Application of variational mode decomposition in vibration analysis of machine components

Monitoring and diagnosis of machinery in maintenance are often undertaken using vibration analysis. The machine vibration signal is invariably complex and diverse, and thus useful information and features are difficult to extract. Variational mode decomposition (VMD) is a recent signal processing method that able to extract some of important features from machine vibration signal. The performance of the VMD method depends on the selection of its input parameters, especially the mode number and balancing parameter (also known as quadratic penalty term). However, the current VMD method is still using a manual effort to extract the input parameters where it subjects to interpretation of experienced experts. Hence, machine diagnosis becomes time consuming and prone to error. The aim of this research was to propose an automated parameter selection method for selecting the VMD input parameters. The proposed method consisted of two-stage selections where the first stage selection was used to select the initial mode number and the second stage selection was used to select the optimized mode number and balancing parameter. A new machine diagnosis approach was developed, named as VMD Differential Evolution Algorithm (VMDEA)-Extreme Learning Machine (ELM). Vibration signal datasets were then reconstructed using VMDEA and the multi-domain features consisted of time-domain, frequency-domain and multi-scale fuzzy entropy were extracted. It was demonstrated that the VMDEA method was able to reduce the computational time about 14% to 53% as compared to VMD-Genetic Algorithm (GA), VMD-Particle Swarm Optimization (PSO) and VMD-Differential Evolution (DE) approaches for bearing, shaft and gear. It also exhibited a better convergence with about two to nine less iterations as compared to VMD-GA, VMD-PSO and VMD-DE for bearing, shaft and gear. The VMDEA-ELM was able to illustrate higher classification accuracy about 11% to 20% than Empirical Mode Decomposition (EMD)-ELM, Ensemble EMD (EEMD)-ELM and Complimentary EEMD (CEEMD)-ELM for bearing shaft and gear. The bearing datasets from Case Western Reserve University were tested with VMDEA-ELM model and compared with Support Vector Machine (SVM)-Dempster-Shafer (DS), EEMD Optimal Mode Multi-scale Fuzzy Entropy Fault Diagnosis (EOMSMFD), Wavelet Packet Transform (WPT)-Local Characteristic-scale Decomposition (LCD)- ELM, and Arctangent S-shaped PSO least square support vector machine (ATSWPLM) models in term of its classification accuracy. The VMDEA-ELM model demonstrates better diagnosis accuracy with small differences between 2% to 4% as compared to EOMSMFD and WPT-LCD-ELM but less diagnosis accuracy in the range of 4% to 5% as compared to SVM-DS and ATSWPLM. The diagnosis approach VMDEA-ELM was also able to provide faster classification performance about 6 40 times faster than Back Propagation Neural Network (BPNN) and Support Vector Machine (SVM). This study provides an improved solution in determining an optimized VMD parameters by using VMDEA. It also demonstrates a more accurate and effective diagnostic approach for machine maintenance using VMDEA-ELM

Application of Sample Entropy Based LMD-TFPF De-Noising Algorithm for the Gear Transmission System

This paper investigates an improved noise reduction method and its application on gearbox vibration signal de-noising. A hybrid de-noising algorithm based on local mean decomposition (LMD), sample entropy (SE), and time-frequency peak filtering (TFPF) is proposed. TFPF is a classical filter method in the time-frequency domain. However, there is a contradiction in TFPF, i.e., a good preservation for signal amplitude, but poor random noise reduction results might be obtained by selecting a short window length, whereas a serious attenuation for signal amplitude, but effective random noise reduction might be obtained by selecting a long window length. In order to make a good tradeoff between valid signal amplitude preservation and random noise reduction, LMD and SE are adopted to improve TFPF. Firstly, the original signal is decomposed into PFs by LMD, and the SE value of each product function (PF) is calculated in order to classify the numerous PFs into the useful component, mixed component, and the noise component; then short-window TFPF is employed for the useful component, long-window TFPF is employed for the mixed component, and the noise component is removed; finally, the final signal is obtained after reconstruction. The gearbox vibration signals are employed to verify the proposed algorithm, and the comparison results show that the proposed SE-LMD-TFPF has the best de-noising results compared to traditional wavelet and TFPF method