# Nonlinear Blind Source Separation and Fault Feature Extraction Method for Mining Machine Diagnosis
## 3 Results  
Experimental tests were carried out to evaluate the proposed method. The vibration datasets were measured from a gearbox in a mining machine with artificial failures on the gears. Four acceleration sensors were installed at two different locations of the transmission system (see Figure 3). Sensors were installed on each location to measure the vibration signals in horizontal and vertical directions. The measured datasets were obtained in the case of two faulty gears in the gear transmission system, and the fault frequency of gear 1 was \(f_{h}\) = 19.5 Hz and the second gear fault frequency was \(f_{l}\) = 13.4 Hz. Figure 4 shows the time waveforms of the vibration signals measured by the four sensors with a spalling failure in gear 1 and a broken gear tooth  
As can be seen in Figures 4-6, the original vibration signals of the mining machine were contaminated by strong background noise, which had a great influence on the amplitude impact of the time waveforms and the frequency distributions. After wavelet de-noising, the influence of noise was effectively suppressed in both the time domain and frequency domain. Comparing Figure 4 with Figure 5, it is noticed that the noise energy in the original signals has been significantly reduced, and the time interval between each two peaks in the de-noised signals is more observable than that in the original ones. The time interval could provide useful periodical information about the mechanical impact of the mining machine for discovering undergoing faults. In Figure 6, after wavelet de-noising the peak locating at 19.9 Hz (\(\approx\) 19.5 Hz) can be clearly observed as the spalling fault frequency. Useless frequency components have been filtered by wavelet processing. However, the broken tooth fault frequency 13.4 Hz is not observed. It is worth noting that the spectral peaks and sidebands of the fault frequencies are strong indicators for the existence of the faults [1]; however, as can be seen from Figure 6, due to different vibration sources (such as vibrations of gears, bearings and shafts) the characteristics of the broken tooth fault frequency is lost. Therefore, it is necessary to separate the spalling fault and the broken tooth fault sources from the measured vibration signals to accurately extract the fault characteristics of the two faults. Figure 5: Time waveforms of measured vibration signals after wavelet de-noising. Figure 6: Spectra of measured vibration signal of Sensor 3. It can be seen from Figure 7 that the separated source signals include the spalling and wear fault frequencies \(f_{h}\) and \(f_{l}\), respectively, and their harmonics. Significant energy lines appear at these characteristic frequencies. The separation results show that different fault vibration sources of the two gears can be extracted from the mixed observation signals. Similar observations can be seen from Figures 8 and 9. However, when the gear fault degree increases, in addition to energy lines at \(f_{h}\) and \(f_{l}\), the separated fault sources present complex coupling frequency components at low frequencies. The coupling frequency (\(f_{h}+f_{l}\)) is clearly observed in Figure 9a. Moreover, the amplitude of the energy lines with broken gear tooth condition is much larger than those of other gear fault types. The reason is probably due to functionally damage of the gear pair. By comparing Figures 7-9 with Figure 6, it can be seen that the proposed nonlinear ICA model can recover the gear fault vibration sources from the multi-vibration measurements. As a result, the compound gear faults can be effectively identified. In order to diagnose the gear faults, the WPD analysis was first applied to the separated sources to calculate 32 fault features for each source. Because db10 mother wavelet was effective for vibration analysis [25], it was used in the WPD processing. Then a RBFNN classifier was used to identify the fault types. The RBFNN classifier consisted of 32 notes in input layer, 35 notes in hidden layer and three notes in output layer.