CN109946076B - Planetary wheel bearing fault identification method of weighted multi-scale dictionary learning framework - Google Patents

Planetary wheel bearing fault identification method of weighted multi-scale dictionary learning framework Download PDF

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CN109946076B
CN109946076B CN201910079232.3A CN201910079232A CN109946076B CN 109946076 B CN109946076 B CN 109946076B CN 201910079232 A CN201910079232 A CN 201910079232A CN 109946076 B CN109946076 B CN 109946076B
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陈雪峰
赵志斌
王诗彬
乔百杰
孙闯
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Xian Jiaotong University
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Abstract

The invention discloses a planet wheel bearing fault identification method of a weighted multi-scale dictionary learning frame, which comprises the following steps: constructing a block operator based on the planet wheel bearing vibration signal; constructing a weighted multi-scale dictionary learning frame based on the blocking operator, and optimally solving the weighted multi-scale dictionary learning frame to obtain a fault characteristic signal; based on Q-switched wavelet and l0Regularly constructing a weighted multi-scale dictionary learning special case, and extracting fault characteristic signals of the planet wheel bearing through the special case; and identifying the fault type through envelope analysis based on the extracted fault characteristic signals.

Description

Planetary wheel bearing fault identification method of weighted multi-scale dictionary learning framework
Technical Field
The invention belongs to the technical field of fault diagnosis methods, and particularly relates to a planet wheel bearing fault identification method of a weighted multi-scale dictionary learning framework.
Background
Electromechanical devices, which are important components of modern industry, are especially important for their operational safety. The traditional regular maintenance mode consumes a large amount of resources such as manpower, material resources, financial resources and the like, and can not adapt to the development trend of modern industry. The on-demand maintenance has the obvious advantages of small scale, high efficiency, good economic affordability and capability of diagnosing and predicting serious disaster accidents. An important prerequisite for effective implementation of the on-demand maintenance is the construction of a complex forecasting and health management system. Vibration signal analysis and fault diagnosis are one of the important components of the health management system, and the vibration signal analysis and fault diagnosis of the electromechanical equipment excavates operation state information by concentrated silk-spinning and cocoon-peeling from numerous and complex observation data, thereby providing a necessary basis for health assessment and operation safety guarantee of the electromechanical equipment. The planetary gearbox is taken as a key component of many important electromechanical devices (such as a helicopter, a wind driven generator and the like), and fault identification and health assessment of core components (a planet wheel, a planet wheel bearing and the like) of the planetary gearbox are very important.
The traditional method (such as wavelet transformation, spectral kurtosis, time-frequency analysis and the like) for constructing a customized filter based on prior knowledge or characteristic indexes is too dependent on the prior knowledge of the system, and neglects the huge value hidden in the observation data. Therefore, there is no way to diagnose such complex signals of the planet wheel bearing.
Dictionary learning can provide a more sparse representation due to its adaptivity to data, and has recently become a focus of signal processing and machine learning research, and is also widely used in mechanical failure diagnosis. However, the dictionary learning algorithm also has the corresponding disadvantages: firstly, before learning a dictionary, an original signal needs to be subjected to block operation, so that the model is only limited to the learning of local information; secondly, the dictionary learning algorithm is very sensitive to harmonic interference, however, a large amount of harmonic interference exists in the vibration signal; thirdly, structural mathematical description of the characteristic signals needs to be established for learning of the structural dictionary, but effective mathematical description cannot be established for many physical characteristics; and fourthly, the dictionary learning model is limited by the dimension of a sample, and the calculation amount is large.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.
Disclosure of Invention
The invention provides a planet wheel bearing fault identification method of a weighted multi-scale dictionary learning frame, aiming at the problems in the prior art, the method utilizes a proper multi-scale transformation which can effectively match with periodic impact characteristics, converts a time domain signal to a multi-scale transformation domain through the multi-scale transformation, then needs to select a prior regular form which can effectively promote sparseness to form a bilinear optimization problem (namely a dictionary learning problem), directly learns a corresponding dictionary from the multi-scale transformation domain to ensure that the dictionary has multi-scale and global characteristics, then realizes the inhibition of the frame on strong harmonic interference by introducing a weighted term of sub-band kurtosis, and finally carries out iterative solution through an alternative optimization algorithm to realize the effective enhancement of characteristic information and the effective attenuation of interference information.
