A mechanical fault diagnosis method based on minimum entropy deconvolution and stochastic resonance

Abstract

The present application relates to a kind of mechanical fault diagnosis systems based on minimum entropy deconvolution and stochastic resonance, comprising: the vibration data of mechanical rotating component is collected as original signal;After frequency scaling, the original signal is input into bistable stochastic resonance system, and correlation kurtosis is used as index function, system parameters are adaptively adjusted, so that the desired signal is output, the numerical solution of nonlinear system output is obtained using 4-order Runge-Kutta algorithm, the impact component in original signal is amplified using stochastic resonance phenomenon, and the signal after noise reduction is obtained;The signal after noise reduction is filtered again using minimum entropy deconvolution, and minimum entropy deconvolution filter signal is obtained;The signal after minimum entropy deconvolution filtering is subjected to hilbert envelope spectrum analysis, and the fault of mechanical rotating component is diagnosed.The present application can autonomously extract the frequency of fault signal by designing corresponding index under the condition that the fault frequency of unknown signal is unknown, and accurate fault diagnosis and positioning are realized.

Description

Technical Field

[0001] This invention belongs to the field of intelligent bearing fault diagnosis, specifically providing a mechanical fault diagnosis method based on minimum entropy deconvolution and random resonance. This system does not need to know the fault characteristic frequency of the original signal and can adaptively diagnose system faults through given indicators and feature extraction techniques. 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 enhancing weak signals with noise rather than eliminating noise.

[0004] The Minimum Entropy Deconvolution (MED) algorithm was initially proposed by Ra. Wiggens in 1978. It was applied to seismic data detection as an iterative algorithm to maximize the kurtosis value of the filtered output signal, a measure of the impulse component of a signal. In 1984, Ca. Cabreli proposed an equivalent kurtosis index, called D-norm, which solved the problem that the MED algorithm could only be solved iteratively; this was called Optimal Minimum Entropy Deconvolution (OMED). To address the limitation that the kurtosis index could only extract a single pulse, a new OMED algorithm, Maximum Correlation Kurtosis Deconvolution (MCKD), was proposed in 2012 as an iterative algorithm. This method can extract multiple pulses simultaneously, but it requires prior knowledge of the fault characteristic frequency of the signal, and parameters such as filter length and fault period need to be selected, which limits its application. In 2016, Geoff L. McDonald improved the D-norm metric, proposed Multi-point Optimal Minimum Entropy Deconvolution (MOMED), and proposed an adjusted convolution algorithm to overcome the discontinuity of the original convolution calculation.

[0005] This invention combines stochastic resonance and minimum entropy deconvolution algorithms. It utilizes the ability of stochastic resonance to enhance low-frequency signals to enhance low-frequency impact signals. The pulse-enhanced signal is then subjected to minimum entropy deconvolution and envelope spectrum feature extraction, which improves the ability of minimum entropy deconvolution to extract pulses and enhances the fault extraction capability. Summary of the Invention

[0006] Based on the aforementioned problem background, this invention provides a mechanical fault diagnosis method based on minimum entropy deconvolution and stochastic resonance. Specifically, it utilizes the characteristic that stochastic resonance can amplify the low-frequency components of a signal. The original signal is first amplified by a stochastic resonance system to produce a low-frequency impact signal while suppressing the high-frequency components. The signal after impact enhancement is then deconvolved with minimum entropy for feature extraction, thereby achieving accurate fault diagnosis.

[0007] The specific technical solution of this invention is as follows:

[0008] S1. Use an accelerometer to collect gearbox vibration data of engineering machinery vehicles as raw signals;

[0009] S2. After frequency scaling, the original signal is passed through a bistable nonlinear system, also known as a bistable stochastic resonance system. The correlation kurtosis (CK) is used as the index function to adaptively adjust the system parameters so that the system outputs the desired signal. The numerical solution of the nonlinear system output is obtained by using the fourth-order Runge-Kutta algorithm. The stochastic resonance (SR) phenomenon is used to amplify the impulse component in the original signal to obtain the noise-reduced signal.

[0010] S3. The signal after noise reduction by the stochastic resonance system is then subjected to minimum entropy deconvolution (MEDA) filtering. The kurtosis is selected as the index function, and the signal with the largest kurtosis is output to obtain the minimum entropy deconvolution filtered signal.

