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 ) 1.5 sin(2f t ) two 3 2 = 1.(17)where the very first component x1 (t ) denotes the periodic impulse series connected to bearing faults, 0 0.1 0.2 0.three 0.four f o would be the bearing fault characteristic frequency and 0.five meets f o = 30 Hz. The second part Time (s) x2 (t ) 5represents the harmonic component with all the frequency of f2 = 20 Hz and f3 = 30 Hz. The third portion n(t ) represents the Gaussian white noise generated by MATLAB function 0 randn(1, N ) . The sampling frequency and sampling length of simulation BI-0115 supplier signal x(t) are set 0 0.1 0.two 0.3 0.4 0.five as 8192 Hz and 4096 points, respectively. Figure three shows time domain waveform of simTime (s) ulation signal x(t) and its corresponding components. Figure 3. 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 elements. would be the proposed PAVME and three regular techniques (VME, VMD and EMD) adopted to method the simulation signal x(t). In PAVME, the penalty factor and mode 3 The proposed PAVME and three common techniques (VME, VMD and EMD) are f are automatically selected3as 1680 and 2025extracted mode WOA. In Hz by using center-frequency The extracted mode elements The adopted to processd the simulation signal x(t). In PAVME, the penalty aspect components and mode 2 two genuine The mode applying WOA. Inside the normal VME,The are mode components chosen (i.e., penalty factorHz by components centercenter-frequency f the combination parameters as 1680 and 2025real and mode automaticallyn(t)1 the 1standard VME, the mixture parameters (i.e., penalty element and mode centerfrequency f d ) are artificially set as 2000 and 2500 Hz. In VMD, the decomposition mode 0 0 number K and penalty aspect are also automatically Folate Receptor alpha (FR-alpha) Proteins Gene ID selected as 4 and 2270 Hz by utilizing -1 -1 WOA. Figure four shows the periodic mode components extracted by diverse methods (i.e., PAVME, VME, VMD and EMD). Noticed from Figure 4, though 3 strategies (PAVME, -2 -2 0 0.1 0.2 0.3 0.four 0.five 0 0.1 0.two 0.three 0.four 0.five VME and VMD) can Time receive the periodic impulse features of simulation signal, but their all (s) Time (s) obtained outcomes are distinct. The periodic mode elements extracted by EMD possess a (a) (b) big distinction with the true mode component x1 (t) with the simulation signal. Therefore, for a far better comparison, fault feature extraction efficiency on the 4 approaches (PAVME, AmplitudeAmplitudedx(t0 0 0 0.1 0.two Time (s) 2 0.3 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 operating time). 0 0.1 0.two 0.3 0.four 0.5 Table 1 lists the calculation benefits. Observed from Table 1, kurtosis and correlation coefficient of Time (s) the proposed PAVME strategy is larger than that of other 3 approaches (i.e., VME, VMD five and EMD). The RMSE of the PAVME system is significantly less than that of other three techniques. This 0 signifies that the proposed PAVME has better feature extraction efficiency. Nevertheless, the operating time of VMD is highest, the second is PAVME and also the smallest running time is 0 0.1 0.two 0.three 0.four 0.five Time (s) EMD. This since the PAVME and VMD are optimized by WOA, so their computational efficiency is lowered, but it is acceptable for many occasions. The above comparison shows Figure 3. Time domain waveform of simulation signal x(t) and its corresponding components. t.