A mechanical fault diagnosis method based on adaptive noise transform and stochastic resonance

Abstract

The application relates to a mechanical fault diagnosis method based on adaptive noise transformation and random resonance. The method comprises the following steps: S1, collecting vibration data of a rotating part by using an acceleration sensor as an original signal; S2, performing discrete wavelet transformation on the original signal, redistributing the decomposed signal, determining a decomposition layer number and a redistribution coefficient, and then reconstructing a new signal containing pink noise; S3, optimizing the decomposition layer number and the redistribution coefficient in S2 by using an artificial bee colony algorithm, and taking a weighted spectral kurtosis as an optimization target; S4, inputting the reconstructed signal into a normalized bistable random resonance system to obtain a denoised signal; and S5, performing envelope spectrum analysis on the finally obtained signal, comparing an envelope spectrum peak frequency with a calculated theoretical fault characteristic frequency, and performing fault diagnosis. The application can adaptively change noise distribution and enhance a signal by using a newly defined index, so that fault diagnosis can be accurately performed.

Description

Technical Field

[0001] This invention belongs to the field of intelligent fault diagnosis of mechanical rotating parts, specifically providing a mechanical fault diagnosis method based on adaptive noise transformation and random resonance. This system transforms the noise distribution in the input signal to obtain the noise distribution most favorable to the random resonance system, and then performs noise reduction through the random resonance system for fault diagnosis. Background Technology

[0002] Mechanical systems play an indispensable role in industrialization, with rotating machinery accounting for the majority. Gearboxes are crucial components of rotating machinery. Due to the harsh industrial environment and their enclosed working conditions, gearbox maintenance is difficult, leading to frequent gearbox failures in rotating machinery, each potentially resulting in significant financial and productivity losses. In the era of the so-called Fourth Industrial Revolution, the factory of the future, and the Industrial Internet of Things, industrial mechanical systems are becoming increasingly intelligent and complex. Therefore, researching and developing data-driven methods and condition monitoring technologies to achieve rapid, reliable, and high-quality automatic diagnostics is essential. Accurate early warning of gearbox failures can prevent major industrial accidents, enabling timely maintenance by workers, which is of great significance to industrial production.

[0003] Stochastic resonance (SR), as a nonlinear signal processing method capable of extracting weak signal features from vibration signals, has been widely studied in the field of mechanical fault diagnosis due to its unique advantage of using noise to enhance weak signals rather than eliminating noise. Summary of the Invention

[0004] Based on the aforementioned problem background, this invention provides a mechanical fault diagnosis method based on adaptive noise transformation and stochastic resonance. By transforming the distribution of noise in the input signal and using the artificial bee colony algorithm to quickly optimize the parameters, the noise distribution most favorable to the stochastic resonance system is obtained. Then, the signal is denoised through the stochastic resonance system, and finally, fault diagnosis is performed through envelope spectrum analysis.

[0005] The specific technical solution of this invention is as follows:

[0006] S1. Use an accelerometer to collect vibration data of rotating mechanical parts as raw signals;

[0007] S2. The original signal is decomposed into signals of different frequency bands by Discrete Wavelet Transform (DWT). The number of decomposition levels is an undetermined coefficient. The decomposed signals are redistributed. The redistribution coefficients are undetermined. The purpose of redistribution is to transform the colored noise in the original signal into pink noise, which is most favorable to the stochastic resonance system. The redistributed noise is then reconstructed by Discrete Wavelet Transform (DWT) to obtain a new signal containing the pink noise distribution.

[0008] S3. The discrete wavelet decomposition level and redistribution coefficients in S2 are optimized using the artificial bee colony algorithm (ABC). The objective function for optimization is weighted spectral kurtosis (CSK). The optimization result is substituted into S2 to obtain the reconstructed signal.

[0009] S4. Input the reconstructed signal into the standardized bistable stochastic resonance system. Through stochastic resonance, the noise energy is used to enhance the low-frequency signal energy and amplify the fault characteristic signal in the original signal to obtain the denoised signal.

[0010] S5. Perform Hilbert envelope spectrum analysis on the final signal after denoising by the stochastic resonance system, compare the peak frequency of the envelope spectrum with the calculated theoretical fault characteristic frequency, and diagnose the fault of the mechanical rotating parts.

