# A State Recognition Approach for Complex Equipment Based on a Fuzzy Probabilistic Neural Network
## 4 Simulation Example
### Constructing the Multi-Level State Space and Training PNN  
The model of a shearer was shown in Figure 4, and three units can be separated according to the structural characteristics of the shearer. The cutting and haulage unit can be divided into the left and right sub-unit separately. The states of each sub-unit and transformer are described by the current and temperature, and each state variable consists of four features. The multi-level state space for the shearer was constructed as shown in Figure 5.  
After preliminary analysis on the current and temperature of the shearer, the average, variance, peak factor, and frequency center are selected as the features. According to the combination of vast statistic data, expert knowledge and experience, the state set of the average value of the left cutting current was {_RS_, _NM_, _RB_, _B_}, the state set of stand deviation was {_NM_, _RB_}, the state set of peak factor was {_RS_, _NM_, _RB_}, and the state set of the frequency center was {_NM_, _AN_}. Then, the fuzzy rule base on each feature of the left cutting current could be shown as below:  
Figure 4: Structure of the shearer. Figure 5: A multi-level state space for the shearer. In the same way, the fuzzy rule base of other parameters, sub-units, units, and the whole shearer were established successively. Then, the feature matrix of the left cutting temperature and other parameters could be summarized as shown:  
\[X_{LC48\times 4}=\left[\begin{array}{c}LC\_A\_RS\ \ LC\_S\_NM\ \ LC\_P\_RS\ \ LC\_F\_NM\\ LC\_A\_RS\ \ LC\_S\_NM\ \ LC\_P\_RS\ \ LC\_F\_AN\\ LC\_A\_RS\ \ LC\_S\_NM\ \ LC\_P\_RS  
\(\mu_{\rm{G}}\) was the membership function of the average value and could be shown as below:  
\[\mu_{cj}=\left\{ \begin{array}{ll}5j/128&(0<j\leq 51.2)\\ 5j/64-2&(51.2<j\leq 76.8)\\ 4&(j>76.8)\end{array} \right. \tag{11}\]  
\(\mu_{cb}\) was the membership function of the standard deviation and could be shown as below:  
\[\mu_{cb}=\left\{ \begin{array}{ll}b/3&(0<b\leq 3)\\ b/7+4/7&(3<b\leq 10)\\ 2&(b>10)\end{array} \right. \tag{12}\]  
\(\mu_{cf}\) was the membership function of the peak factor and could be shown as below:  
\[\mu_{cf}=\left\{ \begin{array}{ll}50f/51&(0<f\leq 1.02)\\ 50f/24-9/8&(1.02<f\leq 1.5)\\ 2f/3+1&(1.5<f\leq 3)\\ 3&(f>3)\end{array} \right. \tag{13}\]  
Moreover, \(\mu_{pf}\) was the membership function of the frequency center and could be shown as below:  
\[\mu_{pf}=\left\{ \begin{array}{ll}1&(0.9\leq p\leq 1.0)\\ 2&(p<0.9\;or\;p>1.0)\end{array} \right. \tag{14}\]  
Then, a quantification matrix of left cutting current was obtained as below:  
\[X_{LCQ8\times 4}=\left[ \begin{array}{llll}1.0559&0.1067&1.0208&1.0000\\ 1.0711&0.1067&1.0417&1.0000\\ 1.0598&0.1533&1.0417&1.0000\\ 1.0816&0.1233&1.0000&1.0000\\ 1.1027&0.1600&1.0833&1.0000\\ 1.1129&0.3300&1.1667&1.0000\\ 1.0738&0.2100&1.0625&1.0000\\ 1.0668&0.2133&1.1458&1.0000\end{array} \right] \tag{15}\]  
Working condition of the shearer was recognized by the trained PNN and the multi-level fuzzy rule base. The state of each left cutting current was obtained by inputting a four-dimensional row vector into the trained PNN. Row vector \(x_{q1\times 4}\) = (1.0599 0.1067 1.0208 1.0000) was inputted into PNN to gain the left cutting current of group 1. In the same way, parameter states of other groups were obtained by the trained PNN as shown below: