Fault diagnosis method for bearing based on GA-VMD and adaptive stochastic resonance

Abstract

This invention discloses a bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance, belonging to the field of early fault diagnosis of rotating machinery. The implementation method is as follows: First, the original rolling bearing vibration signal is acquired. Second, using envelope entropy as the comprehensive objective function, a genetic algorithm is used to search for the minimum value of the comprehensive objective function, determining the optimal combination of the penalty parameter α and the number of modes k in the variational mode decomposition algorithm. Third, the original bearing signal is initially denoised using the optimized variational mode decomposition algorithm. Fourth, using the signal-to-noise ratio of the bearing signal as the comprehensive objective function, a quantum particle swarm optimization algorithm is used to search for the maximum value of the comprehensive objective function, determining the optimal combination of the nonlinear system potential function parameters a and b and the damping coefficient μ, obtaining an optimal parameter-adaptive stochastic resonance system. Fifth, this stochastic resonance system is used to perform stochastic resonance on the bearing vibration signal to improve the signal-to-noise ratio of the bearing signal. Sixth, spectral analysis is performed on the stochastic resonance output signal to achieve accurate extraction of weak fault features and accurate fault identification.

Description

Technical Field

[0001] This invention belongs to the field of early fault diagnosis of rotating machinery, and particularly relates to a bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance. Background Technology

[0002] Rotating machinery is widely used in industries such as aviation, aerospace, military, and vehicles. For example, the core components of aircraft engines, electric motors, and steam turbines are all rotating machinery. These machines often experience failures due to their operation in high-speed, heavy-load, and poorly sealed environments. Rolling bearings, as one of the most widely used components in rotating machinery, are also among the most prone to failure. Their operational status directly affects the function of the entire system. Once a rolling bearing fails, it can reduce equipment precision and affect production quality, or even cause production interruptions, system paralysis, and in severe cases, threaten the safety of people's lives and property.

[0003] However, due to the harsh working environment, the early fault characteristic information of rolling bearings is often submerged in strong noise and difficult to extract. There are two main reasons for this: firstly, the early fault characteristic signals of rolling bearings are weak and the evolution law of the fault characteristic signals is difficult to capture; secondly, the noise under harsh external working environment is too great.

[0004] Methods for extracting early fault features in rolling bearings rely on noise suppression and signal decomposition, such as wavelet transform, empirical mode decomposition, and local mean decomposition. While these methods suppress noise, they also weaken useful fault feature information to some extent. Stochastic resonance, however, does not employ direct noise reduction. Instead, it optimizes the system output through the best matching of the signal, nonlinear system, and noise. By converting noise energy into signal energy through stochastic resonance, it enhances the weak fault feature information against a noisy background.

[0005] Although many signal processing methods have achieved good results in the extraction and diagnosis of early fault features in rolling bearings, many problems still exist. For example, empirical mode decomposition methods sometimes suffer from mode aliasing, failing to successfully decompose the feature signals and leading to low accuracy in the final analysis results. Stochastic resonance methods are greatly affected by system structural parameters, making it difficult to achieve ideal detection results in practical signal processing. Currently, most stochastic resonance methods independently assign values ​​to system parameters, rarely considering the interactions between nonlinear system parameters, resulting in inaccurate extraction of early fault features in rolling bearings. Summary of the Invention

[0006] Because bearings operate in harsh environments, early fault characteristic information of rolling bearings is often submerged in strong noise and difficult to extract. This is mainly due to two reasons: firstly, the early fault characteristic signals of rolling bearings are weak and their evolution is difficult to capture; secondly, the noise under harsh external environments is too great. To solve these technical problems, the main objective of this invention is to provide a bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance. Using the envelope entropy of the original rolling bearing signal containing strong noise as the comprehensive optimization objective function, a genetic algorithm is used to search for the minimum value of the comprehensive optimization objective function, finding the optimal combination of the penalty parameter α and the number of modes k for reducing the noise intensity of the original rolling bearing signal. This yields the optimal parameter variational mode decomposition algorithm GA-VMD. This optimal variational mode decomposition algorithm reduces the noise generated by the harsh external environment in the original rolling bearing signal, resulting in a bearing vibration signal with preliminary noise reduction. The preliminary noise-reduced rolling bearing vibration signal, the added Gaussian white noise, and the signal containing exp(-x) 2 The nonlinear system of the potential function of the modified term together constitutes the improved stochastic resonance system. Using the quantum particle swarm optimization (QPSO) algorithm, with the signal-to-noise ratio (ISNR) of the rolling bearing vibration signal as the comprehensive optimization objective function, the QPSO algorithm searches for the maximum value of the comprehensive optimization objective function to find the optimal combination of the nonlinear system potential function parameters a and b and the damping coefficient μ, thus obtaining an improved stochastic resonance system with optimal parameters and adaptability. This improved stochastic resonance system is used to perform stochastic resonance on the rolling bearing vibration signal, further reducing the noise contained in the rolling bearing vibration signal and improving the SNR of the rolling bearing vibration signal. A short-time Fourier transform is performed on the high SNR rolling bearing vibration signal output from the above stochastic resonance to obtain the spectrum of the high SNR rolling bearing vibration signal, which facilitates the capture of the evolution law of fault characteristic signals. Through spectrum analysis, the early weak fault characteristic frequencies of the rolling bearing are accurately identified, thus enabling accurate extraction of early fault characteristics and accurate identification of fault types even in harsh environments with strong noise.

[0007] The objective of this invention is achieved through the following technical solution.

[0008] The bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance disclosed in this invention includes the following steps:

[0009] Step 1: Obtain the original rolling bearing vibration signal.

[0010] Step 2: Consider the interaction between the penalty parameter α and the number of modes k during variational mode decomposition, avoiding independent values. Using the envelope entropy of the original rolling bearing signal with strong noise as the comprehensive optimization objective function, a genetic algorithm is used to search for the minimum value of the comprehensive optimization objective function. This finds the optimal combination of the penalty parameter α and the number of modes k for reducing the noise intensity of the original rolling bearing signal, resulting in the optimal variational mode decomposition algorithm GA-VMD.