The invention aims to realize the purpose through the following technical scheme, and discloses a planet wheel bearing fault identification method of a weighted multi-scale dictionary learning frame, which comprises the following steps:
in the first step, a block operator is constructed based on a planet wheel bearing vibration signal;
in the second step, a weighted multi-scale dictionary learning framework is constructed based on a blocking operator, and the framework comprises the following two parts:
Figure BDA0001958212500000031
Figure BDA0001958212500000032
wherein the content of the first and second substances,
Figure BDA0001958212500000033
f norm representing the matrix, y representing the signal measured by the sensor, x ∈ Rn×1For fault signature signals (R represents the real number set, n is the length of the signal),
Figure BDA0001958212500000038
representing the characteristic signal obtained by solution, D ∈ RN×LA representation learning dictionary (N is the dimension of each column in the dictionary, L represents the number of columns in the dictionary),
Figure BDA0001958212500000034
representing a solved dictionary, P (A) being a priori representing coefficients, λ representing a regularization parameter, A ∈ RL×MTo represent the coefficients (M represents the number of samples),
Figure BDA0001958212500000035
representing a solved dictionary, Г (·) representing scoresBlock operators (i.e. tiling vectors into a matrix), where WTDenotes the transpose of the multiscale transform w (T denotes the operation of the transpose of the matrix), K is the diagonal matrix containing the sub-band fault features, defined as
Figure BDA0001958212500000036
Where S denotes the maximum number of decomposition levels for the multiscale transform, KlIndicating the kurtosis of the l-th layer,
Figure BDA0001958212500000037
wherein<·>Denotes an averaging operation, |, denotes an absolute value operation, ulRepresenting the signal reconstructed from the first layer coefficients;
in the third step, a weighted multi-scale dictionary learning framework is optimized and solved, and a fault characteristic signal X is obtained;
in the fourth step, according to the weighted multi-scale learning frame established in the second step and the third step, the Q-switched wavelet and the l are combined0Regular substitution into a frame to construct a weighted multi-scale dictionary learning special case, and Q-switched wavelet sum l-based construction0The method comprises the following steps that (1) a regular weighted multi-scale learning special case realizes the extraction of fault characteristic signals of the planet wheel bearing;
and in the fifth step, based on the fault characteristic signals extracted by the multi-scale dictionary learning special case model in the fourth step, identifying the fault type through envelope analysis.
In the method, in the first step, a planet wheel bearing vibration signal y epsilon Rn×1Is y ═ x + h + n, where h ∈ Rn ×1For multi-source harmonic interference, n is equal to Rn×1Extracting a planet wheel bearing fault characteristic signal x under the interference of multi-source harmonic waves and strong background noise, wherein n is the signal length, partitioning the one-dimensional signal by an operator Г, and splicing all the blocks into a matrix, wherein,
X＝[Γ1(x)，Г2(x)，...，ГM-1(x)，ΓM(x)]＝Г(x)，
wherein gamma isi：Rn×1→RN×1Denotes the extraction of the ith block from x into the ith column of the matrix x, Γ-1：RN×M→Rn×1Representing the inverse of the operator Γ-1＝Г-1Г＝I。
In the method described, therefore, the normalized operator satisfies the following relationship:
Figure BDA0001958212500000041
where ⊙ represents a point-by-point multiplication.
