A weak signal detection method based on a hybrid tri-stable stochastic resonance system

Abstract

The application discloses a weak signal detection method based on a mixed three-stable random resonance system, determines a secondary sampling frequency based on collected original equipment fault signals, carries out variable scale random resonance on the secondary sampling frequency, obtains a small parameter system input signal conforming to an adiabatic approximation theory, establishes a mixed three-stable random resonance system based on a controllable potential well condition, and obtains an output signal of the mixed three-stable random resonance system through the small parameter system input signal, and based on the output signal of the mixed three-stable random resonance system, realizes detection and extraction of a weak characteristic signal and equipment fault degree determination. Through establishment of the mixed three-stable random resonance model, the application improves the detection capability of the weak signal.

Description

Technical Field

[0001] This invention belongs to the field of weak characteristic signal detection of mechanical equipment, and specifically relates to a weak signal detection method based on a hybrid tristable stochastic resonance system. Background Technology

[0002] In today's increasingly industrialized society, the safety and reliability of engineering systems and mechanical equipment are fundamental guarantees for the production process and are important issues concerning science, technology, and people's livelihoods. Damage to a component of rotating machinery can negatively impact the entire integrated system, causing economic losses, and in severe cases, potentially leading to major industrial accidents that threaten human lives. In practical applications, the working environment of mechanical equipment is often accompanied by extremely high background noise; when people try to detect early fault signals, they are often polluted by the surrounding noise.

[0003] It is generally believed that the presence of noise interferes with the extraction of effective signals, and previous methods for extracting weak signals have primarily focused on noise suppression. Some methods utilize bearing surface temperature sensors to collect fault information, but these struggle to capture early-stage fault signals with minimal temperature changes. Others employ magnetic effects to observe the distribution of particles on ferrographic plates for diagnosis, but these are only applicable to oil-lubricated bearings and have long analysis cycles. Still other methods use ultrasonic technology to measure axial displacement, but this requires a high degree of surface smoothness from the tested component. In summary, traditional fault detection techniques have limitations in many aspects.

[0004] With the continuous research on nonlinear dynamics, stochastic resonance theory has ushered in a golden age of development. Traditional methods of noise suppression have been broken through, and the idea of ​​transforming "noise" into a "beneficial signal" has attracted widespread attention from researchers. The core of stochastic resonance is the cooperative effect between the input signal, noise, and the nonlinear system (potential function). Through the action of the nonlinear system, after a noisy signal is input, the periodic driving force and noise driving output will change periodically, allowing some noise energy to be successfully transferred to the signal under test. Stochastic resonance is generally suitable for processing low-frequency signals under the adiabatic approximation theory. In this case, a certain amount of noise will help detect weak but effective signals. This unconventional detection method has ample potential in practical mechanical fault detection. Summary of the Invention

[0005] The purpose of this invention is to overcome the insufficient detection capabilities of existing models and provide a weak signal detection method based on a hybrid tristable stochastic resonance system. This method combines the classical Woods-Saxon monostable potential model with a controllable symmetric bistable potential model, allowing the system output to dynamically change with the adjustment of the controllable potential well factor under controllable potential well depth and width. This improves the utilization rate of the stochastic resonance system for noise and enhances the detection capabilities of both the classical monostable and symmetric bistable models for weak signals.

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

[0007] A method for detecting weak signals based on a hybrid tristable stochastic resonance system includes the following steps:

[0008] Based on the sampling frequency f of the collected fault signals from the original equipment s The secondary sampling frequency is determined, and variable-scale random resonance is applied to the secondary sampling frequency to obtain the input signal of the small-parameter system that conforms to the adiabatic approximation theory.

[0009] Based on the controllable potential well condition, a hybrid tristable stochastic resonance system is established, and the output signal of the hybrid tristable stochastic resonance system is obtained through the small parameter system input signal.

[0010] Based on the output signal of a hybrid tristable stochastic resonance system, weak characteristic signals can be detected and the degree of equipment failure can be determined.

[0011] Furthermore, the steps for determining the aforementioned secondary sampling frequency are as follows:

[0012] Based on the original equipment fault signal sampling frequency f s The secondary sampling frequency f is set according to the adiabatic approximation condition of random resonance. sr The secondary sampling frequency satisfies the small parameter constraint of the random resonant input signal and f sr <f s .

