CN110569478A - Improved variational modal decomposition method for encoder signal analysis - Google Patents
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Abstract
The present application provides an improved variational modal decomposition method for encoder signal analysis, comprising: collecting encoder signal x of output shaft of gear box for output shaft encodereprocessing to obtain a preprocessed signal x; initializing an input coefficient of a decomposition method; selecting a proper balance coefficient by utilizing the correlation kurtosis value of the mode signal u in the decomposition process; selecting an optimal balance coefficient by circularly using a variational modal decomposition method; after the optimal balance coefficient is obtained, carrying out sparse processing on the correspondingly decomposed signals; and analyzing the processed encoder signals, and giving a gearbox fault diagnosis result according to the interval distance of fault impact. The invention avoids the selection dependence of the traditional variational modal decomposition method on two parameters, namely a decomposition mode and a balance coefficient; the method has high robustness, does not need to set parameters manually in the circulation process, and is suitable for online health monitoring.
Description
Technical Field
The invention relates to the technical field of fault diagnosis of mechanical equipment, in particular to an improved variational modal decomposition method for signal analysis of an encoder.
Background
The gearbox system is a key transmission component in rotating machinery. The failure of the machine is the main reason for the machine to stop or even cause accidents. Therefore, how to accurately diagnose the gearbox fault has become one of the most popular topics in the field of mechanical fault diagnosis. Generally, a test method for gearbox fault diagnosis is vibration analysis, because state degradation of mechanical equipment often manifests as changes or anomalies in vibration information. However, as mechanical devices become more integrated, vibration-based analysis approaches encounter difficulties in gearbox fault diagnosis. Therefore, finding a new testing means to replace the traditional vibration analysis is also one of the approaches to solve the problem of gearbox fault diagnosis.
Encoders have been widely installed in electromechanical systems for device operation speed and position control. The encoder is usually mounted close to the gearbox system, so that the encoder signal contains abundant mechanical dynamic information. Compared to vibration analysis, analysis based on encoder signals has the following advantages in gearbox fault diagnosis:
1) The fault sensitivity is high: the gear box meshing can generate obvious rigidity change when passing through a fault area, and encoder signals can directly reflect torsional vibration behaviors in a system and are more sensitive to rigidity change caused by faults.
2) The transmission path is short: the fault information needs to pass through a complicated and lengthy transmission path to be tested by the external vibration sensor. The encoder is arranged in the equipment and is closer to key components such as a gear box and the like. Therefore, the transmission path through which the failure information in the encoder information passes is shorter, so the influence by the energy attenuation or the like by the transmission path is smaller.
3) the application range is wide: the running environment of mechanical equipment such as digit control machine tool, excavator, rolling equipment, high-speed railway, aircraft and spacecraft is abominable, and key information can receive a great deal of restriction because of wiring and safety problem through external sensor test equipment. In contrast, the test approach based on built-in coding information does not need to take into account the above limitations.
4) The test cost is low: vibration, current and acoustic emission testing approaches all rely on high precision external sensors and other ancillary equipment. However, since the encoder is widely installed in various mechanical devices as an important speed control sensor, the operation of acquiring the encoder information is simpler and the test cost is lower.
however, the encoder signal is inevitably subjected to noise, which makes it difficult to extract the fault feature efficiently. In 2011, Zhou et al proposed the use of Empirical Mode Decomposition (EMD) for denoising and separating fault information. However, this method is only suitable for the case where the noise content in the signal is small, and is difficult to work under the interference of complex background noise. Therefore, a method for accurately extracting gearbox fault information in an encoder signal under the interference of complex background noise is needed at present.
