CN111507305B - Fractional order self-adaptive stochastic resonance bearing fault diagnosis method based on WCSNR - Google Patents
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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
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 weighted correction signal-to-noise ratio index (WCSNR).
Background
Rotating machinery equipment is prone to failure under severe working conditions, other mechanical failures are further caused by the failure, and the rolling bearing is widely applied to the rotating machinery as a key mechanical part of the rotating machinery. The rolling bearing is a priority target for state monitoring and fault diagnosis of rotary mechanical equipment because the bearing is easy to fail in working environments such as high speed, heavy load, high impact and the like. However, in practical engineering, vibration signals of bearing faults generally show the characteristics that the signals are polluted by strong noise, the fault characteristic frequency is uncertain, and the like, so that the extraction of the fault characteristics of the bearing becomes a very difficult task.
Stochastic Resonance (SR) is an effective feature extraction technique, which was first proposed by Benzi et al in the 80 th 20 th century when studying ancient earth weather, and in recent years, has also been better applied and developed in fractional order systems. Compared with the traditional integer order stochastic resonance method and the traditional filtering method based on noise elimination, the method comprises the following steps: wavelet transformation, empirical mode decomposition, and the like, and the fractional order random resonance technology has multiple advantages: (1) Conventional filtering methods all attempt to suppress or eliminate background noise, which also attenuates weak signal characteristics. The stochastic resonance technique is a technique for enhancing a weak signal by using noise to achieve a certain synergistic effect, and thus is widely used for extracting weak fault features in a defective bearing. (2) Fractional order random resonance has better performance compared with the traditional integer order random resonance, and an output signal with stronger periodicity can be obtained by modifying the fractional order. The advantages enable the fractional order stochastic resonance technology to be very suitable for extracting weak fault characteristics polluted by strong noise in bearing fault signals, and enable the fractional order stochastic resonance technology to become a research hotspot in the field of signal processing. The research is mainly focused on two points: how to use the adaptive algorithm to overcome the problem that the parameters in the stochastic resonance system are difficult to select; how to solve the problem of extracting fault characteristics by using a fractional order stochastic resonance algorithm under the condition that the fault characteristics are unknown.
At present, the fractional order self-adaptive stochastic resonance technology based on the traditional signal-to-noise ratio index can not accurately and stably extract fault characteristics and needs to know specific numerical values of fault characteristic frequency in advance, so that the fault characteristic frequency is more and more difficult to meet the current production requirements.
Disclosure of Invention
Aiming at the problems, the invention provides a random resonance bearing fault diagnosis method, which is used for accurately and stably extracting weak fault characteristics by using a fractional order random resonance technology under the conditions that the fault characteristics are weak and the characteristic frequency is uncertain.
In order to realize the purpose, the invention adopts the technical scheme that: and constructing a weighted correction signal-to-noise ratio index according to the characteristics of the expected output signal and the characteristics of the resonance system, quantizing the output response of the resonance system by using the weighted correction signal-to-noise ratio index, and then establishing an adaptive stochastic resonance system based on a grid search method to process the input signal, thereby accurately, stably and effectively extracting unknown fault characteristics and realizing the diagnosis of the bearing fault.
Further, the method comprises the following specific 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 the 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, a variable scale coefficient beta and the like;
and 5: substituting the vibration signal into a self-adaptive fractional order random 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 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: and 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: and carrying out spectrum analysis on the optimal system response y, extracting fault characteristics and judging the fault type.
Specifically, the structure of weighting and correcting the signal-to-noise ratio index in step 1 still mainly uses the signal-to-noise ratio, but cannot simply use SN R as an evaluation index, and the method for constructing the weighting and correcting the signal-to-noise ratio index WCSNR includes:
(1) performing spectral analysis on the output response using the peak frequency f max Performing signal reconstruction to obtain
Considering the reconstructed signal
And calculating the similarity with the original vibration signal x (t) to obtain the cross correlation coefficient C of the original vibration signal x (t) and introducing the cross correlation coefficient C into the construction of the 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,
respectively, are the average of the two signals.
(2) To further ensure this similarity, the residual noise energy Rvar, residual noise, is considered
Replacing the residual noise energy with the residual noise variance yields Rvar = var (resx). The smaller the residual noise is, the stronger the similarity is, so the C/Rvar cross correlation system is constructedThe large number also results in a small residual noise energy.
