A method for reconstructing bearing vibration signals of strong noise engineering equipment

Abstract

The present invention belongs to the technical field of engineering machinery, and discloses a method for reconstructing the vibration signal of a strong noise engineering bearing, comprising the following steps: step 1, collecting the original signal; step 2, using the particle swarm algorithm to obtain the three-dimensional coordinates and fitness size of the particle with the largest fitness value of the particle swarm; step 3, using the Laplace wavelet basis function constructed with the optimal coordinates (f, ξ), and using the time shift parameter τ as a variable to span, and constructing a Laplace wavelet dictionary; step 4, inputting the signal and the dictionary into a regularization solver, setting the regularization parameter, obtaining the reconstruction coefficient, and generating a reconstructed signal. The present invention realizes the sparse reconstruction of the vibration signal of the bearing of the strong noise engineering equipment, overcomes the problems of the difficulty of denoising and feature extraction of the strong noise vibration signal of the engineering type existing in the prior art, and effectively solves the difficulties of the traditional method in signal acquisition, noise reduction filtering, and analysis and identification.

Description

Technical Field

[0001] The invention belongs to the technical field of engineering machinery, and in particular relates to a method for reconstructing vibration signals of a strong noise engineering bearing. Background Art

[0002] Engineering equipment is often used in open-air working environments such as roads, bridges, and mines. Unlike indoor electromechanical equipment, its complex and changeable working environment brings many challenges to the intelligent diagnosis research of engineering equipment. Common engineering equipment includes road construction machinery, mining equipment, and wind power equipment. When the bearing of engineering equipment fails, the characteristics of the collected signal show the characteristics of instability and nonlinearity. Its characteristic impact waveform is sparse compared with the overall signal and can be extracted separately. There are various signals that transmit information in nature, and the analysis and processing of signals is an important means of scientific research. The signals collected by sensors usually contain a large amount of working information and state characteristics of the collected system. When the signal contains only a limited number of non-zero sampling data of features, and the rest are zero (or approximately equal to zero), the signal is sparse, that is, the degree of freedom of the signal feature is less than or much less than the dimension of the signal itself. Reconstructing using the sparsity of the signal can effectively solve the difficulties of traditional methods in signal acquisition, noise reduction filtering, analysis and recognition. Summary of the invention

[0003] In view of the problems existing in the prior art, the purpose of the present invention is to propose a method for reconstructing the vibration signal of a strong noise engineering bearing, to achieve sparse reconstruction of the vibration signal of the bearing of strong noise engineering equipment, and to overcome the problems existing in the prior art of difficulty in denoising and feature extraction of engineering strong noise vibration signals.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions to achieve it.

[0005] 1. Sparse representation model of vibration signals

[0006] If the signal If the number of non-zero elements of does not exceed K (||x||0≤K), then x is called K-sparse. Furthermore, let x = Aα, where A is a certain framework. If α is K-sparse, then x is K-sparse under framework A. In actual use, due to the influence of factors such as the working environment and background noise, the signal x does not strictly meet the above definition. Therefore, consider the following conventional optimization problem:

[0007]

[0008] The above formula is a 10-norm minimum optimization problem, but this problem has two main disadvantages:

[0009] (1) The equality constraint x=Aα is too strict because it is extremely difficult to represent any vector using the sparse columns in A. Therefore, a certain error is allowed in the actual optimization.

[0010] (2) The sparse measure 10-norm is too sensitive to elements with smaller values ​​in α, so a better measure should be found to adopt a more relaxed measure for small-valued elements.

