CN115655455A - Mechanical fault diagnosis method based on adaptive noise transformation and stochastic resonance - Google Patents
Mechanical fault diagnosis method based on adaptive noise transformation and stochastic resonance Download PDFInfo
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Abstract
The invention relates to a mechanical fault diagnosis method based on adaptive noise transformation and stochastic resonance. The method comprises the following steps: s1, acquiring vibration data of a rotating part by using an acceleration sensor as an original signal; s2, carrying out discrete wavelet transform on the original signal, redistributing the decomposed signal, determining the number of decomposition layers and a redistribution coefficient, and reconstructing to obtain a new signal containing pink noise; and S3, optimizing the decomposition layer number and the redistribution coefficient in the S2 through an artificial bee colony algorithm, wherein the optimization target is the weighted spectrum kurtosis. And S4, inputting the reconstructed signal into a standardized bistable state stochastic resonance system to obtain a denoised signal. And S5, carrying out envelope spectrum analysis on the finally obtained signal, comparing the peak frequency of the envelope spectrum with the calculated theoretical fault characteristic frequency, and carrying out fault diagnosis. The invention utilizes a newly defined index to adaptively change the noise distribution and enhance the signal and accurately diagnose the fault.
Description
Technical Field
The invention belongs to the field of intelligent fault diagnosis of mechanical rotating parts, and particularly provides a mechanical fault diagnosis method based on adaptive noise transformation and stochastic resonance.
Background
Mechanical systems have an indispensable role in industrialization, in which rotating mechanical equipment occupies the majority, and the key in rotating mechanical equipment is a gearbox, which is difficult to maintain due to the harsh industrial environment and its closed working environment, so that various failures of the gearbox in rotating mechanical equipment often occur, and each failure may cause an indispensable loss of money and productivity. In the era of the fourth industrial revolution, future factories and industrial internet of things, industrial mechanical systems are continuously intelligentized and complicated. Therefore, it is necessary to develop and develop data-driven methods and condition monitoring techniques that enable rapid, reliable, and high-quality automatic diagnosis. The early warning can be carried out to gear box early fault, major industrial accident is avoided taking place, and the staff can accomplish in time to maintain, and this has very important meaning to industrial production.
Stochastic Resonance (SR) has been widely studied in the field of mechanical fault diagnosis as a nonlinear signal processing method capable of extracting weak signal features from vibration signals, with its unique advantage of enhancing the weak signals with noise rather than eliminating the noise.
Disclosure of Invention
Based on the problem background, the invention provides a mechanical fault diagnosis method based on adaptive noise transformation and stochastic resonance, which is characterized in that noise distribution which is most beneficial to a stochastic resonance system is obtained by carrying out distribution transformation on noise in an input signal and rapidly optimizing parameters by using an artificial bee colony algorithm, then signal denoising is carried out through the stochastic resonance system, and finally fault diagnosis is carried out through envelope spectrum analysis.
The specific technical scheme of the invention is as follows:
s1, collecting vibration data of a mechanical rotating part by using an acceleration sensor to serve as an original signal;
s2, decomposing the original signal into signals of different frequency bands through Discrete Wavelet Transform (DWT), wherein the number of decomposition layers is a coefficient to be determined, redistributing the decomposed signals, the coefficient to be determined is determined, the purpose of redistributing is to convert colored noise in the original signal into pink noise which is most beneficial to a stochastic resonance system, and reconstructing the obtained redistributed noise through Discrete Wavelet Transform (DWT) to obtain a new signal containing pink noise distribution.
And S3, optimizing the discrete wavelet decomposition layer number and the redistribution coefficient in the S2 through an artificial bee colony Algorithm (ABC), wherein an optimization objective function is weighted spectral kurtosis (CSK), and substituting an optimization result into the S2 to obtain a reconstructed signal.
And S4, inputting the reconstructed signal into a standardized bistable state stochastic resonance system, enhancing the energy of the low-frequency signal by using noise energy through stochastic resonance, and amplifying the fault characteristic signal in the original signal to obtain a denoised signal.
And S5, performing Hilbert envelope spectrum analysis on the finally obtained signal subjected to noise removal by the stochastic resonance system, comparing the peak frequency of the envelope spectrum with the calculated theoretical fault characteristic frequency, and performing fault diagnosis on the mechanical rotating part.
