# Spatiotemporal Monitoring and Evaluation Method for Sand-Filling of Immersed Tube Tunnel Foundation
## 3 Evaluation Model of Foundation Cushion Filling Effect Based on Elastic Wave Monitoring
### Elastic Wave Monitoring: BP Neural Network
#### 3.2.2 Sample Selection and Training  
The elastic wave data with a clear sand-filling state were selected to train the network model. The data collected each time were classified into two states, as listed in Table 3, representing whether the sand deposit under the detection point was in contact with the bottom concrete of the immersed tube.  
Specifically, for the middle holes, there are two ends: a free and a constrained end. The free end is the one where the adjacent sand-filling hole is unfilled, and the constrained end is the end where the adjacent sand-filling hole is filled. The diffusion of the sand deposit at the free end can be considered a state where the initial diffusion radius is 0 and the finished state diffusion radius reaches \(\mathrm{R_{d}}\). The free end data were filtered out, and the corresponding sand deposit state was determined according to the recorded information. The selection of the training data also considered other field information, such as the information of the pressure gauge on the sand-filling vessel, the resulting feedback of the diver's exploration, and the uplift of the pipe section shown in Table 1. During the process  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Classification** & **State** \\ \hline State 1 & Not filled \\ State 2 & Filled \\ \hline \hline \end{tabular}
\end{table}
Table 3: States of monitoring points.  
Figure 9: BP neural network structure of the sand-filling state.  
of sand-filling holes W4 and E3, there was a pipe section uplifting. This was caused by the jacking up of the sand plate. The state of the detection point was state 2. Additional measurements were carried out when the pipe section was raised, and the collected data were defined as state 2. In this way, 1000 sets of data with clear states were selected: 500 sets of data for State 1 and 500 sets of data for State 2.  
Before the BP neural network model training, the Z-score normalization method was used to normalize each group of characteristic data to eliminate the influences of dimension and value range difference between indices. The regularization, momentum, and learning rate parameters were set to 0.2, 0.01, and 0.05, respectively. The parameters were tuned accordingly to obtain optimal performance. The number of hidden layers is set to 3, the numbers of nodes of which are 15, 20 and 10. The tan-sigmoid function was selected as the transfer function. Levenberg-Marquardt algorithm was adopted for the fastest convergence speed for medium-scale BP neural networks. The goal error of the training set was set as 0.001. When the error of the training set during the iteration was less than 0.001, the training process stopped. The error function gradually decreased with an increase in the number of iterations, reaching 0.00099588 at 321 iterations, showing that the neural network was convergent.  
After training, the training set data were input into the trained model for simulation, and the difference between the simulation result and its true value was defined as the error. The error change of the model on the training set is shown in Figure 10. The errors of 800 training datasets were all within 0.01, indicating that the error was small.