[0011] S4. Perform Hilbert envelope spectrum analysis on the signal after minimum entropy deconvolution filtering. Compare the envelope spectrum analysis results with the calculated theoretical bearing fault characteristic frequency values ​​and the frequency components with the highest amplitude in the envelope spectrum to diagnose faults in mechanical rotating parts.

[0012] In a specific embodiment of the present invention, in S2, the method for generating random resonance of the original signal through a nonlinear system is as follows:

[0013] The Langevin equation for the Brownian particle in a nonlinear system under the influence of weak periodic forces and noise is as follows:

[0014]

[0015] Where x(t) is the particle trajectory, γ is the damping coefficient between particles, U(x) is the system potential function, S(t) is the weak periodic external force, and ξ(t) is zero-mean Gaussian white noise with intensity D.

[0016] The potential function U(x) of the bistable system is as follows:

[0017]

[0018] Where a>0, b>0.

[0019] Therefore, the Langevin equation for the bistable overdamped nonlinear system can be obtained as follows:

[0020]

[0021] Assuming S(t) is a periodic signal with period Ω, the escape rate (Kramerrate) of the particle jumping caused by noise is:

[0022]

[0023] Where ΔU is the barrier height, representing the height difference between the stable point and the critical stable point of the bistable system, and is influenced by system parameters a and b. Therefore, the particle escape velocity is affected by system parameters a and b, as well as the noise intensity D. When the particle escape velocity satisfies the following condition, the system undergoes random resonance, utilizing the noise intensity to amplify low-frequency signals.

[0024]

[0025] Since the random resonance theory requires that the input periodic signal be a small amplitude and low frequency signal, the fault frequency and sampling frequency of engineering signals are often very large, which cannot meet the above requirements. Therefore, when the actual engineering signal is input into the random resonance system, it is necessary to first perform frequency scaling transformation.

[0026] In a specific embodiment of the present invention, the specific implementation steps of S2, where the original signal is frequency-scaled and then subjected to random resonance, are as follows:

[0027] S21. Select the frequency scaling factor so that the original input signal meets the characteristics of low frequency and small parameters;

[0028] S22. Initialize the parameters of the nonlinear system, specifying the range for parameter selection;

[0029] S23. Select the correlation kurtosis as the objective function, use the grid search method to traverse the parameter initialization interval, and select the parameter combination with the largest correlation kurtosis.

[0030] S24. Using the optimal parameter combination obtained by the grid search method, set up the random resonance system, input the original signal into the random resonance system to amplify the low-frequency impact signal and suppress the high-frequency part, and return the amplified denoised signal according to the frequency scaling factor selected in S21 to restore the original signal frequency, thus obtaining the random resonance denoised signal.

[0031] In a specific embodiment of the present invention, in S3, the method for the denoised signal to undergo minimum entropy deconvolution filtering is as follows:

[0032] A series of finite-length pulse filters, i.e., FIR filters, are selected to convolve the stochastic resonance denoised signal. During the convolution process, only the non-zero portions of the signal are convolved to avoid discontinuities in the convolution process; this method is called adjusted convolution. Initial filter coefficients and kurtosis are selected as the objective function, and the filter is solved by an iterative algorithm until the objective function is no longer in a decreasing position, thus obtaining the optimal filter parameters and the filtered output signal.

[0033] In a specific embodiment of the present invention, in S4, the method for performing Hilbert envelope spectrum analysis on the signal is as follows:

[0034] 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.

[0035] Compared to existing technologies, this invention has the following advantages. This invention combines stochastic resonance and minimum entropy deconvolution for fault diagnosis of rotating mechanical components. The stochastic resonance phenomenon can effectively utilize the noise component in the original signal, converting noise energy into low-frequency energy. Fault vibration signals often appear in the form of impacts, and their frequencies are relatively low compared to gear meshing frequencies. Therefore, the stochastic resonance phenomenon can effectively enhance the impact component in noisy fault signals and suppress high-frequency components. After performing minimum entropy deconvolution on the enhanced impact signal, a more accurate result can be obtained. All of the above steps do not require prior knowledge of the fault frequency and can yield accurate fault diagnosis results. Attached Figure Description

[0036] Figure 1 This is a flowchart of the present invention;

[0037] Figure 2 This is a time-domain diagram of the bearing outer ring fault in an example of the present invention;

[0038] Figure 3This is a frequency domain diagram of the bearing outer ring fault in an example of the present invention;

[0039] Figure 4 This is a time-domain diagram of the signal after random resonance denoising in an example of the present invention;

[0040] Figure 5 This is a time-domain image of the signal after minimum entropy deconvolution filtering in an example of the present invention;

[0041] Figure 6 This is the envelope spectrum after minimum entropy deconvolution filtering in an example of the present invention. Detailed Implementation

[0042] 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.

