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

September 27, 2022

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 ) two three 2 = 1.(17)where the initial element x1 (t ) denotes the periodic impulse series associated to bearing faults, 0 0.1 0.2 0.3 0.four f o will be the bearing fault characteristic frequency and 0.5 meets f o = 30 Hz. The second component Time (s) x2 (t ) 5represents the harmonic element using 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 0.3 0.four 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 components. Figure three. Time domain waveform of simulation signal x(t) and its corresponding elements. Figure three. Time domain waveform of simulation signal x(t) and its corresponding components. will be the proposed PAVME and 3 normal procedures (VME, VMD and EMD) adopted to course of action the simulation signal x(t). In PAVME, the penalty element and mode three The proposed PAVME and three 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 Seclidemstat supplier components The adopted to processd the simulation signal x(t). In PAVME, the penalty element components and mode 2 2 genuine The mode working with WOA. Within the normal VME,The are mode components 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 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 number K and penalty factor are also automatically selected as 4 and 2270 Hz by utilizing -1 -1 WOA. Figure 4 shows the periodic mode components extracted by various strategies (i.e., PAVME, VME, VMD and EMD). Noticed from Figure four, even though 3 solutions (PAVME, -2 -2 0 0.1 0.2 0.3 0.4 0.five 0 0.1 0.two 0.three 0.four 0.five VME and VMD) can Time get the periodic impulse functions of simulation signal, but their all (s) Time (s) obtained final results are various. The periodic mode components extracted by EMD have a (a) (b) major distinction together with the actual mode component x1 (t) in the simulation signal. Hence, for a greater comparison, fault function extraction Charybdotoxin Autophagy performance on the 4 methods (PAVME, AmplitudeAmplitudedx(t0 0 0 0.1 0.2 Time (s) two 0.three 0.four 0.x 1(t)Entropy 2021, 23,0 5 0 0 0.1 0.two Time (s) 0.3 0.4 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.two 0.three 0.four 0.5 Table 1 lists the calculation final results. Observed from Table 1, kurtosis and correlation coefficient of Time (s) the proposed PAVME system is higher than that of other three strategies (i.e., VME, VMD five and EMD). The RMSE in the PAVME technique is less than that of other three approaches. This 0 suggests that the proposed PAVME has far better feature extraction overall performance. On the other hand, the operating time of VMD is highest, the second is PAVME and also the smallest running time is 0 0.1 0.two 0.3 0.4 0.five Time (s) EMD. This because the PAVME and VMD are optimized by WOA, so their computational efficiency is lowered, but it is acceptable for most occasions. The above comparison shows Figure 3. Time domain waveform of simulation signal x(t) and its corresponding components. t.