CN111507305B - Fault Diagnosis Method of Fractional-Order Adaptive Stochastic Resonance Bearing Based on WCSNR - Google Patents

Abstract

The invention relates to the field of bearing fault diagnosis, and discloses a fractional order self-adaptive stochastic resonance bearing fault diagnosis method based on WCSNR.

Description

Fault Diagnosis Method of Fractional-Order Adaptive Stochastic Resonance Bearing Based on WCSNR

technical field

The invention relates to the field of bearing fault diagnosis, in particular to a fractional-order self-adaptive stochastic resonance fault diagnosis method based on a weighted corrected signal-to-noise ratio index (WCSNR).

Background technique

Rotating mechanical equipment is prone to failure under harsh working conditions, and the failure will further cause other mechanical failures. As a key mechanical component of rotating machinery, rolling bearings are widely used in rotating machinery. Working environments such as high speed, heavy load, and high impact are likely to cause bearing failure. Therefore, rolling bearings are the priority targets for condition monitoring and fault diagnosis of rotating machinery equipment. However, in actual engineering, the vibration signals of bearing faults usually show the characteristics of strong noise pollution and uncertain fault characteristic frequency, which makes the extraction of bearing fault features a very difficult task.

Stochastic resonance (SR) is an effective feature extraction technique. It was first proposed by Benzi et al. in the 1980s when studying the ancient earth weather problem. In recent years, the stochastic resonance technique has also been well applied in fractional order systems. And development. Compared with the traditional integer-order stochastic resonance method and traditional filtering methods based on noise elimination, such as: wavelet transform, empirical mode decomposition, etc., fractional-order stochastic resonance technology has many advantages: (1) Traditional filtering methods try to suppress or eliminate Background noise, which at the same time weakens weak signal features too. The stochastic resonance technology is a technology that uses noise to achieve a certain synergistic effect to enhance weak signals, so it is widely used to extract weak fault features in defective bearings. (2) Compared with the traditional integer order stochastic resonance, the fractional stochastic resonance has superior performance, and a more periodic output signal can be obtained by modifying the fractional order. These advantages make the fractional stochastic resonance technique very suitable for extracting weak fault features polluted by strong noise in bearing fault signals, which also makes it a research hotspot in the field of signal processing. The research mainly focuses on two points: how to use the adaptive algorithm to overcome the problem of difficult selection of parameters in the stochastic resonance system; how to solve the problem of using the fractional stochastic resonance algorithm for fault feature extraction when the fault characteristics are unknown.

At present, the fractional-order adaptive stochastic resonance technology based on the traditional signal-to-noise ratio index cannot accurately and stably extract fault characteristics and needs to know the specific value of the fault characteristic frequency in advance, making it increasingly difficult to meet today's production requirements.

Contents of the invention

Aiming at the above problems, the present invention proposes a stochastic resonance bearing fault diagnosis method to accurately and stably extract weak fault features using fractional stochastic resonance technology when the fault features are weak and the characteristic frequency is uncertain.

In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is: according to the characteristics of the expected output signal and the characteristics of the resonance system, the weighted correction SNR index is constructed, and the output response of the resonance system is quantified by using the weighted correction SNR index, and then based on The grid search method establishes an adaptive stochastic resonance system to process the input signal, and then extracts the unknown fault features accurately, stably and effectively, and realizes the diagnosis of bearing faults.

Further, specific steps of the present invention include:

Step 1: According to the characteristics of the expected output signal and the characteristics of the resonance system, construct the expression of the weighted modified signal-to-noise ratio index WCSNR;

Step 2: collect the vibration signal x of the bearing;

Step 3: Solve the fractional-order overdamped Langevin equation, obtain the discrete form of the fractional-order stochastic resonance equation, and establish a discrete model of the adaptive fractional-order stochastic resonance system;

Step 4: Initialize the system parameters of the discrete model of the adaptive fractional stochastic resonance system, including the barrier parameters a, b and the search range and step size of the fractional order α, variable scaling coefficient β, etc.;

