## 5 Experimental Results and Discussion
### Experimental Results of Steel Cord conveyor Belt Defects
#### 5.2.3 Feature Extraction and Reduction of the Defects Signals  
The frequency domain and time domain features of the weak magnetic signals of the steel cord conveyor belt defects were extracted. The spectral amplitudes corresponding to the different defects are presented in Figure 14. The peaks are observed at similar frequencies, with slight discrepancies at the amplitude. Therefore, the time domain features are selected for the classification.  
Figure 14: _Cont._  
Figure 13: Normalized weak magnetic signals of the rope fatigue defect before and after noise reduction.  
First, twelve common time domain fault features were extracted, which were the peak-to-peak values, root mean square amplitudes, mean amplitudes, variance, root amplitudes, waveform width, kurtosis, wave index, peak index, pulse index, margin index and the kurtosis index. Then, the features were reduced by a neighborhood rough set algorithm. The four time domain features, after reduction were root mean square amplitudes, variance, kurtosis and waveform width. The root mean square amplitudes mainly reflected the signals energy, the variance mainly reflected the degree of the signals dispersion and the kurtosis mainly reflected signal sharpness and impact characteristics. As can be observed in Figures 11-13, the normalized signal features of the splice, broken rope defect and rope fatigue defect were significantly different in waveform width, signals energy, degree of signals dispersion, signal sharpness and impact, the waveform width and kurtosis of splice signals were usually larger than the broken rope defect and the rope fatigue defect. Therefore, according to the features reduction and waveform analysis in Figures 11-13, the four domain features, finally determined, were root mean square amplitude, variance, kurtosis and waveform width.  
For a given the sample signals \(x_{i}\) and the number \(N\), the four time domain features calculation expressions are presented as follows:  
(1) Root Mean Square Amplitude (RMSA)  
\[X_{rms}=\sqrt{\frac{1}{N}{\sum\limits_{i=1}^{N}{x_{i}}^{2}}} \tag{11}\]  
(2) Variance  
\[\sigma_{x}=\frac{1}{N}{\sum\limits_{i=1}^{N}{(x_{i}-\overline{x})^{2}}} \tag{12}\]  
where \(\overline{x}\) is the average value of \(x_{i}\).  
(3) Kurtosis  
\[\beta=\frac{1}{N}{\sum\limits_{i=1}^{N}{x_{i}}^{4}} \tag{13}\]  
(4) Waveform width  
Given the position number \(N_{r5}\) for the first raising edge at 5% of the maximum value of \(|x_{i}|\) and the position number \(N_{f5}\) for the last falling edge at 5% of the maximum value of \(|x_{i}|\). The collection interval \(d_{ci}\) was 0.0005 mm. The waveform width \(P_{wide}\) was given by Equation (14).  
Figure 14: Amplitude spectrum for the weak magnetic signals of the steel cord conveyor belt defects.  
\[P_{wide}=(N_{f5}-N_{r5}\ )\times d_{ci} \tag{14}\]  
The distributions of the four time domain features of the partial sample signals are presented in Figure 15. As can be seen in Figure 15, the four time domain features distribution results of the splices, broken rope defects and the rope fatigue defects were significantly different, which was consistent with the features reduction and waveform analyses (Figures 11-13). As can be observed in Figure 15, the splice could be identified well by the waveform width and the rope fatigue could be identified well by the other three features. However, according to the splice structure, rope fatigue and broken rope defects presented in Figures 11a, 12a and 13a, the length of the splice, fracture width of broken rope defect and the fatigue length of the rope fatigue defect could lead to changes of the waveform width. It may cause overlapping waveform width distribution for three types of weak magnetic signals in actual operating conditions. Therefore, in order to improve the classification accuracy of the steel cord conveyor belt in actual working conditions, four time domain features were used together for classification.