Application Research of a New Adaptive Noise Reduction Method in Fault Diagnosis
Abstract
:1. Introduction
2. Basic Theory
2.1. CEEMD
- (1)
- Two new signals are formed by adding white noise with a certain standard deviation and equal length and opposite signs to the original signal.
- (2)
- EMD decomposition of S+i and S-i to obtain IMF+(i,j) and IMF-(i,j), then the first-order IMF is
- (3)
- Repeat the above steps to add Gaussian white noise 2N times.
- (4)
- Finally, the decomposition results of multiple component combinations are obtained:
2.2. Multi-Scale Sample Entropy (MSE)
- (1)
- From N/Q-m+1 to vector (i)
- (2)
- Calculate the maximum norm between two vectors dm[(i), (j)].
- (3)
- Define function B
- (4)
- Define function A
- (5)
- Then calculate the probability of matching points
- (6)
- The theoretical value of multiscale sample entropy is defined asWhen the data point N/Q is a finite number, the estimate of sample entropy is given by the following formula:It can be seen from Equation (12) that the value of SampEn is related to the value of m,r. At present, there is no definite value, and the empirical value is m = 2, r ∈ (0.1SD~0.5SD). SD is the standard deviation of the original data. In this paper, when studying the complexity of time series, m = 1, r = 0.25SD is taken.
2.3. Optimized CEEMD Method
- (1)
- Employing the CEEMD method to decompose the original signal X(t) containing noise to obtain a series of IMFs.
- (2)
- The selection of the scale factor Q of the MSE will affect the multiscale sample entropy value of each IMF. According to the decomposition characteristics of the IMF, the noise content of each layer is different. In order to better distinguish each layer of signals, this paper chooses a scale factor of 1–20 and signals with different SNRs for simulation to determine the best scale factor Q.
- (3)
- Substitute m = 2, r = 0.25SD, and the Q that was determined in step (2) into the MSE, calculate the multiscale sample entropy value of 10,000 sets of random noise signals, and obtain the minimum value K of the noise multiscale sample entropy.
- (4)
- Calculate the multi-scale sample entropy value of each IMF component, compare the obtained value with K, remove components greater than K value, and reconstruct the remaining IMFs components.
- (5)
- Perform CEEMD decomposition on the reconstructed signal again, and then calculate the multiscale sample entropy value of each IMF component.
- (6)
- Compare the MSE value of each IMF component with the minimum value K, if there is more than K worth of IMF, repeat (2–6); otherwise, continue.
- (7)
- The signal is FFT transformed to obtain the fault signal.
3. Simulation
3.1. Construct a Simulation Signal
3.2. Optimized CEEMD Method
4. Experimental Verification
5. Conclusions
- (1)
- Determine the best scale factor Q = 10 in the MSE by simulation signals with different SNR, and then employ it to calculate the MSE values of noise signals, simulation signals, and vibration signals, which provide support for optimizing the CEEMD method.
- (2)
- Calculate the MSE value of 10,000 sets of random noise, and use the minimum value as the threshold, remove the IMFs component signal greater than the threshold, achieve the purpose of CEEMD noise reduction, and verify the feasibility of the minimum value as the threshold.
- (3)
- Through CEEMD decomposition of the reconstructed signal, the MSE value of each component signal is calculated. The MSE value is compared with the dynamic threshold value, and if there is an IMFs component signal greater than the threshold, it is removed, the remaining signal is reconstructed, and CEEMD decomposition is performed again. After multiple iterations, when it is finally shown that there is no case where the MSE value of the component signal is greater than the threshold, the iteration is terminated. Finally, the obtained signal is analyzed by the frequency spectrum to determine the fault characteristics.
Author Contributions
Funding
Conflicts of Interest
References
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Rotating Speed n | NJ405 | NJ210 |
---|---|---|
1500 rpm | 147.66 Hz | 231.2 Hz |
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Guo, W.; Li, R.; Kou, Y.; Zhang, J. Application Research of a New Adaptive Noise Reduction Method in Fault Diagnosis. Appl. Sci. 2020, 10, 5078. https://doi.org/10.3390/app10155078
Guo W, Li R, Kou Y, Zhang J. Application Research of a New Adaptive Noise Reduction Method in Fault Diagnosis. Applied Sciences. 2020; 10(15):5078. https://doi.org/10.3390/app10155078
Chicago/Turabian StyleGuo, Wenxiao, Ruiqin Li, Yanfei Kou, and Jianwei Zhang. 2020. "Application Research of a New Adaptive Noise Reduction Method in Fault Diagnosis" Applied Sciences 10, no. 15: 5078. https://doi.org/10.3390/app10155078
APA StyleGuo, W., Li, R., Kou, Y., & Zhang, J. (2020). Application Research of a New Adaptive Noise Reduction Method in Fault Diagnosis. Applied Sciences, 10(15), 5078. https://doi.org/10.3390/app10155078