[0011] In a specific embodiment of the present invention, the method for signal-to-noise transformation of the original signal in S2 using discrete wavelet transform is as follows:

[0012] Assuming x(t) is the original input signal, we first perform a discrete wavelet transform on the original signal to obtain a series of detail coefficients and approximation coefficients, as expressed below:

[0013]

[0014]

[0015] in, For scaling function, Let be the mother wavelet function, and j be the decomposition level, j = 1, 2, ..., J, where J is the last level. Thus, we obtain a series of wavelet coefficients in different frequency bands:

[0016] Φ={d1,d2,…,d j ,…,d J ,d J+1} (3)

[0017] Where d J+1 The approximation coefficient a for the last layer J Since the essence of discrete wavelet decomposition lies in constructing a series of low-pass and high-pass filters to filter the original signal and output signals of different frequency bands.

[0018] The number of decomposition layers J is determined by the following formula:

[0019]

[0020] Where f s f0 is the sampling frequency, and f0 is the fault characteristic frequency. The fault characteristic frequency is included in the last layer of detail coefficients, while f0 is usually unknown.

[0021] Next, we redistribute the noise in the signals of different frequency bands to obtain the pink noise most favorable to the stochastic resonance system. The characteristic of pink noise is that the noise intensity decreases with increasing frequency, that is, pink noise is mainly concentrated in the low-frequency part of the signal. The formula for redistributing the wavelet coefficients is as follows:

[0022]

[0023] Where α is the redistribution coefficient, and finally the redistributed signal is reconstructed to obtain a new signal y. n (t):

[0024]

[0025] In a specific embodiment of the present invention, the steps in S3 of using the Artificial Bee Colony Algorithm (ABC) with the newly proposed correlation spectral kurtosis (CSK) as the fitness function to optimize the discrete wavelet decomposition level J and the redistribution coefficient α are as follows:

[0026] S21. Initialize the solution space dimension and range, population size and population solutions, number of scout bees, acceleration constant, maximum number of times the nectar source does not update, and maximum number of iterations.

[0027] S22. Calculate the fitness function value of each nectar source. Hired bees explore and search for new nectar sources near the current nectar source, while follower bees select the optimal nectar source according to a greedy strategy and explore and search for new nectar sources in the vicinity of the current nectar source.

[0028] S23. Repeat step S22. If the number of times a nectar source has not been updated reaches the maximum number of times a nectar source has not been updated, discard the nectar source and randomly generate an optimal nectar source to replace it based on the number of scout bees.

[0029] S24. Repeat S22 and S23 until the maximum number of iterations is reached to obtain the optimal solution.

[0030] In a specific embodiment of the present invention, the principle of using a bistable stochastic resonance system to denoise the signal in S4 is as follows:

[0031] The Langevin equation for a bistable overdamped stochastic resonance system is as follows:

[0032]

[0033] Where x(t) is the particle trajectory, a and b are non-negative system parameters, A0 is the amplitude of the weak signal, f0 is the frequency of the periodic signal, and ξ(t) is zero-mean Gaussian white noise with intensity D.

[0034] To overcome the limitations of small parameters, let τ = at, therefore, equation (7) becomes:

[0035]

[0036] Thus, the standard form of the bistable stochastic resonance system was obtained, and the frequency and amplitude of the input periodic signal were transformed to meet the small parameter constraints.

[0037] In a specific embodiment of the present invention, the principle of the Hilbert envelope spectrum in S5 is as follows:

[0038] The complex part of the original signal is obtained by performing a Hilbert transform on the signal. The original signal and its complex part are combined to obtain the analytic signal. The magnitude of the analytic signal is obtained by calculating the Hilbert envelope signal. The amplitude spectrum is obtained by calculating the Hilbert envelope spectrum, which is mainly used to display the low-frequency modulation part of the original signal.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] This invention first transforms the vibration signal containing a large amount of noise in the engineering process to obtain pink noise, which is more favorable to the random resonance system. Then, the original signal is amplified by low-frequency noise through the random resonance system to obtain a better amplification effect of the original signal. Attached Figure Description

[0041] Figure 1 This is a flowchart of the present invention;

[0042] Figure 2 This is a time-domain diagram of the bearing outer ring fault in this invention;

[0043] Figure 3 This is a frequency domain diagram of the bearing outer ring fault in this invention;