In the method, in the second step (S2), definition is performed
Figure BDA0001958212500000051
Figure BDA0001958212500000052
Wherein (W)Ty)lAnd (W)Tx)lThe coefficients representing the i-th layer of the multi-scale transform,
Figure BDA0001958212500000053
Figure BDA0001958212500000054
wherein the content of the first and second substances,
Figure BDA0001958212500000055
for the l-th layer coefficient of the measurement signal y under the multiscale transformation w, DlA learning dictionary for the l-th layer coefficients,
Figure BDA0001958212500000056
to solve the resulting dictionary of layer l, AlThe coefficients are represented for the dictionary of the l-th layer,
Figure BDA0001958212500000057
to solve for the resulting layer I dictionary representation coefficients, P (A)l) A priori for the dictionary representation coefficients, lambda represents the regularization parameter,
Figure BDA0001958212500000058
the ith layer coefficient under the multi-scale transformation w for the fault signature,
Figure BDA0001958212500000059
and the l-th layer coefficient of the fault characteristic signal obtained by solving under the multi-scale transformation w is shown, and Γ (·) represents a block operator.
In the third step, a weighted multi-scale dictionary learning framework is solved by adopting alternative optimization to obtain a dictionary learning model consisting of sparse coding and dictionary updating, and corresponding P (A) is givenl) Solving to solve the bilinear non-convex problem, solving the convex quadratic optimization problem through an optimal closed-form solution, wherein the optimal closed-form solution is as follows:
Figure BDA00019582125000000510
wherein
Figure BDA00019582125000000511
Blocking operator Γ for ith sampleiIs transposed, (.)-1Representing the inverse of the matrix, M representing the total number of samples,
Figure BDA00019582125000000512
for the layer i dictionary solved in the dictionary update,
Figure BDA0001958212500000061
is the representative coefficient of the ith sample.
In the method, in the fourth step, P (A)l)＝||Al||0(||·||0Representing the number of non-zero elements), the bilinear non-convex problem in the framework is:
Figure BDA0001958212500000062
wherein
Figure BDA0001958212500000063
For the l-th layer coefficient of the measurement signal y under the multiscale transformation w, DlA learning dictionary for the l-th layer coefficients,
Figure BDA0001958212500000064
to solve the resulting dictionary of layer l, AlThe coefficients are represented for the dictionary of the l-th layer,
Figure BDA0001958212500000065
to solve the resulting layer I dictionary representation coefficients, Γ (·) represents the blocking operator, KlAnd expressing the kurtosis of the ith layer, and expressing the deviation of the model by an epsilon-representation model, and solving by a KSVD algorithm.
In the method, a data acquisition system is adopted to obtain the vibration signal of the planet wheel bearing, wherein the sampling frequency is 12800 Hz. Compared with the prior art, the invention has the following advantages:
the method can quickly and effectively realize the identification of the fault mode of the planet wheel bearing, can improve the accuracy and reliability of fault diagnosis, and is favorable for the arrangement and adjustment of the maintenance and overhaul plan of the core component of the mechanical system.
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Various other advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. It is obvious that the drawings described below are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. Also, like parts are designated by like reference numerals throughout the drawings.
In the drawings:
FIG. 1 is a schematic step diagram of a planetary wheel bearing fault identification method of a weighted multi-scale dictionary learning framework according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a flowchart of the method according to the present embodiment;
FIG. 3 is a schematic diagram of a fault simulation test bed and a test device thereof for a planetary gearbox in the embodiment;
FIG. 4 is a schematic diagram of the test stand principle in this embodiment;
5(a) to 5(d) are schematic diagrams of local amplification of the time domain, the frequency spectrum, the square envelope spectrum and the square envelope spectrum of the signal to be identified in the present embodiment;
6(a) to 6(d) are schematic diagrams of local amplification of time domain, frequency spectrum, square envelope spectrum and square envelope spectrum of the feature extracted by the weighted multi-scale dictionary learning in the embodiment;
fig. 7(a) to 7(d) are schematic diagrams of local enlargements of time domain, frequency spectrum, square envelope spectrum and square envelope spectrum of the features extracted with respect to the KSVD in the present embodiment.
The invention is further explained below with reference to the figures and examples.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to fig. 1 to 7 (d). While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present invention is defined by the appended claims.
For the purpose of facilitating understanding of the embodiments of the present invention, the following description will be made by taking specific embodiments as examples with reference to the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present invention.
