Sparse representation diagnosis method for rotating machinery based on feature-oriented regularization parameters

Abstract

A diagnosis method for rotating machinery based on feature-guided regular parameters is disclosed. In the method, the vibration acceleration signal at the bearing end cover of the rotating machinery is collected; the signal decomposition dictionary is set as a composite redundant dictionary composed of Fourier basis and orthogonal wavelet basis; the least angle regression algorithm is used to solve the sparse representation coefficients corresponding to the collected vibration acceleration signal in the composite redundant dictionary, and the solution path of the convex optimization problem constrained by the l1 norm is obtained; multiple candidate feature signals are reconstructed respectively by using the temporary solutions obtained in each step of the least angle regression algorithm, where each candidate feature signal corresponds to the temporary solution of the convex optimization problem under a certain regular parameter; the feature presence index FP of each candidate feature signal is calculated respectively, and the largest feature presence index FP corresponds to the optimal regular parameter setting and the optimal fault feature signal; the rotating machinery fault diagnosis is carried out by judging whether there is a significant fault feature frequency in the envelope demodulation spectrum of the fault feature signal.

Description

Technical Field

[0001] The invention relates to the technical field of rotating machinery fault diagnosis, and in particular to a rotating machinery sparse representation diagnosis method based on feature-oriented regularization parameters. Background Art

[0002] The sparse representation fault diagnosis method decomposes the mechanical vibration signal into a redundant waveform dictionary, and finally reconstructs the fault feature signal through the sparse representation coefficient to realize the fault feature extraction and diagnosis of rotating machinery. [1，2] . The sparse representation algorithm can obtain the corresponding sparse representation coefficient of the signal in the dictionary by solving the optimization problem constrained by the l0 norm or l1 norm. However, the selection of the regularization parameter λ in the sparse representation algorithm plays a crucial role in feature reconstruction. However, the existing regularization parameter selection is mainly based on the fixed parameter setting formula derived under the additive white noise signal model. The noise in the actual signal often does not satisfy the white noise assumption, so the reconstructed denoised signal often cannot reveal the fault characteristics. In addition, the setting of the existing regularization parameters can also adopt the "trial and error" method: under each regularization parameter setting, compare and select the signal with the best feature reconstruction. This type of "trial and error" method has a slow processing speed, and the parameter selection is too dependent on the subjective judgment of the diagnostic personnel.

[0003] 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 to a person of ordinary skill in the art. Summary of the invention

[0004] The purpose of the present invention is to provide a rotating machinery sparse representation diagnosis method based on feature-guided regularization parameters, which solves the problem of difficult regularization parameter selection in existing sparse representation algorithms, realizes effective extraction of fault feature signals under arbitrary noise distribution, and further realizes accurate rotating machinery fault diagnosis.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A sparse representation diagnosis method for rotating machinery based on feature-oriented regularization parameters of the present invention comprises:

[0007] Step 1, collecting vibration acceleration signals of rotating machinery;

[0008] Step 2, setting the signal decomposition dictionary to a composite redundant dictionary composed of a Fourier basis and an orthogonal wavelet basis;

[0009] Step 3, using the minimum angle regression algorithm to solve the sparse representation coefficients corresponding to the collected vibration acceleration signal in the composite redundant dictionary, and obtain the solution path of the convex optimization problem with l1 norm constraints;

[0010] Step 4, using the temporary solutions obtained in each step of the minimum angle regression algorithm, reconstruct multiple candidate feature signals, wherein each candidate feature signal corresponds to a temporary solution of the convex optimization problem under a regularization parameter;

[0011] Step 5, respectively calculating the feature existence index FP of each feature signal to be selected, wherein the largest feature existence index FP corresponds to the optimal regularization parameter setting and the optimal fault feature signal;

[0012] Step 6: Perform rotating machinery fault diagnosis by judging whether there is a significant fault characteristic frequency in the envelope demodulation spectrum of the fault characteristic signal.