[0011] The implementation method for step two is as follows:

[0012] Step 2.1: The original rolling bearing vibration signal is constructed into a variational constraint problem using a variational mode decomposition algorithm. The signal is then adaptively decomposed based on its frequency domain characteristics by solving the variational problem. The original rolling bearing signal containing strong noise is decomposed into multiple sub-signals through the variational mode decomposition process, and then these sub-signals are reconstructed into a preliminarily denoised rolling bearing vibration signal.

[0013] First, a variational problem is constructed. The original rolling bearing vibration signal f is decomposed into k components, ensuring that the decomposed sequence consists of modal components with a finite bandwidth and a center frequency, while minimizing the sum of the estimated bandwidths of each mode. The constraint condition is that the sum of all modes is equal to the original vibration signal. The corresponding constraint variational expression is:

[0014]

[0015] In the formula, k is the number of modes to be decomposed (a positive integer); {u k} represents the k-th modal component after variational mode decomposition; {ω k} represents the k-th center frequency after variational mode decomposition; δ(t) is the Dirac function; * is the convolution operator.

[0016] The IMF expression obtained from variational mode decomposition is:

[0017] u k (t)=A k (t)cos(φ k (t)) (2)

[0018] In the formula, A k (t) is u k The instantaneous amplitude of (t); ω k (t) is u k The instantaneous frequency of (t); u k (t) is a value with amplitude A k (t), with frequency ω k The harmonic signal of (t).

[0019] To ensure the variational discrete problem is highly linearized and non-convex, and thus to guarantee that the original vibration signal can be accurately decomposed into individual sub-signals using the variational mode decomposition algorithm, a quadratic penalty term α and a Lagrange multiplier λ(t) are introduced. The extended Lagrange expression is then:

[0020]

[0021] In the formula, α is the penalty parameter; λ is the Lagrange multiplier. The variational problem is solved using the alternating direction method of multiplication operators, through iterative updates. as well as The optimal value of the above function can be obtained by taking the value of .

[0022] The question of the value of is expressed as:

[0023]

[0024] In the formula, ω k equal equal

[0025] Using Fourier isometric transformation, equation (4) becomes:

[0026]

[0027] The updated center frequency is as follows:

[0028]

[0029] In the formula, Equivalent to the current remaining amount Wiener filtering results; It is the centroid of the power spectrum of the modal function.

[0030] Variational mode decomposition (VMD) algorithms obtain time-domain results by continuously updating the frequency domain and then performing an inverse Fourier transform. The specific implementation method of the VMD algorithm is as follows:

[0031] 1) n = 0, initialization and maximum number of iterations N

[0032] 2) Let n = n + 1, and start executing the loop program.

[0033] 3) Let k = 0, k = k + 1, and update in the frequency domain according to formulas (5) and (6).

[0034] 4) Update in

[0035] 5) Set the precision convergence criterion e > 0. If the condition is not met... If the current iteration count n < N, then return to the second step and continue iterating; otherwise, complete the iteration and output the final result. and

[0036] In the ordinary variational mode decomposition algorithm, the penalty parameter α and the number of modes k are preset parameters. Although the ordinary variational mode decomposition algorithm can avoid the mode aliasing problem in the empirical mode decomposition algorithm, the selection of the penalty parameter α and the number of modes k depends heavily on the experience of the technicians, and the values ​​of the two parameters also have a huge impact on the effect of the variational mode decomposition algorithm.

[0037] Step 2.2: To obtain the optimal variational mode decomposition algorithm for reducing the noise of the original bearing vibration signal, the interaction between the penalty parameter α and the number of modes k during the variational mode decomposition process is considered, avoiding independent values. Using the envelope entropy of the original rolling bearing signal containing strong noise as the comprehensive optimization objective function, a genetic algorithm is used to search for the minimum value of the comprehensive optimization objective function, finding the optimal combination of the penalty parameter α and the number of modes k for reducing the noise intensity of the original rolling bearing signal, thus obtaining the optimal variational mode decomposition algorithm GA-VMD.

[0038] When the genetic algorithm searches for the optimal combination of penalty parameter α and mode number k in the variational mode decomposition algorithm, the Hilbert transform is used to demodulate the rolling bearing vibration signal. The envelope entropy E is selected as the fitness function. If the IMF component obtained after variational mode decomposition contains more periodic fault feature information, the envelope entropy value is smaller; conversely, if the IMF component obtained after variational mode decomposition contains less periodic fault feature information, the envelope entropy value is larger.

[0039] Based on the concept of envelope entropy, the IMF component of the original rolling bearing vibration signal after decomposition by the variational mode algorithm... i The envelope entropy of (j) is expressed as

[0040]

[0041] In the formula, i is the IMF index obtained from the decomposition of the original rolling bearing vibration signal x(j) (i=1,2,3,...); P i,j For a i (j) normalized form; a i (j) represents the signal IMF. i (j) The envelope signal obtained after demodulation by Hilbert transform.

[0042] The optimization objective is expressed as

[0043]

[0044] Generate an initial population. Each individual contains a penalty parameter α and a mode number k. Different individuals have different combinations of penalty parameter α and mode number k. Reserve a position in each individual to store the optimal component index i and fitness value.

[0045] Crossover and mutation are performed on the initial population, and the fitness function value of each individual in the population is solved, E. max E min These represent the maximum and minimum fitness function values ​​for an individual in the population, respectively. Individual X i The envelope entropy function value is C i The fitness solution function is

[0046]

[0047] To avoid premature maturation, individuals with a predetermined probability are eliminated in each generation, and are randomly generated using an initial population method. Individual X i The crossover probability is P i,c The mutation probability is P i,m Adaptive adjustments are made during the computation process, specifically expressed as follows:

[0048]

[0049]

[0050] In the formula, fit avg The average fitness of individuals in the current population; fit i The fitness of an individual to be subjected to crossover or mutation operations; fit max This represents the maximum fitness of individuals within the current population.

[0051] By combining equations (7) to (11), the optimal combination of the penalty parameter α and the number of modes k in the variational mode decomposition algorithm is found.

