# A Feature Extraction Method Using Auditory Nerve Response for Collapsing Coal-Gangue Recognition
## 3 Feature Extraction and Selection
### Feature Extraction
#### 3.2.2 Feature Extraction Based on Auditory Spectrum  
In pattern recognition, it is significant to extract effective features which are significant to boost the recognition accuracy. According to the analysis of time-frequency distribution characteristics of the auditory spectrum, statistical features including auditory spectrum energy (ASE), auditory spectrum energy moment (ASEM), auditory spectrum energy entropy (ASEE), skewness, kurtosis, and variance are extracted on the basis of auditory spectrum. These statistical characteristics are as follows:  
Figure 6: The coal signal’s auditory spectrum. Figure 7: The gauge signal’s auditory spectrum. (1) Auditory spectrum energy (ASE) can intuitively reflect the distribution characteristics of energy under the characteristic frequency. The energy of auditory signals at each characteristic frequency \(E_{i}\) is:  
\[E_{i}=\sum_{t=1}^{N}\left|x_{i}(t)\right|^{2} \tag{5}\]  
where \(x_{i}(t)\) represents the auditory signal at the \(i\)-th characteristic frequency, \(N\) represents the time span of such auditory signal. Moreover, ASE is normalized to better highlight the difference in auditory spectrum distribution property as:  
\[ASE=[E_{1},E_{2},\ldots,E_{\text{M}}]/\sum_{i=1}^{\text{M}}E_{i} \tag{6}\]  
(2) Auditory spectrum energy moment (ASEM) demonstrates both energy and distribution characteristics of auditory signals. The energy moment of signals at each characteristic frequency \(ASEM_{i}\) is:  
\[ASEM_{i}=\sum_{t=1}^{N}\frac{t}{\text{fs}}\cdot|x_{i}(t)|^{2} \tag{7}\]  
where fs represents the sampling frequency of vibration signal, which is equal to 12.8 kHz. (3) Auditory spectrum energy entropy (ASEE) reflects the chaotic degree of energy distribution in the characteristic frequency. The energy distribution gradually tends to be uniform with an increase in energy entropy and a decrease in energy entropy will lead to the disordered energy distribution in this characteristic frequency. The energy entropy of signals at each characteristic frequency \(ASEE_{i}\) is:  
\[ASEE_{i}=-\sum_{t=1}^{N}\frac{\left|x_{i}(t)\right|^{2}}{E_{i}}\cdot\ln(\frac {\left|x_{i}(t)\right|^{2}}{E_{i}}) \tag{8}\]  
where \(E_{i}\) represents the energy of \(i\)-th auditory signal. (4) Skewness represents the degree of skewness in auditory signal distribution within each characteristic frequency, which can be calculated as follows:  
\[Skewness_{i}=\frac{E(x_{i}(t)-\mu)^{3}}{\sigma^{3}} \tag{9}\]  
where \(\mu\) and \(\sigma\) represent mean value and standard deviation of the auditory signal. (5) Kurtosis demonstrates the gentleness of the waveform, which can be calculated as follows:  
\[Kurtosis_{i}=\frac{E(x_{i}(t)-\mu)^{4}}{\sigma^{4}} \tag{10}\]  
(6) Variance reflects the degree of auditory signal fluctuation, which can be calculated as follows:  
\[Variance_{i}=\sum_{t=1}^{N}\frac{(x_{i}(t)-\mu)^{2}}{N-1} \tag{11}\]  
According to Functions (5) to (11), the features of the auditory spectrum are extracted. Figure 6 shows the normalized comparison of various features extracted from coal and gangue. Each row represents the distribution of a type of feature within different characteristic frequencies, and each column demonstrates the distribution of a different type of feature at a certain characteristic frequency. The features of the auditory spectrum extracted from the acoustic signals which are processed by the auditory nerve response model are quite distinct, as represented in Figures 8 and 9. It shows that the difference between features extracted from coal and gangue auditory signals is obvious within low frequency and high frequency. Within the range of 200-409.26 Hz, ASE, ASEE, and variance of falling gangue samples are greater than those of falling coal samples. When the characteristic frequency ranges from 2932.1 to 6000 Hz, skewness and kurtosis of falling coal samples are greater than that of falling gangue samples, but ASEM is less than that of falling coal samples.