In a specific embodiment of the present invention, the method for signal noise transformation of the original signal in S2 by discrete wavelet transform comprises:
assuming that x (t) is an original input signal, firstly, discrete wavelet transform is performed on the original signal to obtain a series of detail coefficients and approximation coefficients, and the expression is as follows:
wherein,
in order to be a function of the scale,
for the mother wavelet function, J is the number of decomposition layers, J =1, 2.. And J, J is the last layer, so we have a series of wavelet coefficients at different bands:
Φ＝{d 1 ,d 2 ,…,d j ,…,d J ,d J+1 } (3)
wherein d is J+1 Is an approximation coefficient a of the last layer J Since the essence of discrete wavelet decomposition is to construct a series of low-pass and high-pass filters to filter the original signal, signals of different frequency bands are output.
The number of decomposition layers J is determined by the following formula:
wherein f is s To sample frequency, f 0 For the fault signature frequency, the fault signature frequency is included in the last layer detail coefficients, and f 0 In generalIs unknown.
Next, we redistribute the noise in each different frequency band signal to obtain the pink noise which is most beneficial to the stochastic resonance system, the pink noise is characterized by the fact that the noise strength becomes smaller with the increase of the frequency, that is, the pink noise is mainly concentrated in the low frequency part of the signal, and the formula for redistributing each wavelet coefficient is as follows:
wherein alpha is a redistribution coefficient, and finally, reconstructing the redistributed signals to obtain a new signal y n (t)：
In a specific embodiment of the present invention, the step of optimizing the number J of discrete wavelet decomposition layers and the redistribution coefficient α using an artificial bee colony Algorithm (ABC) and a newly proposed Correlated Spectral Kurtosis (CSK) as a fitness function in S3 is as follows:
s21, initializing solution space dimensions and ranges, population numbers and population solutions, detecting bee numbers, acceleration constants, maximum honey source non-updating times and maximum iteration times.
And S22, calculating the fitness function value of each honey source. And the bee is hired to search a new honey source near the current honey source, the following bee selects an optimal honey source according to a greedy strategy, and the bee is hired to search a new honey source near the honey source.
And S23, repeating the step S22, if the non-updating times of a certain honey source reach the maximum non-updating times of the honey source, discarding the honey source, and randomly generating an optimal honey source according to the number of the detected bees for replacing.
And S24, continuously repeating the S22 and the S23 until the maximum iteration times are reached to obtain an optimal solution.
In a specific embodiment of the present invention, the principle of denoising the signal by using the bistable stochastic resonance system in S4 is as follows:
the langevin equation for bistable over-damped stochastic resonance systems is as follows:
where x (t) is the particle motion trajectory, a, b are non-negative system parameters, A 0 Is the weak signal amplitude, f 0 For periodic signal frequency, ξ (t) is zero-mean Gaussian white noise with an intensity D.
To overcome the small parameter limitation, order
τ = at, and therefore, the formula (7) becomes:
thus, the standard form of the bistable stochastic resonance system is obtained, and the input periodic signal is subjected to frequency and amplitude conversion, so that the small parameter limit is met.
In one embodiment of the present invention, the principle of the hilbert envelope spectrum in S5 is as follows:
the method comprises the steps of obtaining a complex domain part of an original signal by Hilbert transformation of the signal, combining the original signal and the complex domain part of the original signal to obtain an analytic signal of the signal, solving a model of the analytic signal to obtain a Hilbert envelope signal, obtaining a Hilbert envelope spectrum by solving an amplitude spectrum, and mainly displaying a low-frequency modulation part of the original signal.
Compared with the prior art, the invention has the beneficial effects that:
according to the invention, a pink noise which is more beneficial to a stochastic resonance system is obtained by carrying out noise transformation on a vibration signal containing a large amount of noise in engineering, and then the original signal is amplified through low-frequency noise in the stochastic resonance system, so that a better original signal amplification effect is obtained.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a time domain diagram of a bearing outer race fault of the present invention;
FIG. 3 is a frequency domain plot of bearing outer race faults in the present invention;
FIG. 4 is a time domain diagram of a reconstructed signal after redistribution in accordance with the present invention;
FIG. 5 is an iterative graph of an artificial bee colony algorithm in accordance with the present invention;
FIG. 6 is a time domain diagram of the signals after passing through the stochastic resonance system in accordance with the present invention;
FIG. 7 is a signal envelope spectrum of the present invention after passing through the stochastic resonance system.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention are further described below with reference to the accompanying drawings and practical experiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not delimit the invention.
The invention relates to a mechanical fault diagnosis method based on adaptive noise transformation and stochastic resonance, which comprises the following steps:
s1, collecting vibration data of a mechanical rotating part by using an acceleration sensor to serve as an original signal;
s2, decomposing the original signal into signals of different frequency bands through Discrete Wavelet Transform (DWT), wherein the number of decomposition layers is a coefficient to be determined, redistributing the decomposed signals, the coefficient to be determined is determined, the purpose of redistributing is to convert colored noise in the original signal into pink noise which is most beneficial to a stochastic resonance system, and reconstructing the obtained redistributed noise through Discrete Wavelet Transform (DWT) to obtain a new signal containing pink noise distribution.