[0052] Step 3: Reduce the noise generated by the harsh external environment in the original rolling bearing signal by using the optimal variational mode decomposition algorithm described in Step 2, and obtain the rolling bearing vibration signal with preliminary noise reduction by the optimal variational mode decomposition algorithm.

[0053] Step 4: Based on the preliminary noise reduction of the rolling bearing vibration signal obtained in Step 3, add Gaussian white noise and noise containing exp(-x) 2The modified bistable potential function nonlinear system together constitutes the improved stochastic resonance system. The improved bistable system potential function U(x) is selected. Considering the mutual influence between potential function parameters, a quantum particle swarm optimization (QPSO) algorithm is adopted, using the signal-to-noise ratio (ISNR) of the rolling bearing vibration signal as the comprehensive optimization objective function. The algorithm searches for the maximum value of the comprehensive optimization objective function to find the optimal combination of the nonlinear system potential function parameters a and b and the damping coefficient μ, resulting in a stochastic resonance system with optimal parameters and adaptive behavior. This stochastic resonance system is used to perform stochastic resonance on the rolling bearing vibration signal, further reducing the noise contained in the rolling bearing vibration signal and improving its SNR.

[0054] Based on the preliminary noise reduction of the rolling bearing vibration signal obtained in step three, the added Gaussian white noise and the noise containing exp(-x) 2 The bistable state function nonlinear system with the correction term together constitutes a stochastic resonance system. When the initially denoised rolling bearing vibration signal, the added Gaussian white noise, and the signal containing exp(-x) are combined... 2 When the bistable state function nonlinear system of the correction term reaches the optimal matching relationship, it can realize the conversion of noise energy into signal energy, thereby enhancing or identifying the weak characteristic information of early rolling bearing faults under noise background. Using this random resonance system to perform random resonance on the rolling bearing vibration signal, the noise contained in the rolling bearing vibration signal is further reduced, and the signal-to-noise ratio of the rolling bearing vibration signal is improved.

[0055] The one containing exp(-x) 2 The modified bistable state function nonlinear system is an improved bistable system, described by the nonlinear Langevin equation:

[0056]

[0057] In the formula, a and b are parameters of a non-zero nonlinear system, S(t) is a weak periodic signal, and ξ(t) is zero-mean Gaussian white noise, satisfying the following condition:

[0058] <N(t)> =0,<N(t),N(0)> =2Dδ(t) (13)

[0059] In the formula, D is the noise intensity.

[0060] When considering the inertial term of the system, i.e., the inertial force of the system is not much smaller than the damping force, then equation (12) becomes:

[0061]

[0062] In the formula, μ is the damping coefficient of the system.

[0063] The potential function of the improved bistable system described above is:

[0064]

[0065] In the formula, a and b are the parameters of the non-zero improved nonlinear system.

[0066] The improved bistable potential function nonlinear system consists of two steady states and one unsteady state. When there is no external input, the improved bistable potential function system is at the lowest point of the potential well, with minimal potential energy, and is in a most stable position. When a weak signal is input to the improved bistable potential function system, the signal energy cannot overcome the potential barrier, so the output state of the improved bistable potential function system can only move within one potential well. If noise is added to the improved bistable potential function system, the noise energy will be partially transferred to the signal, causing them to interact and break through the system barrier, resulting in transitions between the two steady states of the improved bistable potential function system at the signal frequency. Since the potential difference between the improved bistable states is much larger than the amplitude of the input signal, it amplifies the input signal, i.e., stochastic resonance.

[0067] The specific steps of the method for finding the optimal combination of parameters a and b and damping coefficient μ of an improved bistable adaptive stochastic resonance structure using the quantum particle swarm optimization algorithm are as follows:

[0068] Specify the optimization range, population size N, and maximum number of iterations T for the improved bistable adaptive stochastic resonance structure parameters a and b and damping coefficient μ. max Given the search space dimension S, set the parameter optimization range for each dimension and initialize the initial position of the population individuals;

[0069] The preliminarily denoised rolling bearing vibration signal obtained in step three is input into a stochastic resonance system. The signal-to-noise ratio (SNR) of the rolling bearing vibration signal output by the stochastic resonance is used as the fitness function of the quantum particle swarm optimization algorithm. The fitness value of the initial position of each particle is calculated according to the traditional SNR calculation formula, and this fitness value is used as the individual optimal position fitness value P of the first generation of particles. best(i) At the same time, P best(i) The maximum value in the range is used as the global optimal fitness value P. g ;

[0070] Calculate the average optimal position M of the particle swarm; calculate the fitness value of the current position, update the fitness value of the individual's optimal position, and compare it with the fitness value of the global optimal position. If it is better than the global optimal position, then take it as the new global optimal.

[0071] Repeat the above quantum particle swarm optimization algorithm to improve the stochastic resonance of the bistable system, and determine whether the number of iterations T has reached the preset maximum number of iterations T. maxIf the maximum number of iterations is reached, proceed to the next step; otherwise, if the number of iterations has not reached T... max If so, continue with the above steps;

[0072] The values ​​of parameters a and b and the damping coefficient μ when the fitness of the quantum particle swarm optimization algorithm reaches its maximum value are saved. The random resonance parameters of the nonlinear system are used to perform random resonance on the rolling bearing vibration signal that has undergone preliminary noise reduction in step three, thereby further reducing the noise contained in the rolling bearing vibration signal and improving the signal-to-noise ratio of the rolling bearing vibration signal.

[0073] Step 5: Perform a short-time Fourier transform on the high signal-to-noise ratio (SNR) rolling bearing vibration signal output by the above random resonance to obtain the spectrum of the high SNR rolling bearing vibration signal, so as to capture the evolution law of early fault characteristic signals of rolling bearings. By analyzing the spectrum, the weak early fault characteristic frequencies of rolling bearings can be accurately identified, thus enabling accurate extraction of early fault characteristics and accurate identification of fault types even in harsh environments with strong noise.

[0074] It also includes step six: Based on the accurate identification results of early fault characteristics and fault types of rolling bearings obtained in step five, it is possible to effectively and accurately determine whether early rolling bearings have failed during operation in the context of strong noise. This is helpful for staff to maintain and repair mechanical equipment, and can effectively prevent the reduction of equipment precision and production quality caused by rolling bearing failure. It can also protect the production status and system operation, and protect the life and property safety of on-site staff to a certain extent.