Disclosure of Invention
In order to accurately extract the gear box fault information in the encoder signal under the interference of complex background noise, the invention provides an improved variational modal decomposition method for encoder signal analysis, and the technical scheme adopted by the invention is as follows: the method comprises the following steps:
The method comprises the following steps: method for collecting encoder signal x of output shaft of gear box by using output shaft encodereSecondly, converting the acquired encoder incremental digital sequence into an instantaneous angular acceleration signal by using a secondary difference, and then removing other noise and interference components irrelevant to the fault information of the gearbox in the signal by using the existing time domain synchronous averaging technology to obtain a preprocessed signal recorded as x;
Step two: initializing input coefficients of the decomposition method, including decomposition mode K, initial center frequency omega0coefficient of equilibrium alpha0And a step size Δ α;
step three: selecting a proper balance coefficient by utilizing a correlation kurtosis value of a mode signal u in the decomposition process in the formula (1);
The expression (1) is an expression used when K is 1, where u is a mode signal obtained after decomposition, i.e., a decomposition mode signal,TsFor a gearbox fault period, P is the data length of signal u; CK (CK)MSetting M to be 1 for the correlation kurtosis value of the mode signal u in the decomposition process, wherein M is the shift number of the correlation kurtosis, so that the correlation kurtosis value of the signal is replaced by CK; wherein m and p are integers;
step four: selecting an optimal balance coefficient through circulation; first, a cyclic coefficient n is set to 1, and a balance coefficient α is usedn-1decomposing the signal x by using the existing variational modal decomposition method to obtain a decomposition mode signal un-1Calculating to obtain the related kurtosis value CKn-1(ii) a Then circularly executing the fifth step to the seventh step;
Step five: increasing a balance coefficient by taking the delta alpha as a step length, and performing variational modal decomposition on the signal x by using the new balance coefficient to obtain decomposition mode signals under different conditions; and (3) circularly selecting the specific operation of the optimal balance coefficient: when the step size is delta alpha, the balance coefficient is reducedand obtaining a decomposition pattern signalCalculating the correlation kurtosis value of the formula (1)Wherein the superscript "-" represents various parameters or signals obtained when the balance coefficient is reduced, and the subscript "n" or "n-1" represents various parameters or signals under different cycle times; when the step size is delta alpha, the balance coefficient is increasedObtaining decomposition mode signalsCalculating the correlation kurtosis value of the formula (1)Wherein the superscript "+" indicates increasing the balance factorObtaining various parameters or signals;
Step six: if it is notThen select alphan-1the optimal balance coefficient is obtained, and the circulation is directly carried out to the step eight;
Step seven: if it is notThen updateOtherwise updateThen according to the updated alphanDecomposing the signal x by using the existing variational modal decomposition method to obtain a mode signal unMeanwhile, updating the cyclic coefficient n to n +1, and returning to the step five;
Step eight: further sparsely processing the decomposed signals;
Step nine: and analyzing the processed encoder signals, and giving a gearbox fault diagnosis result according to the interval distance of fault impact.
preferably, in the second step, the input coefficients for initializing the decomposition method are specifically that the decomposition mode is set to K ═ 1, and the initial center frequency is ω00, balance coefficient α0＝5000，Δα＝500。
Preferably, in the step eight, the further thinning processing is performed on the decomposed signal, specifically, the thinning processing is performed by using equation (2):
un＝un(1-exp(-(un)2/2(w·rms(un))2))(2)
In the formula, w is a weight coefficient. rms (u)n) Is a signal unRoot mean square value of unIs a mode signal.
preferably, a planetary gearbox test stand is used, comprising a drive motor, an input shaft encoder, a planetary gearbox, an output shaft encoder and a brake.
Compared with the prior art, the invention has the following beneficial effects:
a) The invention avoids the selection dependence of the traditional variational modal decomposition method on two parameters, namely a decomposition mode and a balance coefficient.
b) the method can effectively extract the fault characteristics of the gearbox in the encoder signal under the complex interference, and has high robustness.
c) The invention does not need to set parameters manually and is suitable for online health monitoring.
d) the invention provides a new idea for diagnosing the fault of the gearbox by utilizing the encoder signal.
Drawings
FIG. 1 is a schematic diagram of an improved variational modal decomposition method for encoder signal analysis, exemplified by a planetary gearbox test stand, in accordance with the present invention;
FIG. 2 is a flow chart of an improved variational modal decomposition method for encoder signal analysis in accordance with the present invention;
FIG. 3 shows an encoder signal x collected in an embodiment of the present inventioneA schematic diagram of (a);
FIG. 4 is a diagram illustrating a signal x after quadratic difference and time-domain synchronous averaging according to an embodiment of the present invention;
FIG. 5 is a graphical representation of the results obtained using the proposed method in an embodiment of the present invention; and
FIG. 6 is a graphical representation of results obtained using a prior art EMD decomposition on a planetary gearbox test stand.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
Taking a planetary gearbox test bed as an example, as shown in fig. 1, the test bed is composed of a driving motor 1, an input shaft encoder 2, a planetary gearbox 3, an output shaft encoder 4, a brake 5 and the like, as shown in fig. 1. The input shaft encoder 2 is arranged at the input shaft end of the planetary gear box 3, and the output shaft encoder 4 is arranged at the output shaft end of the planetary gear box 3. The prefabricated planet gear flank peeling fault is placed in the planetary gearbox 3 for testing experiments.
As shown in fig. 2, the improved variational modal decomposition method for encoder signal analysis includes the following steps:
the method comprises the following steps: firstly, an output shaft encoder 4 is utilized to acquire an encoder signal x of an output shaft of a gear boxeFig. 3 appears to be continuous, as shown in fig. 3, but it is known to those skilled in the art that this is due to the very high acquisition frequency, the actual acquired encoder signal xeas a discrete signal. Secondly, the acquired encoder incremental digital sequence is converted into an instantaneous angular acceleration signal using a prior art quadratic difference. Then, using the existing time domain synchronous averaging technique, removing other noise and interference components in the signal which are not related to the fault information of the gearbox to obtain a preprocessed signal x, and fig. 4 shows the encoder signal xeA schematic diagram of the signal x after the second difference and the time domain synchronous averaging;
Step two: initializing input coefficients of a decomposition method, setting a decomposition mode to be K-1, and setting an initial center frequency to be omega00, balance coefficient α0＝5000，Δα＝500。
Step three: and (3) setting the formula (1) to select a proper balance coefficient according to the correlation kurtosis value of the mode signal u in the decomposition process.
The expression (1) is an expression used when K is 1, where u is a mode signal obtained after decomposition, i.e., a decomposition mode signal, Tsfor a gearbox failure period, P is the data length of signal u. CK (CK)MFor the correlation kurtosis value of the mode signal u in the decomposition process, M is the shift number of the correlation kurtosis, and M is generally set to 1, so the correlation kurtosis value of the signal is replaced by CK. Wherein m and p are integers.
Step four: the optimal balance coefficient is selected by cycling. First, a cyclic coefficient n is set to 1, and a balance coefficient α is usedn-1Decomposing the signal x by using the existing variational modal decomposition method to obtain a decomposition mode signal un-1Calculating to obtain the related kurtosis value CKn-1In this case, since n is 1, αn-1Is alpha0，un-1Is u0，CKn-1Is CK0。
Step five: and secondly, increasing the balance coefficient by taking the delta alpha as a step length, and performing variation mode decomposition on the signal x by using the new balance coefficient to obtain decomposition mode signals under different conditions. And (3) circularly selecting the specific operation of the optimal balance coefficient: when the step size is delta alpha, the balance coefficient is reducedAnd obtaining a decomposition pattern signalcalculating the correlation kurtosis value of the formula (1)Wherein the superscript "-" represents various parameters or signals obtained when the balance coefficient is reduced, and the subscript "n" or "n-1" represents various parameters or signals under different cycle times; when the step size is delta alpha, the balance coefficient is increasedObtaining decomposition mode signalsCalculating the correlation kurtosis value of the formula (1)Where the superscript "+" indicates the various types of parameters or signals obtained when the balance factor is increased.
Step six: if it is notThen select alphan-1And (5) directly jumping out to circulate to the step eight.
Step seven: if it is notUpdatingOtherwise updatethen according to the updated alphanDecomposing the signal x by using the existing variational modal decomposition method to obtain a mode signal unAnd simultaneously updating the cyclic coefficient n to n +1, returning to the step five, and continuing to circulate until the optimal balance coefficient is found.
step eight: the decomposed signal is further thinned out using equation (2).
un＝un(1-exp(-(un)2/2(w·rms(un))2)) (2)
In the formula, w is a weight coefficient. rms (u)n) Is a signal unRoot mean square value of unIs a mode signal.
Step nine: and analyzing the processed encoder signals by using the prior art, and giving a gearbox fault diagnosis result according to the separation distance of fault impact.
As shown in fig. 5, the result of applying the method proposed by the present invention to the signal x, i.e. the mode signal after sparse processing obtained according to the optimal balance coefficient, is shown, and the impact component of 31 teeth apart can be clearly seen by those skilled in the art according to the signal processing result shown in fig. 5. Since only the planet wheels in the planetary gearbox 3 have 31 teeth, i.e. it turns out that the stiffness fluctuations of the planetary gearbox are reflected in the encoder signal every 31 teeth interval, thereby indicating that a fault has occurred on the planet wheels.
to further illustrate the superiority of this embodiment, fig. 6 shows a schematic diagram of the results obtained by using the existing EMD for the planetary gearbox test stand, and it can be seen from fig. 6 that although many mode signals (8 mode signals are shown in fig. 6) are obtained by using the existing EMD for the signal x, each mode diagram is a position on the abscissa and an amplitude on the ordinate, it can be seen from fig. 6 that it is difficult to find information related to planetary gear faults from any one mode signal. Thereby proving the obvious advantages of the invention compared with the traditional method. The method does not depend on manual selection of the decomposition coefficient, has high intelligent degree and is more applicable to engineering practice.
