Mechanical fault diagnosis method based on parameter adaptive VMD

A technology for mechanical faults and diagnosis methods, applied in the testing of mechanical components, genetic models, genetic laws, etc., can solve problems such as information omission, influence of decomposition results, and difficulty in obtaining satisfactory analysis results, and achieve strong signal detection capabilities and accurate analysis. the effect of the result

Active Publication Date: 2018-10-23
SICHUAN UNIV
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AI-Extracted Technical Summary

Problems solved by technology

However, the decomposition parameters of the VMD method (the number of modal components and the frequency bandwidth control parameters of the modal components) have a significant impact on its decomposition results
At present, in the field of mechanical failure, the VMD decomposition parameters are specified in advance in most studies, and it is difficult to obtain satisfactory analysi...
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Method used

The present invention utilizes weighted kurtosis index (KCI) as fitness function, obtains the VMD decomposition parameter with the best matching of signal to be analyzed by optimization algorithm adaptively, utilizes the VMD decomposition parameter of best matching to carry out VMD to original vibration signal Decomposition, and then realize mechanical fault feature extraction and fault diagnosis. Since the weigh...
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Abstract

The invention relates to the field of mechanical vibration signal processing and fault diagnosis, and discloses a mechanical fault diagnosis method based on a parameter adaptive VMD. The signal detection capability of the VMD method in fault diagnosis is improved, and accurate mechanical fault diagnosis is realized. According to the invention, a weighted kurtosis index is used as a fitness function; a VMD decomposition parameter which best matches a signal to be analyzed is acquired through the self-adaption of an optimization algorithm; the optimal VMD decomposition parameter is used to carryout VMD decomposition on an original vibration signal; and mechanical fault feature extraction and fault diagnosis are realized. The method provided by the invention is suitable for mechanical faultdiagnosis.

Application Domain

Technology Topic

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  • Mechanical fault diagnosis method based on parameter adaptive VMD
  • Mechanical fault diagnosis method based on parameter adaptive VMD
  • Mechanical fault diagnosis method based on parameter adaptive VMD

Examples

  • Experimental program(1)