For better understanding, fig. 1 is a schematic diagram of steps of a method for identifying a fault of a planet wheel bearing of a weighted multi-scale dictionary learning framework according to an embodiment of the present invention, and as shown in fig. 1, the method for identifying a fault of a planet wheel bearing of a weighted multi-scale dictionary learning framework includes the following steps:
in a first step S1, constructing a blocking operator based on the planet wheel bearing vibration signal;
in the second step S2, a weighted multi-scale dictionary learning framework is constructed based on the blocking operator, and the framework includes the following two parts:
Figure BDA0001958212500000081
Figure BDA0001958212500000082
wherein the content of the first and second substances,
Figure BDA0001958212500000083
f norm representing the matrix, y representing the signal measured by the sensor, x ∈ Rn×1For fault signature signals (R represents the real number set, n is the length of the signal),
Figure BDA0001958212500000095
representing the characteristic signal obtained by solution, D ∈ RN×LA representation learning dictionary (N is the dimension of each column in the dictionary, L represents the number of columns in the dictionary),
Figure BDA0001958212500000091
representing a solved dictionary, P (A) being a priori representing coefficients, λ representing a regularization parameter, A ∈ RL×MTo represent the coefficient (M represents the number of samples))，
Figure BDA0001958212500000092
Representing the solved dictionary, and Γ (·) representing the block operator (i.e., tiling the vector into a matrix), where WTDenotes the transpose of the multiscale transform w (T denotes the operation of the transpose of the matrix), K is the diagonal matrix containing the sub-band fault features, defined as
Figure BDA0001958212500000093
Where s denotes the maximum number of decomposition levels for the multi-scale transformation, KlIndicating the kurtosis of the l-th layer,
Figure BDA0001958212500000094
wherein<·>Denotes an averaging operation, |, denotes an absolute value operation, ulRepresenting the signal reconstructed from the first layer coefficients;
in a third step S3, optimizing and solving a weighted multi-scale dictionary learning frame to obtain a fault characteristic signal x;
in the fourth step S4, the Q-switched wavelet and l are combined according to the weighted multi-scale learning frame established in the second step and the third step0Regular substitution into a frame to construct a weighted multi-scale dictionary learning special case, and Q-switched wavelet sum l-based construction0The method comprises the following steps that (1) a regular weighted multi-scale learning special case realizes the extraction of fault characteristic signals of the planet wheel bearing;
in a fifth step S5, based on the fault feature signals extracted from the multi-scale dictionary learning special case model in step four, the fault type is identified through envelope analysis.
According to the method, amplitude modulation, frequency modulation and discrete frequency components in the vibration signals of the planetary gearbox can be effectively inhibited, and fault diagnosis of the bearing of the planetary gearbox is effectively realized by integrating the kurtosis index into a frequency band with sensitive fault characteristics.
In a preferred embodiment of the method, in a first step S1, the planet wheel bearing vibration signal y e Rn×1Is y ═ x + h + n, where h ∈ Rn×1For multi-source harmonic interference, n is equal to Rn×1For strong background noise, n is the signalLength, extracting planet wheel bearing fault characteristic information x under interference of multiple source harmonic waves and strong background noise, partitioning the one-dimensional signals by an operator Г, and splicing all blocks into a matrix, wherein,
X＝[Г1(x)，Г2(x)，...，ГM-1(x)，ГM(x)]＝Γ(x)，
Г thereini：Rn×1→RN×1Indicates that the ith block is extracted from x and placed in the ith column of matrix x, Г-1：RN×M→Rn×1Representing the inverse of operator Г, Γ Г-1＝Г-1Γ＝I
In a preferred embodiment of the method, the normalized operator therefore satisfies the following relation:
Figure BDA0001958212500000101
where ⊙ represents a point-by-point multiplication.
In a preferred embodiment of the method, in a second step S2,
Figure BDA0001958212500000102
Figure BDA0001958212500000103
wherein (W)Ty)lAnd (W)Tx)lThe coefficients representing the i-th layer of the multi-scale transform,
Figure BDA0001958212500000104
Figure BDA0001958212500000105
wherein DlAnd AlRespectively, the dictionary and the coefficient obtained by the learning of the l-th layer.
