## 3 Results and Discussions
### Pattern Recognition  
In order to reduce misjudge and improve evaluable accuracy, a pattern recognition method with multi parameters was introduced in this paper. The network study process repeated a two phase cycle, propagation and weight update. When an input vector was presented to the network, it was propagated forward through the network, layer by layer, until it reached the output layer. The output of the network was then compared to the desired output, using a loss function. The resulting error value was calculated for each of the neurons in the output layer. The error values were then propagated from the output back through the network, until each neuron had an associated error value that reflects its contribution to the original output.  
The BP neural network in this paper was to identify the expulsion defect based on wavelet decomposition from a series of the electrode force signals. The peak-to-peak amplitude and the kurtosis index of the target signal in Section 3.3 were the input parameters ([p,k]) without data (2, 12, and 19), and the classification information expulsion and other conditions ([1,-1]) were the output parameters in this paper. The data 2, 12, and 19 were used as test ones. The structure of the BP neural network in this paper is presented in Figure 10.  
The parameter settings were as follows: net.trainParam.epochs (the highest training times) was set at 500, net.trainParam.lr (the learning rate) was set at 0.01, net.trainParam.goal (the training goal) was set at 0.0001. Figure 11 shows the network training results. The network achieved the goal after six iterations.  
Figure 12 shows the collation map of actual and predicted results. From the figure below, the trained neural network had good predicting results in distinguishing the expulsion and other conditions.  
Figure 11: The network training results.  
Figure 10: The structure of the BP neural network.  
Figure 13 shows the predicted results of the test data using the network trained before. The first data was the expulsion one, while the other two were the ones without expulsion. From the figure below, the first predicted value was around \(1\) which stood for the expulsion defect, while the other two values were lower than \(-1\) which predicted other conditions. Therefore, the expulsion defect identification based on wavelet decomposition and BP neural network with the peak-to-peak amplitude and kurtosis index was effective.  
The peak-to-peak amplitude and kurtosis index of the original signal (without data (2, 12 and 19)) without wavelet decomposition were calculated directly as the input vectors of the BP neural network to present the feature extraction effect of the wavelet analysis. The distributions of these two indexes are shown in Figure 14. From the figures below, the expulsion feature was not so obvious. The peak-to-peak amplitudes presented small differences between the expulsion signals and other signals. The kurtosis indexes of these data stayed in a similar level.  
Figure 12: The collation map of actual and predicted results.  
Figure 13: Test results.  
Then, [k,p] was used as the input parameter, and the classification information expulsion and other conditions ([1,\(-\)1]) were the output parameter as mentioned before. The parameter settings were the same as before. The BP neural net training results and the test data predict results are shown in Figures 15 and 16, respectively. The net training results were not as satisfied, compared with the method before, though the parameter settings were the same. The iteration was 12 times. Misjudgment still existed in the test data. The detailed comparison results are shown in Table 2. Comparing the two methods, it was obvious that the wavelet decomposition is effective in the expulsion feature extraction and improved the identification accuracy.