[0044] Figure 4 This is a time-domain diagram of the reconstructed signal after redistribution in this invention;

[0045] Figure 5 This is an iterative curve diagram of the artificial bee colony algorithm in this invention;

[0046] Figure 6 This is a time-domain diagram of the signal after passing through the random resonance system in this invention;

[0047] Figure 7 This is the signal envelope spectrum after passing through the random resonance system in this invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be further described below in conjunction with the accompanying drawings and actual experiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0049] This invention provides a mechanical fault diagnosis method based on adaptive noise transformation and random resonance, comprising the following steps:

[0050] S1. Use an accelerometer to collect vibration data of rotating mechanical parts as raw signals;

[0051] S2. The original signal is decomposed into signals of different frequency bands by Discrete Wavelet Transform (DWT). The number of decomposition levels is an undetermined coefficient. The decomposed signals are redistributed. The redistribution coefficients are undetermined. The purpose of redistribution is to transform the colored noise in the original signal into pink noise, which is most favorable to the stochastic resonance system. The redistributed noise is then reconstructed by Discrete Wavelet Transform (DWT) to obtain a new signal containing the pink noise distribution.

[0052] S3. The discrete wavelet decomposition level and redistribution coefficients in S2 are optimized using the artificial bee colony algorithm (ABC). The objective function of the optimization is the weighted spectral kurtosis. The optimization result is substituted into S2 to obtain the reconstructed signal.

[0053] S4. Input the reconstructed signal into the standardized bistable stochastic resonance system. Through stochastic resonance, the noise energy is used to enhance the low-frequency signal energy and amplify the fault characteristic signal in the original signal to obtain the denoised signal.

[0054] S5. Perform Hilbert envelope spectrum analysis on the final signal after denoising by the stochastic resonance system, compare the peak frequency of the envelope spectrum with the calculated theoretical fault characteristic frequency, and diagnose the fault of the mechanical rotating parts.

[0055] The following are specific implementation examples of the present invention:

[0056] This example uses bearing data from Case Western Reserve University (CRWU), specifically fault data from the outer ring drive end of the bearing. The fault size is 7mm, and the sampling frequency is f. s Given a value of 12000, a motor speed of 1772 rpm, and a data length N of 2048, the theoretical fault frequency f0 in this example can be calculated to be 159.9. The formula for calculating the theoretical fault characteristic frequency of the bearing inner ring is as follows:

[0057]

[0058] Among them, f i denoted as the theoretical inner ring failure characteristic frequency; D is the bearing pitch diameter; d is the rolling element diameter; Z is the number of rolling elements; α is the contact angle; f n For frequency conversion.

[0059] First, the input signal is reconstructed using discrete wavelet transform, making the noise distribution approximate pink noise:

[0060] x(t) is the original input signal. First, a discrete wavelet transform is performed on the original signal to obtain a series of detail coefficients and approximation coefficients, as expressed below:

[0061]

[0062]

[0063] in, For scaling function, Let be the mother wavelet function, and j be the decomposition level, j = 1, 2, ..., J, where J is the last level. Thus, we obtain a series of wavelet coefficients in different frequency bands:

[0064] Φ={d1,d2,…,d j ,…,d j ,d J+1} (3)

[0065] Where d J+1 The approximation coefficient a for the last layer J Since the essence of discrete wavelet decomposition lies in constructing a series of low-pass and high-pass filters to filter the original signal and output signals of different frequency bands.

[0066] The number of decomposition layers J is determined by the following formula:

[0067]

[0068] Where f s f0 is the sampling frequency, and f0 is the fault characteristic frequency. The fault characteristic frequency is included in the last layer of detail coefficients, while f0 is usually unknown.

[0069] Next, we redistribute the noise in the signals of different frequency bands to obtain the pink noise most favorable to the stochastic resonance system. The characteristic of pink noise is that the noise intensity decreases with increasing frequency, that is, pink noise is mainly concentrated in the low-frequency part of the signal. The formula for redistributing the wavelet coefficients is as follows:

[0070]

[0071] Where α is the redistribution coefficient, and finally the redistributed signal is reconstructed to obtain a new signal yn(t):

[0072]

[0073] The steps for optimizing the discrete wavelet decomposition level J and redistribution coefficient α using the artificial bee colony algorithm (ABC) with the correlation spectral kurtosis as the fitness function are as follows:

[0074] S21. Initialize the solution space dimension to 2, the upper and lower bounds of the decomposition level to [1 8], the range of the redistribution coefficient α to [0 20], the population size to 100, the number of scout bees to 100, the acceleration constant a = 1, the maximum number of times the nectar source does not update to 120, and the maximum number of iterations to 200.