[0013] In a sparse representation diagnosis method for rotating machinery based on feature-oriented regularization parameters, the mathematical expression of the convex optimization problem with l1 norm constraint is as follows:

[0014]

[0015] Where y is the noisy vibration acceleration signal; A is the composite redundant dictionary; x is the sparse representation coefficient; λ is the regularization parameter; ||·||2 represents the l2 norm of the vector; ||·||1 represents the l1 norm of the vector, and argmin represents the corresponding x value when the subsequent function takes the minimum value, which is recorded as

[0016] In a sparse representation diagnosis method for rotating machinery based on feature-oriented regularization parameters, a method for reconstructing multiple candidate feature signals is as follows: in is the sparse representation coefficient on the solution path obtained by the minimum angle regression algorithm; y i is the reconstructed i-th candidate feature signal.

[0017] In a sparse representation diagnosis method for rotating machinery based on feature-oriented regularization parameters, the calculation steps of the feature presence index FP are as follows:

[0018] Step 5-1, calculate the analytical signal of the reconstructed candidate feature signal: in is the Hilbert transform of the reconstructed candidate feature signal y, j is an imaginary unit;

[0019] Step 5-2, calculate the envelope demodulation spectrum ES of the selected characteristic signal y y (f k ):

[0020]

[0021] Where t is time; y a (n) represents the analytical signal y of the feature signal to be selected aThe value at discrete time n; y a The discrete frequency f k = k / N (k = 1, 2, ..., N), k is the number of discrete spectral lines; N is y a Length;

[0022] Step 5-3, using the moving median μ MED and the moving median absolute deviation σ MAD The envelope demodulation spectrum is normalized, and the formula is expressed as: In the formula represents the normalized envelope demodulation spectrum; f k is the discrete frequency; μ MED (f k ),σ MAD (f k ) are the moving median and the moving absolute deviation median at f k The value at

[0023] Step 5-4, in the hypothesis testing framework, set the significance level α to 0.05, then the 95% score of the spectral line amplitude in the standardized envelope demodulation spectrum is λ 0.95 It is determined as the feature significance threshold;

[0024] Step 5-5, at the fault characteristic frequency α c1 Nearby, set the search band to [α c1 -0.05α c1 , α c1 +0.05α c1 ], the highest spectral line amplitude in the search band is m1, then the calculation formula of the characteristic existence index FP component is as follows:

[0025]

[0026] Step 5-6, at the higher harmonics 2α of the fault characteristic frequency c1 , 3α c1 Calculate the index components F2 and F3 according to step 5-5, then the final characteristic existence index FP is the arithmetic mean of each component: FP = (F1 + F2 + F3) / 3.

[0027] In the above technical scheme, a sparse representation diagnostic method for rotating machinery based on feature-guided regularization parameters provided by the present invention has the following beneficial effects: a sparse representation diagnostic method for rotating machinery based on feature-guided regularization parameters of the present invention can efficiently obtain the solution path of the sparse representation optimization problem by using the minimum angle regression algorithm, that is, the curve of the sparse representation coefficient changing with the regularization parameter, and by designing the feature existence index FP, based on the diagnostic principle, directly select the optimal fault feature signal corresponding to the optimal regularization parameter, thereby overcoming the additive white noise assumption based on the traditional fixed regularization parameter setting formula, and improving the scope of application and practical application effect of the sparse fault diagnosis method. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0029] Figure 1 It is a flow chart of the sparse representation diagnosis method of rotating machinery based on feature-oriented regularization parameters in the present invention;

[0030] Figure 2 It is a schematic diagram of the calculation process of the feature existence index FP of the rotating machinery sparse representation diagnosis method based on the feature-oriented regularization parameter in the present invention;

[0031] Figure 3(a) to Figure 3(c) It is a schematic diagram of the envelope demodulation spectrum standardization process of the rotating machinery sparse representation diagnosis method based on feature-oriented regularization parameters in the present invention, wherein FIG3(a) is the envelope demodulation spectrum of the reconstructed selected characteristic signal of the rotating machinery sparse representation diagnosis method based on feature-oriented regularization parameters in the present invention; FIG3(b) is the standardized envelope demodulation spectrum; FIG3(c) is a schematic diagram of the spectral line amplitude feature significance threshold selected according to the 95% quantile;

[0032] Using the moving median μ MED and the moving median absolute deviation σ MAD , the envelope demodulation spectrum 3(a) is standardized, and the result is shown in Figure 3(b). Therefore, the spectrum lines of this standardized envelope demodulation spectrum have approximately the same fluctuation variance and mean. Thanks to the standardization operation, the 95% quantile of the spectrum line can be used as a threshold to determine whether there is a significant feature. The FP index is calculated based on the significant threshold;

