# Weak Multiple Fault Detection Based on Weighted
## 5 Experimental Verification
### Application to a Real Signal Mixture  
While Section 4 describes the effectiveness of the proposed WOGS algorithm with simulated signal, this section deals with the proposed algorithm used to extract the multiple faults of rolling bearings with a test bench (Figure 18a). The test bench is driven by an AC motor via a shaft and composed of a loading system, four rolling bearings, a sensor monitoring system, a signal modulate circuit, and a software monitoring system. Figure 18b shows the loading diagram of four bearings in the test bench. The sensor monitoring system contains three accelerometers, and four thermocouple sensors are installed on the housing of the rolling bearings to collect bearing vibration and temperature signals. Figure 18c depicts the sensor arrangement. The employed accelerometer, i.e., PCB Piezotronics model 608A11, is used to measure the radial vibration signal, with a nominal sensitivity of 100 mV/g and a measurement range of \(\pm\)50 g. NI 9234 is employed for data acquisition, which can simultaneously collect four channels of acceleration signal, and each channel has its own current source to supply the acceleration sensor. The motor speed is 1050 r/min, the signal sampling frequency is 10,240 Hz, and the sampling time is 1 s. Four rolling bearings are mounted on the shaft (Figure 18b). The faulty bearing is equipped on the far left, and the other three positions are mounted with healthy bearings. The type of the experimental bearing is a single row deep groove ball bearing 6205. One rolling bearing is damaged with an electrical discharge from a wire to simulate a faulty bearing (Figure 19). The inner fault size is 1.6 mm (width) \(\times\) 4 mm (depth), and the outer fault size is 1.6 mm (width) \(\times\) 2 mm (depth). Table 3 shows the structural parameters of the rolling bearing 6205. According to the calculations of the fault feature frequencies of rolling bearings, the theoretical results of rolling bearing's characteristic frequencies are shown in Table 4.  
Figure 17: Results of OGS: (**a**) Time-domain waveform. (**b**) Envelope spectrum. Figure 18: Rolling bearing test rig: (**a**) Bearing failure test bench. (**b**) The diagram of loading system. (**c**) Sensor layout. Figure 20a shows the time domain waveform of the collected vibration signal, which is dominated by impulse features. However, determining the time interval of the periodic impulse features is difficult. Figure 20b shows the frequency spectrum corresponding to Figure 20a. The weak multiple fault characteristics of rolling bearings are difficult to extract directly from the frequency spectrum due to the strong background noise. Figure 20c shows the envelope spectrum. Extracting the fault feature frequencies of inner and outer rings is difficult because the multiple fault information may be mixed with noise. The proposed WOGS algorithm is used to process the experimental signal, with the group size \(3\times 7\). Figure 15 shows the denoised results, and Figure 21a depicts that impulse features are apparent. Moreover, Figure 21b shows the frequency spectrum of denoised signals. It reduces wideband noise, such as white noise. From the envelope spectrum shown in Figure 21c, the frequency components at 63, 134, and 201 Hz have the largest magnitudes, and these frequencies are approximately equal to the outer fault feature frequency and its harmonic frequencies. The frequency components at 95 and 190 Hz are close to the inner fault feature frequency. The result is consistent with the setup of the experiment when outer and inner race faults are extracted. For comparison, the same experimental signal is analyzed with TQWT, OGS, and soft threshold denoising to further demonstrate the superiority of the proposed algorithm, respectively.