(3) The zero crossing ratio Zcr is then considered to enhance the periodicity of the output signal at the spectral peak frequencies, with a stronger periodicity indicating a more pronounced stochastic resonance phenomenon of the system. The zero crossing ratio refers to the ratio of the number of actual zero crossings of the system output response to the number of theoretical zero crossings. For a sampling frequency of f s First, calculating the theoretical zero-crossing number N and the 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. Then, a linear interpolation method is used for obtaining the time value { t } of each actual zero crossing point j J =1,2,.. M } and the time interval { ZD (r), r =1,2,... M-1}, remove the spurious zero point caused by noise in the actual zero crossing (ZD (r) ≠ 1/2 f) max ) Then obtaining the actual zero crossing number n1, wherein the judging conditions of the pseudo zero are as follows:
finally, the zero-crossing ratio Zcr = n1/n is obtained by the ratio of the actual zero-crossing to the theoretical zero-crossing. The closer ZCr is to 1, the more pronounced the periodic characteristics of the output response, thus introducing |1-ZCr | into the construction of WCSNR;
the closer Zcr is to 1, the more pronounced the periodic characteristics of the output response, thus introducing |1-Zcr | into the construction of the WCSNR.
(4) We then actually consider the features of stochastic resonance. According to the adiabatic approximation theory of stochastic resonance, the frequency of a weak fault signal needs to be much smaller than 1HZ, so that a variable scale 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 the fault characteristic frequency is much smaller than beta. At this time, we convert this condition into a frequency weighting coefficient Fwc by using a Sigmoid function to weight the measured spectral peak frequency, and introduce the frequency weighting coefficient into the structure of WC SNR, where the expression of Fwc is:
where a is used to adjust the steepness of the function. Then, in order to observe the effect, a difference value Adis between the highest spectral peak and the second highest spectral peak is introduced, and finally, an expression of a weighted correction signal-to-noise ratio index WCSNR is obtained as follows:
further, in step 3, the discrete expression of the numerical solution method of the adaptive fractional order stochastic resonance system is as follows:
in the formula, x is an output signal, and the output signal satisfies an initial condition of zero, i.e., x (0) =0. Alpha is the fractional order, j is the cyclic coefficient, s is the input signal with noise, h is the sampling step and satisfies that h is taken small enough, i.e. the sampling frequency is high enough. k is an index for the output discrete data, i.e., x (kh) is represented as the kth data point of the output signal. w is a j Is a coefficient of a binomial form, w j The solving method comprises the following steps:
w 0 ＝1,
the method can accurately and stably extract weak fault features by using the fractional order random resonance technology under the condition of uncertain feature frequency. The evaluation index comprehensively considers the periodicity and the saliency of the output response and the similarity of the output response and the original signal, so that the defect that the traditional stochastic resonance adaptive method needs to predict the characteristic frequency of the fault can be overcome. In addition, the index is considered aiming at the characteristics of stochastic resonance, a frequency weighting coefficient is introduced, the accuracy of fault feature extraction can be greatly improved, and therefore accurate diagnosis of bearing faults is achieved.
Drawings
FIG. 1 is a flow chart of a stochastic resonance bearing fault diagnosis method of the present invention;
FIG. 2 is a time domain waveform of an original vibration signal in an embodiment of the present invention;
FIG. 3 is an amplitude spectrum of an original vibration signal in an embodiment of the present invention;
FIG. 4 is a time domain waveform of an output signal obtained in an embodiment of the present invention;
FIG. 5 is an amplitude spectrum of the resulting output signal in an embodiment of the present invention;
FIG. 6 is a time domain waveform of an output signal obtained using a conventional signal-to-noise ratio indicator-based adaptive stochastic resonance algorithm;
FIG. 7 is an amplitude spectrum of an output signal obtained using a conventional adaptive stochastic resonance algorithm based on a signal-to-noise indicator.
Detailed Description
According to the method, a weighted correction signal-to-noise ratio index is constructed according to the characteristics of an expected output signal and the characteristics of a resonance system, the W CSNR is utilized to quantize the output response of the resonance system, and then an adaptive fractional order random resonance algorithm is established based on a grid search method, so that unknown fault characteristics are accurately, stably and effectively extracted. The weighted correction signal-to-noise ratio index provided by the invention not only comprehensively considers the periodicity and the saliency of output response and the similarity with an original signal, but also overcomes the defect that the traditional stochastic resonance adaptive method needs to predict the characteristic frequency of a fault. In addition, the index is considered aiming at the characteristics of stochastic resonance, a frequency weighting coefficient is introduced, and the accuracy of fault feature extraction is further improved, so that the accurate and efficient diagnosis of the bearing fault is realized.
Based on the above thought, the embodiment provides a bearing fault diagnosis method, a flow chart of which is shown in fig. 1, and the specific steps are as follows:
step 1: constructing a weighted correction signal-to-noise ratio index according to the characteristics of the expected output signal and the characteristics of the resonance system, wherein the expression of the weighted signal-to-noise ratio index 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.