[0075] As a preferred approach, the accurate identification results of early fault characteristics and fault types of rolling bearings obtained in step five, along with related fault discrimination data, are visualized and output to assist staff in real-time judgment and improve the efficiency and accuracy of early fault judgment of rolling bearings.

[0076] Beneficial effects:

[0077] Because bearings operate in harsh environments, early fault characteristic information of rolling bearings is often submerged in strong noise and difficult to extract. This is mainly due to two reasons: firstly, the early fault characteristic signals of rolling bearings are weak and their evolution is difficult to capture; secondly, the noise level in harsh external environments is too high. To solve the above technical problems, this invention has the following beneficial effects:

[0078] 1. Addressing the challenges of extracting early fault characteristic signals and identifying early fault types in rolling bearings, this invention discloses a bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance. This method, for the first time, combines GA-VMD with adaptive stochastic resonance to achieve synergistic noise reduction of the original rolling bearing vibration signal and further improve the signal-to-noise ratio (SNR) of the rolling bearing vibration signal. A high SNR spectrum of the rolling bearing vibration signal is obtained through short-time Fourier transform, facilitating the capture of the evolution law of early fault characteristic signals. Spectrum analysis accurately identifies the weak early fault characteristic frequencies of rolling bearings, enabling precise extraction of early fault characteristics and accurate identification of fault types even in harsh environments with strong noise.

[0079] 2. The bearing fault diagnosis method based on GA-VMD and adaptive random resonance disclosed in this invention includes preliminary noise reduction of the rolling bearing vibration signal, the addition of Gaussian white noise and noise containing exp(-x) 2 The bistable potential function nonlinear system of the modified term together constitutes the improved stochastic resonance system. Using the quantum particle swarm optimization (QPSO) algorithm, with the signal-to-noise ratio (ISNR) of the rolling bearing vibration signal as the comprehensive optimization objective function, the algorithm searches for the maximum value of the comprehensive optimization objective function to find the optimal combination of the nonlinear system potential function parameters a and b and the damping coefficient μ, thus obtaining an improved stochastic resonance system with optimal parameters and adaptability. This improved stochastic resonance system is then used to perform stochastic resonance on the rolling bearing vibration signal, reducing the noise contained in the rolling bearing vibration signal and improving its SNR.

[0080] 3. The bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance disclosed in this invention uses the envelope entropy of the original rolling bearing signal containing strong noise as the comprehensive optimization objective function. The minimum value of the comprehensive optimization objective function is searched through a genetic algorithm to find the optimal combination of the penalty parameter α and the number of modes k for reducing the noise intensity of the original rolling bearing signal. The optimal parameter variational mode decomposition algorithm GA-VMD is obtained. The noise generated by the harsh external environment in the original rolling bearing signal is reduced by the optimal variational mode decomposition algorithm, and the rolling bearing vibration signal with preliminary noise reduction by the optimal variational mode decomposition algorithm is obtained.

[0081] 4. The bearing fault diagnosis method based on GA-VMD and adaptive random resonance disclosed in this invention, on the basis of achieving the above-mentioned beneficial effects 1, 2, and 3, can effectively and accurately determine whether the rolling bearing has failed in the early stage of operation under strong noise background. It is beneficial to assist the staff in the maintenance of mechanical equipment, can effectively prevent the reduction of equipment precision and production quality caused by rolling bearing failure, and can protect the production status and system operation to a certain extent, and protect the life and property safety of on-site staff. Attached Figure Description

[0082] Figure 1 This is a flowchart of a bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance;

[0083] Figure 2 This is a time-domain plot of the original rolling bearing vibration signal;

[0084] Figure 3 This is the frequency domain diagram of the original rolling bearing vibration signal;

[0085] Figure 4 This is the time-domain plot of the original rolling bearing vibration signal after demodulation by Hilbert transform;

[0086] Figure 5 This is the frequency domain diagram of the original rolling bearing vibration signal after demodulation by Hilbert transform;

[0087] Figure 6 It refers to the change in envelope entropy E during the process of optimizing the optimal combination of penalty parameter α and mode number k in the variational mode decomposition algorithm using a genetic algorithm;

[0088] Figure 7 This is the time-domain diagram of the best components after demodulating the rolling bearing vibration signal using Hilbert transform and performing preliminary noise reduction using a variational mode decomposition algorithm optimized by a genetic algorithm.

[0089] Figure 8 This is the optimal component frequency domain diagram after demodulating the rolling bearing vibration signal using Hilbert transform and performing preliminary noise reduction using a variational mode decomposition algorithm optimized by a genetic algorithm.

[0090] Figure 9 This refers to the change in signal-to-noise ratio (ISNR) during the optimization and improvement of the optimal combination of potential function parameters a and b and damping coefficient μ in a bistable system using the quantum particle swarm optimization algorithm.

[0091] Figure 10 This refers to the change in signal-to-noise ratio (ISNR) during the optimization of the optimal combination of potential function parameters a and b and damping coefficient μ in a classical bistable system using the quantum particle swarm optimization algorithm.

[0092] Figure 11It is the optimal random resonance output of the rolling bearing vibration signal after improvement of adaptive random resonance;

[0093] Figure 12 It is the frequency domain diagram of the optimal random resonance output after the rolling bearing vibration signal is improved by adaptive random resonance;

[0094] Figure 13 It is the random resonance output of the original rolling bearing vibration signal after classical bistable random resonance;

[0095] Figure 14 It is the frequency domain diagram of the random resonance output after applying classical bistable random resonance to the original rolling bearing vibration signal. Detailed Implementation

[0096] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0097] This invention is applicable to early fault diagnosis of rotating machinery, especially early fault diagnosis of rolling bearings. To verify the feasibility of this invention, experimental data were obtained from the drive end acceleration data of an SKF rolling bearing from Case Western Reserve University, USA, at a rotational speed of 1730 r / min and a sample frequency of 48 kHz. The fault type data used was rolling bearing outer ring fault, with a fault characteristic frequency of 108 Hz.