[0013] Furthermore, the aforementioned steps for obtaining the output signal of the hybrid tristable stochastic resonance system include:

[0014] By combining the classic Woods-Saxon monostable system with a controllable symmetric bistable system, a hybrid tristable stochastic resonance system is obtained. The potential function U(x) of the hybrid tristable stochastic resonance system is:

[0015]

[0016] In the formula, p, q, k, A, B, ω0, β are parameters of the mixed tristable system, and

[0017] Based on the potential function, the Langevin equation for the hybrid tristable stochastic resonance system is obtained:

[0018]

[0019] Where s(t) is the weak periodic signal of the input hybrid tristable stochastic resonance system, x(t) is the system output, and ξ(t) is a signal with zero mean and variance. Gaussian white noise, D represents the noise intensity, and g(t) is the noise with a mean of 0 and a variance of 1.

[0020] The Langevin equation is solved using the fourth-order Runge-Kutta method to obtain the output signal of the hybrid tristable stochastic resonance system. The numerical calculation formula of the fourth-order Runge-Kutta method is as follows:

[0021]

[0022] Where x in (i) represents the discretized form of the noisy input signal of the system, and its value is the discretized form of the sum of the input signal s(t) and the noise signal ξ(t) of the small-parameter system, x out (i) represents the discretized form of the system output signal, Δ is the step size, h is the controllable potential well factor, and the Langevin(*) function is the Langevin equation for the hybrid tristable stochastic resonance system.

[0023] Furthermore, when the aforementioned controllable potential well condition is a controllable potential well depth condition, A = B = h in the potential function of the hybrid tristable stochastic resonance system, where h is the controllable potential well factor.

[0024] Furthermore, when the aforementioned controllable potential well condition is a controllable potential well width condition, A = 1 / h in the potential function of the hybrid tristable stochastic resonance system. 2 B = 1 / h 4 h is the controllable potential well factor.

[0025] Furthermore, the aforementioned steps for detecting weak feature signals based on the output signal of a hybrid tristable stochastic resonance system include:

[0026] The power spectrum of the output signal of the hybrid tristable stochastic resonance system is obtained by Fourier transform, and a signal-to-noise ratio (SNR) calculation formula is established based on the power spectrum.

[0027]

[0028] In the formula, A i A is the amplitude corresponding to each spectral line of the power spectrum X(i)i=1,2,...,N / 2 of the system output signal. dis the amplitude at the fault characteristic frequency, and N is the number of samples.

[0029] Based on the above formula, plot the curve of signal-to-noise ratio as a function of noise intensity, and analyze and judge the weak signal detection capability of the hybrid tristable stochastic resonance system according to the peak signal-to-noise ratio.

[0030] Furthermore, the aforementioned steps for determining the degree of equipment failure based on the output signal of a hybrid tristable stochastic resonance system include:

[0031] The output signal of the hybrid tristable stochastic resonance system is sampled at a second sampling frequency f. sr The compression ratio is reduced;

[0032] The time-domain and frequency-domain plots of the restored signal are drawn. The smoothness and periodicity of the time-domain waveform are used to observe the quality of the output signal. The degree of equipment failure is determined based on the amplitude of the frequency-domain waveform at a specific fault frequency.

[0033] The beneficial effects achieved by this invention are as follows:

[0034] 1. Compared with the classical symmetric bistable stochastic resonance model, the hybrid tristable stochastic resonance model proposed in this invention has a higher noise utilization rate due to the introduction of the intermediate potential well, can show a more prominent amplitude at the characteristic fault frequency, and produces a smoother and more periodic time-domain output waveform.

[0035] 2. The hybrid tristable stochastic resonance model proposed in this invention can control the width and depth of the potential well by adjusting the controllable potential well factor, so that the system output can achieve a higher peak signal-to-noise ratio and improve the detection capability of weak signals.

[0036] 3. Variable-scale stochastic resonance is adopted, which overcomes the small parameter limitations of the adiabatic approximation condition of stochastic resonance and better meets the needs of actual industrial production. Attached Figure Description

[0037] Figure 1 The potential function of a hybrid tristable stochastic resonance system as a function of parameters under controllable potential well depth is shown.

[0038] Figure 2 The potential function of a hybrid tristable stochastic resonance system as a function of parameters under the condition of controllable potential well width is shown.

[0039] Figure 3a This is a time-domain plot of the original bearing equipment vibration signal;

[0040] Figure 3b Frequency domain diagram of the original bearing equipment vibration signal

[0041] Figure 4aThe time-domain plot is the output of a controllable deep-mixing tristable stochastic resonance system;

[0042] Figure 4b The frequency domain diagram is the output of a controllable deep-mixing tristable stochastic resonance system.