[0043] This invention provides a mechanical fault diagnosis method based on minimum entropy deconvolution and stochastic resonance, comprising the following steps:

[0044] S1. Use an accelerometer to collect gearbox vibration data of engineering machinery vehicles as raw signals;

[0045] S2. After frequency scaling, the original signal is passed through a bistable nonlinear system, also known as a bistable stochastic resonance system. The system parameters are adaptively adjusted using the correlation kurtosis as an index function to make the system output the desired signal. The numerical solution of the nonlinear system output is obtained by using the fourth-order Runge-Kutta algorithm. The impulse component in the original signal is amplified by using the stochastic resonance phenomenon to obtain the noise-reduced signal.

[0046] S3. After the signal is denoised by the stochastic resonance system, perform minimum entropy deconvolution filtering again, select kurtosis as the index function, and output the signal with the largest kurtosis to obtain the minimum entropy deconvolution filtered signal.

[0047] S4. Perform Hilbert envelope spectrum analysis on the signal after minimum entropy deconvolution filtering. Compare the envelope spectrum analysis results with the calculated theoretical bearing fault characteristic frequency values ​​and the frequency components with the highest amplitude in the envelope spectrum to diagnose the bearing faults of the gearbox of engineering machinery.

[0048] The following are specific implementation examples of the present invention:

[0049] 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. sGiven 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:

[0050]

[0051] 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.

[0052] The principle of stochastic resonance is as follows:

[0053] The Langevin equation for the Brownian particle in a nonlinear system under the influence of weak periodic forces and noise is as follows:

[0054]

[0055] Where x(t) is the particle trajectory, γ is the damping coefficient between particles, U(x) is the system potential function, S(t) is the weak periodic external force, and ξ(t) is zero-mean Gaussian white noise with intensity D.

[0056] The potential function U(x) of the bistable system is as follows:

[0057]

[0058] Where a>0, b>0.

[0059] Therefore, the Langevin equation for the bistable overdamped nonlinear system can be obtained as follows:

[0060]

[0061] Assuming S(t) is a periodic signal with period Ω, the escape rate (Kramerrate) of the particle jumping caused by noise is:

[0062]

[0063] Where ΔU is the barrier height, representing the height difference between the stable point and the critical stable point of the bistable system, and is influenced by system parameters a and b. Therefore, the particle escape velocity is affected by system parameters a and b, as well as the noise intensity D. When the particle escape velocity satisfies the following condition, the system undergoes random resonance, utilizing the noise intensity to amplify low-frequency signals.

[0064]

[0065] Due to the adiabatic approximation theorem, the input signal of random resonance should also satisfy the condition of small parameters, that is, the input signal of the system is a signal with frequency and amplitude much smaller than 1. Specifically, the amplitude of the input signal should satisfy the following conditions:

[0066]

[0067] Where A is the amplitude of the input signal.

[0068] Let the original input signal be x(t). Since the signals actually measured in engineering will definitely contain noise, x(t) contains both periodic and noise signals, satisfying the requirements of a stochastic resonance input signal. Therefore, for this signal, the Langevin equation for the bistable overdamped nonlinear system is:

[0069]

[0070] The Langevin equations for bistable overdamped nonlinear systems are solved using the fourth-order Runge-Kutta algorithm. The solution process is as follows:

[0071] For data lengths n = 1: N

[0072] k1=f(y n ,t n )

[0073]

[0074]

[0075] k4=f(y n +h k1,t n +h)

[0076]

[0077] Where y n The output data is h, where h is the time step.

[0078] The specific steps of the input signal x(t) passing through the stochastic resonance system are as follows:

[0079] S21. The input signal is frequency scaled, with a scaling factor R = 250. Therefore, the sampling frequency f' s =f s / R, correspondingly, the fault characteristic frequency f'0=f0 / R, which makes the input signal satisfy the low-frequency limitation.