[0098] like Figure 1 As shown in the figure, the bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance disclosed in this embodiment has the following specific implementation steps:

[0099] Step 1: Acquire the raw rolling bearing vibration signal using acceleration data from the drive end of an SKF rolling bearing from Case Western Reserve University. The fault type data used is an outer ring fault in the rolling bearing, with a fault characteristic frequency of 108 Hz. Figure 2 The image shown is a time-domain plot of the original rolling bearing vibration signal; as shown... Figure 3 The image shown is a frequency domain diagram of the original rolling bearing vibration signal.

[0100] Step 2: Consider the interaction between the penalty parameter α and the number of modes k during variational mode decomposition, avoiding independent values. Using the envelope entropy of the original rolling bearing signal with strong noise as the comprehensive optimization objective function, a genetic algorithm is used to search for the minimum value of the comprehensive optimization objective function. This finds the optimal combination of the penalty parameter α and the number of modes k for reducing the noise intensity of the original rolling bearing signal, resulting in the optimal variational mode decomposition algorithm GA-VMD.

[0101] The specific process is as follows:

[0102] When using a genetic algorithm to find the optimal combination of penalty parameter α and mode number k for variational mode decomposition, the Hilbert transform is used to demodulate the original rolling bearing vibration signal, such as... Figure 4 The image shown is a time-domain plot of the original rolling bearing vibration signal after demodulation using a Hilbert transform; as shown... Figure 5 The image shown is the frequency domain diagram of the original rolling bearing vibration signal after demodulation by Hilbert transform.

[0103] The envelope entropy E of the original rolling bearing vibration signal is selected as the fitness function. If the IMF component obtained after variational mode decomposition contains more periodic fault feature information, the envelope entropy value is smaller. Conversely, if the IMF component obtained after variational mode decomposition contains less periodic fault feature information, the envelope entropy value is larger.

[0104] Based on the concept of envelope entropy, the IMF component of the original rolling bearing vibration signal after decomposition by the variational mode algorithm... i The envelope entropy of (j) is expressed as

[0105]

[0106] In the formula, i is the IMF index obtained from the decomposition of the original rolling bearing vibration signal x(j); P i,j For a i (j) normalized form; a i (j) represents the signal IMF. i (j) The envelope signal obtained after Hilbert demodulation.

[0107] The optimization objective is expressed as

[0108]

[0109] Generate an initial population. Each individual contains a penalty parameter α and a mode number k. Different individuals have different combinations of penalty parameter α and mode number k. Reserve a position in each individual to store the optimal component index i and fitness value.

[0110] Crossover and mutation are performed on the initial population, and the fitness function value of each individual in the population is solved, E. max E min These represent the maximum and minimum fitness function values ​​for an individual in the population, respectively. Individual X i The envelope entropy function value is C i The fitness solution function is

[0111]

[0112] To avoid premature maturation, one-quarter of the individuals in each generation are eliminated, and the initial population is randomly generated using an initial population method. Individual X iThe crossover probability is P i,c The mutation probability is P i,m Adaptive adjustments are made during the computation process, specifically expressed as follows:

[0113]

[0114]

[0115] In the formula, fit avg The average fitness of individuals in the current population; fit i The fitness of an individual to be subjected to crossover or mutation operations; fit max This represents the maximum fitness of individuals within the current population.

[0116] By combining equations (16) to (20), the optimal combination of the penalty parameter α and the number of modes k in the variational mode decomposition algorithm is found.

[0117] like Figure 6 The figure shows the change in envelope entropy E during the process of optimizing the optimal combination of penalty parameter α and mode number k in the variational mode decomposition algorithm using a genetic algorithm.

[0118] Step 3: Reduce the noise generated by the harsh external environment in the original rolling bearing signal by using the optimal variational mode decomposition algorithm described in Step 2, and obtain the rolling bearing vibration signal with preliminary noise reduction by the optimal variational mode decomposition algorithm.

[0119] like Figure 7 The image shown is a time-domain plot of the optimal component data after demodulating the rolling bearing vibration signal using Hilbert transform and performing preliminary noise reduction using a variational mode decomposition algorithm optimized by a genetic algorithm. Figure 8 The image shown is a frequency domain diagram of the optimal component data after demodulating the rolling bearing vibration signal using Hilbert transform and denoising using a variational mode decomposition algorithm optimized by a genetic algorithm.

[0120] Step 4: Based on the preliminary noise reduction of the rolling bearing vibration signal obtained in Step 3, add Gaussian white noise and noise containing exp(-x) 2 The modified bistable potential function nonlinear system together constitutes the improved stochastic resonance system. The improved bistable system potential function U(x) is selected. Considering the mutual influence between potential function parameters, a quantum particle swarm optimization (QPSO) algorithm is adopted, using the signal-to-noise ratio (ISNR) of the rolling bearing vibration signal as the comprehensive optimization objective function. The algorithm searches for the maximum value of the comprehensive optimization objective function to find the optimal combination of the nonlinear system potential function parameters a and b and the damping coefficient μ, resulting in a stochastic resonance system with optimal parameters and adaptive behavior. This stochastic resonance system is used to perform stochastic resonance on the rolling bearing vibration signal, further reducing the noise contained in the rolling bearing vibration signal and improving its SNR.

[0121] Based on the preliminary noise reduction of the rolling bearing vibration signal obtained in step three, the added Gaussian white noise and the noise containing exp(-x) 2 The bistable state function nonlinear system with the correction term together constitutes a stochastic resonance system. When the initially denoised rolling bearing vibration signal, the added Gaussian white noise, and the signal containing exp(-x) are combined... 2 When the bistable state function nonlinear system of the correction term reaches the optimal matching relationship, it can realize the conversion of noise energy into signal energy, thereby enhancing or identifying the weak characteristic information of early rolling bearing faults under noise background. Using this random resonance system to perform random resonance on the rolling bearing vibration signal, the noise contained in the rolling bearing vibration signal is further reduced, and the signal-to-noise ratio of the rolling bearing vibration signal is improved.