[0033] Figure 4 It is a schematic diagram for collecting vibration acceleration signals at the end cover of the rotating machinery bearing;

[0034] Figure 5(a) to Figure 5(b) In order to use the minimum angle regression algorithm to solve the solution path and characteristic existence index FP curve of the convex optimization problem with l1 norm constraint, the meaning of the solution path in Figure 5(a) is: the ordinate value of all curves corresponding to a horizontal axis is the solution of the optimization problem under a regularization parameter. Figure 5(b) shows the curve of the index FP changing with the l1 norm of the representation coefficient, where the maximum characteristic existence index FP corresponds to the optimal regularization parameter setting and the optimal fault characteristic signal;

[0035] Figure 6(a) to Figure 6(b) Schematic diagram of the sparse representation diagnosis effect of rotating machinery based on feature-oriented regularization parameter setting, where Fig. 6(a) is the optimal fault feature signal extracted according to the maximum value of the feature existence index FP; Fig. 6(b) is the envelope demodulation spectrum of the optimal fault feature signal, where BPFI is the characteristic frequency of the inner race fault of the bearing;

[0036] As shown in Figure 6(a), the rotating machinery sparse representation diagnosis method based on feature-oriented regularization parameter setting selects the optimal fault feature signal corresponding to the optimal regularization parameter. In Figure 6(b), there are obvious spectral peaks at BPFI and its multiples, indicating that this method can effectively extract impact fault features and break the additive white noise assumption of the collected signal. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described in combination with the embodiments of the present invention. Obviously, the described embodiments are 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 creative work are within the scope of protection of the present invention.

[0038] Therefore, the following Figure 1 to Figure 6(b) The detailed description of the embodiments of the present invention provided in the present invention is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention.

[0039] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0040] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0041] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0042] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be directly connected or indirectly connected through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0043] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may include that the first and second features are in direct contact, or may include that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, a first feature being "above", "above" and "above" a second feature includes that the first feature is directly above and obliquely above the second feature, or simply indicates that the first feature is higher in level than the second feature. A first feature being "below", "below" and "below" a second feature includes that the first feature is directly below and obliquely below the second feature, or simply indicates that the first feature is lower in level than the second feature.

[0044] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings. A sparse representation diagnosis method for rotating machinery based on feature-oriented regularization parameters includes:

[0045] Step 1, collecting the vibration acceleration signal of the rotating machinery;

[0046] Step 2, setting the signal decomposition dictionary to a composite redundant dictionary composed of a Fourier basis and an orthogonal wavelet basis;

[0047] Step 3, using the minimum angle regression algorithm to solve the sparse representation coefficients corresponding to the collected vibration acceleration signal in the composite redundant dictionary, and obtain the solution path of the convex optimization problem with l1 norm constraints;

[0048] Step 4, respectively using the temporary solution obtained in each step of the minimum angle regression algorithm to reconstruct multiple candidate feature signals, wherein each candidate feature signal corresponds to a temporary solution of the convex optimization problem under a regularization parameter.

[0049] In step 5, the characteristic existence index FP of each characteristic signal to be selected is calculated respectively, wherein the largest characteristic existence index FP corresponds to the optimal regularization parameter setting and the optimal fault characteristic signal; the optimal fault characteristic signal is used to calculate the envelope demodulation spectrum in step 6; by setting the optimal regularization parameter, the optimal fault characteristic signal can be obtained.

[0050] Step 6, by judging whether there is a significant fault characteristic frequency in the envelope demodulation spectrum of the fault characteristic signal to perform rotating machinery fault diagnosis, if the spectrum line amplitude at the fault characteristic frequency is significantly higher than the other spectrum line amplitudes, it indicates that there is a significant fault characteristic frequency. For example, the 95% quantile of all spectrum lines is used as a threshold, where the spectrum line amplitude exceeds the threshold, it is considered that there is a significant fault characteristic frequency.

