Fault diagnosis method for rotating machinery based on time-frequency supergroup sparse decomposition model

Abstract

The present application relates to the technical field of electromechanical equipment fault diagnosis, and particularly relates to a rotating machinery fault diagnosis method based on a time-frequency supergroup sparse decomposition model, comprising: obtaining a vibration acceleration signal sequence of the rotating machinery in a same period, an instantaneous rotating frequency signal sequence of a rotating shaft of the rotating machinery, and a theoretical fault characteristic order of each component in the rotating machinery; obtaining a time-frequency supergroup sparse decomposition model; optimizing a parameter combination of the time-frequency supergroup sparse decomposition model to obtain an optimal parameter combination corresponding to the time-frequency supergroup sparse decomposition model of each component; obtaining a time-domain reconstruction signal sequence corresponding to each component; obtaining an equiangular sampling signal sequence corresponding to each component; and obtaining a fault component of the rotating machinery. The present application realizes accurate extraction of a non-periodic fault impact characteristic signal of the rotating machinery under a variable rotating speed condition, thereby accurately determining the fault component of the rotating machinery.

Description

Technical Field

[0001] This invention relates to the field of fault diagnosis technology for electromechanical equipment, and specifically to a fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model. Background Technology

[0002] Aero-engines and wind turbines, as crucial pieces of equipment, play a significant role in driving national economic and technological development. Rotating machinery components, such as bearings, gears, and rotors, are key parts of the transmission systems in these systems. Under harsh operating conditions of high temperature, high pressure, and alternating loads, rotating machinery components are prone to localized damage that can spread, potentially leading to equipment downtime or even catastrophic accidents. Therefore, monitoring the operational status and diagnosing early faults of rotating machinery components in critical equipment is of paramount importance for safe operation and maintenance. In recent years, vibration-based rotating machinery condition monitoring has gained widespread attention due to its ease of installation and high cost-effectiveness.

[0003] When localized damage occurs to rotating mechanical components, the collision between the damaged area and contacting parts during operation will generate vibration and impact signals. Aero engines and wind turbines typically operate at variable speeds, and the fault impact signals generated by damage to rotating mechanical components under these conditions exhibit non-periodic characteristics. These fault characteristic signals are often submerged in strong background noise and vibration signals from other components, necessitating the extraction and characterization of fault features using advanced signal processing methods. Commonly used fault characteristic signal characterization methods under variable speed conditions include order tracking, order-spectral correlation analysis, and time-frequency analysis.

[0004] Existing computational order tracking, order-spectral correlation analysis, and time-frequency analysis methods are susceptible to noise, making it difficult to extract weak fault features in early damage or under strong noise environments. High-fidelity extraction of non-periodic fault impact signals is the key to early fault diagnosis of rotating machinery components under variable speed conditions.

[0005] Therefore, existing technologies have proposed sparse decomposition theory, which has the advantage of high-fidelity feature signal extraction. It represents the signal as a linear combination of an overcomplete dictionary, and then obtains the reconstruction coefficients of the feature signal by solving the sparse decomposition model. Existing technologies have conducted extensive research on sparse decomposition theories and methods for periodic fault impact signals under constant speed conditions, proposing enhanced sparse decomposition models including adjustable quality factor wavelet transform dictionaries, learned dictionaries, and overcomplete dictionary matrices. However, these periodic dictionaries cannot match aperiodic fault impact signals under variable speed conditions, making these constant-speed sparse decomposition methods difficult to directly apply to the extraction of aperiodic fault impact feature signals under variable speed conditions, thus affecting the accurate identification of faulty components in rotating machinery.

[0006] Therefore, a fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model is needed to solve the above problems. Summary of the Invention

[0007] This invention provides a fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model. This addresses the problem that existing sparse decomposition models, which obtain feature signal reconstruction coefficients based on periodic fault impact signals under constant speed conditions, cannot match aperiodic fault impact signals under variable speed conditions. Consequently, these periodic dictionaries cannot be directly applied to extract aperiodic fault impact feature signals under variable speed conditions, thus affecting the accurate identification of faulty components in rotating machinery.

[0008] The present invention provides a fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model, which adopts the following technical solution, including:

[0009] Obtain the vibration acceleration signal sequence of rotating machinery within the same time period, the instantaneous rotation frequency signal sequence of rotating machinery shaft, and the theoretical fault characteristic order of each component in rotating machinery;

[0010] Based on symmetric Laplace wavelet basis functions, a time-frequency overlap group sparse decomposition model enhanced by continuous symmetric Laplace wavelet transform is established.

[0011] The parameter combination of the time-frequency overlap group sparse decomposition model is optimized using a multi-objective optimization algorithm to obtain the optimal parameter combination for each component with respect to the time-frequency overlap group sparse decomposition model. The parameters in the parameter combination include: the number of rows of the time-frequency block, the number of columns of the time-frequency block, the sparsity parameter, and the damping ratio parameter of the time-frequency overlap group sparse decomposition model.

[0012] Based on the optimal parameter combination of each component with respect to the time-frequency overlap group sparse decomposition model, the corresponding target time-frequency overlap group sparse decomposition model is obtained. The vibration acceleration signal sequence of the rotating machinery is decomposed using the target time-frequency overlap group sparse decomposition model corresponding to each component. The decomposition result is then subjected to continuous symmetric Laplace wavelet inverse transform to obtain the time-domain reconstructed signal sequence corresponding to each component.