[0011] Research has shown that the P0 problem in general is a non-deterministic polynomial problem, which brings many conceptual challenges. Therefore, for the problem in the above formula, try to relax the 10 function, relax 10 to the 11 norm, and introduce the error tolerance threshold ∈, and you can get the following change of formula (P1):

[0012]

[0013] This form of transformation is called basis pursuit denoising (BPDN). Equation (3.2) can be described as a standard optimization problem with linear penalty terms and quadratic linear inequality constraints. By introducing a suitable Lagrange multiplier λ, the solution of equation (3.2) can be transformed into:

[0014]

[0015] The above formula is a solution to a common unconstrained optimization problem. The penalty parameter λ determines the sparseness of the vector obtained in the final solution. The bearing of engineering equipment is affected by environmental factors, and the collected signals usually contain a large amount of background noise, which seriously affects the determination of the working state of the bearing. Decomposing the original signal x, the fault vibration signal of the bearing can be linearly expressed by the following formula:

[0016] x=∑c r g r +ε (3.4)

[0017] Among them, g r is the wavelet atom that expresses the fault characteristics, c r is the sparse representation coefficient, and ε is the noise signal.

[0018] A is the fault feature wavelet atom g rThe constructed dictionary, α is a one-dimensional vector composed of various sparse representation coefficients. By multiplying a finite number of non-zero atoms in the vector with the dictionary, the original vibration signal can be restored as much as possible. Fault features often appear periodically in vibration signals, and the impact waveforms they produce have relatively fixed oscillation frequencies and damping ratios, so they are sparse compared to the original signals. The noise component ε is distributed throughout the entire signal, has no fixed characteristic waveform, cannot be represented by a finite number of features, and is not sparse, which provides a theoretical possibility for sparse reconstruction to remove background noise.

[0019] Substituting the bearing vibration signal of formula (3.4) into the sparse representation model of formula (3.3), we get:

[0020]

[0021] In formula (3.5), ξ is the signal reconstruction error. In the process of signal reconstruction, the sparsity of the reconstructed signal is adjusted by adjusting the regularization term λ in the model, and the noise signal ε can be processed as the residual between the acquired signal and the reconstructed signal. According to the selection of different sparsities, the sparse reconstruction of the signal is expected to eliminate the background noise and achieve dynamic balance while maintaining the original data characteristics, that is, the ξ value is as small as possible. The entire reconstruction process can be regarded as the process of extracting the fault impact features of the bearing vibration signal. The original signal is projected into a feature space composed of a series of non-orthogonal basis functions. The projection coefficient of each basis function is the sparse representation coefficient (sparse coding). Each group of basis functions represents a fault feature atom, and these atoms together constitute a sparse representation dictionary. The construction of the dictionary and the solution of the representation coefficient are crucial to the quality of the final reconstructed signal.

[0022] 2. Laplace wavelet dictionary construction and representation coefficient solution based on PSO

[0023] In the sparse model formula (3.3), dictionary A is the basic component for defining sparse signals and completing the reconstruction process. The energy of sparse signals is usually concentrated in a small number of representation atoms. The main features of the original signal can be represented by sparse representation coefficients and representation atoms to achieve the reconstruction process of the original signal. Common dictionary forms include pre-constructed dictionaries and adaptive dictionaries. Adaptive dictionaries can represent any signal that conforms to the sparse structure to a certain extent. Its internal atoms are composed of a series of unstructured matrices. Since they need to be fitted with the help of learning and training algorithms, the amount of calculation is greater in practical applications and is limited to low-dimensional data signals.

[0024] According to the sparseness of the impact characteristics when the bearing failure of the engineering equipment occurs, consider selecting a pre-constructed dictionary, in which the atomic structure is controlled by specific parameters. Common ones include:

[0025] (1) Wavelet packets dictionary

[0026] Wavelet packets use a set of orthogonal, rapidly decaying wavelet packet basis functions for signal fitting, such as dBN wavelet, sym wavelet, etc. There are many types of wavelet packet basis function families, which can characterize most vibration signals. Its basic wavelet expression is as follows:

[0027]

[0028] Where a is the scale parameter, which controls the scale (frequency) of the wavelet by scaling, and b is the wavelet translation parameter, which controls its position in the time domain.

[0029] (2) Laplace wavelet dictionary

[0030] The Laplace wavelet is a non-orthogonal, unilaterally decaying complex exponential wavelet. Its characteristic waveform is similar to the impact waveform of a bearing fault. By adjusting the (ω, ξ, τ) in the function, a variety of unilaterally decaying impact waveforms can be simulated.