[0080] S22. Given the initial values ​​of the potential function parameters of a bistable system, b = 1, a = [0.016] with a step size of 0.05, h = [0.10.5] with a step size of 0.1.

[0081] S23. Set the objective function to be the product of the correlation coefficient between the input and output signals of the nonlinear system and the kurtosis value of the output signal. Use the grid search method to traverse the parameter initialization interval and select the parameter combination with the largest correlation kurtosis (CK).

[0082] S24. Use the optimal parameter combination obtained by the grid search method to set up the stochastic resonance system, use the fourth-order Runge-Kutta algorithm to obtain the numerical solution of the nonlinear system output, input the original signal into the stochastic resonance system to amplify the low-frequency impulse signal and suppress the high-frequency part, and return the amplified denoised signal according to the frequency scaling factor selected in S21 to restore the original signal frequency, thus obtaining the stochastic resonance denoised signal.

[0083] The signal after stochastic resonance denoising is then subjected to feature extraction using the minimum entropy deconvolution algorithm. The principle of the minimum entropy deconvolution (MEDA) algorithm is as follows:

[0084] Deconvolution: The fault signal is smoothed by convolving with a source signal or system function, producing a signal that we can observe. We hope to reconstruct the fault signal based on certain characteristics of the fault signal or an approximate representation of the system function of the source signal.

[0085] The specific steps of the minimum entropy deconvolution algorithm are as follows:

[0086] Let the enhanced impulse signal be x(t), the deconvolution output signal be y(t), and the inverse filter be g(l). The original convolution process is as follows:

[0087]

[0088] To avoid discontinuities during the convolution padding process, adjusted convolution is used, which only performs convolution on the non-zero parts of the signal. The adjusted convolution process is as follows:

[0089]

[0090] The objective function is chosen to be kurtosis, and the expression is as follows:

[0091]

[0092] The problem becomes finding the filter coefficients that maximize the kurtosis index. Setting the partial derivative of the kurtosis index with respect to the filter coefficients to zero yields the following:

[0093]

[0094] The above equation can be written in matrix form as b = Af, where b is the cube of the output vector and a multiple of the cross-correlation vector of the input vector, A is the Toeplitz autocorrelation matrix of the inverse filter input signal, and f is the filter vector. Due to the highly nonlinear nature of the above equation, an iterative algorithm is used to solve it. The steps of the iterative algorithm are as follows:

[0095] S31. First, calculate the Toeplitz autocorrelation matrix A and initialize the filter coefficients. Generally, it is set as a time delay filter, i.e., [0,1,0,…,0].

[0096] S32. According to formula (9), using the known signal and filter coefficients f (k) Calculate the output signal y (k) Where k represents the number of iterations, k = 0, 1, 2, ...;

[0097] S33, Calculation formula (10) Left side term b (k+1) and using f (k+1) =A -1 b (k+1) Calculate the new filter coefficients f (k +1) ;

[0098] S34. Calculate the cycle error:

[0099] E(err)=E[(f (k) -μf (k-1) ) / μf (k-1) ]

[0100] μ=(E(f (k-1) )) 2 / (E(f (k) )2) 1 / 2

[0101] S35. Compare the calculated error with the convergence threshold. When the error is greater than the convergence threshold, i.e., E(err) > tolerance, proceed to S32. The loop continues until the error is less than the convergence threshold, at which point the loop ends, finally obtaining the minimum entropy deconvolution FIR filter parameters f. (end) .

[0102] S36. According to formula (9), y can be calculated using the known signal x(t) and the final filter coefficients. (end) This yields the output of the minimum entropy deconvolution.

[0103] First, time-frequency domain analysis is performed on the signal. The time-domain and frequency-domain plots of the acquired original signal are as follows: Figure 2 and Figure 3As 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.

[0104] in accordance with Figure 1 The method flowchart shown analyzes the acquired signals.

