## 5 Experiment
### Case 1: Outer Race Fault with Circumferential Width of 1 mm  
The parameters of MCKD are set as follows: the period of deconvolution \(T\) is equal to 195, the length of filter \(L\) is equal to 90, the order of iteration is equal to 30, and the number of shift \(M\) is equal to 4, according to the method mentioned in Section 3.  
From Figure 21a, it can be seen that the 1 mm outer race fault signal waveforms are buried in background noise. Figure 21b shows the signal is preprocessed by MCKD. It can be seen that MCKD helps clarify the impact of the signal. Figure 21c shows the spectrum of the outer race fault signal, and only rotational frequency and its harmonics can be found in the spectrum. In Figure 21d, the Fourier spectrum of the preprocessed signal is segmented by EWT and the result can be seen in Figure 22.  
Figure 21: The collected signal of the bearing with 1 mm outer race fault and the result of the collected signal processed by the MCKD-EWT method: (**a**) the original signal; (**b**) the de-noised signal processed by MCKD method; (**c**) the spectrum of the original signal; (**d**) the Fourier spectrum segmentation result of the de-noised signal obtained by Improved EWT method.  
Figure 20: The experiment apparatus: (**a**) The Machine Fault Simulator with an eccentric disk; (**b**) the bearing with the inner race fault; (**c**) the bearing with the outer race fault.  
The kurtosis values of these modes are, respectively, 4.773, 9.035, 3.021, and 11.68. Figure 23 displays the squared envelope spectrum and teager energy operator spectrum of signal mode 4. In the squared envelope spectrum and teager energy operator spectrum, it can be seen that both methods successfully extract the outer race fault feature. The frequency 262 Hz and its harmonics (i.e., \(f_{o}\), \(2f_{o}\), and \(3f_{o}\)) are obvious in the strong background noise in Figure 23.  
The FK is presented in Figure 24a. It implies that the center frequency and the bandwidth of the optimal filter equal 4800 Hz and 3200 Hz, respectively. The recommended frequency band of FK is \(\left[\begin{array}{cc}3.2&6.4\\ \end{array}\right]\) kHz. Figure 24b illustrates the squared envelope spectrum of the filtered signal obtained by the recommended filter of FK. It can be seen that only rotational frequency and its harmonics can be found.  
Figure 23: The diagnosis result obtained by IMF4 of the collected signal of the bearing with 1 mm outer race fault: (**a**) the squared envelope spectrum of IMF4; (**b**) the teager energy spectrum of IMF4.  
Figure 22: The IMFs of the collected signal of bearing with 1 mm outer race fault processed by the Improved EWT method: (**a**) IMF1; (**b**) IMF2; (**c**) IMF3; (**d**) IMF4.  
The robust performance of the OWPT model is shown in Figure 25a. It can be seen that the mean fitness of the GA training is 0.1331. The algorithm tends to be stable at the 5 th epoch and the fitness value reaches 0.056 at the 57 th epoch. Figure 25b is the squared envelope spectrum obtained by OWPT. Apparently, no fault feature can be noticed and it implies that the architecture and parameters selected in the OWPT are not effective and feasible for noisy signals.