Example Embodiment

[0052] The present invention uses the weighted kurtosis index (KCI) as the fitness function, adaptively obtains the VMD decomposition parameter that best matches the signal to be analyzed through the optimization algorithm, and uses the best matching VMD decomposition parameter to perform VMD decomposition on the original vibration signal, and then Realize mechanical fault feature extraction and fault diagnosis. Since the weighted kurtosis index comprehensively considers the characteristics of the modal components and the correlation between the modal components and the original signal, using it as the optimization objective function can effectively avoid the problem of information omission, thereby improving the signal detection ability of the VMD method in mechanical fault diagnosis. , to achieve accurate diagnosis of mechanical faults.
[0053] The embodiment provides a method for diagnosing mechanical faults, and the workflow is as follows: figure 1 shown, the specific steps are as follows:
[0054] Step 1: Obtain the original vibration signal x(t) of the monitored object through the acceleration sensor.
[0055] Step 2: Set the VMD decomposition parameter range, including setting the number of decomposed modal components k and the modal component frequency bandwidth control parameter α; initialize the optimization algorithm. In this example, the optimization algorithm uses a common genetic algorithm, so the initialization optimization algorithm includes : Initialize the population number p and the maximum number of iterations L.
[0056] In specific applications, other optimization algorithms can also be selected, such as particle swarm optimization (PSO) and gray wolf optimization (WOA).
[0057] Step 3: Within the range of the set parameters, perform VMD decomposition on the vibration signal of the monitoring object to obtain multiple component signals. The decomposition process of VMD can be regarded as the construction and solution of the constrained variational problem described by equation (1):
[0058]
[0059] Among them, x(t) is the input signal; t is the time; Indicates that the formula in parentheses is derived from t; δ(t) is the Dirac function; u k is the component signal decomposed by VMD, k is an integer greater than 1; w k is the center frequency of the component signal; j is the imaginary number symbol; α is the component frequency bandwidth control parameter, which is used to ensure the reconstruction accuracy of the signal under Gaussian noise, λ is the Lagrangian multiplier, and its augmented Lagrangian equation is as follows ( 2) as shown:
[0060]
[0061] It can be seen that the saddle point of equation (2) corresponds to the solution of equation (1), which can be solved by using the multiplier alternate iteration method.
[0062] Further, the specific steps of solving the saddle point of equation (2) (corresponding to the solution of equation (1)) by using the alternate iteration method of multipliers include:
[0063] First, pre-specify the number of decomposed components, and initialize the frequency of the components to obtain the initial component frequency and The corresponding initial center frequency and the initial Lagrange multiplier;
[0064] Then, update the component frequency and the center frequency according to equations (3) and (4), respectively;
[0065]
[0066]
[0067] Among them, n is the current iteration number;
[0068] And after each update to get the corresponding component signal and its center frequency, update the Lagrangian multiplier according to equation (5):
[0069]
[0070] where τ is the update parameter of the Lagrangian multiplier.
[0071] Then, it is judged whether the updated iterative component frequency satisfies the condition of convergence equation (6), if not, continue to update, if so, the iteration ends, and then the component signal decomposed by VMD is obtained.
[0072]
[0073] where ε is the convergence criterion tolerance value.
[0074] Step 4: Calculate the KCI value of each component signal; the KCI value can be calculated according to the following formula:
[0075] KCI=KI·|C|
[0076]
[0077]
[0078] In the formula, KCI is the weighted kurtosis index value, KI is the kurtosis value of the signal sequence y(m), and n>0 is an integer; C is the correlation coefficient between the signal r and the signal s; M is the value of the signal sequence y(m). length, E[ ] represents the mathematical expectation notation.
[0079] Step 5: Determine whether the optimization algorithm satisfies the iteration termination condition, that is, whether the current iteration number l of the genetic algorithm is greater than or equal to the preset maximum iteration number L, if the iteration condition is met, go to step 6, otherwise, let l=l+1, and Return to step 3 and continue to execute the algorithm;
[0080] Step 6: save the decomposition parameters when the component signal KCI obtains the maximum value, that is, the optimal VMD decomposition parameters;
[0081] Step 7: Using the best decomposition parameters obtained in Step 6, perform VMD decomposition on the original vibration signal to obtain a plurality of component signals, and calculate the KCI value of each component signal, and the calculation method of the KCI value can refer to Step 4;
[0082] Step 8: Select the component signal with the largest weighted kurtosis index value in step 7 to be the component signal with the most fault feature information, and use it as a sensitive component;
[0083] Step 9: Perform envelope analysis on sensitive components to obtain envelope spectrum;
[0084] Step 10: Identify the fault type according to the envelope spectrum of the sensitive component.
[0085] The embodiments are further described below with reference to a specific example—gearbox fault diagnosis. The specifications of the test gearbox are shown in Table 1:
[0086] Table 1 Test Gearbox Specifications
[0087] gear ratio
[0088] During the test, the motor drives the gearbox to rotate through a V-belt with a transmission ratio of 2.527:1, and the motor rotates at a constant speed of 5400 rpm. Therefore, the fault characteristic frequency f of the faulty gear (pinion) is tested. s =5400/(60×2.527)=35.62Hz.
[0089] Step 1: Obtain the vibration signal (unit g) of the gearbox through the acceleration sensor, figure 2 are the time-domain waveform and envelope spectrum of the original vibration signal. It can be seen from the figure that due to the influence of background noise and other interference components, no obvious periodic shock can be observed in the time domain of the vibration signal, although the characteristic frequency f of the pinion fault can be observed in the envelope spectrum. s , but the interference is strong, and it is difficult to accurately diagnose the gearbox fault.
[0090] Step 2: Specify the VMD decomposition parameter range and initialize the genetic algorithm. That is, the number k of the decomposed modal components is an integer in the interval [2,7]; the frequency bandwidth control parameter α of the modal component takes a value in the interval [1000, 10000]; the number of populations p=30; the maximum number of iterations L= 10.
[0091] Step 3: Perform VMD decomposition on the original signal within the set parameter range to obtain multiple component signals.
[0092] Step 4: Calculate the KCI value of each component signal after decomposition.
[0093] Step 5: Determine whether the algorithm satisfies the iteration termination condition, that is, whether the current iteration number l of the genetic algorithm is greater than or equal to the preset maximum iteration number L, if the iteration condition is met, go to step 6, otherwise let l=l+1, and Return to step 3 and continue to execute the algorithm;
[0094] The sixth step: save the optimal VMD decomposition parameter combination searched by the genetic algorithm, namely: k=2, α=9000. image 3 Genetic algorithm convergence curve for the optimal decomposition parameter search process for VMD.
[0095] Step 7: Use the optimal parameter combination (k=2, α=9000) obtained in the sixth step to decompose the original signal by VMD, and calculate the KCI value of each component signal, the result is as follows Figure 4 shown.
[0096] Step 8: Select sensitive components. Depend on Figure 4 It can be seen that the original signal is divided into two component signals, and the KCI value of component 1 is larger than 1.51. Therefore, component 1 is the sensitive component with the most fault feature information, and component 1 is regarded as the sensitive component.
[0097] Step 9: Perform envelope analysis on component 1, and its envelope spectrum is as follows Figure 5 shown.
[0098] Step 10: Identify the fault type according to the envelope spectrum of component 1. from Figure 5 The pinion fault characteristic frequency f can be clearly observed in s and its multiplier (2f s , 3f s , 4f s , 5f s ), therefore, it can be judged that the pinion of the gearbox is faulty, and the diagnosis results are consistent with the test plan.
[0099] Meanwhile, in order to further illustrate the superiority of the method of the present invention, Image 6 , Figure 7 The result diagram of analyzing the same vibration signal by the traditional VMD method (pre-specified parameters: k=4, α=2000) is given. Image 6 are the four component signals obtained by the traditional VMD method, Figure 7 is the envelope spectrum of each component signal. Compared Figure 5 , 7 , it can be clearly seen that the present invention has better effects in mechanical vibration signal processing and fault diagnosis, and the analysis results are more accurate.
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