteration time Iter is maxIter, stopping the iteration; otherwise, Iter +1, returning to step d), and continuing the iteration.
L) if i ═ L, stopping the iteration; otherwise, returning to the step c) and continuing the iteration, wherein i is equal to i + 1.
m) output
Figure BDA00019813396700000712
A，B。
In an embodiment of the invention, in the step S5, the signal of block reconstruction is integrally learned ∑ Yi＝Y'。
In one embodiment of the present invention, dictionary Ai∈Rm×n，Bi∈Rm×nIs a dictionary DiI.e. by
Figure BDA00019813396700000713
In the embodiment of the invention, after SeDiL and FMSeDiL processing is carried out on a horizontal vibration (1H) signal of a rear bearing of a wind turbine, the obtained spectrogram is shown in FIGS. 8 and 9. The peak signal-to-noise ratio and the reconstruction time of the former method are 23.473 s and 24.461s respectively, and the peak signal-to-noise ratio and the reconstruction time of the method used by the invention are 23.568 s and 19.097s respectively. Therefore, the accuracy of the wind turbine fault detection reaches 100%, the frequency multiplication of the fault signal can be reconstructed, and the reconstruction time is greatly shortened.
Although the present invention has been described in detail with reference to specific embodiments thereof, it will be understood by those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (7)

1. The wind turbine bearing fault diagnosis method based on the fast multi-separation dictionary learning is characterized by comprising the following steps of:
s1, collecting a bearing signal of the wind turbine, and constructing a training sample matrix through phase space reconstruction;
step S2, the sample matrix is partitioned, and the sample matrix is divided into L types according to different types through a K _ means classifier;
step S3, the ith matrix signal is optimized and updated through separable dictionary learning, and sparse coefficient is output
Figure FDA0001981339660000011
Separable dictionary Ai，Bi；
Step S4, repeating the step S3, obtaining all sparse coefficient and dictionary matrix sets, and reconstructing through a 2D _ OMP algorithm;
step S5, for signal YiAnd performing integrated processing to obtain Y ', and outputting a signal Y' reflecting fault characteristics.
2. The wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning as claimed in claim 1, wherein the signal in the step S1 is recorded as yiWherein i ═ 1,2,3, …, N; introducing phase space reconstruction, reconstructing the signal to a phase space of l dimension, and the sequence expression after reconstruction is yi＝(yi+(l-1)τ,…,yi+τ,yi) (ii) a Line vector yiSingle position information representing a phase space reconstruction; nonlinear dynamical system definition refers toOut, these vectors are connected in columns to form a trajectory matrix, creating the following phase space reconstruction matrix: y ═ Y1+(l-1)τY2+(l-2)τ… YN)T(ii) a In the formula: y isiIs the ith phase point; l is the embedding dimension; τ is the delay time.
3. The method as claimed in claim 1, wherein in step S2, the signal matrix is classified by a K _ means classifier, where L is the number of small matrices divided and depends on the size of the signal matrix.
4. The method as claimed in claim 1, wherein in step S3, the 2D _ OMP algorithm and the separable dictionary are introduced to update the coefficient matrix and the dictionary matrix of each matrix type respectively, and there are three unknowns in the optimization process of the separable dictionary of each matrix type, which are respectively the separated dictionary aiAnd BiAnd a sparse coefficient matrix
Figure FDA0001981339660000012
In the known optimization theory, because0The norm is non-convex and cannot be solved by a convex optimization algorithm, so that l is often taken as a sparse measurement function0Norm relaxation of l1Solving the norm;
if the sample signal matrix Y is divided into L blocks in step S1, the number of signal matrices of the ith block is Ni，A＝{A1,A2,…,ALB ═ B1,B2,…,BLThe dictionary sequences composed of separate dictionaries are respectively represented, so the objective function of a multi-separate dictionary can be represented as:
Figure FDA0001981339660000013
because the signal sample matrixes are independent from each other, the formula (1) can be divided into the sum of a plurality of independent objective functions, wherein the ith objective function comprises:
Figure FDA0001981339660000021
introducing a new sequence of Lambertian operators
Figure FDA0001981339660000022
Solving by taking the above constraint conditions as a regular term in the objective function, the formula (2) can be converted into:
Figure FDA0001981339660000023
wherein liThe most common solving algorithm for the problem is an Alternating Direction Multiplier (ADM), and aiming at different variable constraint conditions, the whole objective function is divided into a plurality of independent solving problems to realize the optimization of the whole objective.
5. The method for diagnosing the bearing fault of the wind turbine based on the fast multi-separation dictionary learning as claimed in claim 1, wherein the multi-separation underdetermined dictionary learning algorithm in the steps S3 and S4 is specifically solved as follows:
a) inputting a clustering number L, a positive sparsity parameter lambda, a mean value mu and a maximum mean value mumaxCoefficient ρ, i-th matrix
Figure FDA0001981339660000024
A＝{A1,A2,…,AL}、Ai∈Rm×a(a＜m)、B＝{B1,B2,…,BL}、Bi∈Rm×b(b＜m)；
b) Dividing the matrix samples into L clusters, and selecting the ith sample
Figure FDA0001981339660000025
Optimizing;
c) setting the number of samples i to 1(i is less than or equal to L);
d) initializing residual error kappa, iteration number Iter 1, introducing new Lagrange multiplier, and forming Lagrange multiplier matrix
Figure FDA0001981339660000026
Updating orthogonal matrix A by QR decompositioniNamely:
Figure FDA0001981339660000027
e) if j is 1, combined with T(w)i＝(|wi|-)+sgn(wi) This soft threshold operator updates the independent sparse coefficient matrix
Figure FDA0001981339660000028
The method can obtain the product with the advantages of high yield,
Figure FDA0001981339660000029
f) if j is equal to NiThen stop
Figure FDA00019813396600000210
Otherwise, j is j +1, returning to the step e), and continuing the iteration;
g) updating orthogonal matrix BiAnalogously to A in step d)iThe update of (a), namely:
Figure FDA0001981339660000031
h) if j is equal to 1, updating the independent matrix
Figure FDA0001981339660000032
Then there are:
Figure FDA0001981339660000033
i) if j is equal to NiThen stop
Figure FDA0001981339660000034
Iteration of (2); otherwise, j equals j +1, and returns to the step h) to continue iteration;
j) updating lagrange multiplier matrices
Figure FDA0001981339660000035
The following can be obtained:
Figure FDA0001981339660000036
k) if it is
Figure FDA0001981339660000037
Or if the iteration time Iter is equal to max Iter, stopping the iteration; otherwise, Iter is equal to Iter +1, returning to the step d), and continuing iteration;
l) if i ═ L, stopping the iteration; otherwise, returning to the step c) and continuing iteration, wherein i is i + 1;
m) output
Figure FDA0001981339660000038
A，B。
6. The wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning as claimed in claim 1, wherein in the step S5, the signals reconstructed by the blocks are subjected to ensemble learning ∑ Yi＝Y'。
7. The wind turbine bearing fault diagnosis method based on fast multi-separation dictionary learning as claimed in claim 1, wherein the dictionary A isi∈Rm×n，Bi∈Rm×nIs a dictionary DiI.e. by
Figure FDA0001981339660000039
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