[0013] The instantaneous frequency switching signal sequence is accumulated and integrated to obtain the angle domain signal sequence. The mapping relationship between the angle domain signal sequence and the time domain reconstructed signal sequence is obtained. Based on the mapping relationship, the interpolation method is used to interpolate on the preset equal angle sampling sequence to obtain the equal angle sampling signal sequence corresponding to each component.

[0014] The faulty components of rotating machinery are obtained based on the envelope signal and envelope order spectrum of the equal-angle sampled signal sequence.

[0015] Preferably, the expression for the symmetric Laplace wavelet basis function is:

[0016]

[0017] In the formula, Represents the symmetric Laplace wavelet basis functions;

[0018] B represents the normalization factor;

[0019] ω0 represents the oscillation frequency of the symmetric Laplace wavelet basis function;

[0020] ζ represents the damping ratio parameter;

[0021] j represents an imaginary number;

[0022] t represents time;

[0023] e represents the natural constant.

[0024] Preferably, the steps for establishing a time-frequency overlap group sparse decomposition model based on continuous symmetric Laplace wavelet transform enhancement are as follows:

[0025] Obtaining continuous symmetric Laplace wavelet transform operators based on symmetric Laplace wavelet basis functions;

[0026] A sparse decomposition model of time-frequency overlapping groups is obtained by using the inverse transform operator of the continuous symmetric Laplace wavelet transform operator.

[0027] Preferably, the inverse transform operator expression of the continuous symmetric Laplace wavelet transform algorithm is:

[0028] y n =AW n (s l )

[0029]

[0030] In the formula, A represents the inverse transform operator of the continuous symmetric Laplace wavelet transform algorithm;

[0031] y n This represents the vibration acceleration signal sequence of rotating machinery at time n;

[0032] W n (s l () represents the time-scale domain decomposition coefficients obtained by decomposing the vibration acceleration signal sequence of rotating machinery at time n using the continuous symmetric Laplace wavelet transform algorithm;

[0033] This represents the vibration acceleration signal sequence y of rotating machinery at the nth time point within the time interval N-1. n The discrete Fourier spectrum;

[0034] s l This represents the l-th scale layer in the scale layer sequence;

[0035] δt represents the sampling time interval of the vibration acceleration signal sequence;

[0036] ω m This represents the m-th angular frequency in the angular frequency sequence;

[0037] j represents an imaginary number;

[0038] The scale layer is s l angular frequency ω m The conjugate of the Fourier spectrum of the symmetric Laplace wavelet basis functions.

[0039] Preferably, the expression for the time-frequency overlap group sparse decomposition model is:

[0040]

[0041] In the formula, This indicates finding the minimum value of the function F(x);

[0042] x represents the reconstruction coefficient of the non-periodic fault impact feature signal to be extracted from the vibration acceleration signal sequence. The reconstruction coefficient is represented as a two-dimensional matrix in the time-scale plane.

[0043] x i,K This represents a one-dimensional vector composed of all elements within the time-frequency block region K, starting from the i-th data point, in a two-dimensional matrix.

[0044] 'a' represents the regularization parameter;

[0045] λ represents the sparsity parameter of the time-frequency overlap group sparse decomposition model;

[0046] A represents the inverse transform operator of the continuous symmetric Laplace wavelet transform algorithm;

[0047] y represents the vector formed by the vibration acceleration signal of the rotating machinery.

[0048] Preferably, the steps for optimizing the parameter combination of the time-frequency overlap group sparse decomposition model using a multi-objective optimization algorithm to obtain the optimal parameter combination for each component with respect to the time-frequency overlap group sparse decomposition model are as follows:

[0049] Based on the harmonic-to-noise ratio of the envelope order spectrum feature corresponding to the theoretical fault characteristic order of each component and the correlation kurtosis of the angle domain envelope signal sequence, a multi-objective optimization model for the combination of parameters of the time-frequency overlap group sparse decomposition model corresponding to each component is established.

[0050] The NSGAII algorithm of the multi-objective optimization genetic algorithm is used to solve the multi-objective optimization model corresponding to each component to obtain the Pareto front;

[0051] The optimal parameter combination for each component is obtained based on the distance density of the non-dominated solutions contained in the Pareto front, with respect to the sparse decomposition model of the time-frequency overlap group.

[0052] Preferably, the expression for the multi-objective optimization model is:

[0053] ming(Ω)=[g1(Ω),g2(Ω)]

[0054] g1(Ω)=1 / HNR-OS(FCO k )

[0055] g2(Ω)=1 / CK-AE M (FCO k )

[0056] In the formula, ming(Ω) represents a multi-objective optimization model;

[0057] Ω represents the parameter combination of the time-frequency overlap group sparse decomposition model;

[0058] HNR-OS(FCO k The ) represents the envelope order spectral harmonic noise ratio under the theoretical fault characteristic order corresponding to the k-th component;

[0059] CK-AE M (FCO k ) represents the correlation kurtosis of the angle domain envelope signal sequence under the theoretical fault characteristic order corresponding to the k-th component.

[0060] Preferably, the step of obtaining the optimal parameter combination for each component with respect to the time-frequency overlap group sparse decomposition model based on the distance density of the non-dominated solutions contained in the Pareto front is as follows:

[0061] Normalize each nondominated solution in the Pareto front;

[0062] Obtain the first distance between each normalized nondominated solution and the origin;

[0063] Sort the first distance in ascending order to obtain the distance sequence;

[0064] In order, a preset number of normalized non-dominated solutions corresponding to distances in the distance sequence are selected as the target non-dominated solutions, and a parameter combination sequence is obtained based on the parameter combination corresponding to the target non-dominated solutions.