[0105] First, the original signal is denoised using a stochastic resonance system. The original signal is first frequency-scaled. The potential function parameter b = 1 of the bistable nonlinear system is fixed. The grid search method is used to optimize the bistable system parameter a and the time step h of the Runge-Kutta algorithm. The optimization range is a = [0.16] with a step size of 0.05, and h = [0.1-0.5] with a step size of 0.1. The correlation kurtosis is selected as the index function, and the parameter combination with the largest index function is chosen. The final result is a = 5.51 and h = 0.3. The time-domain plot of the signal after stochastic resonance enhancement is shown below. Figure 4 As shown, the enhanced signal is processed using a minimum entropy deconvolution algorithm for feature extraction, with 100 iterations, to obtain the filtered signal, as shown. Figure 5 As shown, many obvious impact signals can now be observed. The filtered signal is then subjected to Hilbert envelope spectrum analysis to obtain the Hilbert envelope spectrum, as shown below. Figure 6 As shown, the peak frequency of the envelope spectrum corresponds to 158.2, while the theoretical fault frequency calculated is 159.7. Since the theoretical fault frequency is not obtained under actual working 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.

[0106] 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 minimum entropy deconvolution 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 frequency-scaled and then input into a bistable stochastic resonance system. The system parameters are adaptively adjusted using the correlation kurtosis as an index function to produce the desired output signal. The numerical solution of the nonlinear system output is obtained using the fourth-order Runge-Kutta algorithm. The impulse component in the original signal is amplified using the stochastic resonance phenomenon to obtain the denoised signal. The specific steps for inputting the original signal into the stochastic resonance system after frequency scaling are as follows: S21. Select the frequency scaling factor so that the original input signal meets the low-frequency characteristics; S22. Initialize the parameters of the nonlinear system, specifying the range for parameter selection; S23. Select the correlation kurtosis as the objective function, use the grid search method to traverse the parameter initialization interval, and select the parameter combination with the largest correlation kurtosis. S24. Use the optimal parameter combination obtained by the grid search method to set up the stochastic resonance system. Input the original signal into the stochastic resonance system to amplify the low-frequency impact signal and suppress the high-frequency part. Then, restore the original signal frequency by the frequency scaling factor selected in S21 to obtain the stochastic resonance denoised signal. S3. After the signal is denoised by the bistable stochastic resonance system, perform minimum entropy deconvolution filtering. Select kurtosis as the index function and output the signal with the largest kurtosis to obtain the minimum entropy deconvolution filtered signal. S4. Perform Hilbert envelope spectrum analysis on the signal after minimum entropy deconvolution filtering. Compare the envelope spectrum analysis results with the calculated theoretical bearing fault characteristic frequency values ​​and the frequency components with the highest amplitude in the envelope spectrum to diagnose faults in mechanical rotating parts.

2. The mechanical fault diagnosis method based on minimum entropy deconvolution and stochastic resonance according to claim 1, characterized in that, In S2, methods for generating stochastic resonance through a nonlinear system include: The Langevin equation for the Brownian particle in a nonlinear system under the influence of weak periodic forces and noise is as follows: (1) Where x(t) is the trajectory of the particle over time, γ is the damping coefficient between particles, U(x) is the system potential function, S(t) is a weak periodic external force that varies with time, and ξ(t) is zero-mean Gaussian white noise with intensity D. The potential function U(x) of the bistable system is as follows: (2) Where a>0, b>0; Therefore, the Langevin equation for the bistable overdamped nonlinear system can be obtained as follows: (3) Assuming S(t) is a periodic signal with period Ω, the escape velocity of the particle caused by noise is: (4) Where ΔU is the barrier height, which is the height difference between the stable point and the critical stable point of the bistable system, and is affected by system parameters a and b. Therefore, it can be seen that the particle escape velocity is affected by system parameters a and b and noise intensity D. When the particle escape velocity satisfies the following condition, the system undergoes random resonance, and the low-frequency signal is amplified using noise intensity: (5)。 3. The mechanical fault diagnosis method based on minimum entropy deconvolution and stochastic resonance according to claim 1, characterized in that, In S3, the methods for deconvolution filtering the denoised signal using minimum entropy include: A series of FIR filters are selected to convolve the signal after stochastic resonance denoising. During the convolution process, only the non-zero parts of the signal are selected for convolution to avoid discontinuities in the convolution process. The initial filter coefficients and kurtosis are selected as the objective function, and the filter is solved by an iterative algorithm until the objective function no longer decreases, thus obtaining the optimal filter coefficients and the filtered output signal.

4. The mechanical fault diagnosis method based on minimum entropy deconvolution and stochastic resonance according to claim 1, characterized in that, In S4, the method for performing Hilbert envelope spectrum analysis on the signal is as follows: The complex part of the original signal is obtained by performing a Hilbert transform on the signal. The analytic signal is obtained by combining the original signal and its complex part. 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.

Images