In a preferred embodiment of the method, in the third step S3, a weighted multi-scale dictionary learning framework is solved by using an alternative optimization method to obtain a model-based modelA dictionary learning model consisting of sparse codes and dictionary updates by giving corresponding P (A)l) Solving to solve the bilinear non-convex problem, solving the convex quadratic optimization problem through an optimal closed-form solution, wherein the optimal closed-form solution is as follows:
Figure BDA0001958212500000111
wherein
Figure BDA0001958212500000112
And
Figure BDA0001958212500000113
is a solution to the bilinear non-convex problem.
In a preferred embodiment of the method, in a fourth step S4, P (a)l)＝||Al||0The bilinear non-convex problem in the frame is:
Figure BDA0001958212500000114
wherein epsilon represents the deviation of the model and is solved by a KSVD algorithm.
In the preferred embodiment of the method, a data acquisition system is adopted to acquire the vibration signal of the planet wheel bearing, wherein the sampling frequency is 12800 Hz.
In order to further understand the present invention, referring to fig. 2, the present embodiment provides a method for identifying a fault of a planet wheel bearing of a weighted multi-scale dictionary learning framework, including the following steps:
step 1 (S1): firstly, defining a planet wheel bearing vibration signal y epsilon Rn×1Comprises the following steps:
y＝x+h+n
wherein X ∈ Rn×1For the fault signature, h ∈ Rn×1For multi-source harmonic interference, n is equal to Rn×1Is a strong background noise. Our basic goal is to extract the planet wheel bearing fault signature information x from strong harmonic and noise interference.
Then block operators Γ and Γ are defined-1And the operator gamma realizes the blocking of the one-dimensional signals and splices all the blocks into a matrix. We can express it by the following formula:
X＝[Г1(x)，Γ2(x)，...，ГM-1(x)，ΓM(x)]＝Γ(x)
wherein gamma isi：Rn×1→RN×1Indicating that the ith block is extracted from x and placed in the ith column of matrix x. Similarly, Γ-1：RN ×M→Rn×1Representing the inverse of the operator Γ. Due to the overlap between blocks, the operator needs to be constrained as follows:
ΓΓ-1＝Γ-1Γ＝I
thus, the normalized operator satisfies the following relationship:
Figure BDA0001958212500000121
wherein ⊙ represents point-by-point multiplication;
step 2 (S2): based on the above operator definition, we can construct a weighted multi-scale dictionary learning framework, which comprises the following two parts:
Figure BDA0001958212500000122
Figure BDA0001958212500000123
wherein D ∈ RN×LRepresenting a learning dictionary, P (A) being a priori representing coefficients, λ representing a regularization parameter, A ∈ RL×MTo represent the coefficients. Wherein wTExpressing multi-scale transformation, K is a diagonal matrix containing sub-band fault characteristics and is defined as:
Figure BDA0001958212500000124
where s represents the maximum number of decomposition levels for the multi-scale transform, Kl represents the calculated kurtosis:
Figure BDA0001958212500000131
wherein<·>Denotes an averaging operation, ulRepresenting the signal reconstructed from the first layer coefficients. To simplify the derivation of the solution after, let us
Figure BDA0001958212500000132
And
Figure BDA0001958212500000133
wherein (W)Ty)lAnd (W)Tx)lRepresenting coefficients of the l-th layer of the multi-scale transform. Since the layers are independent from one another, we can consider the optimization model of only one layer (the remaining layers are similar), as follows:
Figure BDA0001958212500000134
Figure BDA0001958212500000135
wherein DlAnd AlRespectively obtaining a dictionary and a coefficient obtained by the learning of the l-th layer;
step S3: the solution of the weighted multi-scale dictionary learning framework constructed as step S2 is decomposed into a series of optimization problems on different levels l. Since the first optimization problem in the framework is a bilinear non-convex problem, we cannot find the optimal solution by using the traditional convex optimization algorithm. Therefore, we use an alternate optimization strategy to solve this non-convex optimization problem. The main idea of alternating optimization is to alternately optimize one variable with the other fixed. In fact, we can derive the optimization problem by using an alternating optimization strategy to be just a dictionary learning model consisting of sparse coding and dictionary updating, by giving the corresponding P (A)l) Many existing dictionary learning algorithms can be found to solve the problem.