The foregoing is a preferred embodiment of the present application, and it should be noted that those skilled in the art can make several improvements and modifications without departing from the technical principle, and these improvements and modifications should also be considered as the protection scope of the present application.
Claims (4)
1. an improved variational modal decomposition method for encoder signal analysis, characterized by: the method comprises the following steps:
the method comprises the following steps: method for collecting encoder signal x of output shaft of gear box by using output shaft encodereSecondly, converting the acquired encoder incremental digital sequence into an instantaneous angular acceleration signal by using a secondary difference, and then removing other noise and interference components irrelevant to the fault information of the gearbox in the signal by using the existing time domain synchronous averaging technology to obtain a preprocessed signal recorded as x;
Step two: initializing an input coefficient of a decomposition method;
Step three: selecting a proper balance coefficient by utilizing a correlation kurtosis value of a mode signal u in the decomposition process in the formula (1);
wherein u is a decomposed mode signal, i.e. a decomposed mode signal, TsFor a gearbox fault period, P is the data length of signal u; CK (CK)Mthe correlation kurtosis value of the mode signal u in the decomposition process, and M is the shift frequency of the correlation kurtosis; m and p are positive integers;
Step four: selecting an optimal balance coefficient through circulation; first, a cyclic coefficient n is set to 1, and a balance coefficient α is usedn-1The existing variational modal decomposition method is utilized to carry out credit agreementDecomposing the number x to obtain a decomposition pattern signal un-1Calculating to obtain the related kurtosis value CKn-1；
Step five: secondly, increasing a balance coefficient by taking the delta alpha as a step length, and performing variational modal decomposition on the signal x by using the new balance coefficient to obtain decomposition mode signals under different conditions; and (3) circularly selecting the specific operation of the optimal balance coefficient: when the step size is delta alpha, the balance coefficient is reducedand obtaining a decomposition pattern signalCalculating the correlation kurtosis value of the formula (1)Wherein the superscript "-" represents various parameters or signals obtained when the balance coefficient is reduced, and the subscript "n" or "n-1" represents various parameters or signals under different cycle times; when the step size is delta alpha, the balance coefficient is increasedObtaining decomposition mode signalsCalculating the correlation kurtosis value of the formula (1)Wherein the superscript "+" indicates various parameters or signals obtained when the balance coefficient is increased;
step six: if it is notThen select alphan-1the optimal balance coefficient is obtained, and the circulation is directly carried out to the step eight;
Step seven: if it is notThen updateOtherwise updateThen according to the updated alphandecomposing the signal x by using the existing variational modal decomposition method to obtain a mode signal unMeanwhile, updating the cyclic coefficient n to n +1, and returning to the step five;
Step eight: carrying out sparse processing on the decomposed signals; and
Step nine: and analyzing the processed encoder signals, and giving a gearbox fault diagnosis result according to the interval distance of fault impact.
2. the improved variational modal decomposition method for encoder signal analysis according to claim 1, characterized in that: in the second step, the input coefficients of the initialized decomposition method are specifically that the decomposition mode is set to K ═ 1, and the initial center frequency is ω00, balance coefficient α0＝5000，Δα＝500。
3. the improved variational modal decomposition method for encoder signal analysis according to claim 1, characterized in that: in the step eight, performing further sparse processing on the decomposed signal specifically performs sparse processing by using an equation (2):
un＝un(1-exp(-(un)2/2(w·rms(un))2)) (2)
Wherein w is a weight coefficient, rms (u)n) Is a signal unRoot mean square value of unIs a mode signal.
4. The improved variational modal decomposition method for encoder signal analysis according to claim 1, characterized in that: the improved variational modal decomposition method for the encoder signal analysis uses a planetary gearbox test bed, and comprises a driving motor, an input shaft encoder, a planetary gearbox, an output shaft encoder and a brake.
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