[0043] Figure 5 The output signal-to-noise ratio of a hybrid tristable system varies with noise intensity under controllable potential well depth conditions;

[0044] Figure 6a The output of the controllable-width hybrid tristable stochastic resonance system is shown in the time domain.

[0045] Figure 6b The frequency domain diagram is the output of a controllable-width hybrid tristable stochastic resonance system.

[0046] Figure 7 The signal-to-noise ratio of the output of a hybrid tristable system varies with noise intensity under controllable potential well width conditions. 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 invention provides a weak signal detection method based on hybrid tristable stochastic resonance, the method comprising the following steps:

[0049] Step (1): Determine the secondary sampling frequency based on the collected original bearing equipment fault signals, and perform variable-scale random resonance based on the secondary sampling frequency to obtain the small-parameter system input signal that conforms to the adiabatic approximation theory.

[0050] At the original sampling frequency f s Based on this, the secondary sampling frequency f is set according to the adiabatic approximation condition of random resonance. sr (f sr <f s This allows the signal to meet the small parameter constraints of the random resonance input signal, and the output signal is then restored using this scale after the random resonance process ends.

[0051] Step (2): Under controllable potential well conditions, combining the Woods-Saxon monostable and controllable symmetric bistable models, the potential function of the hybrid tristable stochastic resonance model is obtained. Its derivative is calculated, and noise is added to derive the Langevin equation for the system. The small-parameter system input signal obtained in step (1) is used as the input to the hybrid tristable stochastic resonance system. The fourth-order Runge-Kutta method is used for numerical solution to obtain the output signal of the hybrid tristable stochastic resonance system.

[0052] 2.1) The potential function U(x) of the mixed tristable stochastic resonance model under controllable potential well conditions can be described as the sum of the Woods-Saxon monostable potential function and the potential function of the controllable symmetric bistable system:

[0053]

[0054] In the formula, p, q, k, A, B, ω0, β are parameters of the mixed tristable system. h is the controllable well factor. Under the condition of controllable well depth, A = B = h, and under the condition of controllable well width, A = 1 / h. 2 B = 1 / h 4 When parameters p, q, k, and h change, the potential structure of the mixed tristable model changes accordingly. The potential functions under controllable depth and width conditions are as follows: Figure 1 and Figure 2 As shown, adjusting the parameters can control the depth and width of the potential wells, thereby affecting the dynamic characteristics of the Brownian particle transitions in the three potential wells and improving the output signal-to-noise ratio of the system.

[0055] 2.2) Further, the Langevin equation for this system can be described as:

[0056]

[0057] Where s(t) is the weak periodic signal of the input hybrid tristable stochastic resonance system, x(t) is the system output, and ξ(t) is a signal with zero mean and variance. Gaussian white noise, D represents the noise intensity, and g(t) is the noise with a mean of 0 and a variance of 1.

[0058] To verify the effectiveness of the method, the open dataset of inner ring fault signals from the signal database of deep groove ball bearings at Western Reserve University was used for processing. The bearing model at the drive end was SKF 6205. Using electrical discharge machining (EDM), the bearing fault state can be reflected in the form of electrical signals with a sampling frequency of 12000 Hz and an inner ring speed of 1730 r / min. The bearing parameters are shown in Table 1.

[0059] Table 1: SKF 6205 Bearing Parameters

[0060]

[0061] inner ring failure frequency f at the drive end of rolling bearing m As shown below:

[0062]

[0063] Figure 3a and Figure 3b The time-domain and frequency-domain plots of the original bearing equipment vibration signal are presented. It can be found that the characteristic signal is basically buried by noise, and it is difficult to identify any fault characteristics in the time-domain waveform. It is not periodic, and the signal energy in the frequency spectrum is also relatively dispersed, indicating that the high-frequency noise signal has a large interference with the characteristic signal.

[0064] Figure 4a and Figure 4b The time-domain and frequency-domain plots of the output from a controllable deep-mixed tristable stochastic resonance system are presented. Comparison reveals that the waveform output from the hybrid tristable system exhibits characteristics closer to a sine wave than the original disordered state. The amplitude changes more orderly and clearly with the sampling points, displaying a certain periodicity and regularity. The frequency-domain output amplitude is more stable and concentrated, noise energy is significantly reduced, and the output signal energy shows an overall shift from the high-frequency region to the low-frequency region. This effectively improves the phenomenon where characteristic frequencies are masked by noise, causing noise to permeate the entire frequency band, thus enhancing the ability to detect weak signals.