The second optimization problem in the framework belongs to the convex quadratic optimization problem, and the closed-form solution of this optimization problem can be obtained directly by making the derivative of the objective function zero, whose optimal closed-form solution is:
Figure BDA0001958212500000141
wherein
Figure BDA0001958212500000142
And
Figure BDA0001958212500000143
is the solution to the first optimization problem.
After the two optimization problems are solved, the finally extracted fault characteristic information can be obtained by performing multi-scale inverse transformation
Figure BDA0001958212500000144
Step S4: giving a wavelet sum l based on Q modulation0The method comprises the steps of learning a special case of a frame by using a weighted scale dictionary, and realizing the extraction of fault characteristics of the planet wheel bearing by using the special case to verify the effectiveness of an algorithm on the fault identification of the planet wheel bearing. Let P (A) herel)＝||Al||0The first optimization problem in the framework can be rewritten as:
Figure BDA0001958212500000145
where epsilon represents the deviation of the model. Thus, the optimization problem can be solved directly by the classic KSVD algorithm.
Step S5: and aiming at the extracted fault characteristic signals, identifying the specific type of the fault through envelope analysis.
In a preferred embodiment of the method according to the present invention, in the first step S1, a normalized blocking operator is constructed to formulate a one-dimensional signal block representation.
In a preferred embodiment of the method of the present invention, in the second step S2, a weighted multi-scale dictionary learning framework is established, so as to overcome the disadvantage of the conventional dictionary learning for extracting fault features.
In a preferred embodiment of the method of the present invention, in the third step S3, the first optimization problem of the weighted multi-scale dictionary learning framework is solved by using an alternating optimization strategy, a closed-form solution of the second optimization problem is derived, and the extracted fault features are reconstructed by multi-scale transformation.
In a preferred embodiment of the method according to the invention, in a fourth step S4, the method is based on Q-adjusted wavelets and l0The regularization constructs special cases of weighted multi-scale dictionary learning, so that the effectiveness of the frame is proved by utilizing the effectiveness of the special cases.
In a preferred embodiment of the method of the present invention, in the fifth step S5, the specific type of the fault is identified through envelope analysis with respect to the extracted fault feature signal, so as to locate the fault of the planet wheel bearing.
Referring to fig. 3 and 4, the planetary gearbox fault simulation test bed and the test equipment thereof and the test bed principle of the embodiment of the invention are schematically illustrated. The test bed mainly comprises a driving motor, a two-stage planetary gear train, a two-stage ordinary gear train and a magnetic powder actuator. Acceleration sensor installs in the input and output position of first level planet wheel, and vibration signal passes through sony COC080 data collection station and gathers. The sampling frequency and the output frequency of the drive motor were 12800Hz and 30Hz, respectively.
Frequency conversion f of sun gearsun30Hz, number of teeth of the sun gear ZsNumber of teeth Z of planet gear 20pNumber of teeth Z of ring gear, 40r100. Using these parameters and the first two equations below, we can calculate the carrier rotation frequency fc5Hz and the absolute frequency of the planet carrier (the absolute frequency of the outer ring of the planet wheel bearing) fc (a)12.5 Hz. The revolution frequency of the planet wheel can be calculated by the following third formula
Figure BDA0001958212500000151
Thus, according to 61800 bearingThe outer ring fault characteristic frequency f of the planet wheel bearing can be obtained by calculating the corresponding fault characteristic frequency under the unit frequencyo34.48Hz inner ring fault characteristic frequency fi48.02Hz, rolling element fault characteristic frequency frm22.22Hz, characteristic frequency f of the cage failurecg＝3.14Hz。
Figure BDA0001958212500000161
Figure BDA0001958212500000162
Figure BDA0001958212500000163
Referring to fig. 5(a) to 5(d), the time domain, the frequency spectrum, the square envelope spectrum and the square envelope spectrum of the signal to be identified according to the embodiment of the present invention are partially enlarged. The time-domain vibration pattern 5(a) does not have a significant impact component, and the frequency spectrum pattern 5(b) is mainly based on the Mesh Frequency (MF) and its multiple frequency, and no significant resonance band is found. The square envelope spectrogram 5(c) -5 (d) also mainly takes the meshing frequency and the frequency multiplication thereof as the main part, and the fault characteristic frequency is completely submerged in the interference.
