## 4 Evaluations of Prediction Results Using Accuracy Metrics
### Evaluations of Performance of Different Training Algorithms
#### 4.1.2 Evaluations of Performance Using Percentage-Dependent Metrics  
The evaluation results of the performance of the six different training algorithms using percentage-dependent metrics are shown in Table 4 and Figure 7. As there were zero values in the actual values of the prediction model, the calculation results of MAPE were infinite. The reason for this was that the actual values were denominators in the calculation algorithm of MAPE (refer to Equation (7)). To eliminate the influences of zero values on the calculation results, the MAPE scores were calculated after the zero values were removed from the actual values.  
Calculation results of the MAPE without zero values are shown in Table 4. The evaluation result of the MAPE for the algorithm was 14.61%, and it was the minimum of the evaluation results of the six training algorithms. The evaluation result of MAPE for the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multirow{2}{*}{**R**} & \multirow{2}{*}{**R\({}^{2}\)**} & **MPAE** & **MAPE** & **SMAPE** & **SMAPE** \\  & & & **(Include Zero** & **(Remove Zero** & **(Include Zero** & **(Remove Zero** \\  & & & **Values)** & **Values)** & **Values)** \\ \hline TRAINBFG & 0.9449 & 0.8760 & Infinite & 21.35 \% & 58.09 \% & 21.65 \% \\ TRAINCGB & 0.9480 & 0.8784 & Infinite & 20.34 \% & 56.94 \% & 20.20 \% \\ TRAINCGP & _0.9314_ & _0.8499_ & Infinite & _25.02_ \% & **62.12** \% & **26.71** \% \\ TRAINSLCM & _0.9690_ & _0.9318_ & Infinite & _14.61_ \% & 52.94 \% & **15.17** \% \\ TRAINRP & 0.9531 & 0.8909 & Infinite & 19.39 \% & 56.35 \% & 19.46 \% \\ TRAINSCG & 0.9458 & 0.8709 & Infinite & 21.17 \% & 57.68 \% & 21.13 \% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Evaluation results of six training algorithms using percentage-dependent metrics.  
Figure 7: Evaluation results of six training algorithms using percentage-dependent metrics. Evaluation results of the “TRAINGLM” are minimum, and evaluation results of the “TRAINCGP” are maximum.  
\"TRAINCGP\" algorithm was 25.02%, and it was the maximum of the evaluation results of the six training algorithms.  
The calculation results of the SMAPE were discussed in two groups, as shown in Table 4. In one group, the SMAPE was calculated with all actual values. In another group, the zero values were removed from the actual values, and then the SMAPE was calculated. The comparison of the results of these two groups indicated that the zero values in the actual values could increase the calculation results of the SMAPE. This caused errors in the evaluations of prediction results.  
As shown in Table 4, the evaluation result of SMAPE without zero values for the \"TRAINGLM\" algorithm was 15.17%, and it was the minimum of the evaluation results of the six training algorithms. The evaluation result of the SMAPE without zero values for the \"TRAINCGP\" algorithm was 26.71%, and it was the maximum of the evaluation results of the six training algorithms.  
We conclude with regard to the evaluation results of the percentage-dependent metrics that the MAPE could be infinite or undefined if there are zero values in the actual values. The zero values can maximize the evaluation results of the SMAPE. Thus, the zero values should be removed from the actual values when using the MAPE or SMAPE. Evaluation results of the percentage-dependent metrics add further proof that \"TRAINGLM\" is the best training algorithm among the six training algorithms for predicting the damage locations of deep piles using the ANN prediction model.