[0031] Traditional signal representation methods rely on orthogonal basis functions and reconstruct signals through linear combinations of basis functions. For a set of orthogonal basis functions (such as the family of wavelet packet basis functions), they can accurately and uniquely represent any signal, but due to strict orthogonal restrictions, their expansion is simple and the sparsity is not ideal. If the basis function is not selected properly, a large number of representation coefficients may be required to approximately fit the original signal, which brings problems in data calculation and processing. Therefore, the Laplace wavelet basis function close to the fault characteristic waveform is selected, and the non-orthogonal basis function is used as the atom of the dictionary. Sparse representation can replace the orthogonal basis of the traditional method with the redundant basis in the complete dictionary, breaking through the limitations of basis function selection, thereby obtaining a reconstructed signal that better matches the original signal characteristics.

[0032] When the complexity of the original signal is not high and the characteristic structure is relatively simple, the Laplace wavelet correlation filtering method is used to search for the time, natural frequency and damping ratio of the fault impact characteristics in the signal through a one-to-one comparison to complete the construction of the wavelet characteristic structure. However, this method takes a long time and has low efficiency when processing complex vibration signals such as engineering equipment bearings, and it is difficult to meet actual engineering needs. Particle swarm optimization (PSO) is a parameter optimization algorithm that is inspired by the mutual cooperation of bird flocks for prey, and realizes the search for optimal parameters through mutual cooperation and information sharing between individuals and groups. The specific update rules are as follows:

[0033]

[0034] x i =x i +υ i (3.8)

[0035] In formula (3.7) and formula (3.8): i = 1, 2, ..., N is the total number of particles in the group; υ i , x i are the current speed and position of the particle respectively. The particle swarm optimization algorithm continuously adjusts its own speed and position through information sharing between different particles, and finally makes all particles tend to the same optimal value to realize the search of the optimal Laplace wavelet characteristic atom. The three basic parameters of the Laplace wavelet (f, ξ, τ) are used as the three-dimensional coordinates of the particle, and the correlation coefficient between the wavelet basis function and the original signal is used as the fitness function of the algorithm to evaluate the similarity between the Laplace wavelet composed of many particles and the original vibration signal fault characteristics. The calculation method is as follows:

[0036]

[0037] According to the known original parameter range, each particle can continuously adjust its own parameters through calculation, and finally obtain the optimal matching characteristic parameters which are faster and more efficient than the original method. After the optimal wavelet atom is obtained through algorithm search, the time-shift parameter is used as a variable for expansion to complete the construction of the Laplace wavelet dictionary.

[0038] Solving the sparse representation coefficients is a key step in obtaining sparse signals. The optimization methods for the classic sparse model of formula (3.1) mainly include greedy algorithms and convex relaxation methods. The greedy algorithm is represented by orthogonal matching pursuit. In each iteration, the residual signal of the previous step is searched for the item that best matches the dictionary A and puts it into the solution coefficient. Then the new residual signal is obtained to enter the next iteration until the allowable error threshold is met. The basis pursuit denoising model of formula (3.3) is a convex relaxation algorithm, which relaxes l0 to the l1 norm. At present, for the problem of solving l1 regularization, EWOUT V, DEN B and others proposed a root-finding algorithm for any point on the least squares solution curve. The proposed method is converted into a problem form that can be solved by the optimizer.

[0039] Based on the above algorithm models, the reconstruction algorithm model of the bearing vibration signal can be finally realized according to the following steps:

[0040]

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows: utilizing the sparsity of the signal for reconstruction can effectively solve the difficulties of traditional methods in signal acquisition, noise reduction filtering, analysis and identification, and overcome the problems existing in the prior art of difficulty in denoising engineering strong noise vibration signals and difficulty in feature extraction. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] Figure 1 a bearing data acquisition platform for Case Western Reserve University;

[0044] Figure 2 is the original vibration signal of the laboratory;

[0045] Figure 3 This is the spectrum of the original vibration signal in the laboratory;

[0046] Figure 4 shows the Laplace wavelet optimal parameter optimization process;

[0047] Figure 4(a) shows the optimization of normal bearing vibration signal parameters;

