## 4 Evaluations of Prediction Results Using Accuracy Metrics  
### Evaluations of Performance of Different Training Algorithms  
Evaluations of Performance Using Scale-Dependent Metrics  
Figure 5 shows the regression plot of backpropagation ANN prediction models with the six network training algorithms as illustrated in Table 2 [45]. The ANN prediction model was trained using the 600 AE signal dataset. In Figure 5, the target values refer to the actual value of damage locations, while the output values refer to the prediction values of damage locations. The black circles represent the individual data points. It can be observed from Figure 5 that the regression plots of the six algorithms were approximately the same, and it was difficult to evaluate the performance of the six algorithms. Thus, it is essential to compare the performance of different algorithms using accuracy metrics. Figure 4: Schematic diagram of backpropagation ANN prediction model for damage locations. In the ANN prediction model, AE signals were input from the input layer and the damage locations output from the output layer. There were 10 neurons in the hidden layer. The evaluation results of the performance of six different training algorithms using scale-dependent metrics are shown in Table 3 and Figure 6. In Figure 6, the R and R\({}^{2}\) are shown with columns to evaluate the goodness of linear fit for the regression model. The MSE, RMSE and MAE are shown with a variation curve to evaluate the errors of prediction. \begin{table}
\begin{tabular}{l l} \hline \hline
**Algorithm** & **Description** \\ \hline TRAINBFG & It is a network training algorithm that updates weight and bias values in terms of the BFGS quasi-Newton method. \\ \hline TRAINCGB & It is a network training algorithm that updates weight and bias values in terms of the conjugate gradient backpropagation with Powell-Beale restarts. \\ \hline TRAINCGP & It is a network training algorithm that updates weight and bias values in terms of conjugate gradient backpropagation with Polak-Ribière updates. \\ \hline TRAINGLM & It is a network training algorithm that updates weight and bias values in terms of Levenberg-Marquardt optimization. \\ \hline TRAINRP & It is a network training algorithm that updates weight and bias values in terms of the resilient backpropagation algorithm (Rprop). \\ \hline TRAINSCG & It is a network training algorithm that updates weight and bias values in terms of the scaled conjugate gradient method. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The illustrations of abbreviation and functions of the six training algorithms. Figure 5: Regression plot of the six training algorithms. (**a**) Regression plot of TRAINBFG; R value is 0.9449. (**b**) Regression plot of TRAINCGB; R value is 0.9480. (**c**) Regression plot of TRAINCGP; R value is 0.9314. (**d**) Regression plot of TRAINGLM; R value is 0.9690. (**e**) Regression plot of TRAINRP; R value is 0.9531. (**f**) Regression plot of TRAINSCG; R value is 0.9458. The R value of the \"TRAINGLM\" algorithm was 0.9690, and it was the maximum of the six training algorithms. The R value of the \"TRAINCGP\" algorithm was 0.9314, and it was the minimum of the six training algorithms. According to the degree of correlations, as shown in Figure 2, all of the six regression models (prediction models) showed very strong correlations between the actual value and predicted value. For the R\({}^{2}\), the value of the \"TRAINGLM\" algorithm was 0.9318, and it was also the maximum of the six training algorithms. The R\({}^{2}\) value of the \"TRAINCGP\" algorithm was 0.8499, and it was also the minimum of the six training algorithms. The R\({}^{2}\) values of the six training algorithms were greater than 0.80, indicating that the regression models explained the predicted values very well. The evaluation results of MSE, RMSE and MAE for the \"TRAINGLM\" algorithm were 315.45 cm\({}^{2}\), 17.76 cm and 13.62 cm, respectively. They were the minima of the evaluation values of the six training algorithms.