Referring to fig. 6(a) to 6(d), the weighted multi-scale dictionary learning of the embodiment of the present invention extracts time domain, frequency spectrum, square envelope spectrum and local enlargement of square envelope spectrum of features. As can be seen from the spectrum chart of fig. 6(b), the proposed algorithm can effectively locate the resonance band excited by the outer ring fault of the planet wheel bearing. In addition, as shown in fig. 6(c) to 6(d), the meshing frequency component is effectively suppressed in the square envelope spectrum and its partial enlarged view, and the outer ring fault characteristic frequency is effectively enhanced. Because the outer ring of the planet wheel bearing revolves along with the planet wheel, a component with the planet carrier rotation frequency as the side frequency exists at the outer ring fault characteristic frequency. In conclusion, the algorithm can effectively inhibit harmonic waves (meshing frequency) and noise interference and extract weak fault characteristic signals.
Referring to fig. 7(a) to 7(d), we can find that the outer ring fault characteristic frequency of the planet wheel bearing still cannot be identified in the square envelope spectrogram 7(c) -7 (d), and the meshing frequency still occupies the main energy. Therefore, the two methods cannot successfully extract the fault characteristics when the planet wheel bearing fault is analyzed.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and application fields, and the above-described embodiments are illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto without departing from the scope of the invention as defined by the appended claims.

Claims (7)

1. A planet wheel bearing fault identification method of a weighted multi-scale dictionary learning framework comprises the following steps:
in a first step (S1), constructing a blocking operator based on the planet wheel bearing vibration signal;
in the second step (S2), a weighted multi-scale dictionary learning framework is constructed based on the blocking operator, the framework comprising the following two parts:
Figure FDA0002313761970000011
Figure FDA0002313761970000012
wherein the content of the first and second substances,
Figure FDA0002313761970000013
f norm representing the matrix, y representing the signal measured by the sensor, x ∈ Rn×1For fault signature, R represents a real number set, n is the length of the signal,
Figure FDA0002313761970000014
representing the characteristic signal obtained by solution, D ∈ RN×LRepresenting a learning dictionary, wherein N is the dimension of each column in the dictionary, L represents the number of columns in the dictionary,
Figure FDA0002313761970000015
representing a solved dictionary, P (A) being a priori representing coefficients, λ representing a regularization parameter, A ∈ RL×MTo represent coefficients, where M represents the number of samples,
Figure FDA0002313761970000016
representing a solved dictionary, Γ (·) representing a blocking operator, where WTRepresents the transpose of the multi-scale transform w, K is a diagonal matrix containing the sub-band fault features, defined as
Figure FDA0002313761970000017
Where S denotes the maximum number of decomposition levels for the multiscale transform, KlIndicating the kurtosis of the l-th layer,
Figure FDA0002313761970000018
wherein<·>Denotes an averaging operation, |, denotes an absolute value operation, ulRepresenting the signal reconstructed from the first layer coefficients;
in the third step (S3), a weighted multi-scale dictionary learning framework is optimized and solved to obtain a fault characteristic signal X;
in the fourth step (S4), the Q-switched wavelet and l are combined according to the weighted multi-scale learning frame established in the second step and the third step0Regular substitution into a frame to construct a weighted multi-scale dictionary learning special case, and Q-switched wavelet sum l-based construction0The method comprises the following steps that (1) a regular weighted multi-scale learning special case realizes the extraction of fault characteristic signals of the planet wheel bearing;
in the fifth step (S5), the fault type is identified by envelope analysis based on the fault feature signal extracted by the multi-scale dictionary learning special case model in step four.