[0048] Figure 4(b) shows the optimization of the inner race fault vibration signal parameters;

[0049] Figure 4(c) shows the optimization of the outer ring fault vibration signal parameters;

[0050] Figure 5 Sparse reconstruction of vibration signals of fault-free bearings;

[0051] Figure 6 Sparse reconstruction of vibration signals of bearings with inner ring faults;

[0052] Figure 7 Sparse reconstruction of vibration signals of bearings with rolling element faults;

[0053] Figure 8 Sparse reconstruction of bearing vibration signals with outer ring fault. DETAILED DESCRIPTION

[0054] The embodiments of the present invention will be described in detail below with reference to examples, but those skilled in the art will understand that the following examples are only used to illustrate the present invention and should not be construed as limiting the scope of the present invention.

[0055] 1. Sparse representation model of vibration signals

[0056] If the signal If the number of non-zero elements of does not exceed K (||x||0≤K), then x is called K-sparse. Furthermore, let x = Aα, where A is a certain framework. If α is K-sparse, then x is K-sparse under framework A. In actual use, due to the influence of factors such as the working environment and background noise, the signal x does not strictly meet the above definition. Therefore, consider the following conventional optimization problem:

[0057] (P0):

[0058] The above formula is a 10-norm minimum optimization problem, but this problem has two main disadvantages:

[0059] (1) The equality constraint x=Aα is too strict because it is extremely difficult to represent any vector using the sparse columns in A. Therefore, a certain error is allowed in the actual optimization.

[0060] (2) The sparse measure 10-norm is too sensitive to elements with smaller values ​​in α, so a better measure should be found to adopt a more relaxed measure for small-valued elements.

[0061] Research has shown that the P0 problem in general is a non-deterministic polynomial problem, which brings many conceptual challenges. Therefore, for the problem in the above formula, try to relax the 10 function, relax 10 to the 11 norm, and introduce the error tolerance threshold ∈, and you can get the following change of formula (P1):

[0062]

[0063] This form of transformation is called basis pursuit denoising (BPDN). Equation (3.2) can be described as a standard optimization problem with linear penalty terms and quadratic linear inequality constraints. By introducing a suitable Lagrange multiplier λ, the solution of equation (3.2) can be transformed into:

[0064]

[0065] The above formula is a solution to a common unconstrained optimization problem. The penalty parameter λ determines the sparseness of the vector obtained in the final solution. The bearing of engineering equipment is affected by environmental factors, and the collected signals usually contain a large amount of background noise, which seriously affects the determination of the working state of the bearing. Decomposing the original signal x, the fault vibration signal of the bearing can be linearly expressed by the following formula:

[0066] x=∑c r g r +ε (3.4)

[0067] Among them, g ris the wavelet atom that expresses the fault characteristics, c r is the sparse representation coefficient, and ε is the noise signal.

[0068] A is the fault feature wavelet atom g r The constructed dictionary, α is a one-dimensional vector composed of various sparse representation coefficients. By multiplying a finite number of non-zero atoms in the vector with the dictionary, the original vibration signal can be restored as much as possible. Fault features often appear periodically in vibration signals, and the impact waveforms they produce have relatively fixed oscillation frequencies and damping ratios, so they are sparse compared to the original signals. The noise component ε is distributed throughout the entire signal, has no fixed characteristic waveform, cannot be represented by a finite number of features, and is not sparse, which provides a theoretical possibility for sparse reconstruction to remove background noise.

[0069] Substituting the bearing vibration signal of formula (3.4) into the sparse representation model of formula (3.3), we get:

[0070]

[0071] In formula (3.5), ξ is the signal reconstruction error. In the process of signal reconstruction, the sparsity of the reconstructed signal is adjusted by adjusting the regularization term λ in the model, and the noise signal ε can be processed as the residual between the acquired signal and the reconstructed signal. According to the selection of different sparsities, the sparse reconstruction of the signal is expected to eliminate the background noise and achieve dynamic balance while maintaining the original data characteristics, that is, the ξ value is as small as possible. The entire reconstruction process can be regarded as the process of extracting the fault impact features of the bearing vibration signal. The original signal is projected into a feature space composed of a series of non-orthogonal basis functions. The projection coefficient of each basis function is the sparse representation coefficient (sparse coding). Each group of basis functions represents a fault feature atom, and these atoms together constitute a sparse representation dictionary. The construction of the dictionary and the solution of the representation coefficient are crucial to the quality of the final reconstructed signal.