And S3, optimizing the discrete wavelet decomposition layer number and the redistribution coefficient in the S2 through an artificial bee colony Algorithm (ABC), wherein an optimization objective function is weighted spectral kurtosis, and substituting an optimization result into the S2 to obtain a reconstructed signal.
And S4, inputting the reconstructed signal into a standardized bistable state stochastic resonance system, enhancing the energy of the low-frequency signal by using noise energy through stochastic resonance, and amplifying the fault characteristic signal in the original signal to obtain a denoised signal.
And S5, performing Hilbert envelope spectrum analysis on the finally obtained signal subjected to noise removal by the stochastic resonance system, comparing the peak frequency of the envelope spectrum with the calculated theoretical fault characteristic frequency, and performing fault diagnosis on the mechanical rotating part.
The following are specific examples of the present invention:
in the embodiment, bearing data of Keiss West university of storage (CRWU) is adopted, fault data of a bearing outer ring driving end is selected, the fault size is 7mm, and the sampling frequency f s 12000, the rotating speed of the motor 1772rmp, the intercepted data length N2048 and the theoretical fault frequency f of the example can be calculated 0 At 159.9, the theoretical failure characteristic frequency calculation formula of the bearing inner ring is as follows:
wherein f is i Is the theoretical inner ring fault characteristic frequency; d is the bearing pitch diameter; d is the diameter of the rolling body; z is the number of rolling bodies; alpha is a contact angle; f. of n Is the frequency conversion.
First, the input signal is reconstructed using discrete wavelet transform, so that the noise distribution approaches pink noise:
x (t) is an original input signal, firstly, discrete wavelet transform is carried out on the original signal to obtain a series of detail coefficients and approximate coefficients, and the expression is as follows:
wherein,
in order to be a function of the scale,
for the mother wavelet function, J is the number of decomposition layers, J =1, 2., J is the last layer, so we have a series of wavelet coefficients at different bands:
Φ＝{d 1 ,d 2 ,…,d j ,…,d j ,d J+1 } (3)
wherein d is J+1 Is an approximation coefficient a of the last layer J Since the essence of discrete wavelet decomposition is to construct a series of low-pass and high-pass filters to filter the original signal, signals of different frequency bands are output.
The number of decomposition layers J is determined by the following formula:
wherein f is s To sample frequency, f 0 For the fault signature frequency, the fault signature frequency is included in the last layer detail coefficients, and f 0 Is generally unknown.
Next, we redistribute the noise in each different frequency band signal to obtain the pink noise which is most beneficial to the stochastic resonance system, the pink noise is characterized by the fact that the noise strength becomes smaller with the increase of the frequency, that is, the pink noise is mainly concentrated in the low frequency part of the signal, and the formula for redistributing each wavelet coefficient is as follows:
wherein, α is a redistribution coefficient, and finally, reconstructing the redistributed signal to obtain a new signal yn (t):
the steps of optimizing the discrete wavelet decomposition layer number J and the redistribution coefficient alpha by using an artificial bee colony Algorithm (ABC) and taking the related spectral kurtosis as a fitness function are as follows:
s21, initializing the solution space dimension to be 2, setting the upper and lower bounds of the decomposition layer number to be [1 8], setting the redistribution coefficient alpha range to be [ 0], setting the population number to be 100, setting the number of the detection bees to be 100, setting the acceleration constant a =1, setting the maximum non-updating times of the honey sources to be 120 and setting the maximum iteration times to be 200.
And S22, calculating the fitness function value of each honey source. And the bee is hired to search a new honey source near the current honey source, the following bee selects an optimal honey source according to a greedy strategy, and the bee is hired to search a new honey source near the honey source.
And S23, repeating the step S22, if the non-updating times of a certain honey source reach the maximum non-updating times of the honey source, discarding the honey source, and randomly generating an optimal honey source according to the number of the detected bees for replacing.
And S24, continuously repeating the S22 and the S23 until the maximum iteration times is reached to obtain the optimal solution.
The fitness function weighted spectral kurtosis (CSK) is calculated as follows:
where x (t) is the input signal, y (t) is the output signal, y ES (f) To output the signal envelope spectrum, N is the data length.
And (5) carrying the obtained optimal solution into discrete wavelet transform to obtain a reconstructed signal x _ new (t).