[0075] S22. Calculate the fitness function value of each nectar source. Hired bees explore and search for new nectar sources near the current nectar source, while follower bees select the optimal nectar source according to a greedy strategy and explore and search for new nectar sources in the vicinity of the current nectar source.

[0076] S23. Repeat step S22. If the number of times a nectar source has not been updated reaches the maximum number of times a nectar source has not been updated, discard the nectar source and randomly generate an optimal nectar source to replace it based on the number of scout bees.

[0077] S24. Repeat S22 and S23 until the maximum number of iterations is reached to obtain the optimal solution.

[0078] The formula for calculating the fitness function weighted spectral kurtosis (CSK) is as follows:

[0079]

[0080] Where x(t) is the input signal, y(t) is the output signal, and y ES (f) represents the envelope spectrum of the output signal, and N represents the data length.

[0081] Substituting the obtained optimal solution into the discrete wavelet transform, we obtain the reconstructed signal x_new(t).

[0082] The reconstructed signal is scaled and then input into a standardized bistable stochastic resonance system for denoising. In this example, the signal frequency scaling factor is R = 500, and the amplitude scaling factor is... The expression for a bistable stochastic resonance system is as follows:

[0083] The Langevin equation for a bistable overdamped stochastic resonance system is as follows:

[0084]

[0085] Where x(t) is the particle trajectory, a and b are non-negative system parameters, A0 is the amplitude of the weak signal, f0 is the frequency of the periodic signal, and ξ(t) is zero-mean Gaussian white noise with intensity D.

[0086] To overcome the limitations of small parameters, let τ = at, therefore, equation (7) becomes:

[0087]

[0088] The Langevin equations for bistable overdamped nonlinear systems are solved using the fourth-order Runge-Kutta algorithm. The solution process is as follows:

[0089] For data lengths n = 1: N

[0090] k1=f(y n ,t n )

[0091]

[0092]

[0093] k4=f(y n +h k1,t n +h)

[0094]

[0095] Where y n For the output data, h is the time step, which is set to 1 / f in this example. s .

[0096] First, time-frequency domain analysis was performed on the signal. The time-domain and frequency-domain plots of the acquired original signal are attached. Figure 2 and Figure 3 As shown, the time-domain plot reveals a clear signal pulse component, but the pulse is surrounded by significant noise. The frequency-domain plot shows numerous high-frequency components and some modulated sidebands, while low-frequency components are almost nonexistent. Therefore, the signal requires further analysis as follows.

[0097] The collected signals are analyzed using the method described above. The specific process of using this method in this particular example is described below.

[0098] First, the original signal is decomposed using discrete wavelet transform, with the db6 wavelet chosen as the wavelet basis function. The decomposed signal is then redistributed so that the noise in the original input signal is approximately equal to pink noise, meaning the noise energy is concentrated near the low frequency. The number of decomposition layers and redistribution coefficients are obtained using an artificial bee colony algorithm, with the number of bees set to 100 and the maximum number of iterations set to 200. The fitness function is the product of the spectral kurtosis of the output signal and the correlation coefficient between the output and input signals, with solutions ranging from [1 8] to [0 20]. The optimal solution is then substituted into the signal reconstruction part, and the reconstructed signal is as follows: Figure 4 As shown, the iterative curve of the artificial bee colony algorithm is as follows: Figure 5 As shown in the figure. The reconstructed signal is passed through a stochastic resonance system, where noise energy is added to the low-frequency components of the signal to amplify the low-frequency signal. The amplified output signal is shown in the figure. Figure 6 As shown in Figure 7, the envelope spectrum of the output signal corresponds to a peak frequency of 158.2 Hz. The theoretical fault frequency calculated is 159.9 Hz. Since the theoretical fault frequency is not obtained under actual operating conditions, friction and sliding will occur in the bearing under its specific operating environment, leading to a deviation in the fault frequency. However, the magnitude of this error does not affect the actual fault diagnosis performance. It can be seen that this method can effectively enhance and extract the impulse component of the signal and accurately extract the fault characteristic frequency, proving the effectiveness of this method.