[0051] In a preferred implementation of a sparse representation diagnosis method for rotating machinery based on feature-oriented regularization parameters, the mathematical expression of the convex optimization problem with l1 norm constraint is as follows:

[0052]

[0053] Where y is the noisy vibration acceleration signal; A is the composite redundant dictionary; x is the sparse representation coefficient; λ is the regularization parameter; ||·||2 represents the l2 norm of the vector; ||·||1 represents the l1 norm of the vector, and argmin represents the corresponding x value when the subsequent function takes the minimum value, which is recorded as

[0054] In a preferred implementation of a rotating machinery sparse representation diagnosis method based on feature-oriented regularization parameters, a method for reconstructing multiple candidate feature signals is: in is the sparse representation coefficient on the solution path obtained by the minimum angle regression algorithm; y i is the reconstructed i-th candidate feature signal.

[0055] In a preferred implementation of a rotating machinery sparse representation diagnosis method based on feature-oriented regularization parameters, the calculation steps of the feature presence index FP are:

[0056] Step 5-1, calculate the analytical signal of the reconstructed candidate feature signal: in is the Hilbert transform of the reconstructed candidate feature signal y;

[0057] Step 5-2, calculate the envelope demodulation spectrum ES of the selected characteristic signal y y (f k ):

[0058]

[0059] Where t is time; y a (n) represents the analytical signal y of the feature signal to be selected a The value at discrete time n; y a The discrete frequency f k = k / N (k = 1, 2, ..., N), k is the number of discrete spectral lines; N is y a Length;

[0060] Step 5-3, using the moving median μ MED and the moving median absolute deviation σ MAD The envelope demodulation spectrum is normalized, and the formula is expressed as: like Figure 3(a) to Figure 3(c) As shown;

[0061] Step 5-4, in the hypothesis testing framework, set the significance level α = 0.05, then the 95% score of the spectral line amplitude in the standardized envelope demodulation spectrum is λ 0.95 It is determined as the feature significance threshold;

[0062] Step 5-5, at the fault characteristic frequency α c1 Nearby, set the search band to [α c1 -0.05α c1 , α c1 +0.05α c1 ], the highest spectral line amplitude in the search band is m1, then the calculation formula of the characteristic existence index FP component is as follows:

[0063]

[0064] Step 5-6, at the higher harmonics 2α of the fault characteristic frequency c1 , 3α c1 Calculate the index components F2 and F3 according to step 5-5, then the final characteristic existence index FP is the arithmetic mean of each component: FP = (F1 + F2 + F3) / 3.

[0065] In one embodiment, Figure 4 Take the vibration acceleration signal in as an example. The vibration acceleration signal collected at the end cover of the rotating machinery bearing is as follows Figure 4 As shown;

[0066] The signal decomposition dictionary is set to be a composite redundant dictionary composed of a Fourier basis and an orthogonal wavelet basis;

[0067] The minimum angle regression algorithm is used to solve the sparse representation coefficients corresponding to the collected signal in the composite redundant dictionary, and the solution path of the convex optimization problem with l1 norm constraint is obtained, as shown in Figure 5(a);

[0068] The temporary solutions obtained in each step of the minimum angle regression algorithm are used to reconstruct multiple candidate feature signals, each of which corresponds to the solution of the optimization problem under a certain regularization parameter;

[0069] The characteristic existence index FP of each candidate reconstructed signal is calculated separately, and the curve of the characteristic existence index FP changing with the representation coefficient l1 norm is shown in Figure 5(b), where the maximum characteristic existence index FP corresponds to the optimal regularization parameter setting and the optimal fault characteristic signal, and the optimal fault characteristic signal is shown in Figure 6(a); the envelope demodulation spectrum of the final fault characteristic signal is calculated, as shown in Figure 6(b), and it is found that there is a significant bearing inner ring fault characteristic frequency BPFI and its frequency multiple components in the envelope demodulation spectrum, so it is diagnosed that the inner ring of the rotating machinery bearing has local damage in this case.

[0070] In one embodiment, the rotating machine includes a rotating shaft.

[0071] In one embodiment, a vibration acceleration signal at an end cover of a rotating machinery bearing is collected.

[0072] Finally, it should be noted that the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without making any creative work are within the scope of protection of the present application.