[0065] Normalize each parameter combination in the parameter combination sequence and obtain the distance density of each normalized parameter combination in the parameter combination sequence;

[0066] The normalized parameter combination corresponding to the minimum distance density is used as the target parameter combination;

[0067] The parameter combination before normalization corresponding to the target parameter combination is taken as the optimal parameter combination.

[0068] Preferably, the expression for the envelope order spectrum of the equal-angle sampled signal sequence is:

[0069]

[0070] In the formula, os represents the envelope order spectrum of the equiangularly sampled signal sequence.

[0071] FFT[] is the Fourier transform operator;

[0072] abs() represents the modulo operator;

[0073] This indicates that the Hilbert transform is performed on the equiangular sampled signal sequence.

[0074] Preferably, the step of obtaining the faulty component of the rotating machinery is as follows:

[0075] Obtain the main order components in the envelope order spectrum of the equiangular sampling signal sequence corresponding to each component, and whether there are fault impact signal groups with an interval equal to the reciprocal of the theoretical fault characteristic order in the envelope signal;

[0076] If the main order components corresponding to a certain component include the theoretical fault characteristic order and the order components that are integer multiples of the theoretical fault characteristic order, then the component is faulty.

[0077] If the main order component corresponding to a certain component does not include the theoretical fault characteristic order, but has an integer multiple of the theoretical fault characteristic order, and the envelope signal contains a group of fault impulse signals with an interval equal to the reciprocal of the theoretical fault characteristic order, then the component is faulty.

[0078] Preferably, the theoretical fault characteristic order of each component in the rotating machinery is calculated based on the type and geometry of the rotating machinery.

[0079] The beneficial effects of this invention are:

[0080] The constructed continuous symmetric Laplace wavelet basis functions can meet the decomposition and reconstruction framework requirements of continuous wavelet transform. Compared with discrete wavelet transform, the wavelet basis functions of continuous symmetric Laplace wavelet transform are time-shifted continuously along the time axis, which can more effectively match the impact characteristic signals of non-periodic faults in rotating machinery under variable speed conditions. Therefore, based on the continuous symmetric Laplace wavelet basis functions, a time-frequency overlap group sparse decomposition model is established. That is, the constructed time-frequency overlap group sparse decomposition model is obtained from the continuous symmetric Laplace wavelet basis functions. Thus, the time-frequency overlap group sparse decomposition model of this invention can well describe the sparse characteristics of the impact characteristic signals of non-periodic faults in rotating machinery under variable speed conditions on the time-frequency surface. Then, this invention optimizes the parameter combination of the time-frequency overlap group sparse decomposition model through a multi-objective optimization algorithm to obtain the optimal parameter combination. The target time-frequency overlap group sparse decomposition model is obtained using the optimal parameter combination. That is, this invention uses the target time-frequency overlap group sparse decomposition model obtained by the optimal parameter combination to accurately extract the impact characteristic signals of non-periodic faults in rotating machinery under variable speed conditions, thereby accurately determining the faulty components of rotating machinery.

[0081] Secondly, the adaptive optimization strategy for the parameter combination of the time-frequency overlapping group sparse decomposition model based on the multi-objective optimization genetic algorithm NSGAII adopted in this embodiment, compared with the traditional single-objective optimization strategy, takes the richness of fault feature information in both the time domain and the order domain of the sparse decomposition signal as multiple optimization objectives, and can obtain the optimal combination parameters of the sparse decomposition model more robustly. Attached Figure Description

[0082] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0083] Figure 1 This is a flowchart of a fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model according to the present invention.

[0084] Figure 2 The vibration acceleration signal collected from the QI test bench in an embodiment of the present invention;

[0085] Figure 3 The instantaneous frequency conversion signal of the rotating shaft is collected from the QI experimental platform in an embodiment of the present invention;

[0086] Figure 4The normalized Pareto front and acceptable solution set are obtained by the multi-objective optimization genetic algorithm NSGAII in the embodiments of the present invention.

[0087] Figure 5 Visualization of the parameter combinations corresponding to the acceptable solution set;

[0088] Figure 6 The waveform and a magnified view of the time-domain reconstructed signal sequence after the vibration test signal is decomposed based on the time-frequency overlap group sparse decomposition model corresponding to the optimal parameter combination are shown.

[0089] Figure 7 The waveform diagrams corresponding to the equal-angle sampling signal sequences in this embodiment are shown below.

[0090] Figure 8 This is the envelope order spectrum corresponding to the equiangular sampling signal sequence. Detailed Implementation

[0091] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0092] An embodiment of the fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model of the present invention is as follows: Figure 1 As shown, it includes:

[0093] S1. Obtain the vibration acceleration signal sequence of the rotating machinery within the same time period, the instantaneous rotation frequency signal sequence of the rotating machinery shaft, and the theoretical fault characteristic order of each component in the rotating machinery.

[0094] Specifically, in this embodiment, an acceleration sensor installed on the bearing housing or casing monitors the vibration acceleration signal of the rotating machinery, and the vibration acceleration signal at time n is y. n By setting n = 0, 1, ..., N-1, the vibration acceleration signal sequence can be obtained, where N is the length of the vibration acceleration signal sequence.

[0095] In this embodiment, the instantaneous rotational frequency signal of the rotating machinery shaft is measured using a tachometer. The instantaneous rotational frequency signal at time n is f. r (n), n=0,1,...,N-1, can be used to obtain the instantaneous frequency conversion signal sequence. The instantaneous frequency conversion signal sequence and the vibration acceleration signal sequence have the same discrete time sequence t. n n = 0, 1, ..., N-1.

