T ,1 f 0 ) (s) x (t ) Time3 sin( 2f t )

T ,1 f 0 ) (s) x (t ) Time3 sin( 2f t ) 1.5 sin(2f
T ,1 f 0 ) (s) x (t ) Time3 sin( 2f t ) 1.5 sin(2f t ) 2 3 two = 1.(17)where the very first aspect x1 (t ) denotes the periodic impulse series related to bearing faults, 0 0.1 0.2 0.three 0.four f o could be the bearing fault characteristic frequency and 0.five meets f o = 30 Hz. The second portion Time (s) x2 (t ) 5represents the harmonic element with all the frequency of f2 = 20 Hz and f3 = 30 Hz. The third component 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.two 0.3 0.4 0.5 as 8192 Hz and 4096 points, respectively. Figure three 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 elements. Figure 3. Time domain waveform of simulation signal x(t) and its corresponding components. are the proposed PAVME and 3 normal approaches (VME, VMD and EMD) adopted to process the simulation signal x(t). In PAVME, the penalty element and mode three The proposed PAVME and 3 standard approaches (VME, VMD and EMD) are f are automatically selected3as 1680 and 2025extracted mode WOA. In Hz by utilizing center-frequency The extracted mode elements The adopted to processd the simulation signal x(t). In PAVME, the penalty aspect elements and mode 2 2 true The mode making use of WOA. Inside the normal VME,The are mode elements selected (i.e., penalty factorHz by elements centercenter-frequency f the mixture C2 Ceramide Metabolic Enzyme/Protease parameters as 1680 and 2025real and mode automaticallyn(t)1 the 1standard VME, the mixture 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 quantity K and penalty aspect are also automatically chosen as 4 and 2270 Hz by using -1 -1 WOA. Figure 4 shows the periodic mode components extracted by Tenidap custom synthesis diverse solutions (i.e., PAVME, VME, VMD and EMD). Seen from Figure 4, even though 3 approaches (PAVME, -2 -2 0 0.1 0.2 0.3 0.four 0.5 0 0.1 0.2 0.3 0.4 0.five VME and VMD) can Time obtain the periodic impulse features of simulation signal, but their all (s) Time (s) obtained results are different. The periodic mode elements extracted by EMD possess a (a) (b) significant difference with all the actual mode element x1 (t) of the simulation signal. Hence, for any far better comparison, fault function extraction efficiency from the 4 solutions (PAVME, AmplitudeAmplitudedx(t0 0 0 0.1 0.2 Time (s) two 0.three 0.4 0.x 1(t)Entropy 2021, 23,0 5 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 running time). 0 0.1 0.2 0.three 0.4 0.5 Table 1 lists the calculation results. Noticed from Table 1, kurtosis and correlation coefficient of Time (s) the proposed PAVME process is greater than that of other 3 methods (i.e., VME, VMD five and EMD). The RMSE from the PAVME process is much less than that of other three techniques. This 0 implies that the proposed PAVME has far better function extraction functionality. Nevertheless, the running time of VMD is highest, the second is PAVME and also the smallest operating time is 0 0.1 0.2 0.three 0.4 0.five Time (s) EMD. This because the PAVME and VMD are optimized by WOA, so their computational efficiency is reduced, however it is acceptable for many occasions. The above comparison shows Figure three. Time domain waveform of simulation signal x(t) and its corresponding components. t.