CN111504640B - Weighted sliding window second-order synchronous compression S transformation bearing fault diagnosis method - Google Patents
Weighted sliding window second-order synchronous compression S transformation bearing fault diagnosis method Download PDFInfo
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Abstract
The invention relates to the field of bearing fault diagnosis, and discloses a weighted sliding window second-order synchronous compression S transform bearing fault diagnosis method which is used for improving the precision of bearing fault feature extraction and fault type identification. The method comprises the steps of constructing an optimal weighted sliding window module according to the characteristics of bearing fault vibration signals, transforming and integrating second-order synchronous compression S into a plurality of step length modules, adaptively obtaining a Gaussian window which is best matched with fault characteristic signals in the signal time-frequency analysis process through an optimization algorithm, calculating weights by using the obtained time-frequency analysis Rinyi entropy, and then realizing overall signal reconstruction output. The bearing fault characteristics are accurately extracted and the fault types are accurately identified through the time-frequency spectrogram, and the method is suitable for fault diagnosis of the rolling bearing.
Description
Technical Field
The invention relates to the field of bearing fault diagnosis, in particular to a method for diagnosing a fault of a bearing by weighted sliding window second-order synchronous compression S transformation.
Background
The rolling bearing is used as a key mechanical part of a rotary machine and widely applied to various industrial fields, and the operation state monitoring and fault diagnosis of the rolling bearing have important significance for ensuring the reliability of equipment and avoiding safety accidents. However, in practical engineering, since the bearing fault characteristic information is often submerged by strong background noise and other unstable components, the extraction of the bearing fault characteristic information becomes a difficult task.
The time-frequency analysis of the signal can describe frequency information of each fault component changing along with time, and common signal time-frequency analysis methods, such as: short-time fourier transform, wavelet transform, S-transform, etc. have several advantages: (1) besides obtaining each frequency component, the time when each component appears, the change of signal frequency along with time, and the instantaneous frequency and amplitude at each moment can be known. (2) The instantaneous frequency of the vibration signal changing along with time under the non-stationary condition can be effectively estimated. Because of these advantages, signal time-frequency analysis has recently become a research hotspot in the field of signal processing, and many researchers have proposed various time-frequency post-processing methods in order to improve the accuracy of instantaneous frequency estimation. The synchronous compression transformation is a time-frequency post-processing method obtained by transformation with a mathematical principle, can effectively improve energy aggregation, and can well reflect the time-frequency characteristics of signal weak amplitude components by combining with S transformation. In addition, aiming at a strong noise background, the optimal weighted sliding window algorithm is constructed, so that the instantaneous frequency enhancement estimation of weak features can be realized.
At present, the traditional frequency spectrum analysis method has poor effects of extracting the fault characteristics of the bearing and accurately identifying the fault type, and is more and more difficult to meet the current production requirements.
Disclosure of Invention
Aiming at the problems, the invention provides a weighted sliding window second-order synchronous compression S transform bearing fault diagnosis method which is used for improving the precision of bearing fault feature extraction and fault type identification.
In order to achieve the purpose, the invention adopts the technical scheme that: an optimal weighted sliding window is constructed according to the bearing fault vibration signal characteristics, an optimal weighted sliding window algorithm is combined with a second-order synchronous compression S transformation method, a Gaussian window which is best matched with fault characteristic signals is obtained in a self-adaptive mode in the signal time-frequency analysis process through the optimization algorithm, a plurality of variable step length analysis modules are arranged in the sliding window, weighted reconstruction is carried out on the signals according to the Rinyi entropy after time-frequency analysis is carried out, a high-resolution time-frequency spectrogram is obtained, and therefore accurate extraction of the bearing fault characteristics and accurate identification of fault types are achieved.
Further, the bearing fault diagnosis method provided by the invention specifically comprises the following steps:
step 1: collecting a vibration signal f of a bearing;
step 2: specifying a sliding window length w;
and step 3: specifying the category number M of the variable step size analysis module;
and 4, step 4: decomposing the vibration signal f according to the sliding window length w and the variable step length analysis module category number M to obtain a multi-section variable step length analysis module input signal;
and 5: performing second-order synchronous compression S transformation algorithm analysis on the input signal of the ith variable step size analysis module;
step 6: after the input signal of the ith variable-step-size analysis module is subjected to second-order synchronous compression S transformation algorithm analysis, the weight rho of each variable-step-size analysis module is calculated according to the corresponding renai entropy valueiThen, let i ═ i + 1;
and 7: judging whether i is larger than M, if so, entering step 8; if not, entering step 5;
and 8: outputting the plurality of variable step length modules according to the weight rhoiReconstructing to obtain a total signal time-frequency spectrogram;
and step 9: and (3) extracting the significant fault characteristic component in the time-frequency spectrogram of the total signal, and comparing the theoretical fault frequency to judge the fault type of the bearing.
Specifically, step 1 acquires a vibration signal f of the bearing through an acceleration sensor.
Specifically, the expression of the second-order synchronous compression S transformation is:
in the formula, gσ(0) Is a variable Gaussian window function;
in order to perform the S-transform,
correcting instantaneous frequency for second orderIt is estimated that δ represents a dirac distribution, γ is a predetermined threshold, η is a frequency factor, ω is a phase factor, and t is time.
Further, in step 4, the formula for configuring the step length according to the variable step length analysis module category number M is as follows:
in the formula, λiThe step length of the ith variable step length analysis module; w is the width of the sliding window.
Further, in step 6, a formula for configuring the weight according to the time-frequency analysis renyi entropy value is as follows:
ρi＝[(1-α)(Rα(yi)-μmin[Rα(yi)])]-1
where α is the order of the entropy of the renai used, typically taken to be 3; mu is a scale parameter, and the value range mu belongs to [0,1 ]]，Rα(yi) Is the output result y of the ith variable step size analysis moduleiThe entropy value of R é nyi.
Further, in step 8, the reconstruction formula of the total signal time-frequency spectrogram is as follows:
wherein, yw[d]For the output result of the d-th weighted sliding window of the total signal, yiAnd w is the width of the weighted sliding window, and is the output result of the ith variable step size analysis module in the weighted sliding window.
The method can construct an optimal weighted sliding window according to the bearing fault vibration signal characteristics, adaptively obtains a Gaussian window which is optimally matched with the fault characteristic signal in the signal time-frequency analysis process through an optimization algorithm, performs time-frequency analysis and then performs weighted reconstruction in the sliding window, retains the energy of the weak amplitude signal, finally obtains a high-resolution time-frequency spectrogram, and realizes accurate extraction of the bearing fault characteristics and accurate identification of the fault type.
Drawings
FIG. 1 is a flow chart of a bearing fault diagnosis method of the present invention;
FIG. 2 is a time domain waveform and a frequency domain waveform of an original vibration signal according to an embodiment of the present invention;
FIG. 3 is a second-order synchronous compressed S-transform time-frequency spectrogram based on an optimal weighted sliding window;
FIG. 4 is a time-frequency spectrum of a conventional short-time Fourier transform;
FIG. 5 is a time-frequency spectrum of S transform;
Detailed Description
The invention will now be described in further detail with reference to the following figures and examples, which are given by way of illustration and not of limitation.
The method comprises the steps of constructing an optimal weighted sliding window according to the bearing fault vibration signal characteristics, combining an optimal weighted sliding window algorithm with a second-order synchronous compression S transformation method, adaptively obtaining a Gaussian window which is optimally matched with a fault characteristic signal in the signal time-frequency analysis process through the optimization algorithm, enabling a plurality of variable step length analysis modules to be arranged in the sliding window, conducting time-frequency analysis, conducting weighted reconstruction on the signal according to the Rinyi entropy to obtain a high-resolution time-frequency spectrogram, and further achieving accurate extraction of the bearing fault characteristics and accurate identification of fault types. The second-order synchronous compression S change is used as a time-frequency analysis method, and the wheel set bearing vibration signal with the instantaneous frequency showing nonlinear change along with time can be effectively processed. In addition, by utilizing the frequency change periodic characteristics of the mechanical bearing, the optimal weighting sliding window algorithm aiming at the weak amplitude fault component is provided, so that the instantaneous frequency enhancement estimation of the weak characteristic under the background of strong noise is realized, and the accurate and efficient diagnosis of the bearing fault is realized.
Based on the above thought, the invention provides a bearing fault diagnosis method, the flow chart of which is shown in fig. 1, and the specific steps are as follows:
step 1: and acquiring a bearing vibration signal f through an acceleration sensor.
Step 2: specifying a sliding window length w
And step 3: the number M of variable step size analysis modules is specified.