[0073] The above description is only by way of illustration of certain exemplary embodiments of the present invention. It is undoubted that those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the above drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A sparse representation diagnosis method for rotating machinery based on feature-oriented regularization parameters, characterized in that: It includes the following steps: Step 1, collecting vibration acceleration signals of rotating machinery; Step 2, setting the signal decomposition dictionary to a composite redundant dictionary composed of a Fourier basis and an orthogonal wavelet basis; Step 3, using the minimum angle regression algorithm to solve the sparse representation coefficients corresponding to the collected vibration acceleration signal in the composite redundant dictionary, and obtain the solution path of the convex optimization problem with l1 norm constraints, wherein the solution path is a solution set of the optimization problem corresponding to different regularization parameters; Step 4, using the temporary solutions obtained in each step of the minimum angle regression algorithm, reconstruct multiple candidate feature signals, where each candidate feature signal corresponds to a temporary solution of a convex optimization problem under a regularization parameter; Step 5, respectively calculating the feature existence index FP of each feature signal to be selected, wherein the regularization parameter corresponding to the largest feature existence index and the feature signal to be selected are the optimal regularization parameter setting and the optimal fault feature signal; Step 6, by judging whether there is a significant fault characteristic frequency in the envelope demodulation spectrum of the optimal fault characteristic signal to diagnose the rotating machinery fault, wherein the spectrum line amplitude at the fault characteristic frequency is significantly higher than the amplitudes of other spectrum lines, indicating that there is a significant fault characteristic frequency, wherein the 95% quantile of all spectrum lines is used as the threshold, and the spectrum line amplitude exceeding the threshold is considered to be the presence of a significant fault characteristic frequency.

2. A rotating machinery sparse representation diagnosis method based on feature-oriented regularization parameters according to claim 1, characterized in that: Preferably, the mathematical formulation of the convex optimization problem with l1 norm constraint is as follows: Where y is the noisy vibration acceleration signal; A is the composite redundant dictionary; x is the sparse representation coefficient; λ is the regularization parameter; ||·||2 represents the l2 norm of the vector; ||·||1 represents the l1 norm of the vector, and argmin represents the corresponding x value when the subsequent function takes the minimum value, which is recorded as 3. A rotating machinery sparse representation diagnosis method based on feature-oriented regularization parameters according to claim 2, characterized in that: The method for reconstructing multiple feature signals to be selected is: in is the sparse representation coefficient on the solution path obtained by the minimum angle regression algorithm; y i is the reconstructed i-th candidate feature signal.

4. A rotating machinery sparse representation diagnosis method based on feature-oriented regularization parameters according to claim 3, characterized in that: The calculation steps of the feature presence index FP are: Step 5-1, calculate the analytical signal y of the reconstructed candidate feature signal a : in is the Hilbert transform of the reconstructed candidate feature signal y, j is an imaginary unit; Step 5-2, calculate the envelope demodulation spectrum ES of the selected characteristic signal y y (f k ): Where t is time; y a (n) represents the analytical signal y of the feature signal to be selected a The value at discrete time n; y a The discrete frequency f k = k / N (k = 1, 2, ..., N), k is the number of discrete spectral lines; N is y a Length; Step 5-3, normalizing the envelope demodulation spectrum to obtain a standardized envelope demodulation spectrum Where μ MED (f k ),σ MAD (f k ) are the moving medians μ MED and the moving median absolute deviation σ MAD In f k The value at Step 5-4, in the hypothesis testing framework, set the significance level α to 0.05, then the 95% quantile λ of the spectral line amplitude in the standardized envelope demodulation spectrum 1-α It is determined as the feature significance threshold; Step 5-5, at the fault characteristic frequency α c1 Nearby, set the search band to [α c1 -0.05α c1 ,α c1 +0.05α c1 ], the highest spectral line amplitude in the search band is m1, then the calculation formula of the characteristic existence index FP component is as follows: In the formula, m1 represents the highest spectral line amplitude in the search frequency band, and F1 represents the component of the feature existence index FP; Step 5-6, at the higher harmonics 2α of the fault characteristic frequency c1 , 3α c1 At 2α c1 , 3α c1 Replace α c1 , execute steps 5-5 respectively to obtain new index components, which are recorded as index components F2 and F3 respectively. Then the final feature existence index FP is the arithmetic mean of each component: FP = (F1+F2+F3) / 3.

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