Step 5: Substituting the vibration signal into the discrete model of the adaptive fractional stochastic resonance system to obtain the output response, calculating the weighted correction signal-to-noise ratio index WCSNR according to the output response, and saving the calculated weighted correction signal-to-noise ratio index WCSNR and the corresponding system parameters;

Step 6: Judging whether the calculated weighted corrected signal-to-noise ratio index WCSNR is greater than the maximum WCSNR max_WCSNR that has occurred at present, if it is greater, then go to step 7; if not, go to step 8;

Step 7: Let max_WCSNR=WCSNR, max_a=a, and max_α=α at this time;

Step 8: Determine whether the system parameters have been traversed. If the traverse has been completed, execute Step 9. Otherwise, modify the parameters a and α according to the grid search method to continue the traverse, and enter Step 5;

Step 9: Get the optimal system parameters max_a and max_α by maximizing the weighted correction SNR index search;

Step 10: Substituting the optimal system parameters into the discrete model of the adaptive fractional stochastic resonance system to obtain the optimal output response y.

Step 11: Spectrum analysis is performed on the optimal system response y to extract fault features and identify fault types.

Specifically, the construction of the weighted modified SNR index in step 1 is still based on the SNR, but SNR cannot be used simply as an evaluation index. The construction method of the weighted modified SNR index WCSNR is as follows:

考虑重构信号

与原始振动信号x(t)的相似性，计算得到两者的互相关系数C并将其引入到WCSNR指标的构造中。对于长度为N的离散信号X，X₁,两个信号互相关系数C的表达式为：① Spectrum analysis is performed on the output response, and the signal is reconstructed using the spectral peak frequency f _max to obtain

Consider Refactoring Signals

Based on the similarity with the original vibration signal x(t), the cross-correlation coefficient C between the two is calculated and introduced into the construction of the WCSNR index. For a discrete signal X of length N, X ₁ , the expression of the cross-correlation coefficient C of two signals is:

分别是两个信号的平均值。In the formula,

are the mean values of the two signals, respectively.

利用残余噪声方差替代残余噪声能量得到Rvar＝var(resx)。残余噪声越小表明这种相似性越强，因此构造出C/Rvar让互相关系数大的同时使残余噪声能量小。② To further ensure this similarity, consider the residual noise energy Rvar, the residual noise

Substituting the residual noise variance for the residual noise energy yields Rvar=var(resx). The smaller the residual noise is, the stronger the similarity is, so C/Rvar is constructed to make the cross-correlation coefficient large while making the residual noise energy small.

③ Then consider the zero-crossing ratio Zcr to enhance the periodicity of the output signal at the peak frequency of the spectrum. The stronger the periodicity, the more obvious the stochastic resonance phenomenon appears in the system. The zero-crossing ratio refers to the ratio of the actual number of zero-crossings to the theoretical zero-crossings of the system output response. For a discrete sequence X(K) with a sampling frequency of f _s and a data length of N, first calculate the number n of theoretical zero-crossing points and the pair of actual zero-crossing points H(j):

In the formula, f _max is the spectral peak frequency, M is the logarithm of the zero-crossing point, and the search restriction condition is X(K _j )*X(K _j +1)<0. Then use the linear interpolation method to get the time value {t _j ,j=1,2,...,M} and the time interval {ZD(r),r=1,2,...,M} of each actual zero-crossing point -1}, after removing the false zero point caused by noise in the actual zero crossing point (ZD(r)≠1/2f _max ), the actual number of zero crossing points n1 is obtained, and the judgment condition of the false zero point is:

Finally, we obtain the zero-crossing ratio Zcr=n1/n through the ratio of the actual zero-crossing point and the theoretical zero-crossing point. The closer Zcr is to 1, the more obvious the periodic characteristics of the output response, so |1-Zcr| is introduced into the construction of WCSNR;

The closer Zcr is to 1, the more obvious the periodic characteristics of the output response, so |1-zcr| is introduced into the construction of WCSNR.