And 4, step 4: and decomposing the original signal according to the sliding window length w and the class number M of the variable step length analysis module to obtain a multi-section variable step length analysis module input signal. The formula for configuring the step length according to the number M of the division modules is as follows:
in the formula, λiStep length of the ith module; w is the width of the sliding window.
And 5: performing second-order synchronous compression S transformation algorithm analysis on the input signal of the ith variable step size analysis module;
the process of the second order synchronous compression S transform is represented as:
in the formula, gσ(0) Is a variable Gaussian window function;
for the S-transform of the input signal f,
for the second-order modified instantaneous frequency estimation, δ represents the dirac distribution, γ is a predetermined threshold, η is a frequency factor, ω is a phase factor, and t is time.
Step 6: after the second-order synchronous compression S transformation algorithm analysis is carried out on the ith variable step size analysis module, the weight rho of each ith variable step size analysis module is calculated according to the corresponding renyi entropy valueiThen, let i ═ i + 1;
ρi＝[(1-α)(Rα(yi)-μmin[Rα(yi)])]-1
where α is the order of the entropy of the renai used, typically taken to be 3; mu is a scale parameter, and the value range mu belongs to [0,1 ]]，Rα(yi) For the ith variable step sizeOutput result (time-frequency analysis result) y of analysis moduleiThe entropy value of R é nyi.
And 7: judging whether i is larger than M, if so, entering step 8; if not, entering step 5;
and 8: outputting the plurality of variable step length modules according to the weight rhoiReconstructing to obtain a total signal time-frequency spectrogram;
the reconstruction formula of the total signal time-frequency spectrogram is as follows:
wherein, yw[d]For the output result of the d-th weighted sliding window of the total signal, yiAnd w is the width of the weighted sliding window, and is the output result of the ith variable step size analysis module in the weighted sliding window.
And step 9: and (3) extracting the significant fault characteristic component in the time-frequency spectrogram of the total signal, and comparing the theoretical fault frequency to judge the fault type of the bearing.
The embodiment is further described below with reference to a specific example, namely fault diagnosis of an outer ring of a rolling bearing. The test bearing specifications are shown in table 1 below:
TABLE 1 test bearing Specifications
During the experiment, the motor drives the rotation of test bearing, and wherein the motor frequency of transfer is 10.3Hz, and signal sampling frequency is 10kHz, and the number N of sampling points is 5000, can obtain test bearing rolling element fault characteristic frequency according to bearing specification and motor frequency of transfer and be: fR＝32.7Hz。
Step 1: collecting a vibration signal f of a bearing;
step 2: specifying a sliding window length w;
and step 3: specifying the category number M of the variable step length module;
and 4, step 4: decomposing the original signal according to the sliding window length w and the variable step size module category number M to obtain a multi-section module signal;
and 5: after each module carries out second-order synchronous compression S transformation algorithm analysis, the weight rho is calculated according to the corresponding Rynyi entropy valuei；
Step 6: outputting the plurality of variable step length modules according to the weight rhoiReconstructing to obtain a total signal time-frequency spectrogram;
and 7: and (4) extracting the significant fault characteristic components in the time-frequency spectrogram, and comparing the theoretical fault frequency to judge the bearing fault.
The first step is as follows: an acceleration sensor is used to obtain an original vibration signal f (unit g) of the vibration of the test bearing, and fig. 1 shows a time-domain waveform and a frequency-domain waveform of the original vibration signal f. It can be seen from the figure that due to the existence of noise and other interference components, obvious periodic impact is difficult to observe in the time domain waveform of the vibration signal, and meanwhile, the bearing outer ring fault characteristic frequency in the frequency waveform is almost submerged by the surrounding strong interference frequency, so that the bearing fault is difficult to accurately distinguish.
The second step is that: the sliding window length w is specified, in this example w is 1000.
The third step: specifying the category number M of the variable step size analysis module; in this example, M is 3.
The second-order synchronous compression S transform time-frequency spectrogram based on the optimal weighted sliding window is finally obtained by the calculation method in the steps 4-7 and is shown in FIG. 3. As can be seen from FIG. 3, the frequency characteristic component of the bearing rolling element fault and the bearing rotation frequency component are accurately extracted, and a clear frequency band can be seen. The characteristic frequency of the bearing rolling element fault is the reciprocal of the periodic impact time interval, and in fig. 3, the impact period T is 0.0311s, that is, the frequency f is 32.15 Hz. Characteristic frequency F of theoretical fault of bearing rolling bodyRApproximately equal to 32.7 Hz. Therefore, the rolling element fault of the experimental bearing can be judged, the diagnosis result is consistent with the experimental scheme, and the effectiveness of the embodiment is proved.