[0072] 2. Laplace wavelet dictionary construction and representation coefficient solution based on PSO

[0073] In the sparse model formula (3.3), dictionary A is the basic component for defining sparse signals and completing the reconstruction process. The energy of sparse signals is usually concentrated in a small number of representation atoms. The main features of the original signal can be represented by sparse representation coefficients and representation atoms to achieve the reconstruction process of the original signal. Common dictionary forms include pre-constructed dictionaries and adaptive dictionaries. Adaptive dictionaries can represent any signal that conforms to the sparse structure to a certain extent. Its internal atoms are composed of a series of unstructured matrices. Since they need to be fitted with the help of learning and training algorithms, the amount of calculation is greater in practical applications and is limited to low-dimensional data signals.

[0074] According to the sparseness of the impact characteristics when the bearing failure of the engineering equipment occurs, consider selecting a pre-constructed dictionary, in which the atomic structure is controlled by specific parameters. Common ones include:

[0075] (1) Wavelet packets dictionary

[0076] Wavelet packets use a set of orthogonal, rapidly decaying wavelet packet basis functions for signal fitting, such as dBN wavelet, sym wavelet, etc. There are many types of wavelet packet basis function families, which can characterize most vibration signals. Its basic wavelet expression is as follows:

[0077]

[0078] Where a is the scale parameter, which controls the scale (frequency) of the wavelet by scaling, and b is the wavelet translation parameter, which controls its position in the time domain.

[0079] (2) Laplace wavelet dictionary

[0080] The Laplace wavelet is a non-orthogonal, unilaterally decaying complex exponential wavelet. Its characteristic waveform is similar to the impact waveform of a bearing fault. By adjusting the (ω, ξ, τ) in the function, a variety of unilaterally decaying impact waveforms can be simulated.

[0081] Traditional signal representation methods rely on orthogonal basis functions and reconstruct signals through linear combinations of basis functions. For a set of orthogonal basis functions (such as the family of wavelet packet basis functions), they can accurately and uniquely represent any signal, but due to strict orthogonal restrictions, their expansion is simple and the sparsity is not ideal. If the basis function is not selected properly, a large number of representation coefficients may be required to approximately fit the original signal, which brings problems in data calculation and processing. Therefore, the Laplace wavelet basis function close to the fault characteristic waveform is selected, and the non-orthogonal basis function is used as the atom of the dictionary. Sparse representation can replace the orthogonal basis of the traditional method with the redundant basis in the complete dictionary, breaking through the limitations of basis function selection, thereby obtaining a reconstructed signal that better matches the original signal characteristics.

[0082] When the complexity of the original signal is not high and the characteristic structure is relatively simple, the Laplace wavelet correlation filtering method is used to search for the time, natural frequency and damping ratio of the fault impact characteristics in the signal through a one-to-one comparison to complete the construction of the wavelet characteristic structure. However, this method takes a long time and has low efficiency when processing complex vibration signals such as engineering equipment bearings, and it is difficult to meet actual engineering needs. Particle swarm optimization (PSO) is a parameter optimization algorithm that is inspired by the mutual cooperation of bird flocks for prey, and realizes the search for optimal parameters through mutual cooperation and information sharing between individuals and groups. The specific update rules are as follows:

[0083]

[0084] x i =x i +υ i (3.8)

[0085] In formula (3.7) and formula (3.8): i = 1, 2, ..., N is the total number of particles in the group; υ i , x i are the current speed and position of the particle respectively. The particle swarm optimization algorithm continuously adjusts its own speed and position through information sharing between different particles, and finally makes all particles tend to the same optimal value to realize the search of the optimal Laplace wavelet characteristic atom. The three basic parameters of the Laplace wavelet (f, ξ, τ) are used as the three-dimensional coordinates of the particle, and the correlation coefficient between the wavelet basis function and the original signal is used as the fitness function of the algorithm to evaluate the similarity between the Laplace wavelet composed of many particles and the original vibration signal fault characteristics. The calculation method is as follows:

[0086]

[0087] According to the known original parameter range, each particle can continuously adjust its own parameters through calculation, and finally obtain the optimal matching characteristic parameters which are faster and more efficient than the original method. After the optimal wavelet atom is obtained through algorithm search, the time-shift parameter is used as a variable for expansion to complete the construction of the Laplace wavelet dictionary.

[0088] Solving the sparse representation coefficients is a key step in obtaining sparse signals. The optimization methods for the classic sparse model of formula (3.1) mainly include greedy algorithms and convex relaxation methods. The greedy algorithm is represented by orthogonal matching pursuit. In each iteration, the residual signal of the previous step is searched for the item that best matches the dictionary A and puts it into the solution coefficient. Then the new residual signal is obtained to enter the next iteration until the allowable error threshold is met. The basis pursuit denoising model of formula (3.3) is a convex relaxation algorithm, which relaxes 10 to 11 norms. At present, for the 11 regularization solution problem, EWOUT V, DEN B and others proposed a root-finding algorithm for any point on the least squares solution curve. The proposed method is converted into a problem form that can be solved by the optimizer.

[0089] Based on the above algorithm models, the reconstruction algorithm model of the bearing vibration signal can be finally realized according to the following steps:

[0090]

[0091] The experimental data of this embodiment comes from the fault bearing data of the electrical engineering laboratory of Case Western Reserve University (CWRU). Figure 1 As shown. The equipment includes acceleration and torque sensors to record vibration signals and real-time speed. The remote load can adjust the radial load of the bearing. The test bearings include SKF6203 on the fan end and SKF6205 on the drive end of the test bench. The sampling frequencies are 12kHz and 48kHz.

[0092] Taking the faulty bearing at the drive end as an example, its basic information is shown in Table 1, and the time domain and frequency domain graphs of some vibration signals are shown in Table 1. Figure 2 , Figure 3 shown.

[0093] Table 1 Parameters of faulty bearings to be tested

[0094]

[0095] From the vibration signal, it can be found that the amplitude of the normal bearing signal does not change much, and there is no obvious impact component. The inner and outer ring bearings have obvious periodic impact oscillation components and noise interference components, and the rolling element fault impact waveform is aliased. The characteristic waveforms of the three faults all show a certain sparse characteristic, that is, they are expressed in a certain number of features in the time domain diagram. Figure 3 ,from Figure 3 According to the signal frequency domain analysis results, the frequency energy of normal bearings is concentrated in the low frequency band, while the frequency energy of faulty bearings is concentrated in the range of 2000-4000Hz, and there is weak noise energy expression in the other frequency bands.

[0096] To achieve the modal parameter identification of the measured object, the particle swarm optimization algorithm is used to calculate the fitness information of each particle containing the wavelet parameter information, and the moving speed and orientation are continuously adjusted to finally make the parameters tend to the optimal. The correlation coefficient between the Laplace wavelet atom and the measured signal is used as the metric of the fitness function. The three parameter characteristics of the Laplace wavelet f, ξ, τ are set as the three-dimensional coordinates of the particle. Among them, according to the spectrum analysis of the fault vibration signal, as shown in Figure 4, the fault impact natural frequency is concentrated in the frequency band of 2000-4000Hz, so the parameter range is preliminarily defined: f[2000, 4000 (Hz)], ξ[0, 0.2], τ[0, 0.2], and the particle swarm algorithm optimization process of the vibration signals of the healthy bearing and the inner and outer ring fault bearings shown in Figure 4 is obtained.

