A method for detecting fault signals based on plastic and controllable slope random resonance

Abstract

This invention discloses a fault signal detection method for a plastic and controllable slope stochastic resonance system, comprising the following steps: acquiring fault vibration signals of mechanical equipment and preprocessing them to obtain the system input signal; performing a global optimal solution for the parameters of the plastic and controllable slope stochastic resonance system based on the system output signal-to-noise ratio to obtain the best-matching system parameters; using the system input signal as the input to the plastic and controllable slope stochastic resonance system; and based on the aforementioned solved best-matching system parameters, outputting the optimal enhancement result of the plastic and controllable slope stochastic resonance system; and performing fault feature extraction and qualitative analysis based on this result. This invention effectively solves the saturation system response problem of classical bistable stochastic resonance systems, significantly improving the spectral amplitude and signal-to-noise ratio of the system output signal.

Description

Technical Field

[0001] This invention belongs to the field of weak fault signal detection and relates to a fault signal detection method with plastic and controllable slope random resonance. Background Technology

[0002] With the advent of Industry 4.0, advanced intelligent machinery and equipment are widely used in various industrial fields, often in relatively harsh working environments. Equipment malfunctions can have a significant impact on production and daily life, ranging from production stoppages to catastrophic accidents involving loss of manpower. Regardless of size, all equipment requires regular cleaning and maintenance. Due to the complex working environment of machinery, often operating under high noise levels—including complex time-varying transmission paths, coupling of multiple vibration sources, and external environmental interference—fault characteristics are frequently masked by severe background noise. This results in extremely low signal-to-noise ratios in the acquired fault vibration signals, making fault characteristics difficult to identify, extract, and diagnose.

[0003] Traditional methods for extracting fault features from signals mostly focus on noise removal. However, noise removal inevitably damages the fault features. Stochastic resonance, a promising signal processing tool, transforms noise removal into noise utilization, turning noise into a valuable resource. It breaks with traditional thinking by enhancing fault features through the use of noise. Stochastic resonance is a nonlinear phenomenon where the synergistic effect between a nonlinear system, noise, and weak features leads to the enhancement of weak features.

[0004] As classical bistable stochastic resonance systems are widely used in mechanical fault diagnosis, some of their shortcomings have gradually been discovered. Due to the steep potential well walls on both sides of the classical bistable stochastic resonance system, the range of Brownian particle transitions is limited, causing the output performance of the stochastic resonance system to reach a saturation state. This enhances the detection capability of the classical bistable stochastic resonance system for weak fault signals. This shortcoming directly weakens the classical bistable stochastic resonance system's ability to extract enhanced fault features of mechanical equipment, making it impossible to perform qualitative analysis of the degree of fault development. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a fault signal detection method based on plastic and controllable slope stochastic resonance. This method addresses the limitation of enhancement capability caused by output saturation in classical bistable stochastic resonance systems by controllably modifying the steep potential well walls on both sides of the classical bistable potential structure stochastic resonance system to achieve adjustable slope. This allows for adaptive matching of system parameters and increases the transition range of particles within the potential well. This plastic and controllable slope stochastic resonance fault signal detection method is applied to the extraction of fault features of different degrees in mechanical equipment, thereby enhancing the fault feature detection performance.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for detecting fault signals with plastic and controllable slope random resonance includes the following steps:

[0008] The fault vibration signal c(t) of the mechanical equipment is collected and preprocessed to obtain the system input signal s(t). s(t) satisfies the small parameter signal input condition under the constraint of the adiabatic approximation theory.

[0009] Establish a plastic and controllable slope stochastic resonance system;

[0010] A particle swarm optimization (PSO) fitness function is established for a plastic and controllable slope stochastic resonance system. Based on the fitness function, the global optimal solution for the parameters of the plastic and controllable slope stochastic resonance system is obtained to obtain the best-matching system parameters. The PSO fitness function is the system output signal-to-noise ratio.