The reconstructed signal is subjected to scale transformation 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 R =500
The bistable stochastic resonance system expression is as follows:
the langevin equation for bistable over-damped stochastic resonance systems is as follows:
where x (t) is the particle motion trajectory, a, b are non-negative system parameters, A 0 Is the weak signal amplitude, f 0 For periodic signal frequency, ξ (t) is zero-mean Gaussian white noise with an intensity of D.
To overcome the small parameter limitation, order
τ = at, and therefore, the formula (7) becomes:
solving the Langmuir equation of the bistable state over-damping nonlinear system by adopting a 4-order Rungestota algorithm, wherein the solving process is as follows:
for data length n =1
k 1 ＝f(y n ,t n )
k 4 ＝f(y n +h k 1 ,t n +h)
Wherein y is n For output data, h is the time step, which is set to 1/f in this example s 。
Firstly, the time-frequency domain analysis is carried out on the signal, and the time domain graph and the frequency domain graph of the collected original signal are shown in fig. 2 and fig. 3, wherein the time domain graph can observe the obvious pulse part of the signal, but a plurality of noise components exist around the pulse. From the frequency domain diagram, many high frequency components of the original signal and some modulated side bands can be observed, and the low frequency components are almost 0, so that the signal needs to be analyzed as follows.
The collected signals were analyzed as described above, and the specific procedure for using this method in this embodiment is described below.
Firstly, decomposing an original signal by using discrete wavelet transform, selecting db6 wavelets by wavelet basis functions, and redistributing the decomposed signal so that noise in the original input signal is approximately equal to pink noise, namely noise energy is concentrated near low frequency. The decomposition layer number and the redistribution coefficient are obtained by optimizing an artificial bee colony algorithm, the bee colony number is set to be 100, the maximum iteration number is 200, a fitness function is the product of the spectral kurtosis of an output signal and the correlation coefficient of an output input signal, the solution ranges are [1 ] and [ 0] respectively, an optimal solution carry-in signal reconstruction part is obtained, the reconstruction signal is shown in a graph 4, and an artificial bee colony algorithm iteration curve is shown in a graph 5. The reconstructed signal passes through a stochastic resonance system, noise energy is added to the low-frequency component of the signal, the low-frequency signal is amplified, the amplified output signal is shown in fig. 6, the envelope spectrum of the output signal is shown in the table 7, the corresponding frequency of the peak value of the observed envelope spectrum is 158.2, the theoretical fault frequency obtained through actual calculation is 159.9, and because the theoretical fault frequency is not obtained in the actual working environment, the bearing can generate the phenomena of friction and sliding under the specific working environment of the bearing, so that the fault frequency is deviated, and the error magnitude does not influence the actual fault diagnosis performance. The method can effectively strengthen and extract the impact component of the signal, accurately extract the fault characteristic frequency and prove the effectiveness of the method.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (5)
1. A method for diagnosing mechanical failure based on adaptive noise transformation and stochastic resonance, the method comprising the steps of:
s1, collecting vibration data of a mechanical rotating part by using an acceleration sensor to serve as an original signal;
s2, decomposing the original signal into signals of different frequency bands through discrete wavelet transform, wherein the decomposition layers are coefficients to be determined, redistributing the decomposed signals, amplifying low-frequency signals, determining the redistribution coefficients, and reconstructing the redistributed signals through discrete wavelet transform to obtain new signals containing pink noise;
s3, optimizing the discrete wavelet decomposition layer number and the redistribution coefficient in the S2 through an artificial bee colony algorithm, wherein an optimized objective function is weighted spectral kurtosis, and substituting an optimization result into the S2 to obtain a reconstructed signal;
s4, inputting the reconstructed signal into a standardized bistable state stochastic resonance system, enhancing low-frequency signal energy by using noise energy through stochastic resonance, and amplifying a fault characteristic signal in an original signal to obtain a denoised signal;
and S5, performing Hilbert envelope spectrum analysis on the finally obtained signal subjected to noise removal by the stochastic resonance system, comparing the peak frequency of the envelope spectrum with the calculated theoretical fault characteristic frequency, and performing fault diagnosis on the mechanical rotating part.