2. The method of claim 1Method, wherein in a first step (S1) a planet wheel bearing vibration signal y ∈ Rn×1Is y ═ x + h + n, where h ∈ Rn×1For multi-source harmonic interference, n is equal to Rn×1Extracting fault characteristic signals X of the planet wheel bearing under the interference of multi-source harmonic waves and strong background noise, partitioning a one-dimensional signal by an operator gamma, and splicing all the blocks into a matrix, wherein the n is the signal length,
X＝[Γ1(x)，Γ2(x)，…，ΓM-1(x)，ΓM(x)]＝Γ(x)，
wherein gamma isi：Rn×1→RN×1Denotes the extraction of the ith block from X into the ith column of the matrix X, Γ-1：RN×M→Rn×1Representing the inverse of the operator Γ-1＝Γ-1Γ ═ I, I is the identity matrix.
3. The method of claim 2, wherein, therefore, the normalized operator satisfies the relationship:
Figure FDA0002313761970000028
where □ represents a point-by-point multiplication.
4. The method according to claim 1, in a second step (S2),
Figure FDA0002313761970000022
wherein (W)Ty)lAnd (W)Tx)lThe coefficients representing the i-th layer of the multi-scale transform,
Figure FDA0002313761970000023
Figure FDA0002313761970000024
wherein the content of the first and second substances,
Figure FDA0002313761970000025
for the l-th layer coefficient of the measurement signal y under the multiscale transformation w, DlA learning dictionary for the l-th layer coefficients,
Figure FDA0002313761970000026
to solve the resulting dictionary of layer l, AlThe coefficients are represented for the dictionary of the l-th layer,
Figure FDA0002313761970000027
to solve for the resulting layer I dictionary representation coefficients, P (A)l) A priori for the dictionary representation coefficients, lambda represents the regularization parameter,
Figure FDA0002313761970000031
the ith layer coefficient under the multi-scale transformation w for the fault signature,
Figure FDA0002313761970000032
and the l-th layer coefficient of the fault characteristic signal obtained by solving under the multi-scale transformation w is shown, and Γ (·) represents a block operator.
5. The method according to claim 4, wherein in the third step (S3), the weighted multi-scale dictionary learning framework is solved by using the alternative optimization, the dictionary learning model consisting of sparse coding and dictionary updating is obtained, and the corresponding P (A) is givenl) Solving to solve the bilinear non-convex problem, solving the convex quadratic optimization problem through an optimal closed-form solution, wherein the optimal closed-form solution is as follows:
Figure FDA0002313761970000033
wherein
Figure FDA0002313761970000034
Blocking operator Γ for ith sampleiIs transposed, (.)-1Representing the inverse of the matrix, M representing the total number of samples,
Figure FDA0002313761970000035
for the layer i dictionary solved in the dictionary update,
Figure FDA0002313761970000036
is the representative coefficient of the ith sample.
6. The method of claim 1, wherein in the fourth step (S4), P (A)l)＝||Al||0，||·||0The number of non-zero elements is represented, and the bilinear non-convex problem in the framework is as follows:
Figure FDA0002313761970000037
wherein
Figure FDA0002313761970000038
For the l-th layer coefficient of the measurement signal y under the multiscale transformation w, DlA learning dictionary for the l-th layer coefficients,
Figure FDA0002313761970000039
to solve the resulting dictionary of layer l, AlThe coefficients are represented for the dictionary of the l-th layer,
Figure FDA00023137619700000310
to solve the resulting layer I dictionary representation coefficients, Γ (·) represents the blocking operator, KlAnd expressing the kurtosis of the ith layer, and expressing the deviation of the model by an epsilon-representation model, and solving by a KSVD algorithm.
7. The method of claim 1, wherein the planet wheel bearing vibration signal is acquired using a data acquisition system with a sampling frequency of 12800 Hz.
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