T ,1 f 0 ) (s) x (t ) Time3 sin( 2f t ) 1.five sin(2f
T ,1 f 0 ) (s) x (t ) Time3 sin( 2f t ) 1.five sin(2f t ) 2 three 2 = 1.(17)where the initial portion x1 (t ) denotes the periodic impulse series related to bearing faults, 0 0.1 0.two 0.three 0.four f o will be the bearing fault characteristic frequency and 0.five meets f o = 30 Hz. The second aspect Time (s) x2 (t ) 5represents the harmonic element with all the frequency of f2 = 20 Hz and f3 = 30 Hz. The third part n(t ) represents the Gaussian white noise generated by MATLAB function 0 randn(1, N ) . The sampling frequency and sampling length of simulation signal x(t) are set 0 0.1 0.2 0.three 0.4 0.5 as 8192 Hz and 4096 points, respectively. Figure 3 shows time domain waveform of simTime (s) ulation signal x(t) and its corresponding elements. Figure three. Time domain waveform of simulation signal x(t) and its corresponding components. Figure three. Time domain waveform of simulation signal x(t) and its corresponding elements. will be the proposed PAVME and three typical strategies (VME, VMD and EMD) adopted to process the simulation signal x(t). In PAVME, the penalty aspect and mode 3 The proposed PAVME and three normal solutions (VME, VMD and EMD) are f are automatically selected3as 1680 and 2025extracted mode WOA. In Hz by utilizing center-frequency The extracted mode components The adopted to processd the simulation signal x(t). In PAVME, the penalty aspect elements and mode 2 two real The mode employing WOA. In the regular VME,The are mode elements chosen (i.e., penalty factorHz by elements centercenter-frequency f the combination parameters as 1680 and 2025real and mode automaticallyn(t)1 the 1standard VME, the combination parameters (i.e., penalty factor and mode centerfrequency f d ) are artificially set as 2000 and 2500 Hz. In VMD, the decomposition mode 0 0 number K and penalty factor are also automatically chosen as four and 2270 Hz by utilizing -1 -1 WOA. Figure 4 shows the periodic mode elements extracted by unique methods (i.e., PAVME, VME, VMD and EMD). Seen from Figure 4, while three methods (PAVME, -2 -2 0 0.1 0.two 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 VME and VMD) can Time get the periodic impulse attributes of simulation signal, but their all (s) Time (s) obtained results are distinctive. The periodic mode elements extracted by EMD have a (a) (b) massive IL-24 Proteins Molecular Weight distinction with the true mode component x1 (t) of your simulation signal. Therefore, to get a much better comparison, fault Inositol nicotinate Protocol feature extraction performance in the four procedures (PAVME, AmplitudeAmplitudedx(t0 0 0 0.1 0.2 Time (s) two 0.three 0.four 0.x 1(t)Entropy 2021, 23,0 five 0 0 0.1 0.two Time (s) 0.3 0.four 0.9 ofVME, VMD and EMD) is quantitatively compared by calculating 4 evaluation indexes (i.e., kurtosis, correlation coefficient, root-mean-square error (RMSE) and operating time). 0 0.1 0.2 0.three 0.four 0.five Table 1 lists the calculation results. Noticed from Table 1, kurtosis and correlation coefficient of Time (s) the proposed PAVME process is larger than that of other 3 techniques (i.e., VME, VMD 5 and EMD). The RMSE in the PAVME approach is much less than that of other three methods. This 0 indicates that the proposed PAVME has superior feature extraction performance. Nonetheless, the running time of VMD is highest, the second is PAVME as well as the smallest running time is 0 0.1 0.two 0.3 0.four 0.five Time (s) EMD. This because the PAVME and VMD are optimized by WOA, so their computational efficiency is reduced, nevertheless it is acceptable for most occasions. The above comparison shows Figure 3. Time domain waveform of simulation signal x(t) and its corresponding elements. t.