[0011] The system input signal s(t) is used as the input of the plastic and controllable slope stochastic resonance system. Based on the system's optimal matching parameters obtained above, the optimal enhancement result of the plastic and controllable slope stochastic resonance system is output. Based on this result, fault feature extraction and qualitative analysis are performed.

[0012] Furthermore, the aforementioned steps of collecting the fault vibration signal c(t) of the mechanical equipment and preprocessing it to obtain the system input signal s(t) include:

[0013] Based on the collected fault vibration signal c(t) of the mechanical equipment, the fault characteristic frequency f is obtained through theoretical calculation of the mechanical equipment parameters. d ;

[0014] Based on the fault characteristic frequency f d Set the compression scale n;

[0015] The system input signal s(t) is obtained by compressing the collected fault signal c(t) by the compression scale n.

[0016] Furthermore, the method for establishing the aforementioned plastic and controllable slope stochastic resonance system is as follows:

[0017] By controlling the slope of the steep potential well wall in the classic bistable stochastic resonance model, a plastic and controllable slope stochastic resonance system is obtained.

[0018] The potential function U(x) of a plastic, controllable slope stochastic resonance system is expressed as follows:

[0019]

[0020] In the formula, p, q and k are system parameters;

[0021] Based on Langevin's equations, the plastic, controllable slope stochastic resonance system can be further described as follows:

[0022]

[0023] In the formula, x(t) is the output signal of the plastic and controllable slope random resonance system.

[0024] Furthermore, the calculation steps for the aforementioned system output signal-to-noise ratio (SNR) include:

[0025] The output signal x(t) of the aforementioned plastic and controllable slope stochastic resonance system is solved using the fourth-order Runge-Kutta method.

[0026] The system output signal-to-noise ratio is obtained by performing a fast Fourier transform on the output signal x(t).

[0027]

[0028] In the formula, A i A is the amplitude corresponding to each spectral line in the spectrum X(i) of the system output signal x(t). d It is the amplitude at the fault characteristic frequency, and N is the number of sampling points.

[0029] Furthermore, the aforementioned steps for finding the global optimal solution for the parameters of a plastic, controllable slope stochastic resonance system based on the fitness function to obtain the best-matched system parameters include:

[0030] Set the maximum number of iterations T for the particle swarm optimization algorithm. max =200, continuously update the optimal position of the individual and the optimal position of the group until the maximum number of iterations is met;

[0031] Get the maximum SNR max and its corresponding best-matching system parameters (p) best ,q best ,k best ).

[0032] Furthermore, the aforementioned steps for fault feature extraction and qualitative analysis based on this result include:

[0033] The best matching system parameters (p) best ,q best ,k best Substituting the system potential function U(x), the optimal enhancement result of the plastic and controllable slope stochastic resonance system is obtained by using the fourth-order Runge-Kutta method. The step size of the fourth-order Runge-Kutta method is h = n / f. s f s This refers to the data sampling frequency;

[0034] Based on the compression scale n, the optimal enhancement result is restored to obtain the enhanced signal of c(t);

[0035] Spectral analysis is performed on the enhanced signal to extract fault characteristics of mechanical equipment, and the severity of the fault is qualitatively determined based on the magnitude of the spectral peaks at the fault characteristic frequencies.

[0036] The beneficial effects achieved by this invention are as follows:

[0037] The core feature of this invention is the controllable slope modification of the steep potential well walls on both sides of the potential function of a classical bistable stochastic resonance system. This proposes a plastic and controllable slope stochastic resonance system, which expands the transition range of Brownian particles, thereby overcoming the limitation on the output performance improvement of classical bistable stochastic resonance systems. It also enhances the detection capability of weak fault signals in classical bistable stochastic resonance systems. The plastic and controllable slope stochastic resonance method is used to extract mechanical fault feature information, thereby realizing effective fault diagnosis and qualitative analysis of mechanical equipment. Attached Figure Description

[0038] Figure 1 This is a flowchart of the present invention;

[0039] Figure 2 The graph of the plasticity controllable slope potential function;