[0099] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A mechanical fault diagnosis method based on adaptive noise transform and stochastic resonance, characterized in that, The method includes the following steps: S1. Use an accelerometer to collect vibration data of rotating mechanical parts as raw signals; S2. The original signal is decomposed into signals of different frequency bands through discrete wavelet transform. The number of decomposition levels is an undetermined coefficient. The decomposed signals are redistributed to amplify the low-frequency signals. The redistribution coefficients are undetermined. The redistributed signals are then reconstructed through discrete wavelet transform to obtain a new signal containing pink noise. The method for transforming signal noise using discrete wavelet transform on the original signal is as follows: Assuming x(t) is the original input signal, we first perform a discrete wavelet transform on the original signal to obtain a series of detail coefficients and approximation coefficients, as expressed below: (1) (2) where a J (k) is an approximation coefficient, d j (k) is a detail coefficient, is a scaling function, is a mother wavelet function, j is the decomposition level, J is the last level, and some columns of wavelet coefficients in different frequency bands are obtained: (3) where d J+1 is the approximation coefficient a J of the last layer, The number of decomposition layers J is determined by the following formula: (4) where f s is the sampling frequency, f0is the fault feature frequency, and the fault feature frequency is contained in the last layer of detail coefficients. The noise in different frequency bands is redistributed to obtain pink noise. The formula for redistributing the wavelet coefficients is as follows: (5) where a is a redistribution coefficient, and the redistributed signal is finally reconstructed to obtain a new signal y n (t): (6) S3. The discrete wavelet decomposition level J and redistribution coefficient α in S2 are optimized using the artificial bee colony algorithm. The objective function of the optimization is the weighted spectral kurtosis. The optimization result is substituted into S2 to obtain the reconstructed signal. The steps for optimizing the discrete wavelet decomposition level J and the redistribution coefficient α using the artificial bee colony algorithm are as follows: S31. Initialize the solution space dimension to 2, the upper and lower bounds of the decomposition level to [1 8], the range of the redistribution coefficient α to [0 20], the population size to 100, the number of scout bees to 100, the acceleration constant a=1, the maximum number of times the nectar source does not update to 120, and the maximum number of iterations to 200. S32. Calculate the fitness function value of each nectar source, hire bees to explore and search for new nectar sources near the current nectar source, follow the bees to select the optimal nectar source according to the greedy strategy, and explore and search for new nectar sources near the current nectar source. S33. Repeat step S32. If the number of times a nectar source has not been updated reaches the maximum number of times a nectar source has not been updated, discard the nectar source and randomly generate an optimal nectar source to replace it based on the number of scout bees. S34. Repeat S32 and S33 until the maximum number of iterations is reached to obtain the optimal solution; S4. Input the reconstructed signal into the standardized bistable stochastic resonance system. Through stochastic resonance, the noise energy is used to enhance the low-frequency signal energy, amplify the fault characteristic signal in the original signal, and obtain the denoised signal. Methods for denoising signals using bistable stochastic resonance systems include: The Langevin equation for a bistable overdamped stochastic resonance system is as follows: (7) Where x(t) is the particle trajectory, a and b are non-negative system parameters, A0 is the amplitude of the weak signal, f0 is the frequency of the periodic signal, and ξ(t) is zero-mean Gaussian white noise with intensity D. To overcome the small parameter restriction, let , τ = at, so that (7) becomes (8) The standard form of the bistable stochastic resonance system is obtained, and the frequency and amplitude of the input periodic signal are transformed to meet the small parameter constraints. S5. Perform Hilbert envelope spectrum analysis on the final signal after denoising by the stochastic resonance system, compare the peak frequency of the envelope spectrum with the calculated theoretical fault characteristic frequency, and diagnose the fault of the mechanical rotating parts. 2.The mechanical fault diagnosis method based on adaptive noise transform and stochastic resonance according to claim 1, characterized in that, The methods for Hilbert envelope spectrum analysis in S5 include: The signal is subjected to Hilbert transform to obtain the complex domain part of the original signal, the analytic signal of the signal is obtained by combining the original signal and the complex domain part, the Hilbert envelope signal is obtained by solving the modulus of the analytic signal, and the Hilbert envelope spectrum is obtained by solving the amplitude spectrum.

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