2. The mechanical failure diagnosis method based on adaptive noise transformation and stochastic resonance according to claim 1, wherein the method for performing signal noise transformation on the original signal by discrete wavelet transformation in S2 comprises the following steps:
assuming that x (t) is an original input signal, firstly, discrete wavelet transform is performed on the original signal to obtain a series of detail coefficients and approximation coefficients, and the expression is as follows:
wherein, a J (k) To approximate the coefficients, d j (k) In order to be a coefficient of detail,
as a function of the scale, the ratio of the linear characteristic,
for the mother wavelet function, J is the number of decomposition layers, J =1, 2.. And J, J is the last layer, resulting in a series of wavelet coefficients at different frequency bands:
Φ＝{d 1 ,d 2 ,…,d j ,…,d J ,d J+1 } (3)
wherein d is J+1 Is an approximation coefficient a of the last layer J ，
The number of decomposition layers J is determined by the following formula:
wherein f is s To the sampling frequency, f 0 The fault characteristic frequency is contained in the detail coefficient of the last layer;
redistributing the noise in the signals of different frequency bands to obtain pink noise, wherein the formula for redistributing the wavelet coefficients is as follows:
wherein alpha is a redistribution coefficient, and finally, reconstructing the redistributed signals to obtain a new signal y n (t)：
3. The method for diagnosing mechanical failure based on adaptive noise transformation and stochastic resonance as claimed in claim 1, wherein the step of optimizing the number of discrete wavelet decomposition layers J and the redistribution coefficient α using an artificial bee colony algorithm in S3 is as follows:
s21, initializing solution space dimensions and ranges, population numbers and population solutions, detecting bee numbers, acceleration constants, maximum honey source non-updating times and maximum iteration times;
s22, calculating fitness function values of the honey sources, exploring and searching a new honey source by employing the bees near the current honey source, selecting an optimal honey source according to a greedy strategy by following the bees, and exploring and searching a new honey source near the honey source;
s23, repeating the step S22, if the number of times of non-updating of a certain honey source reaches the maximum number of times of non-updating of the honey source, discarding the honey source, and randomly generating an optimal honey source for replacing according to the number of the detected bees;
and S24, continuously repeating the S22 and the S23 until the maximum iteration times is reached to obtain the optimal solution.
4. The method for diagnosing mechanical failure based on adaptive noise transformation and stochastic resonance of claim 1, wherein the method for denoising the signal by using the bistable stochastic resonance system in S4 comprises:
the langevin equation for bistable over-damped stochastic resonance systems is as follows:
where x (t) is the particle motion trajectory, a, b are non-negative system parameters, A 0 Is the weak signal amplitude, f 0 Is the periodic signal frequency, xi (t) is zero mean Gaussian white noise, and the intensity is D;
to overcome the small parameter limitation, order
Therefore, the formula (7) becomes:
and obtaining a standard form of the bistable stochastic resonance system, and performing frequency and amplitude transformation on the input periodic signal to meet the small parameter limit.
5. The mechanical fault diagnosis method based on the adaptive noise transformation and the stochastic resonance as claimed in claim 1, wherein the Hilbert envelope spectrum analysis method in S5 comprises:
the method comprises the steps of obtaining a complex domain part of an original signal by Hilbert transformation of the signal, combining the original signal and the complex domain part of the original signal to obtain an analytic signal of the signal, solving a model of the analytic signal to obtain a Hilbert envelope signal, and solving an amplitude spectrum to obtain a Hilbert envelope spectrum.
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| CN116304848A (en) * | 2023-05-26 | 2023-06-23 | 广东石油化工学院 | Rolling bearing fault diagnosis system and method |
| CN117905711A (en) * | 2024-03-20 | 2024-04-19 | 江苏海拓宾未来工业科技集团有限公司 | Multi-shaft centrifugal compressor and fault diagnosis method for impeller of multi-shaft centrifugal compressor |
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| CN116222750A (en) * | 2023-03-22 | 2023-06-06 | 哈尔滨工程大学 | Stochastic resonance detector and method suitable for high-frequency narrow pulse width acoustic beacon signals |
| CN116304848A (en) * | 2023-05-26 | 2023-06-23 | 广东石油化工学院 | Rolling bearing fault diagnosis system and method |
| CN116304848B (en) * | 2023-05-26 | 2023-08-22 | 广东石油化工学院 | Rolling bearing fault diagnosis system and method |
| CN117905711A (en) * | 2024-03-20 | 2024-04-19 | 江苏海拓宾未来工业科技集团有限公司 | Multi-shaft centrifugal compressor and fault diagnosis method for impeller of multi-shaft centrifugal compressor |
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Inventor after: Chi Feng Inventor after: Wang Yong Inventor after: Huang Xiaoyan Inventor after: Gao Xiang Inventor after: Yang Qinmin Inventor after: Weng Deyu Inventor after: Chen Xu Inventor after: Cao Weiwei Inventor before: Chi Feng Inventor before: Wang Yong Inventor before: Huang Xiaoyan Inventor before: Gao Xiang Inventor before: Yang Qinmin Inventor before: Weng Deyu Inventor before: Chen Xu Inventor before: Cao Weiwei |