④ Then we combine the characteristics of stochastic resonance for practical consideration. According to the adiabatic approximation theory of stochastic resonance, the frequency of the weak fault signal needs to be much less than 1HZ, so in the traditional stochastic resonance, the variable scale coefficient β is introduced to make the weak fault signal meet the adiabatic approximation theory, that is, the requirement of the fault characteristic frequency becomes much smaller than β. At this time, we use the Sigmoid function to convert this condition into a frequency weighting coefficient Fwc to weight the measured spectral peak frequency, and introduce the frequency weighting coefficient into the construction of WC SNR. The expression of Fwc is:

In the formula, a is used to adjust the steepness of the function. Then, in order to observe the effect, we introduce the difference Adis between the highest spectral peak and the second highest spectral peak, and finally obtain the expression of the weighted modified signal-to-noise ratio index WCSNR as follows:

Further, the discrete expression of the numerical solution method of the adaptive fractional stochastic resonance system in step 3 is:

In the formula, x is the output signal, and the output signal satisfies the zero initial condition, that is, x(0)=0. α is the fractional order, j is the cyclic coefficient, s is the input signal with noise, h is the sampling step size and satisfying that h is small enough, that is, the sampling frequency is high enough. k is the subscript of the output discrete data, that is, x(kh) is expressed as the kth data point of the output signal. w _j is the binomial coefficient, and the solution method of w _j is:

w ₀ =1,

The invention can realize weak fault features, and accurately and stably extract weak fault features by using fractional order stochastic resonance technology under uncertain characteristic frequency. Since the evaluation index comprehensively considers the periodicity, salience and similarity of the output response to the original signal, it can break through the defect that the traditional stochastic resonance adaptive method needs to predict the fault characteristic frequency. In addition, this index considers the characteristics of stochastic resonance itself, and introduces frequency weighting coefficients, which can greatly improve the accuracy of fault feature extraction, thereby realizing accurate diagnosis of bearing faults.

Description of drawings

Fig. 1 is the flow chart of stochastic resonance bearing fault diagnosis method of the present invention;

Fig. 2 is the time-domain waveform of original vibration signal in the embodiment of the present invention;

Fig. 3 is the amplitude spectrum of original vibration signal in the embodiment of the present invention;

Fig. 4 is the output signal time-domain waveform obtained in the embodiment of the present invention;

Fig. 5 is the amplitude spectrum of the output signal gained in the embodiment of the present invention;

Fig. 6 is the time-domain waveform of the output signal obtained by using the traditional adaptive stochastic resonance algorithm based on the signal-to-noise ratio index;

Fig. 7 is the amplitude spectrum of the output signal obtained by using the traditional adaptive stochastic resonance algorithm based on the signal-to-noise ratio index.

Detailed ways

The present invention constructs a weighted correction signal-to-noise ratio index according to the characteristics of the expected output signal and the characteristics of the resonance system, and uses W CSNR to quantify the output response of the resonance system, and then establishes an adaptive fractional stochastic resonance algorithm based on the grid search method, thereby achieving accuracy and stability , Effectively extract unknown fault features. The weighted modified signal-to-noise ratio index proposed by the present invention not only comprehensively considers the periodicity, prominence and similarity with the original signal of the output response, but also breaks through the defect that the traditional stochastic resonance self-adaptive method needs to predict the fault characteristic frequency. In addition, this index considers the characteristics of stochastic resonance itself, and introduces frequency weighting coefficients to further improve the accuracy of fault feature extraction, thereby realizing accurate and efficient diagnosis of bearing faults.

Based on the above ideas, the embodiment provides a bearing fault diagnosis method, the flow chart of which is shown in Figure 1, and the specific steps are as follows:

Step 1: According to the characteristics of the expected output signal and the characteristics of the resonance system, the weighted modified SNR index is constructed. The expression of the weighted SNR index is:

In the formula, SNR is the signal-to-noise ratio index, and the other indexes are Zcr—zero-crossing ratio, Rvar—participating noise energy, C—correlation coefficient, Adis—spectral peak protrusion coefficient, and Fwc—frequency weighting coefficient.