[0096] In this embodiment, based on the type and geometry of the rotating machinery, the theoretical fault characteristic order of each component of the rotating machinery is calculated. The calculation of the theoretical fault characteristic order of each component of the rotating machinery adopts the method described in patent CN202311458124.X, entitled "A Method for Bearing Fault Diagnosis Based on Order Analysis and in a System," with the theoretical fault characteristic order FCO. k k = 1, 2, ..., K, where k is the serial number of the rotating machinery component and K is the total number of rotating machinery components; for rolling bearings, k = 1, 2, 3, 4 correspond to the outer ring, inner ring, rolling element, and cage, respectively; for gears, k = 1, 2 correspond to the two gears of the meshing gear pair, respectively; for rotor components, K = 1 is satisfied.

[0097] S2. Obtain the sparse decomposition model of the time-frequency overlap group;

[0098] Specifically, a continuous symmetric Laplace wavelet transform algorithm is constructed based on symmetric Laplace wavelet basis functions, and the inverse transform operator of the continuous symmetric Laplace wavelet transform algorithm is obtained. Based on the inverse transform operator of the continuous symmetric Laplace wavelet transform operator, a sparse decomposition model of the time-frequency overlapping group is obtained.

[0099] Step 21, the expression for the symmetric Laplace wavelet basis function is:

[0100]

[0101] In the formula, Represents the symmetric Laplace wavelet basis functions;

[0102] B represents the normalization factor and satisfies... η represents an intermediate parameter.

[0103] ω0 represents the oscillation frequency of the symmetric Laplace wavelet basis function;

[0104] ζ represents the damping ratio parameter and satisfies 0 < ζ < 1;

[0105] j represents an imaginary number,

[0106] t represents time;

[0107] e represents the natural constant.

[0108] In this embodiment, the oscillation frequency of the basis function is selected as ω0 = 10 to ensure its Fourier spectrum. The amplitude at ω = 0 is approximately 0. The constructed symmetric Laplace wavelet basis function... Fourier spectrum for:

[0109]

[0110] It can be verified that the symmetric Laplace wavelet basis functions are symmetric about t=0, and satisfy the following condition as |t|→∞: It possesses frequency-domain compact support and satisfies the allowable conditions for continuous wavelet transform decomposition and reconstruction. Therefore, the constructed symmetric Laplace wavelet basis functions can decompose and reconstruct the input signal through the continuous wavelet transform (CWT) framework.

[0111] Step 22, the steps of the inverse transform operator of the continuous symmetric Laplace wavelet transform algorithm are as follows:

[0112] A continuous symmetric Laplace wavelet transform algorithm is established based on symmetric Laplace wavelet basis functions. This algorithm is then used to analyze the vibration test signal y of rotating machinery. n Decomposition is performed to obtain the time-scale domain decomposition coefficients W. n (s l The expression for the time-scale domain decomposition coefficients is:

[0113]

[0114] In the formula, A represents the inverse transform operator of the continuous symmetric Laplace wavelet transform algorithm;

[0115] y n This represents the vibration acceleration signal sequence of rotating machinery at time n;

[0116] W n (s l () represents the time-scale domain decomposition coefficients obtained by decomposing the vibration acceleration signal sequence of rotating machinery at time n using the continuous symmetric Laplace wavelet transform algorithm;

[0117] This represents the vibration acceleration signal sequence y of rotating machinery at the nth time point within the time interval N-1. n The discrete Fourier spectrum, and satisfying m = 1, 2, ... N-1;

[0118] s l Let represent the l-th scale layer in the scale layer sequence, and satisfy s l =2δt·2 lδjl = 0, 1, ..., J, where J is the largest scale layer number in the scale layer sequence and satisfies J = log2(N / 2) / δj; δj represents the scale layer parameter and satisfies 0 < δj < 1;

[0119] δt represents the sampling time interval of the vibration acceleration signal sequence, and satisfies δt=t2-t1, where t2 represents the second sampling time and t1 represents the first sampling time;

[0120] ω m Let ω represent the m-th angular frequency in the angular frequency sequence, where m = 0, 1, ..., N-1. When m ≤ N / 2, ω m = 2πm / Nδt, when m>N / 2, ω m = -2πm / Nδt;

[0121] The scale layer is s l angular frequency ω m The conjugate of the Fourier spectrum of the symmetric Laplace wavelet basis functions;

[0122] For ease of description, the transform operator of the continuous symmetric Laplace wavelet transform algorithm will be written as A. T That is, W n (s l ) = A T y n On the other hand, based on the framework of symmetric Laplace wavelet basis functions and continuous wavelet inverse transform, the inverse transform operator of the continuous symmetric Laplace wavelet transform algorithm can be established and expressed as A, that is, the expression of the inverse transform operator of the continuous symmetric Laplace wavelet transform algorithm is:

[0123] y n =AW n (s l )

[0124] In the formula, A represents the inverse transform operator of the continuous symmetric Laplace wavelet transform algorithm;

[0125] y n This represents the vibration acceleration signal sequence of rotating machinery at time n;

[0126] W n (s l ) represents the time-scale domain decomposition coefficients obtained by decomposing the vibration acceleration signal sequence of rotating machinery at time n using the continuous symmetric Laplace wavelet transform algorithm.