[0065] 2.3) The output signal of the hybrid tristable stochastic resonance system is obtained by solving the Langevin equation of the system using the fourth-order Runge-Kutta method. The numerical calculation formula of the fourth-order Runge-Kutta method is as follows:

[0066]

[0067] Where x in (i) represents the discretized form of the noisy input signal of the system, and its value is the discretized form of the sum of the input signal s(t) and the noise signal ξ(t) of the small-parameter system, x out (i) represents the discretized form of the system output signal, Δ is the step size, h is the controllable potential well factor, and the Langevin(*) function is the Langevin equation for the hybrid tristable stochastic resonance system.

[0068] Step (3) is to detect, extract, and determine the degree of equipment failure based on the output signal of the hybrid tristable stochastic resonance system.

[0069] 3.1 The steps for detecting and extracting weak feature signals are as follows:

[0070] The power spectrum of the output signal of the hybrid tristable stochastic resonance system is obtained by performing a Fourier transform, and then the signal-to-noise ratio of the system output is calculated.

[0071]

[0072] Where A i A is the amplitude corresponding to each spectral line of the power spectrum X(i)i=1,2,...,N / 2 of the system output signal. d Let be the amplitude at the fault characteristic frequency, and N be the number of samples. Specifically, this formula means: after obtaining a numerical solution to the Langevin equation using the fourth-order Runge-Kutta method, perform a Fourier transform on the output signal, multiply it by its conjugate complex number, divide by the number of samples, sum the amplitudes of terms 1 to N / 2, subtract the amplitude at the fault characteristic frequency, and perform a logarithmic operation to obtain the signal-to-noise ratio (SNR) versus noise intensity D curve.

[0073] The signal-to-noise ratio (SNR) can be plotted as a function of noise intensity based on this formula. The detection capability of a stochastic resonance system for weak signals can be analyzed and judged based on the peak SNR.

[0074] 3.2 The steps for determining the degree of equipment failure are as follows:

[0075] The output signal of the hybrid tristable stochastic resonance system is restored according to the second sampling compression ratio. The time-domain and frequency-domain plots of the restored signal are then drawn. The smoothness and periodicity of the time-domain waveform are used to observe the quality of the output signal. The degree of equipment failure is determined based on the amplitude of the frequency-domain waveform at a specific fault frequency.

[0076] Figure 5 The variation of the output signal-to-noise ratio (SNR) of a hybrid tristable system with noise intensity under controllable well depth conditions is presented. The system output of the stochastic resonance is restored using a quadratic sampling compression ratio. By adjusting the controllable well factor h, the peak SNR of the system output is increased from -6.0301 dB after traditional processing to 2.7956 dB. At the fault frequency of 156 Hz, the amplitude increases from the original 0.1938 m / s². -2 Compared with 0.05771 m·s after traditional processing -2 It rose to 0.4353 m·s -2 The results show a significant improvement. The system demonstrates excellent detection capabilities in detecting weak signals from mechanical equipment, with noise interference largely eliminated.

[0077] For step (2), under the condition of controllable potential well width, change the potential function and Langevin equation of the model, and repeat the step to process the noisy signal through the hybrid tristable stochastic resonance system to obtain a clear fault frequency output time-frequency diagram, thereby improving the system signal-to-noise ratio.

[0078] Figure 6a and Figure 6b The time-domain and frequency-domain plots of the output from the controllable deep-mixing tristable stochastic resonance system are presented. Comparison reveals that the time-domain waveform of the output signal from the inner ring of the experimental bearing is improved, exhibiting a smoother shape, and its amplitude value is generally within -2 m·s⁻¹. -2 up to 2 m·s -2 The signal exhibits a periodic oscillation trend with a clearer regularity. The signal spectrum shows a prominent amplitude at the fault frequency, significantly higher than the amplitude at surrounding non-characteristic frequencies. The amplitude at the fault characteristic frequency ranges from 0.06025 m / s. -2 Increased to 0.5436 m·s -2 . Figure 7 The variation of the output signal-to-noise ratio (SNR) of a hybrid tristable system with noise intensity under controllable potential well width conditions is presented. The controllable potential well factor h only controls the width of the two symmetrical potential wells. By controlling the controllable potential well factor, the dynamic characteristics of particle transitions in the hybrid tristable stochastic resonance system are altered, thereby improving the system output. Compared with the peak SNR of -5.9354 obtained by the conventional method, the peak SNR of the hybrid tristable system is 2.3347. This result demonstrates that the hybrid tristable stochastic resonance system of this invention, due to the introduction of the intermediate potential well, has higher noise utilization and obtains a more ideal output waveform.