Step 2: Collect the vibration signal x(t) of the bearing.

Step 3: Solve the fractional-order overdamped Langevin equation, obtain the discrete form of the fractional-order stochastic resonance equation, and establish a discrete model of the system. The numerical solution expression of the fractional-order stochastic resonance system is:

In the formula, x is the input signal, w _j is the binomial coefficient, α is the fractional order, h is the sampling step;

Step 4: Initialize the system parameters of the adaptive stochastic resonance system, including the barrier parameters a, b and the search range and step size of the fractional order α, variable scaling coefficient β, etc.;

Step 5: Substitute the vibration signal x(t) into the system to obtain the output response, calculate the weighted signal-to-noise ratio index WCS NR according to the output response, and save the index and corresponding system parameters;

Step 6: Determine whether the system parameters have been traversed. If the traverse has been completed, execute step 8. Otherwise, modify the parameters according to the grid search method and execute step 5;

Step 7: Get the optimal system parameters a, b, α by maximizing the weighted correction SNR index search;

Step 8: Substituting the optimal parameters into the system to obtain the optimal output response y(t);

Step 9: Perform spectrum analysis on the optimal system response y(t), extract unknown fault features, and identify bearing faults.

The embodiment will be further described below in conjunction with a specific example—fault diagnosis of a certain generator bearing. The test bearing parameters of the generator are shown in the table below:

In this experiment, the motor drives the test bearing to rotate. The rotation frequency of the generator obtained from vibration data collection is 25.76Hz, the sampling frequency is 12800Hz, and the data length is N=16384. Combining the bearing parameters and generator speed information in the above table, it can be known that the bearing external The fault characteristic frequency of the circle is 80.72Hz.

Step 1: Measure the original vibration signal x (unit g) of the generator bearing vibration through the acceleration sensor. Figure 2 and Figure 3 are the time-domain waveform and amplitude spectrum of the original vibration signal x respectively. It can be seen from the figure that the time-domain waveform of the vibration signal of the rear bearing of the generator contains impact components of varying strengths, and it is difficult to observe reliable period information. In the amplitude spectrum, the signal energy is mainly concentrated in the middle frequency band. In the low frequency component, there are frequency components with a switching frequency of 25.78Hz and an insignificant 80.47Hz. When the influence of frequency resolution is ignored, the fault characteristic frequency is f ₀ =80.47Hz , which is consistent with the theoretical value of fault characteristic frequency. At the same time, it can be seen that the characteristic frequency of the generator bearing fault in the amplitude spectrum is almost submerged by the strong interference frequency in the middle frequency band, so it is difficult to accurately identify the bearing fault.

Step 2: Initialize the system parameters according to the vibration signal. In this example, β=300, b=50, a∈[0.01, 1], α∈[1.04, 1.9], and the search step size is 0.02.

Execute according to the above steps 5-9, search to obtain the optimal parameters a=0.01, b=50, α=1.72, and the system output time-domain waveform under the optimal parameters is shown in Figure 4. It can be seen from Figure 4 that the periodic impact of bearing outer ring faults has been accurately extracted, and there is an obvious stochastic resonance phenomenon. By analyzing the frequency spectrum of the time-domain signal in Figure 4, the amplitude spectrum of the output signal shown in Figure 5 is obtained. In the amplitude spectrum, the characteristic frequency f ₀ of the bearing fault can be clearly observed, indicating that the system generates a fault at f ₀ The stable stochastic resonance phenomenon is obtained, and the weak fault features are accurately extracted. Therefore, it can be judged that there is a fault in the bearing after the test generator, and the diagnosis result is consistent with the experimental plan, which proves the effectiveness of the embodiment.