[0122] The one containing exp(-x) 2 The modified bistable state function nonlinear system is an improved bistable system, described by the nonlinear Langevin equation:

[0123]

[0124] In the formula, a and b are parameters of a non-zero nonlinear system, S(t) is a weak periodic signal, and ξ(t) is zero-mean Gaussian white noise, satisfying the following condition:

[0125] <N(t)> =0,<N(t),N(0)> =2Dδ(t) (22)

[0126] In the formula, D is the noise intensity.

[0127] When considering the system's inertial term, i.e., the inertial force of the system is not much smaller than the damping force, then equation (21) becomes:

[0128]

[0129] In the formula, μ is the damping coefficient of the system.

[0130] The potential function of the improved bistable system described above is:

[0131]

[0132] In the formula, a and b are the parameters of the non-zero nonlinear system.

[0133] The specific steps of the method for finding the optimal combination of parameters a and b and damping coefficient μ of an improved bistable adaptive stochastic resonance structure using the quantum particle swarm optimization algorithm are as follows:

[0134] Specify the optimization range, population size N, and maximum number of iterations T for the improved bistable adaptive stochastic resonance structure parameters a and b and damping coefficient μ. maxGiven the search space dimension S, we set the parameter optimization range for each dimension and initialize the initial positions of individuals in the population. Here, we set the optimization range of the quantum particle swarm optimization algorithm's structural parameters a and b, and the damping coefficient μ, to [0.001, 5], the population size to 50, and the maximum number of iterations T. max The value is 100, and the spatial search dimension is 3.

[0135] The preliminarily denoised rolling bearing vibration signal obtained in step three is input into a stochastic resonance system. The signal-to-noise ratio (SNR) of the rolling bearing vibration signal output by the stochastic resonance is used as the fitness function of the quantum particle swarm optimization algorithm. The fitness value of the initial position of each particle is calculated according to the traditional SNR calculation formula, and this fitness value is used as the individual optimal position fitness value P of the first generation of particles. best(i) At the same time, P best(i) The maximum value in the range is used as the global optimal fitness value P. g ;

[0136] Calculate the average optimal position M of the particle swarm; calculate the fitness value of the current position, update the fitness value of the individual's optimal position, and compare it with the fitness value of the global optimal position. If it is better than the global optimal position, then take it as the new global optimal.

[0137] Repeat the above quantum particle swarm optimization algorithm to improve the stochastic resonance of the bistable system, and determine whether the number of iterations T has reached the preset maximum number of iterations T. max If the maximum number of iterations is reached, proceed to the next step; otherwise, if the number of iterations has not reached T... max If so, continue with the above steps;

[0138] like Figure 9 The figure shows the change in signal-to-noise ratio (ISNR) during the optimization and improvement of the optimal combination of potential function parameters a and b and damping coefficient μ in a bistable system using the quantum particle swarm optimization algorithm. Figure 10 This describes the change in signal-to-noise ratio (ISNR) during the optimization of the optimal combination of potential function parameters a and b and damping coefficient μ in a classical bistable system using the quantum particle swarm optimization algorithm. (Comparison) Figure 9 and Figure 10 It is evident that, in the process of using the quantum particle swarm optimization algorithm to find the potential function of a stochastic resonance system, the improved potential function significantly improves the signal-to-noise ratio of the rolling bearing vibration signal compared to the classical bistable potential function.

[0139] The values ​​of parameters a and b, and the damping coefficient μ, when the fitness of the quantum particle swarm optimization algorithm reaches its maximum value are stored. Furthermore, the random resonance parameters of the nonlinear system are used to perform random resonance on the rolling bearing vibration signal obtained from the initial noise reduction in step three, further reducing the noise contained in the rolling bearing vibration signal and improving its signal-to-noise ratio. Figure 11The figure shows the optimal stochastic resonance output of the rolling bearing vibration signal after improvement of adaptive stochastic resonance.

[0140] Step 5: Perform a short-time Fourier transform on the high signal-to-noise ratio (SNR) rolling bearing vibration signal output by the above random resonance to obtain the spectrum of the high SNR rolling bearing vibration signal, so as to capture the evolution law of early fault characteristic signals of rolling bearings. By analyzing the spectrum, the weak early fault characteristic frequencies of rolling bearings can be accurately identified, thus enabling accurate extraction of early fault characteristics and accurate identification of fault types even in harsh environments with strong noise.

[0141] The results of accurate extraction of early fault characteristics and identification of fault types in rolling bearings, along with related fault judgment data, are visualized and output to assist staff in real-time judgment, thereby improving the efficiency and accuracy of early fault diagnosis in rolling bearings. For example... Figure 12 The figure shown is the frequency domain diagram of the optimal random resonance output of the rolling bearing vibration signal after the improvement of adaptive random resonance. Figure 12 The highest spectral peak corresponds to a frequency of 108 Hz, which is the same as the characteristic frequency of the rolling bearing outer ring fault. This indicates that an early fault, such as fatigue wear, exists in the outer ring of the rolling bearing.

[0142] Meanwhile, to further illustrate the advantages of the method of the present invention, such as Figure 13 The image shows the random resonance output of the original rolling bearing vibration signal after applying classical bistable random resonance; as shown... Figure 14 The image shown is the frequency domain diagram of the random resonance output after applying classical bistable random resonance to the original rolling bearing vibration signal. (Comparison) Figure 12 and Figure 14 It is obvious that Figure 12 The signal-to-noise ratio (ISNR) of rolling bearing vibration signals is higher than that of rolling bearing vibration signals. Figure 14 The vibration signal of rolling bearings exhibits a higher signal-to-noise ratio (ISNR) and a more prominent peak frequency. Compared to traditional rolling bearing fault diagnosis based on classical bistable random resonance, this invention can effectively and accurately determine whether an early-stage rolling bearing failure has occurred during operation, even in a high-noise environment. This assists workers in maintaining and repairing mechanical equipment, effectively preventing reduced equipment precision and production quality caused by rolling bearing failures. Furthermore, it can protect production status, system operation, and the lives and property of on-site personnel to a certain extent.