To further illustrate the superiority of the method of the present invention, fig. 4 shows a time-frequency spectrum of the conventional short-time fourier transform, and fig. 5 shows a time-frequency spectrum of the S transform. Comparing fig. 3 and 4 and fig. 3 and 5, respectively, it is clear that the resolution of the time-frequency spectrogram obtained by the embodiment is higher. In fig. 4 and 5, the energy concentration of the time-frequency analysis result is poor, and besides the rolling element fault component of the marked position, a large amount of noise energy is scattered nearby, so that the identification of the fault component is difficult. In addition to the fault component of the rolling element, the rest of noises in the figure 3 are effectively suppressed, and the fault type of the bearing can be identified more accurately.
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 (8)
1. A second-order synchronous compression S transform bearing fault diagnosis method for a weighted sliding window is characterized by comprising the following steps:
step 1: collecting a vibration signal f of a bearing;
step 2: specifying a sliding window length w;
and step 3: specifying the category number M of the variable step size analysis module;
and 4, step 4: decomposing the vibration signal f according to the length w of the sliding window and the category number M of the variable step length analysis modules to obtain a multi-section variable step length analysis module input signal;
and 5: performing second-order synchronous compression S transformation algorithm analysis on the input signal of the ith variable step size analysis module;
step 6: after the input signal of the ith variable-step-size analysis module is subjected to second-order synchronous compression S transformation algorithm analysis, the weight rho of the ith variable-step-size analysis module is calculated according to the corresponding renai entropy valueiThen, let i ═ i + 1;
and 7: judging whether i is larger than M, if so, entering step 8; if not, entering step 5;
and 8: a plurality of variable step length analysis modules are output according toThe weight ρiReconstructing to obtain a total signal time-frequency spectrogram;
and step 9: extracting significant fault characteristic components in a time-frequency spectrogram of the total signal, and judging the type of the bearing fault by comparing theoretical fault frequency;
wherein, the expression of the second-order synchronous compression S transformation in the step 5 is:
in the formula, gσ(0) Is a variable Gaussian window function;
in order to perform the S-transform,
for the second-order modified instantaneous frequency estimation, δ represents the dirac distribution, γ is a predetermined threshold, η is a frequency factor, ω is a phase factor, and t is time.
2. The method for diagnosing the fault of the weighted sliding window second-order synchronous compression S transform bearing according to claim 1, wherein the step 1 is specifically as follows: and acquiring a vibration signal f of the bearing through an acceleration sensor.
3. The method for diagnosing the fault of the weighted sliding window second-order synchronous compression S transform bearing according to claim 2, wherein the formula for configuring the step length according to the class number M of the variable step length analysis module in the step 4 is as follows:
in the formula, λiThe step length of the ith variable step length analysis module; w is the sliding window length.
4. The method for diagnosing the fault of the S transform bearing with the weighted sliding window second-order synchronous compression as recited in claim 3, wherein the formula for configuring the weight according to the corresponding entropy of R < nyi > in the step 6 is as follows:
ρi＝[(1-α)(Rα(yi)-μmin[Rα(yi)])]-1
in the formula, alpha is the order of the entropy value of the used Rwenyi; mu is a scale parameter, and the value range mu belongs to [0,1 ]]，Rα(yi) Is the output result y of the ith variable step size analysis moduleiThe entropy value of R é nyi.
5. The method for diagnosing the fault of the S-transform bearing with the weighted sliding window second-order synchronous compression as recited in claim 4, wherein the order alpha of the entropy value of the used Rnyi is 3.
6. The method for diagnosing the fault of the S transform bearing by the weighted sliding window second-order synchronous compression as claimed in claim 5, wherein the reconstruction formula of the time-frequency spectrogram of the total signal in the step 8 is as follows:
wherein, yw[d]As output result of the d-th sliding window of the total signal, yiAnd w is the length of the sliding window, and is the output result of the ith variable step size analysis module in the sliding window.
7. The method for diagnosing the fault of the weighted sliding window second-order synchronous compression S-transform bearing according to claim 6, wherein the length w of the sliding window is 1000.
8. The method for diagnosing the fault of the S transform bearing by the weighted sliding window second-order synchronous compression as claimed in claim 7, wherein the number M of the classes of the variable step size analysis module is 3.
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