In order to further clarify the superiority of the inventive method, a traditional fractional-order adaptive stochastic resonance algorithm based on the signal-to-noise ratio index is used to process the signal. In this process, assuming that the spectrum peak frequency is the fault characteristic frequency, the time-domain waveform and its amplitude spectrum of the output signal obtained by maximizing the SNR are shown in Figure 6 and Figure 7. Comparing Figures 4 and 6 with Figures 5 and 7 respectively, it can be seen that the traditional adaptive algorithm cannot correctly extract the fault cycle characteristics of the vibration signal, and it can be clearly seen that the output signal in the embodiment produces a more obvious and stable Random resonance phenomenon, so the embodiment has a better effect in the fault diagnosis of the rear bearing of the generator.

The above is only a specific embodiment of the present invention. Any feature disclosed in this specification, unless specifically stated, can be replaced by other equivalent or alternative features with similar purposes; all the disclosed features, or Steps in all methods or processes, except for mutually exclusive features and/or steps, can be combined in any way; any non-essential additions and substitutions made by those skilled in the art based on the technical features of the technical solution of the present invention, All belong to the protection scope of the present invention.

Claims (5)

1. A fractional order self-adaptive stochastic resonance bearing fault diagnosis method based on WCSNR is characterized by comprising the following steps:

step 1: constructing an expression of a weighted correction signal-to-noise ratio index WCSNR according to the characteristics of the expected output signal and the characteristics of the resonance system;

step 2: collecting a vibration signal x of a bearing;

and step 3: solving a fractional order over-damping Langmuim equation to obtain a discrete form of a fractional order stochastic resonance equation, and establishing a discrete model of a self-adaptive fractional order stochastic resonance system;

and 4, step 4: initializing system parameters of a discrete model of the self-adaptive fractional order stochastic resonance system, wherein the system parameters comprise potential barrier parameters a and b, a search range and step length of a fractional order alpha, and a variable scale coefficient beta;

and 5: substituting the vibration signal into the self-adaptive fractional order stochastic resonance system discrete model to obtain an output response, calculating a weighted correction signal-to-noise ratio index WCSNR according to the output response, and storing the calculated weighted correction signal-to-noise ratio index WCSNR and corresponding system parameters;

step 6: judging whether the calculated weighted correction signal-to-noise ratio index WCSNR is larger than the current WCSNR maximum value max _ WCSNR or not, and if so, entering a step 7; if not, entering step 8;

and 7: let max _ WCSNR = WCSNR, max _ a = a, and max _ α = α at this time;

and step 8: judging whether the system parameters are traversed or not, if so, executing a step 9, otherwise, modifying the parameters a and alpha according to a grid search method to continue traversing, and entering a step 5;

and step 9: obtaining optimal system parameters max _ a and max _ alpha by weighted correction signal-to-noise ratio index maximization search;

step 10: substituting the optimal system parameters into the discrete model of the self-adaptive fractional order stochastic resonance system to obtain the optimal output response y;

step 11: carrying out spectrum analysis on the optimal output response y, extracting fault characteristics and judging the fault type;

wherein, the constructing an expression of the weighted modified snr index WCSNR in step 1 specifically includes:

the construction of the weighting correction signal-to-noise ratio index WCSNR still takes the signal-to-noise ratio as the main, but the SNR can not be simply adopted as the evaluation index, and the construction method of the weighting correction signal-to-noise ratio index WCSNR is as follows:

(1) performing spectral analysis on the output response using the peak frequency f _max Performing signal reconstruction to obtain

Considering the reconstructed signal

Calculating the similarity of the original vibration signal x (t) to obtain a cross correlation coefficient C of the original vibration signal x (t) and the cross correlation coefficient C, and introducing the cross correlation coefficient C into a structure of a WCSNR index; for a discrete signal X, X of length N ₁ The expression for the cross correlation coefficient C of the two signals is:

in the formula (I), the compound is shown in the specification,

are the average of the two signals, respectively;

(2) to further ensure this similarity, the residual noise energy Rvar, residual noise, is considered

Replacing residual noise energy with residual noise variance to obtain Rvar = var (resx), wherein the smaller the residual noise is, the stronger the similarity is, so that the C/Rvar is constructed to make the cross correlation coefficient large and make the residual noise energy small;