[0097] Referring to Figure 4, the similarity in Figure 4 is determined by the Laplace wavelet atom and Figure 2 The correlation coefficient of the overall vibration signal in is calculated and multiplied by a certain coefficient. The purpose is to find the most matching signal feature in the local range as much as possible. It can be seen that after 140 iterations, the correlation between the wavelet atom and the fault feature of the measured signal gradually increases, and the three-dimensional coordinates of the optimal particle, that is, the optimal Laplace wavelet parameter, are calculated. From the PSO optimization process, it can be seen that the normal bearing does not contain relevant fault features, and there is no optimal Laplace wavelet atom with a high matching degree after the iteration. As the number of iterations increases, the matching degree of the inner and outer ring faults gradually increases.

[0098] refer to Figures 5 to 8 , which is the reconstructed signal obtained after sparse representation of the original vibration signal of each working condition of the bearing. From the reconstruction result, the reconstructed signal effectively filters out irrelevant signal interference components compared with the original signal. Among them, for the inner and outer ring fault bearings, due to the existence of periodic feature information, its reconstructed signal shows a certain regularity. For the rolling element fault bearing, it collides with the inner and outer rings of the bearing at the same time during high-speed rotation, the feature periodicity is slightly worse, and the fault feature is more complex than the previous two. Since there is no fault feature for the fault-free bearing, its feature sparsity is poor, and the reconstruction result is not much different from the original signal.

[0099] Although the present invention has been described in detail in general terms and in specific embodiments in this specification, it is obvious to those skilled in the art that some modifications or improvements may be made to the present invention. Therefore, these modifications or improvements made without departing from the spirit of the present invention all fall within the scope of protection claimed by the present invention.

Claims

1. A method for reconstructing bearing vibration signals of strong noise engineering equipment, characterized in that: The following steps are involved: Step 1, collect the original signal; Step 2, using the particle swarm algorithm to obtain the three-dimensional coordinates and fitness value of the particle with the largest fitness value in the particle swarm; Step 3, the Laplace wavelet basis function constructed with the optimal coordinates (f0, ξ0) is spanned with the time shift parameter τ as a variable to construct a Laplace wavelet dictionary; f0 is the wavelet oscillation frequency that best matches the local characteristics of the signal obtained by the particle swarm optimization algorithm, and ξ0 is the damping coefficient that best matches the local characteristics of the signal obtained by the particle swarm optimization algorithm; Step 4: Input the signal and dictionary into the regularization solver, set the regularization parameters, obtain the reconstruction coefficients, and generate the reconstructed signal; The sub-steps of step 2 are: Sub-step 2.1, set the range of initial parameter coordinates (f, ξ, τ), as well as the number of particle swarms Num, the maximum moving speed Veo and the number of iterations iter; the initial parameter coordinates (f, ξ, τ) are the three basic parameters of the Laplace wavelet and serve as the three-dimensional coordinates of the particles, f represents the oscillation frequency of the wavelet function, ξ is the damping coefficient, which is used to control the exponential decay rate of the wavelet, and τ is the time shift parameter, which is used to describe the translation position of the wavelet on the time axis; Sub-step 2.2, using the correlation coefficient between the wavelet basis function and the original signal as the fitness function of the particle swarm algorithm to evaluate the similarity between the Laplace wavelet composed of many particles and the fault characteristics of the original vibration signal, the calculation method is as follows: k in formula (3) r It is the optimal correlation coefficient, i.e. the covariance matrix; the larger its value is, the closer it is to 1, the higher the correlation is; the smaller its value is, the closer it is to 0, the lower the correlation is; Sub-step 2.3, using the particle swarm algorithm to calculate the three-dimensional coordinates and fitness value of the particle with the largest fitness value in the particle swarm; Specifically, the update rules of the particle swarm optimization algorithm are as follows: v i =v i +c1×rand()×(pbest i -x i )+c2×rand()×(gbest i -x i ) (1) x i =x i +v i (2) In equations (1) and (2), i = 1, 2, ..., N is the total number of particles in the group; υ i , x i are the current speed and position of the particle respectively; Each particle calculates the fitness value of the particle swarm at the new position by continuously adjusting its own parameters, and iterates iter times; finally, through multiple iterations of the particle swarm, the three-dimensional coordinates and fitness size of the particle with the largest fitness value in the particle swarm at the final position are given.

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