## 4 Case Study
### Results and Discussion
#### 4.2.2 Prediction Results of the Optimum BPNN  
In the proposed case study, the data collected from five settlement observation points in the same column, i.e., 350-1, 350-2, 350-3, 350-4, and 350-5, were used as testing samples, and the data collected from the other 326 settlement observation points were used for training the optimum BPNN. To comprehensively understand the prediction accuracy of the optimum BPNN, two error measurements, i.e., absolute error \(E_{a}\) and absolute error percentage \(E_{p}\), are introduced as follows [13]:  
\[E_{a}=|o_{i}-t_{i}| \tag{15}\]  
\[E_{p}=\frac{|o_{i}-t_{i}|}{|t_{i}|}\times 100\% \tag{16}\]  
where \(o_{i}\) is the output of the BPNN, i.e., the predicted ground settlement at a settlement observation point; \(t_{i}\) is the target output of the BPNN, i.e., the actual ground settlement  
Figure 6: Exploration of the optimum number of neurons in the hidden layer.  
at a settlement observation point. Accordingly, the average absolute error \(\overline{E_{a}}\) and average absolute error percentage \(\overline{E_{p}}\) at a settlement observation point can be calculated as follows:  
\[\overline{E_{a}}=\frac{1}{M}\sum_{i=1}^{M}\lvert o_{i}-t_{i}\rvert \tag{17}\]  
\[\overline{E_{p}}=\frac{1}{M}\sum_{i=1}^{M}\frac{\lvert o_{i}-t_{i}\rvert}{ \lvert t_{i}\rvert}\times 100\% \tag{18}\]  
where \(M\) is the number of prediction data.  
The comparisons of the prediction results and the actual ground settlements at these five settlement observation points from day 4, i.e., 11 June 2021, to day 74, i.e., 20 August 2021, are shown in Figure 7. Particularly, the monitoring data collected from day 1 to day 3 were used to predict ground settlements on day 4. The results show that the variation tendency of the predicted ground settlements is generally consistent with the variation tendency of the actual ground settlements. Specifically, the absolute error \(E_{a}\) of more than 95% of the predicted ground settlements are less than 2 mm, as shown in Figure 8, and the average absolute error \(\overline{E_{a}}\) of the prediction results is 0.57 mm, as shown in Table 2. It can be concluded that the prediction results are fairly close to the actual settlement monitoring results, and thus it is safe to say that the proposed BPNN is able to accurately predict ground settlements on a daily basis. On the other hand, the maximum absolute error of prediction results is 7.6 mm at settlement observation point 350\(-\)1 on day 14, when the actual ground settlement at this location sharply increased by 7.43 mm. Such a sharp increase in ground settlement mainly resulted from over-excavation and the slow erection of steel supports. Accordingly, unnormal variation of ground settlements due to unnormal construction conditions may lead to significant prediction errors of the proposed BPNN model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Error Measurement** & **350-1** & **350-2** & **350-3** & **350-4** & **350-5** & **Total** \\ \hline \(\overline{E_{a}}\) (mm) & 0.81 & 0.70 & 0.62 & 0.35 & 0.39 & 0.57 \\ \(\overline{E_{p}}\) (\%) & 6.33 & 3.37 & 3.41 & 4.44 & 17.55 & 7.02 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average prediction errors of the optimum BPNN.  
Figure 7: _Cont._  
Moreover, the absolute error percentage \(E_{p}\) of more than 80% of the predicted ground settlements are less than 10%, as shown in Figure 8, and the average absolute error percentage \(\overline{E_{p}}\) of the prediction results is 7.02%, as shown in Table 2. The value of \(\overline{E_{p}}\) at settlement observation point 350-5 is significantly larger than the values of \(\overline{E_{p}}\) at the other four settlement observation points, probably because settlement observation point 350-5 is far away from the outer edge of the foundation pit, and other factors, such as heavy truckloads, may significantly affect ground settlement at this location, while these factors were not considered in the proposed study.