(3) then, zero-crossing ratio ZCr is considered to enhance the periodicity of the output signal at the frequency of the spectral peak, the more strong the periodicity indicates that the system has more obvious stochastic resonance phenomenon, and the zero-crossing ratio refers to the ratio of the actual zero-crossing number and the theoretical zero-crossing number of the output response of the system; for a sampling frequency of f _s The discrete sequence X (K) with the data length N, the solution method of ZCr is as follows:

firstly, calculating the number n of theoretical zero-crossing points and an actual zero-crossing pair H (j):

in the formula (f) _max For spectral peak frequency, M is the logarithm of zero crossing, and the search constraint is X (K) _j )*X(K _j + 1) < 0, and then obtaining the time value { t ] of each actual zero crossing point by using a linear interpolation method _j J =1,2,.. M } and the time interval { ZD (r), r =1,2,... M-1}, remove the spurious zero point ZD (r) ≠ 1/2f caused by noise in the actual zero crossing _max Then obtaining the number n1 of the actual zero crossing points, wherein the judgment conditions of the pseudo zero points are as follows:

finally, obtaining a zero-crossing ratio Zcr = n1/n through the ratio of an actual zero-crossing and a theoretical zero-crossing, wherein the closer Zcr is to 1, the more obvious the periodic characteristic of the output response is, so that |1-Zcr | is introduced into the structure of the WCSNR;

(4) then, the characteristics of stochastic resonance are combined for practical consideration, according to the adiabatic approximation theory of stochastic resonance, the frequency of a weak fault signal needs to be far less than 1HZ, therefore, a scale-variable coefficient beta is introduced in the traditional stochastic resonance to enable the weak fault signal to meet the adiabatic approximation theory, namely, the requirement of fault characteristic frequency becomes far less than beta, at this time, a Sigmoid function is utilized to convert the condition into a frequency weighting coefficient Fwc for weighting the measured spectral peak frequency, the frequency weighting coefficient is introduced into the structure of WCSNR, and the expression of Fwc is as follows:

wherein a is used to adjust the steepness of the function; then introducing a difference value Adis of a highest spectral peak and a second highest spectral peak for observation effect, and finally obtaining an expression of the weighted correction signal-to-noise ratio index WCSNR, wherein the expression is as follows:

in the formula, SNR is a signal-to-noise ratio index, and the other indexes are respectively ZCr-zero crossing point ratio, rvar-participating noise energy, C-cross correlation coefficient, adis-spectral peak protrusion coefficient and Fwc-frequency weighting coefficient.

2. The fractional order adaptive stochastic resonance bearing fault diagnosis method based on WCSNR of claim 1, wherein the solving of the fractional order over damping Langmuim equation in step 3 to obtain the discrete form of the fractional order stochastic resonance equation specifically comprises:

the numerical solution method discrete expression of the fractional order stochastic resonance system is as follows:

where x is the output signal, the output signal satisfies the initial condition of zero, i.e. x (0) =0, α is the fractional order, j is the cyclic coefficient, s is the input signal with noise, h is the sampling step size, k is the subscript of the output discrete data, i.e. x (kh) is the kth data point of the output signal, w _j Is a coefficient of a binomial form, w _j The solving method comprises the following steps:

3. the fractional order adaptive stochastic resonance bearing fault diagnosis method based on WCSNR according to claim 2, wherein the sampling frequency is 12800Hz and the data length N =16384.

4. The WCSNR fractional order-based adaptive stochastic resonance bearing fault diagnosis method according to claim 3, wherein system parameters of the adaptive fractional order stochastic resonance system discrete model are initialized to be β =300, b =50, a ∈ [0.01,1], α ∈ [1.04,1.9], and search step sizes are all 0.02.

5. The fractional order adaptive stochastic resonance bearing fault diagnosis method based on WCSNR according to claim 4, wherein the optimal system parameter max _ a =0.01, max _ α =1.72.

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