[0127] Step 23, the expression for the time-frequency overlap group sparse decomposition model is:

[0128]

[0129] In the formula, denotes finding the minimum value of the function F(x); x represents the reconstruction coefficient of the non-periodic fault impact feature signal to be extracted in the vibration acceleration signal sequence, and the reconstruction coefficient is represented as a two-dimensional matrix in the time-scale plane, and this two-dimensional matrix is the quantity to be solved in the time-frequency overlapping group sparse decomposition model, x = {x(i), i ∈ Z J ×Z N}, that is, x is a two-dimensional matrix of J rows and N columns, i is the element position serial number in the two-dimensional matrix x, and x(i) represents the i-th element in the two-dimensional matrix; x i,K represents a one-dimensional vector composed of all elements within the time-frequency block region K starting from the i-th element in the two-dimensional matrix. At , it represents a one-dimensional vector composed of all elements within the time-frequency block region K starting from the i-th element in the two-dimensional matrix; f is the serial number of the elements within the time-frequency block region K, and K1 and K2 represent the number of rows and columns within the time-frequency block region K in sequence; a represents the regularization term parameter, and 0 < a ≤ 1 / (K1K2λ); λ represents the sparsity parameter of the time-frequency overlapping group sparse decomposition model; A represents the inverse transform operator of the continuous symmetric Laplace wavelet transform algorithm; y represents the vector composed of the vibration acceleration signals of the rotating machinery; || ||2 = (∑ N || 2 ) 1 / 2 is the L2 norm operator, that is, the root mean square of the sum of the squares of each element in the two-dimensional vector; ψ(||x i,K ||2; a) is the regularization term of the sparse decomposition model and is represented as where atan() is the arctangent operator.至此,即可得到x通过连续对称Laplace小波逆变换的时域重构信号

[0130] S3. Optimize the parameter combinations of the time-frequency overlapping group sparse decomposition model to obtain the optimal parameter combination corresponding to each component with respect to the time-frequency overlapping group sparse decomposition model;

[0131] Since the parameter combinations of the number of rows K1, the number of columns K2, the sparsity parameter λ, and the damping ratio parameter ζ of the time-frequency overlap group sparse decomposition model will affect the extraction effect of non-periodic fault feature signals of rotating machinery, this embodiment establishes a multi-objective optimization model for each component based on the envelope order spectral feature harmonic ratio and the angular domain envelope signal sequence correlation kurtosis corresponding to the theoretical fault feature order of each component. The NSGAII algorithm of the multi-objective optimization genetic algorithm is used to solve the multi-objective optimization model for each component to obtain the Pareto front. The optimal parameter combination for each component with respect to the time-frequency overlap group sparse decomposition model is obtained according to the distance density of the non-dominated solutions contained in the Pareto front. The parameters in the parameter combination include: the number of rows, the number of columns, the sparsity parameter, and the damping ratio parameter of the time-frequency overlap group sparse decomposition model.

[0132] Step 31, the expression for the multi-objective optimization model is:

[0133] min g(Ω)=[g1(Ω),g2(Ω)]

[0134] g1(Ω)=1 / HNR-OS(FCO k )

[0135] g2(Ω)=1 / CK-AE M (FCO k )

[0136] In the formula, ming(Ω) represents the multi-objective optimization model; Ω represents the parameter combination of the time-frequency overlap group sparse decomposition model; HNR-OS(FCO) k ) represents the envelope order spectral characteristic harmonic ratio under the theoretical fault characteristic order corresponding to the k-th component; CK-AE M (FCO k ) represents the correlation kurtosis of the angle domain envelope signal sequence under the theoretical fault characteristic order corresponding to the k-th component.

[0137] Wherein, the signal sequence length of the envelope order spectrum os is N1 / 2, denoted as os(f i ), i = 0, 1, ..., N1 / 2, f i For each order component, the eigenharmonic-noise ratio of the envelope order spectrum is defined as:

[0138]

[0139] Wherein, os(α×FCO k ), α=1,2,...,M0 represents the amplitude of the first M0 order fault characteristic order in the envelope order spectrum os. It is recommended that M0 be 3≤M0≤5, and in this embodiment, it is 4.

[0140] Angular domain envelope signal correlation kurtosis CK-AE M (FCO k ) is defined as:

[0141]

[0142] Among them, T θ =round[1 / (δθ·FCO)] k )], round[] is the rounding operator; ∏() is the multiplication operator; The envelope signal representing the sequence of equally sampled signals; Indicates envelope signal Mid-data points The product of the data points at intervals mT, where m = 1, 2, ..., M; the recommended value for parameter M is 3 ≤ M ≤ 5, and in this embodiment, it is 4.

[0143] Step 32: In this embodiment, the multi-objective optimization model is solved using the NSGAII multi-objective optimization genetic algorithm to obtain the Pareto front (g1(Ω)). h ),g2(Ω h h = 1, 2, ..., H, where H represents the number of non-dominated solutions in the Pareto front, and the parameter combination corresponding to each non-dominated solution is Ω. h =(K 1,h ,K 2,h ,ζ h ,λ h The optimal parameter combination for each component is obtained based on the distance density of the non-dominated solutions contained in the Pareto front, with respect to the sparse decomposition model of the time-frequency overlap group.

[0144] The steps for obtaining the optimal parameter combination based on the distance density of the non-dominated solutions contained in the Pareto front are as follows:

[0145] Normalize each nondominated solution in the Pareto front:

[0146]

[0147] Where min() is the minimum value operator; max() is the maximum value operator, and each non-dominated solution in the normalized Pareto front is represented as: h = 1, 2, ..., H.

[0148] Obtain each normalized nondominated solution The first distance between i=1,2 and the origin

[0149]

[0150] First distance in ascending order The distance sequence is obtained by sorting: A preset number of normalized non-dominated solutions corresponding to the distances in the distance sequence are selected sequentially (in this embodiment, the preset number is the first Q distances in the distance sequence) as the target non-dominated solution. The parameter combination Ω corresponding to the target non-dominated solution is then used... i =(K 1i ,K 2i ,ζ i ,λ i ), i = 1, 2, ..., Q, to obtain the parameter combination sequence Γ = {Ω i ,i=1,2,...,Q}.