Step 2: and acquiring a vibration signal x (t) of the bearing.
And step 3: solving a fractional order over-damping Langmuim equation to obtain a discrete form of a fractional order random resonance equation, and establishing a system discrete model, wherein a numerical solution expression of the fractional order random resonance system is as follows:
wherein x is the input signal, w j Is a binomial coefficient, alpha is a fractional order, and h is a sampling step length;
and 4, step 4: initializing system parameters of the self-adaptive 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, a variable scale coefficient beta and the like;
and 5: substituting the vibration signal x (t) into the system to obtain an output response, calculating a weighted signal-to-noise ratio index WCS NR according to the output response, and storing the index and corresponding system parameters;
step 6: judging whether the system parameters are traversed or not, if so, executing a step 8, otherwise, modifying the parameters according to a grid search method, and executing a step 5;
and 7: obtaining optimal system parameters a, b and alpha by weighted correction signal-to-noise ratio index maximization search;
and step 8: substituting the optimal parameters into the system to obtain optimal output response y (t);
and step 9: and carrying out spectrum analysis on the optimal system response y (t), extracting unknown fault characteristics, and judging the bearing fault.
The embodiment is further described below with reference to a specific example, a generator bearing fault diagnosis. The generator experimental bearing parameters are shown in the following table:
in this experiment, the motor drives the test bearing and rotates, and the generator that vibration data acquisition obtained changes the frequency and is 25.76Hz, and sampling frequency is 12800Hz, and data length N =16384, combines the bearing parameter and the generator rotational speed information in the table above, and the trouble characteristic frequency of knowing the bearing outer lane is 80.72Hz.
The first step is as follows: an original vibration signal x (unit g) of the vibration of the generator bearing is measured by an acceleration sensor, and fig. 2 and 3 are a time domain waveform and an amplitude spectrum of the original vibration signal x respectively. As can be seen from the figure, the time domain waveform of the vibration signal of the rear bearing of the generator contains impact components with different strengths, and reliable periodic information is difficult to observe. The signal energy in the amplitude spectrum is mainly concentrated in the middle frequency band, the low frequency component has frequency components of 25.78Hz in the rotating frequency and 80.47Hz in the unobvious frequency, and the fault characteristic frequency is f under the condition of neglecting the influence of frequency resolution 0 =80.47Hz, which corresponds to the fault characteristic frequency setpoint value. Meanwhile, the characteristic frequency of the bearing fault of the generator in the amplitude spectrum is almost submerged by the strong interference frequency of the middle frequency band, so that the bearing fault is difficult to accurately distinguish.
The second step: the system parameters are initialized according to the vibration signals, wherein the parameters are beta =300, b =50, a epsilon [0.01,1], alpha epsilon [1.04,1.9] and the search step is 0.02.
The method of the above steps 5-9 is performed, and the optimal parameters a =0.01, b =50, and α =1.72 are obtained by searching, and the system output time-domain waveform under the optimal parameters is shown in fig. 4. As can be seen from fig. 4, the periodic impact of the bearing outer ring fault is accurately extracted, and a significant stochastic resonance phenomenon occurs. The output signal shown in fig. 5 is obtained by performing a spectral analysis of the time domain signal of fig. 4In the amplitude spectrum, the characteristic frequency f of the bearing fault can be very clearly observed 0 Description of the System in f 0 Stable stochastic resonance phenomenon is generated, and weak fault features are accurately extracted. Therefore, the fault of the rear bearing of the generator can be judged, the diagnosis result is consistent with the experimental scheme, and the effectiveness of the embodiment is proved.
In order to further clarify the superiority of the method, the traditional fractional order self-adaptive stochastic resonance algorithm based on the signal-to-noise ratio index is used for processing the signal. In the process, assuming that the spectrum peak frequency is the fault characteristic frequency, the output signal time domain waveform and its amplitude spectrum obtained by SNR maximization are as shown in fig. 6 and fig. 7. Comparing fig. 4 and 6 with fig. 5 and 7, respectively, it can be seen that the fault cycle characteristic of the vibration signal cannot be correctly extracted by the conventional adaptive algorithm, and it can be clearly seen that the output signal in the embodiment generates a more obvious and stable stochastic resonance phenomenon, so that the embodiment has a better effect in the generator rear bearing fault diagnosis.
While the invention has been described with reference to specific embodiments, any feature disclosed in this specification may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except mutually exclusive features and/or steps; any non-essential addition and replacement made by the technical characteristics of the technical scheme of the invention by a person skilled in the art belong to the protection scope of the 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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