[0079] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that 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 defined by the submitted claims. Therefore, the present invention should not be limited to the content disclosed in the embodiments and drawings of the present invention.

Claims

1. A method for detecting weak signals based on a hybrid tristable stochastic resonance system, characterized in that, Includes the following steps: Based on the sampling frequency of the collected fault signals from the original equipment The secondary sampling frequency is determined, and variable-scale random resonance is applied to the secondary sampling frequency to obtain the input signal of the small-parameter system that conforms to the adiabatic approximation theory. Based on the controllable potential well condition, a hybrid tristable stochastic resonance system is established, and the output signal of the hybrid tristable stochastic resonance system is obtained through the small parameter system input signal. Based on the output signal of a hybrid tristable stochastic resonance system, weak characteristic signals can be detected and the degree of equipment failure can be determined. The steps for obtaining the output signal of the hybrid tristable stochastic resonance system include: By combining the classic Woods-Saxon monostable system with a controllable symmetric bistable system, a hybrid tristable stochastic resonance system is obtained. The potential function of this hybrid tristable stochastic resonance system is... for: ； In the formula, p, q, k, , , , For parameters of a mixed tristable system, and Determined by the controllable potential well factor h, and ; Based on the potential function, the Langevin equation for the hybrid tristable stochastic resonance system is obtained: ； in To input a weak periodic signal into a hybrid tristable stochastic resonance system, For system output, The mean is 0 and the variance is Gaussian white noise, D is the noise intensity. It is noise with a mean of 0 and a variance of 1; The Langevin equation is solved using the fourth-order Runge-Kutta method to obtain the output signal of the hybrid tristable stochastic resonance system. The numerical calculation formula of the fourth-order Runge-Kutta method is as follows: ； in This is a discretized form of the noisy input signal of the system, and its value is the input signal of the small parameter system. With noise signal Discretized form of the sum of additions This is the discretized form of the system output signal. The step size is Langevin(*), and the function is the Langevin equation for a mixed tristable stochastic resonance system.

2. The weak signal detection method based on a hybrid tristable stochastic resonance system according to claim 1, characterized in that, The steps for determining the secondary sampling frequency are as follows: Based on the fault signal sampling frequency of the original equipment The secondary sampling frequency is set according to the adiabatic approximation condition of variable-scale random resonance. The secondary sampling frequency satisfies the small parameter constraint of the random resonant input signal and .

3. The weak signal detection method based on a hybrid tristable stochastic resonance system according to claim 1, characterized in that, When the controllable potential well condition is the controllable potential well depth condition, the potential function of the hybrid tristable stochastic resonance system is... h is the controllable potential well factor.

4. The weak signal detection method based on a hybrid tristable stochastic resonance system according to claim 1, characterized in that, When the controllable potential well condition is the controllable potential well width condition, the potential function of the hybrid tristable stochastic resonance system is... h is the controllable potential well factor.

5. A method for detecting weak signals based on a hybrid tristable stochastic resonance system according to claim 3 or 4, characterized in that, The steps for detecting weak feature signals based on the output signal of a hybrid tristable stochastic resonance system include: The power spectrum of the hybrid tristable stochastic resonance system is solved by performing a Fourier transform on the output signal. Signal-to-noise ratio based on power spectrum Calculate the signal-to-noise ratio The calculation formula is: ； In the formula, It is the amplitude corresponding to each spectral line in the power spectrum of the system output signal. is the amplitude at the fault characteristic frequency, and N is the number of samples. Based on the above formula, plot the curve of signal-to-noise ratio as a function of noise intensity, and analyze and judge the weak signal detection capability of the hybrid tristable stochastic resonance system according to the peak signal-to-noise ratio.

6. A method for detecting weak signals based on a hybrid tristable stochastic resonance system according to claim 3 or 4, characterized in that, The steps for determining the degree of equipment failure based on the output signal of the hybrid tristable stochastic resonance system include: The output signal of the hybrid tristable stochastic resonance system is sampled at a second sampling frequency. The compression ratio is reduced; The time-domain and frequency-domain plots of the restored signal are drawn. The smoothness and periodicity of the time-domain waveform are used to observe the quality of the output signal. The degree of equipment failure is determined based on the amplitude of the frequency-domain waveform at a specific fault frequency.

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