[0151] For the parameter combination sequence Γ={Ω i Normalize each parameter combination in {i = 1, 2, ..., Q}:

[0152] i = 1, 2, ..., Q, β = 1, 2, 3, 4

[0153] Among them, Ω i (1) = K 1i Ω i (2) = K 2i Ω i (3)=ζ i Ω i (4)=λ i If there exists max(Ω) i (β))=min(Ω i (β)), then the normalization parameter combination is set to The number of elements in the acceptable solution set Γ is generally 20% to 40% of the number of elements in the Pareto front, that is, the value of Q is Q = (0.2 to 0.4)H.

[0154] And obtain each normalized parameter combination Distance density in parameter combination sequences;

[0155]

[0156] In the formula, This represents the distance density in the i-th parameter combination; Represents the combination of normalized parameters Combination with normalized parameters The distance, of which, The expression is:

[0157]

[0158] The normalized parameter combination corresponding to the minimum distance density among all distance densities is used as the target parameter combination. The expression for the normalized parameter combination is:

[0159]

[0160] Combine target parameters The corresponding parameter combination before normalization As the optimal parameter combination, the optimal parameter combination corresponding to the time-frequency overlap group sparse decomposition model for each component can be obtained.

[0161] S4. Obtain the time-domain reconstructed signal sequence corresponding to each component;

[0162] Specifically, based on the optimal parameter combination corresponding to the time-frequency overlap group sparse decomposition model for each component, the corresponding target time-frequency overlap group sparse decomposition model is obtained. The vibration acceleration signal sequence of the rotating machinery is decomposed using the target time-frequency overlap group sparse decomposition model corresponding to each component, and the decomposition result is subjected to continuous symmetric Laplace wavelet inverse transform to obtain the time-domain reconstructed signal sequence corresponding to each component.

[0163] In this embodiment, when using parameter groups At that time, the vibration acceleration signal sequence is decomposed by the target time-frequency overlap group sparse decomposition model corresponding to the parameter combination to obtain the reconstruction coefficients. The reconstruction coefficients are then subjected to continuous symmetric Laplace wavelet inverse transform to reconstruct the signal in the time domain, and the time domain reconstructed signal sequence is obtained. The length of the time domain reconstructed signal sequence is the same as the length of the vibration acceleration signal sequence.

[0164] S5. Obtain the equiangular sampling signal sequence corresponding to each component;

[0165] Specifically, the instantaneous frequency switching signal sequence is accumulated and integrated to obtain the angle domain signal sequence. The mapping relationship between the angle domain signal sequence and the time domain reconstructed signal sequence is obtained. Based on the mapping relationship, the interpolation method is used to interpolate on the preset equal angle sampling sequence to obtain the equal angle sampling signal sequence corresponding to each component.

[0166] In this embodiment, the instantaneous frequency conversion signal f r (n), n = 0, 1, ..., N-1, are cumulatively integrated. The angle domain signal is obtained, and the angle domain signal sequence has a one-to-one mapping relationship with the time domain reconstructed signal sequence; the angle domain sampling interval is selected as δθ, and the sampling interval is [θ0, θ...]. N-1 Within the range, an equal-angle sampling sequence θ is constructed with an interval of δθ. ang =[θ0,θ0+δθ,θ0+2δθ,...,θ N-1The length of its equal-angle sampling sequence is denoted as N1; the mapping value at time n in the mapping relationship is obtained through interpolation. In the equiangular sampling sequence θ ang Interpolation is performed on the above to obtain a sequence of equal-angle sampled signals, denoted as . n = 0, 1, ..., N1-1, where, θ is the angle sampled signal at time n in the equal-angle sampled signal sequence; n Let be the angle domain signal corresponding to time n in the angle domain signal sequence. This is the time-domain reconstructed signal corresponding to time n in the time-domain reconstructed signal sequence. Thus, the equal-angle sampled signal sequence is obtained.

[0167] S6. Obtain the faulty components of the rotating machinery;

[0168] Specifically, the faulty components of rotating machinery are obtained based on the envelope signal and envelope order spectrum of the equal-angle sampled signal sequence.

[0169] Step 61: In this embodiment, the expression for the envelope order spectrum of the equal-angle sampled signal sequence is:

[0170]

[0171] In the formula, os represents the envelope order spectrum of the equal-angle sampled signal sequence;

[0172] FFT[] is the Fourier transform operator;

[0173] abs() represents the modulo operator;

[0174] This indicates performing a Hilbert transform on a sequence of equally sampled signals.

[0175] The expression for the envelope signal of an equal-angle sampled signal sequence is:

[0176]

[0177] This represents the envelope signal of a sequence of equally sampled signals.

[0178] Step 62, the steps for obtaining the faulty component of the rotating machinery are as follows:

[0179] Step 621: Obtain the main order components in the envelope order spectrum of the equal-angle sampling signal sequence corresponding to each component, and whether there is a fault impact signal group with an interval that is the reciprocal of the theoretical fault characteristic order in the envelope signal.

[0180] Step 622: If the main order components corresponding to a certain component include the theoretical fault characteristic order and the order components that are integer multiples of the theoretical fault characteristic order, then the component is faulty.

[0181] Step 623: If the main order component corresponding to a certain component does not include the theoretical fault characteristic order, but has an integer multiple of the theoretical fault characteristic order, and the envelope signal contains a fault impulse signal group with an interval equal to the reciprocal of the theoretical fault characteristic order, then the component is faulty.