[0143] It should be noted that the above description only illustrates some basic principles of the present invention. Since it is easy for those skilled in the art to make various modifications and alterations based on this, this specification is not intended to limit the invention to the specific structures and applications shown and described. Therefore, all possible modifications and equivalents fall within the scope of the patent claims made in this invention.

Claims

1. A bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance, characterized in that: Comprising the following steps, Step one: obtaining the original rolling bearing vibration signal; Step two: considering the mutual influence of the penalty parameter alpha and the mode number k in the process of variational mode decomposition, avoid independent value; With the envelope entropy of the original rolling bearing signal containing strong noise as the comprehensive optimization objective function, search for the minimum value of the comprehensive optimization objective function through genetic algorithm, find the optimal combination of the penalty parameter alpha and the mode number k for reducing the noise intensity of the original rolling bearing signal, and obtain the variational mode decomposition algorithm with optimal parameters GA-VMD; Step three: reducing the noise in the original rolling bearing signal caused by the harsh environment outside through the variational mode decomposition algorithm with optimal parameters in step two, and obtaining the rolling bearing vibration signal with preliminary noise reduction by the optimal variational mode decomposition algorithm; Step four: based on the preliminary noise reduction rolling bearing vibration signal obtained in step three, added Gaussian white noise and potential function nonlinear system containing exp(-x 2 ) correction term jointly constitute improved stochastic resonance system; select the improved bistable system potential function U(x), consider the mutual influence between the parameters of the potential function, adopt quantum particle swarm algorithm, take the signal-to-noise ratio ISNR of the rolling bearing vibration signal as the comprehensive optimization objective function of the quantum particle swarm algorithm, search for the maximum value of the comprehensive optimization objective function through the quantum particle swarm algorithm, find the optimal combination of the nonlinear system potential function parameters a and b and the damping coefficient μ, obtain the optimal parameters and the self-adaptive stochastic resonance system; use this stochastic resonance system to perform stochastic resonance on the rolling bearing vibration signal, further reduce the noise contained in the rolling bearing vibration signal, and improve the signal-to-noise ratio of the rolling bearing vibration signal; Step five: performing short-time Fourier transform on the high signal-to-noise ratio rolling bearing vibration signal output by the above stochastic resonance to obtain the frequency spectrum of the high signal-to-noise ratio rolling bearing vibration signal, so as to capture the evolution law of the early fault characteristic signal of the rolling bearing; Through the analysis of the frequency spectrum, the early weak fault characteristic frequency of the rolling bearing is accurately identified, and then the accurate extraction of the early fault feature and the accurate identification of the fault type of the rolling bearing can still be realized in the harsh environment with strong noise.

2. The bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance according to claim 1, characterized in that: Step six: according to the early rolling bearing fault feature and fault type accurate identification result obtained in step five, the early rolling bearing fault can be effectively and accurately judged in the background of strong noise, which is beneficial to assist the staff to maintain the mechanical device, can effectively prevent the decrease of equipment precision and production quality caused by rolling bearing fault, and can protect the production state and system operation to a certain extent, and protect the life and property safety of the on-site staff.

3. The bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance according to claim 2, characterized in that: The early rolling bearing fault feature and fault type accurate identification result and related fault discrimination data obtained in step five are output visually, which is convenient for assisting the staff to judge in real time, and improves the early rolling bearing fault judgment efficiency and accuracy.

4. The bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance according to claim 1, 2 or 3, characterized in that: The implementation method of step two is as follows: Step 2.1: the original rolling bearing vibration signal is constructed into a variational constraint problem through the variational mode decomposition algorithm, and the signal is adaptively decomposed according to its own frequency domain characteristics through solving the variational constraint problem; the original rolling bearing signal containing strong noise is decomposed into multiple sub-signals through the variational mode decomposition process, and then the sub-signals are reconstructed into the rolling bearing vibration signal with preliminary noise reduction; First, construct the variational problem, the original rolling bearing vibration signal f is decomposed into k components, ensure that the decomposition sequence is a modal component with a central frequency and a limited bandwidth, and the sum of the estimated bandwidths of each mode is minimum, the constraint condition is that the sum of all modes is equal to the original vibration signal, then the corresponding constraint variational expression is: where k is the number of modes to be decomposed, k is a positive integer;{u k} is the kth mode component after variational mode decomposition;{ω k} is the kth center frequency after variational mode decomposition; δ(t) is the Dirac function; * is the convolution operator; The IMF expression obtained by variational mode decomposition is: u k (t) = A k (t) cos(φ k (t)) (2) where A k (t) is u k (t) is the instantaneous amplitude of u ω k (t) is u k (t) is the instantaneous frequency of u k (t) is a harmonic signal of u k (t) with amplitude A k (t) with frequency ω In order to make the variational discrete problem highly linear and non-convex, and then ensure that the original vibration signal can be accurately decomposed into a single sub-signal through the variational mode decomposition algorithm, by introducing the quadratic penalty term alpha and the Lagrange multiplier lambda(t), the extended Lagrange expression is: In the formula, a is a penalty parameter; λ is a Lagrange multiplier; the variational problem is solved by using a multiplicative operator alternating direction method, and is updated by iteration and The optimal value of the above function is obtained by taking the value of The problem of the value of is expressed as: wherein ω k is equal to is equal to Using Fourier shift transformation, equation (4) becomes: The updated result of the center frequency is: wherein is equivalent to the current remaining amount is the Wiener filter result; is the center of gravity of the modal function power spectrum; The VMD algorithm is updated in the frequency domain, and then the inverse Fourier transform is performed to obtain the time-domain result; Step 2.2: In order to obtain the best VMD algorithm for reducing the noise of the original bearing vibration signal, the mutual influence of the penalty parameter α and the mode number k in the VMD process is considered to avoid independent value selection; the envelope entropy of the original rolling bearing signal containing strong noise is taken as the comprehensive optimization objective function, and the minimum value of the comprehensive optimization objective function is searched through the genetic algorithm to find the optimal combination of the penalty parameter α and the mode number k for reducing the noise intensity of the original bearing signal, and the VMD algorithm with the optimal parameters GA-VMD is obtained; When the genetic algorithm finds the optimal combination of the penalty parameter α and the mode number k of the VMD algorithm, the Hilbert transform is used to demodulate the vibration signal, and the envelope entropy E is selected as the fitness function; if the periodic fault feature information contained in the IMF component obtained after VMD is more, the envelope entropy value is smaller, and vice versa; According to the concept of envelope entropy, the original rolling bearing vibration signal is decomposed into components IMF i The envelope entropy of (j) is represented as In the formula, i is the IMF serial number (i = 1, 2, 3,...) obtained by decomposing the original rolling bearing vibration signal x(j); P i,j is a i normalized form of (j); a i (j) is the signal IMF i (j) is the envelope signal obtained after demodulation of the Hilbert transform of the signal The optimization objective is represented as An initial population is generated, each individual contains a penalty parameter α and a mode number k, and the penalty parameter α and the mode number k of different individuals are different, and a position for storing the best component serial number i and the fitness value is reserved in the individual; The initial population is crossed and mutated, and the fitness function value of each individual in the population is solved, E max , E min represent the maximum and minimum fitness function values of the individuals in the population, respectively; the envelope entropy function value of individual X i is C i , and the fitness solving function is To avoid the phenomenon of precocity, the individuals with preset probability in each generation are eliminated, and the initial population method is used to generate randomly; the individual X i The crossover probability P i,c and the mutation probability P i,m are adjusted adaptively during the operation process, and the specific expression is In the formula, fit avg The average fitness of individuals in the current population; fit i The fitness of an individual to be subjected to crossover or mutation operations; fit max The maximum fitness of individuals in the current population; By combining equations (7) to (11), the optimal combination of the penalty parameter α and the mode number k in the VMD algorithm is found.