[0040] Figure 3 Comparison of Kramers transition rates between classical bistable potential stochastic resonance systems and plastic, controllable slope stochastic resonance systems;

[0041] Figure 4a This is a time-domain plot of the original mechanical inner ring bearing fault signal;

[0042] Figure 4b This is the frequency domain diagram of the original mechanical inner ring bearing fault signal;

[0043] Figure 5a The time-domain plot of the mechanical inner ring bearing fault signal after passing through a plastic and controllable slope random resonance system;

[0044] Figure 5b The frequency domain diagram of the mechanical inner ring bearing fault signal after passing through a plastic and controllable slope random resonance system;

[0045] Figure 6a The time-domain plot of the mechanical inner ring bearing fault signal after passing through a classical bistable structure stochastic resonance system;

[0046] Figure 6b This is the frequency domain diagram of the mechanical inner ring bearing fault signal after passing through a classic bistable structure stochastic resonance system. Detailed Implementation

[0047] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0048] This embodiment discloses a fault signal detection method for plastic and controllable slope random resonance, such as... Figure 1 As shown, it includes the following steps:

[0049] (1) The collected signals c(t) of different fault levels of mechanical equipment are preprocessed to obtain the system input signal s(t) required for subsequent operation. s(t) satisfies the small parameter signal input condition under the constraint of the adiabatic approximation theory:

[0050] The fault characteristic frequency f is obtained through theoretical calculation of mechanical equipment parameters. d Based on the fault characteristic frequency f d Set the compression scale n; based on n and the data sampling frequency f s Determine a quadratic sampling frequency f sr =f s / n, the computational step size h of the fourth-order Runge-Kutta method is 1 / f s Magnified to 1 / f sr That is, the accuracy of numerical calculation also changes accordingly; according to the compression scale n, the collected fault signal c(t) is compressed so that the preprocessed system input signal s(t) meets the small parameter requirements under the adiabatic approximation theory.

[0051] (2) The preprocessed system input signal s(t) from step (1) is used as the input of the plastic and controllable slope stochastic resonance system, and U(x) is the potential function of the system:

[0052]

[0053] In the formula, p, q, and k are system parameters, and p∈(0,10], q∈(0,10], k∈(0,10]). This stochastic resonance system is described by the Langevin equation:

[0054]

[0055] In the formula, x(t) is the system output, and s(t) is the preprocessed input signal for different fault levels. Figure 2The potential function of a plastic and controllable slope stochastic resonance system is presented. Unlike the classical bistable stochastic resonance system, the potential well walls on both sides are linearized and their slopes are adjustable. This effectively overcomes the system output saturation problem caused by the excessively steep potential well walls in the classical bistable stochastic resonance system, thereby improving the weak characteristic enhancement capability of the classical bistable stochastic resonance system.

[0056] (3) Solve for the output signal x(t) of the plastic and controllable slope stochastic resonance system in step (2) using the fourth-order Runge-Kutta method, and then use the fast Fourier transform to solve for the system output signal-to-noise ratio:

[0057]

[0058] In the formula A i A is the amplitude corresponding to each spectral line in the spectrum X(i) of the system output signal x(t). d It is the amplitude at the fault characteristic frequency, and N is the number of sampling points.

[0059] The SNR is used as the fitness function of the particle swarm optimization algorithm to optimize the system parameters (p, q, k), and the maximum number of iterations T of the particle swarm optimization algorithm is set. max =200, to obtain the maximum SNR max and its corresponding best-matching system parameters (p) best ,q best ,k best ).

[0060] (4) The optimal matching system parameters (p) obtained by the particle swarm optimization algorithm are then used to optimize the system. best ,q best ,k best Substituting the plasticity-controlled slope stochastic resonance system from step (2), and using the fourth-order Runge-Kutta method to obtain the optimal system enhancement output, with the calculation step size h of the fourth-order Runge-Kutta method being 1 / f s Magnified to 1 / f sr Then, the output signal x(t) of the plastic and controllable slope random resonance system is restored according to the compression scale n to obtain the enhanced signal of the original signal c(t). Finally, the spectrum analysis is performed to extract the fault characteristics of the mechanical equipment, and the severity of the fault is qualitatively judged according to the size of the spectral peak at the fault characteristic frequency.