[0182] Step 624: If the intervals in the main order components and envelope signals corresponding to a certain component do not satisfy steps 622 and 623, then the rotating machinery is normal.

[0183] The present invention will now be described in conjunction with specific embodiments.

[0184] This embodiment was conducted on the SQI rotating machinery failure simulation test bench of SpectraQuest. The rolling bearing tested was model ER-12K. Before the experiment, a crack with a width of 0.1 mm and a depth of 0.4 mm was pre-fabricated on the inner ring of the test bearing. Based on the geometric parameters of the bearing under test, the failure characteristic order of each component of the test rolling bearing was calculated as shown in Table 1.

[0185] Table 1 Test bearing geometric parameters and fault characteristic order

[0186]

[0187] In the experiment, the instantaneous rotational speed of the shaft was measured using a laser rangefinder sensor mounted above the shaft and a reflective strip on the shaft. The vibration acceleration signal of the rolling bearing was measured using an accelerometer mounted on the bearing housing. The sampling frequency was 10kHz. The collected vibration acceleration signals are shown below. Figure 2 As shown, the corresponding instantaneous frequency conversion signal is as follows: Figure 3 As shown. For the inner ring failure mode of rolling bearings, the optimal combination parameters of the sparse decomposition model are first determined using a multi-objective optimization method. Based on the NSGAII method, the Pareto front containing 40 solutions is obtained, as shown... Figure 4 The diagram shows the normalized non-dominated solutions. Based on this, the acceptable solution set of the multi-objective optimization model (i.e., the parameter combination set corresponding to the first Q normalized non-dominated solutions corresponding to the first distance) is determined by the first distance of each normalized non-dominated solution from the origin, containing a total of 8 solutions, as shown below. Figure 4 As shown, the visualization results of the parameter combinations (K1, K2, ζ, λ) corresponding to each solution are as follows: Figure 5 As shown. Then, the parameter combinations corresponding to each solution in the feasible solution set are normalized, and the distance density of each feasible solution is calculated to obtain the optimized parameter combination. ζ* =0.3938, λ * =2.3044.

[0188] The target time-frequency overlap group sparse decomposition model is obtained by using the optimal parameter combination, and then the target time-frequency overlap group sparse decomposition model is used to... Figure 2 The vibration acceleration signal in the image is subjected to continuous symmetric Laplace wavelet transform to enhance time-frequency overlap group sparse decomposition, and the resulting domain waveform is shown below. Figure 6 As shown in the enlarged view, the impact characteristics of the extracted signal can be clearly observed. Next, the extracted signal is resampled in the angle domain, resulting in an equal-angle sampled signal, as shown below. Figure 7 As shown, the equal-angle sampling signal exhibits significant periodic impulse characteristics. Meanwhile, Figure 7 During one revolution of the display shaft, there are approximately five cycle intervals of fault impacts, which are very close to the fault characteristic order FCO of the bearing inner ring. I =4.95, which allows for a preliminary judgment that these extracted fault impact signals are caused by damage to the bearing inner ring. Then, the envelope order spectrum of the equal-angle sampled signals is calculated, such as... Figure 8 As shown, the main component in the envelope order spectrum is the FCO, which is close to the inner circle fault characteristic order. I The components 1X1 = 4.7325 and their integer multiples indicate the presence of an inner ring fault in the tested rolling bearing. This demonstrates that the method proposed in this invention can accurately extract the non-periodic fault impact characteristic signal under variable speed operating conditions of rotating machinery, and characterize and identify faults in rotating machinery.

[0189] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model, characterized in that, include: Obtain the vibration acceleration signal sequence of rotating machinery within the same time period, the instantaneous rotation frequency signal sequence of rotating machinery shaft, and the theoretical fault characteristic order of each component in rotating machinery; Based on symmetric Laplace wavelet basis functions, a sparse decomposition model of time-frequency overlap groups enhanced by continuous symmetric Laplace wavelet transform is established. The steps for establishing the sparse decomposition model of time-frequency overlap groups enhanced by continuous symmetric Laplace wavelet transform are as follows: obtaining the continuous symmetric Laplace wavelet transform operator based on the symmetric Laplace wavelet basis functions; obtaining the sparse decomposition model of time-frequency overlap groups based on the inverse transform operator of the continuous symmetric Laplace wavelet transform operator. The expression for the symmetric Laplace wavelet basis function is: In the formula, Represents the symmetric Laplace wavelet basis functions; Indicates the normalization factor; This represents the oscillation frequency of the symmetric Laplace wavelet basis function; Indicates the damping ratio parameter; represents an imaginary number; Indicates time; Represents the natural constant; The inverse transform operator expression for the continuous symmetric Laplace wavelet transform algorithm is: In the formula, This represents the inverse transform operator of the continuous symmetric Laplace wavelet transform algorithm; This represents the vibration acceleration signal sequence of rotating machinery at time n; The time-scale domain decomposition coefficients are obtained by decomposing the vibration acceleration signal sequence of rotating machinery at time n using the continuous symmetric Laplace wavelet transform algorithm. Indicates the time period of rotating machinery Vibration acceleration signal sequence at time n within The discrete Fourier spectrum; Represents the first in the scale layer sequence Each scale layer; This represents the sampling time interval of the vibration acceleration signal sequence; This represents the m-th angular frequency in the angular frequency sequence; represents an imaginary number; The scale layer is represented as angular frequency The conjugate of the Fourier spectrum of the symmetric Laplace wavelet basis functions; The parameter combination of the time-frequency overlap group sparse decomposition model is optimized using a multi-objective optimization algorithm to obtain the optimal parameter combination for each component with respect to the time-frequency overlap group sparse decomposition model. The parameters in the parameter combination include: the number of rows of the time-frequency block, the number of columns of the time-frequency block, the sparsity parameter, and the damping ratio parameter of the time-frequency overlap group sparse decomposition model. Based on the optimal parameter combination of each component with respect to the time-frequency overlap group sparse decomposition model, the corresponding target time-frequency overlap group sparse decomposition model is obtained. The vibration acceleration signal sequence of the rotating machinery is decomposed using the target time-frequency overlap group sparse decomposition model corresponding to each component. The decomposition result is then subjected to continuous symmetric Laplace wavelet inverse transform to obtain the time-domain reconstructed signal sequence corresponding to each component. The instantaneous frequency switching signal sequence is accumulated and integrated to obtain the angle domain signal sequence. The mapping relationship between the angle domain signal sequence and the time domain reconstructed signal sequence is obtained. Based on the mapping relationship, the interpolation method is used to interpolate on the preset equal angle sampling sequence to obtain the equal angle sampling signal sequence corresponding to each component. The faulty components of rotating machinery are obtained based on the envelope signal and envelope order spectrum of the equal-angle sampled signal sequence.