5. The bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance according to claim 4, characterized in that: The implementation method of step four is, The random resonance system is composed of the preliminary denoised rolling bearing vibration signal obtained in step three, added Gaussian white noise and a potential function nonlinear system with exp(-x 2 ) correction term; when the preliminary denoised rolling bearing vibration signal, added Gaussian white noise and the potential function nonlinear system with exp(-x 2 ) correction term reach the best matching relationship, the conversion of noise energy to signal energy can be realized, so as to enhance or identify the weak feature information of early fault of the rolling bearing in the noise background; the rolling bearing vibration signal is subjected to random resonance by using the random resonance system, the noise contained in the rolling bearing vibration signal is further reduced, and the signal-to-noise ratio of the rolling bearing vibration signal is improved. The potential function containing the exp(-x 2 The potential function containing the exp(-x 2 The potential function containing the exp(-x In the formula, a and b are parameters of a nonlinear system, S(t) is a certain weak periodic signal, and ξ(t) is a zero-mean Gaussian white noise satisfying the following conditions: <N(t)>=0,<N(t),N(0)>=2Dδ(t) (13) In the formula, D is the noise intensity; When considering the inertia term of the system, that is, the inertia force of the system is much smaller than the damping force, equation (12) becomes: In the formula, μ is the damping coefficient of the system; The potential function of the improved bistable system is: In the formula, a and b are parameters of a nonlinear system; The improved bistable potential function nonlinear system has two stable states and one unstable state; when there is no external input, the improved bistable potential function system is at the lowest point of the potential well, and the potential energy is minimum, so the improved bistable potential function system is at a most stable position; when a weak signal is input to the improved bistable potential function system, the signal energy cannot overcome the barrier, so the output state of the improved bistable potential function system can only move within a potential well; If noise is added to the improved bistable potential function system, the noise energy will partially transfer to the signal to interact with the signal and break through the barrier of the system, so that the signal jumps between the two stable states of the improved bistable potential function system at the frequency of the signal; since the potential difference between the improved bistable states is much larger than the amplitude of the input signal, the input signal is amplified, that is, random resonance occurs. The specific steps of the method for finding the optimal combination of the parameters a and b of the nonlinear system and the damping coefficient μ by using the quantum particle swarm algorithm are as follows: Optimization range of parameters a and b of specified nonlinear system and damping coefficient μ, population quantity N, maximum iteration number T max and search space dimension S, set the parameter optimization range under each dimension respectively, and initialize the initial position of population individuals; The primary noise-reduced rolling bearing vibration signal obtained in step three is input into the random resonance system, the signal-to-noise ratio of the random resonance output rolling bearing vibration signal is taken as the fitness function of the quantum particle swarm algorithm, the fitness value of the initial position of each particle is calculated according to the traditional signal-to-noise ratio calculation formula, and taken as the individual optimal position fitness value P of the first generation of particles best(i) , and the maximum value in P best(i) is taken as the global optimal position fitness value P g ; The average optimal position M of the particle swarm is calculated; the fitness value of the current position is calculated, the individual optimal position fitness value is updated, and the fitness value is compared with the fitness value of the global optimal position, if the fitness value is better than that of the global optimal position, the fitness value is taken as the new global optimal position; The process of improving the stochastic resonance of the bistable system by repeating the above quantum particle swarm algorithm is performed to determine whether the iteration number T reaches the preset maximum iteration number T max . If the maximum iteration number is reached, the next operation is performed. If the iteration number does not reach T max , the operation of the above step is continued. The values of the parameters a and b and the damping coefficient μ when the fitness value of the quantum particle swarm algorithm reaches the maximum value are saved, and the random resonance of the rolling bearing vibration signal preliminarily denoised in step three is performed by using the random resonance parameters of the nonlinear system, so that the noise contained in the rolling bearing vibration signal is further reduced, and the signal-to-noise ratio of the rolling bearing vibration signal is improved.

6. The bearing fault diagnosis method based on GA-VMD and adaptive stochastic resonance according to claim 5, characterized in that: The specific implementation method of the variational mode decomposition algorithm is as follows: 1) n = 0, initialization and a maximum number of iterations N 2) Let n=n+1, start executing the loop program 3) Let k = 0, k = k + 1, update in frequency domain according to equation (5) and equation (6) 4) update wherein 5) Set precision convergence criterion e>0, if not satisfied and current iteration number n<N, go back to step 2 to continue iteration, otherwise finish iteration and output final and

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