[0061] A comparative experiment between classical bistable systems and plastic, controllable-slope stochastic resonance systems:

[0062] The Cramers transition rate is the rate at which a Brownian particle transitions between two steady states in a bistable system. The Cramers transition rate of a classical bistable system is... Cramers transition rate with plasticity, controllable slope, and stochastic resonance Figure 3The parameters of the plastic controllable slope system and the classical bistable structure system are both p=1 and q=1. It can be seen that as the noise intensity D increases, the Kramers transition of both systems first gradually increases and then gradually tends to stabilize. Unlike the classical bistable system, the Kramers transition rate of the plastic controllable slope system also increases with the increase of the slope k, and both are greater than those of the classical bistable system.

[0063] To further demonstrate the enhanced performance of the plasticity-controllable slope stochastic resonance fault feature extraction method, data from the experimental setup at Western Reserve University were used as an example. The drive-end bearing was an SKF 6205-2RSJEM, the sampling frequency was 12kHz, and the rotational speed was 1728 r / min. The dimensions of the drive roller bearing are shown in Table 1. The theoretical value of the inner ring fault frequency is 155.96Hz. To meet the small parameter constraints of the adiabatic approximation theory of stochastic resonance, the secondary sampling frequency was set to 6Hz.

[0064] Table 1: Data on Drive Roller Bearings

[0065]

[0066] Figure 4a , 4b These are the time-domain and frequency-domain plots of the bearing inner ring fault signal. No obvious impact components are observed in the time-domain waveform. In the frequency-domain plot, the spectral energy is distributed over a wide frequency range, with a peak value in the range of 1-2kHz. This is caused by the first natural mode vibration of the bearing component. Therefore, no obvious vibration characteristics of the fault signal are visible in the low-frequency region of the original signal's spectrum.

[0067] Figure 5a , 5b To utilize the plasticity-controlled slope stochastic resonance fault feature extraction method for diagnosis, the optimal output of the plasticity-controlled slope stochastic resonance system was finally obtained through particle swarm optimization. Figure 5a , 5b As shown, at this time, (p best ,q best ,k best = (3.2053, 1.9880, 3.7407), the signal-to-noise ratio (SNR) of the output signal. best = -10.1715. After passing through the plastic and controllable slope random resonance system, the inner ring fault frequency at the detection point is 156Hz, which is close to the theoretical value of 155.96Hz. At this time, the amplitude is 0.4223, and other frequencies near the fault frequency are significantly lower than the fault frequency.

[0068] To demonstrate the superiority of the plasticity-controllable slope stochastic resonance fault feature extraction method, in Figure 1Under the same testing procedure, the testing results obtained by replacing the plastic and controllable slope stochastic resonance system with a classical bistable potential structure stochastic resonance system are as follows: Figure 6a , 6b As shown, the optimal parameters (p) of the classical bistable potential structure stochastic resonance system obtained through particle swarm optimization are... best ,q best = (3.3973, 3.0425), output signal-to-noise ratio (SNR) best = -11.2923, which can also detect the fault frequency, but its amplitude and signal-to-noise ratio are significantly lower than those of the plastic and controllable slope stochastic resonance system. Its capability is limited by the output saturation of the system itself, so its enhancement capability is not as good as the plastic and controllable slope stochastic resonance fault feature extraction method.

[0069] In summary, by controlling the slope of the steep potential well walls of a classical bistable stochastic resonance system, the slopes of both sides of the potential well walls can be adjusted. A swarm intelligence optimization algorithm is used to find the optimal matching slope, expanding the transition range of Brownian particles. This overcomes the limitation on output performance improvement in classical bistable stochastic resonance systems and enhances their ability to detect weak fault signals. Furthermore, the plasticity-controllable slope stochastic resonance method is used to extract mechanical fault feature information, thereby achieving effective fault diagnosis and qualitative analysis of mechanical equipment. This is of great significance for the detection of weak fault signals.

