# InSAR-CTPIM-Based 3D Deformation Prediction in Coal Mining Areas of the Baisha Reservoir, China
## 6 Discussion and Analysis
### Sensitivity Analysis of Model Parameters  
According to existing studies, the accuracy of deformation prediction depends to some extent on the estimation accuracy of model parameters, and sensitivity analysis refers to the uncertainty analysis of the degree of influence on the final results when the relevant  
Figure 14: Baisha Reservoir Coal Mine area temperature and precipitation data (December 2015 to March 2017).  
influencing factors are changed. In this paper, it was used to study the change in the model parameters corresponding to the change in the size of the error of the deformation prediction results: i.e., for the more-sensitive parameters, even a small change in the parameter estimation value will lead to a large error in the deformation prediction results. Conversely, if the parameter is not sensitive, the parameter estimate will have a limited effect on the deformation prediction results [19]. Therefore, this paper investigated the influence of InSAR-3D-CTPIM model parameters on deformation prediction results using simulated data. Firstly, the simulated values of eight model parameters of a mining area were assumed, as shown in Table 4, and they were used as input data substituted into Equations (4) and (5) to obtain the vertical and horizontal deformation values as the initial values to carry out the experiments. Table 4 lists the range corresponding to the error of each parameter, and the parameter uncertainty of the model is defined according to the equation [\(\frac{UP^{2}-UP^{1}}{UP^{1}}\)100%].  
Figure 15a,b show the errors in the vertical and horizontal deformations with respect to the corresponding maximum value of the simulated deformations due to variations in each model parameter, respectively. Taking the vertical deformation as an example, it can be defined as \(W/w_{0}\), where \(\mathrm{w_{0}}\) is the maximum vertical settlement. As can be seen from Figure 15, for the prediction results of the vertical and horizontal deformation, the subsidence coefficient \(q\), the tangent of the main influence angle \(\mathrm{tan}\beta\) and the propagation angle of mining influence \(\theta_{0}\) are model parameters with higher sensitivity, in addition to the higher sensitivity of the parameter of the horizontal displacement constant \(d\), which has a greater impact on the prediction results of the horizontal displacement. To summarize, the model parameters have a greater effect on the deformation and are mainly focused on \(q\), \(\mathrm{tan}\beta\), \(\theta_{0}\) and \(d\). Therefore, accurate estimation of the subsidence coefficient \(q\), the main influence angle tangent \(\mathrm{tan}\beta\), the mining influence propagation angle \(\theta_{0}\) and the horizontal displacement constant \(d\) is the key to accurately predicting the three-dimensional deformation of the coal mine area.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Parameter Analog Values (UP 1)** & **Tolerance Range (UP 2)** & **Parametric Uncertainty** \\ \hline \(q\) & 0.5 & 0.25–0.75 & \(-\)50–50\% \\ \(d\) & 0.3 & 0.1–0.5 & \(-\)67–67\% \\ \(\mathrm{tan}\beta\) & 1.5 & 1–2 & \(-\)33–33\% \\ \(\theta_{0}\) & 85 & 80–90 & \(-\)5.9–5.9\% \\ \(S_{1}\) & 20 & 0–40 & \(-\)100–100\% \\ \(S_{2}\) & 20 & 0–40 & \(-\)100–100\% \\ \(n\) & 0.35 & 0.2–0.5 & \(-\)42–42\% \\ \(c\) & 11.5 & 6\(\sim\)17 & \(-\)46–46\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Uncertainty of InSAR-3D-CTPIM parameters.  
Figure 15: Results of sensitivity analysis of model parameters.