2. The fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model according to claim 1, characterized in that, The expression for the sparse decomposition model of the time-frequency overlap group is: In the formula, Expressing the search function It reaches a minimum value; Represents the reconstruction coefficients of the non-periodic fault impact feature signal to be extracted from the vibration acceleration signal sequence. The reconstruction coefficients are represented as a two-dimensional matrix in the time-scale plane. This represents the time-frequency block region in a two-dimensional matrix, starting from the i-th data point. A one-dimensional vector consisting of all elements within it; This represents the regularization parameter, and , and The time-frequency block regions are represented sequentially. The number of rows and columns within; This represents the sparsity parameter of the time-frequency overlap group sparse decomposition model; This represents the inverse transform operator of the continuous symmetric Laplace wavelet transform algorithm; This represents a vector composed of vibration acceleration signals of rotating machinery.

3. The fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model according to claim 1, characterized in that, The steps for optimizing the parameter combination of the time-frequency overlap group sparse decomposition model using a multi-objective optimization algorithm to obtain the optimal parameter combination for each component with respect to the time-frequency overlap group sparse decomposition model are as follows: Based on the harmonic-to-noise ratio of the envelope order spectrum feature corresponding to the theoretical fault characteristic order of each component and the correlation kurtosis of the angle domain envelope signal sequence, a multi-objective optimization model for the combination of parameters of the time-frequency overlap group sparse decomposition model corresponding to each component is established. The NSGAII algorithm of the multi-objective optimization genetic algorithm is used to solve the multi-objective optimization model corresponding to each component to obtain the Pareto front; The optimal parameter combination for each component is obtained based on the distance density of the non-dominated solutions contained in the Pareto front, with respect to the sparse decomposition model of the time-frequency overlap group.

4. The fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model according to claim 3, characterized in that, The expression for the multi-objective optimization model is: In the formula, This represents a multi-objective optimization model; This represents the parameter combination of the time-frequency overlap group sparse decomposition model; This represents the envelope order spectral harmonic-to-noise ratio under the theoretical fault characteristic order corresponding to the k-th component; It represents the correlation kurtosis of the angular domain envelope signal sequence under the theoretical fault characteristic order corresponding to the k-th component.

5. The fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model according to claim 3, characterized in that, The steps to obtain the optimal parameter combination for each component in the time-frequency overlap group sparse decomposition model based on the distance density of the non-dominated solutions contained in the Pareto front are as follows: Normalize each nondominated solution in the Pareto front; Obtain the first distance between each normalized nondominated solution and the origin; Sort the first distance in ascending order to obtain the distance sequence; In order, a preset number of normalized non-dominated solutions corresponding to distances in the distance sequence are selected as the target non-dominated solutions, and a parameter combination sequence is obtained based on the parameter combination corresponding to the target non-dominated solutions. Normalize each parameter combination in the parameter combination sequence and obtain the distance density of each normalized parameter combination in the parameter combination sequence; The normalized parameter combination corresponding to the minimum distance density is used as the target parameter combination; The parameter combination before normalization corresponding to the target parameter combination is taken as the optimal parameter combination.

6. The fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model according to claim 1, characterized in that, The expression for the envelope order spectrum of an equal-angle sampled signal sequence is: In the formula, The envelope order spectrum represents the sequence of equally sampled signals at equal angles; For Fourier transform operators; This represents the modulo operator; This indicates that the Hilbert transform is performed on the equiangular sampled signal sequence.

7. The fault diagnosis method for rotating machinery based on a time-frequency overlap group sparse decomposition model according to claim 1, characterized in that, The steps for identifying the faulty component of rotating machinery are as follows: Obtain the main order components in the envelope order spectrum of the equiangular sampling signal sequence corresponding to each component, and whether there are fault impact signal groups with an interval equal to the reciprocal of the theoretical fault characteristic order in the envelope signal; If the main order components corresponding to a certain component include the theoretical fault characteristic order and the order components that are integer multiples of the theoretical fault characteristic order, then the component is faulty. If the main order component corresponding to a certain component does not include the theoretical fault characteristic order, but has an integer multiple of the theoretical fault characteristic order, and the envelope signal contains a group of fault impulse signals with an interval equal to the reciprocal of the theoretical fault characteristic order, then the component is faulty.

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