[0070] The above description is a further detailed explanation of the present invention in conjunction with specific preferred embodiments. It should not be considered that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of patent protection determined by the submitted claims.

Claims

1. A method for detecting fault signals with plastic and controllable slope random resonance, characterized in that, Includes the following steps: Collect fault vibration signals of mechanical equipment The system input signal is then preprocessed to obtain the input signal. The It satisfies the small parameter signal input condition under the constraints of the adiabatic approximation theory; Establishing a plastic and controllable slope stochastic resonance system specifically includes: By controlling the slope of the steep potential well wall in the classic bistable stochastic resonance model, a plastic and controllable slope stochastic resonance system is obtained. The potential function of the plastic and controllable slope stochastic resonance system The expression is: ； In the formula , and These are system parameters; Based on Langevin's equations, the plastic, controllable slope stochastic resonance system can be further described as follows: ； In the formula The output signal is for a plastic, controllable slope random resonance system. A particle swarm optimization (PSO) fitness function is established for a plastic and controllable slope stochastic resonance system. Based on the fitness function, a global optimal solution is found for the parameters of the plastic and controllable slope stochastic resonance system to obtain the best-matching system parameters. The PSO fitness function is the system output signal-to-noise ratio. System input signal As input to the plastic and controllable slope stochastic resonance system, and based on the previously solved optimal matching system parameters, the optimal enhancement result of the plastic and controllable slope stochastic resonance system is output, and fault feature extraction and qualitative analysis are performed based on the result.

2. The fault signal detection method based on plastic and controllable slope random resonance according to claim 1, characterized in that, The fault vibration signal of the collected mechanical equipment The system input signal is then preprocessed to obtain the input signal. The steps include: Based on the collection of fault vibration signals from mechanical equipment Fault characteristic frequencies were obtained through theoretical calculations using mechanical equipment parameters. ; Based on fault characteristic frequency Set compression scale ; According to compression scale For the collected fault signals Compression scale to obtain system input signal .

3. The fault signal detection method based on plastic and controllable slope random resonance according to claim 1, characterized in that, The system output signal-to-noise ratio The calculation steps include: The output signal of the aforementioned plastic and controllable slope stochastic resonance system is solved using the fourth-order Runge-Kutta method. ; Output signal The system output signal-to-noise ratio is obtained by performing a fast Fourier transform: ； In the formula, It is the system output signal Spectrum The amplitude corresponding to each spectral line in the spectrum. It is the amplitude at the fault characteristic frequency. It represents the number of sampling points.

4. The fault signal detection method based on plastic and controllable slope random resonance according to claim 3, characterized in that, The steps for finding the global optimal solution for the parameters of a plastic, controllable slope stochastic resonance system based on the fitness function to obtain the best-matched system parameters include: Set the maximum number of iterations for the particle swarm optimization algorithm. The optimal position of the individual and the optimal position of the group are continuously updated until the maximum number of iterations is satisfied; Get the maximum and its corresponding optimal matching system parameters .

5. The fault signal detection method based on plastic and controllable slope random resonance according to claim 4, characterized in that, The steps for fault feature extraction and qualitative analysis based on this result include: Best matching system parameters Substitute the system potential function The optimal enhancement result of the plasticity-controllable slope stochastic resonance system is obtained by using the fourth-order Runge-Kutta method. The step size of the fourth-order Runge-Kutta method is... The This refers to the data sampling frequency; According to compression scale The best enhancement result is restored to obtain The enhanced signal; Spectral analysis is performed on the enhanced signal to extract fault characteristics of mechanical equipment, and the severity of the fault is qualitatively determined based on the magnitude of the spectral peaks at the fault characteristic frequencies.

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