## 4 Engineering Example
### Simulation Results
#### 4.5.2 Hydraulic Head  
To confirm the precision of the acquired hydraulic conductivity values, they were applied to conduct seepage calculations. The reliability of the IWOA-SVR inversion analysis model was determined by comparing the calculated hydraulic head values with the measured values. Table 5 presents the absolute and relative errors between the calculated results and the monitored values. The relative error is calculated using Equation (19).  
\[e_{r}=\frac{H_{i}-H}{\Delta H}\times 100\% \tag{19}\]  
where \(H_{i}\) and \(H\), respectively, denote the calculated and measured hydraulic heads. \(\Delta H\) represents the difference in water level between the upstream and downstream, which is taken as 109.47 m.  
As shown in Table 5 and Figure 9, the relative errors between the monitored and calculated hydraulic head values for the eight monitoring points are all within 2%, with  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Materials** & **Search Range** & **Hydraulic Conductivity (m/s)** \\ \hline Q = 5–10 Lu rock layer & \(1.5\times 10^{-7}\)–\(1.5\times 10^{-5}\) & \(5.21\times 10^{-6}\) \\ Q = 10–100 Lu rock layer & \(3.0\times 10^{-7}\)–\(3.0\times 10^{-5}\) & \(2.67\times 10^{-5}\) \\ Q \(\geq 100\) Lu rock layer & \(3.0\times 10^{-6}\)–\(3.0\times 10^{-4}\) & \(1.24\times 10^{-4}\) \\ Fracture zone & \(3.0\times 10^{-6}\)–\(1.0\times 10^{-4}\) & \(9.89\times 10^{-5}\) \\ Defective grout curtain & \(1.0\times 10^{-7}\)–\(3.0\times 10^{-6}\) & \(1.79\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Hydraulic conductivity inversion results.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Materials** & **Factors** & **1** & **2** & **3** & **4** & **5** \\ \hline Q = 5–10 Lu rock layer & \(1\) & \(1.50\times 10^{-7}\) & \(3.86\times 10^{-6}\) & \(7.58\times 10^{-6}\) & \(1.13\times 10^{-5}\) & \(1.50\times 10^{-5}\) \\ Q = 10–100 Lu rock layer & \(2\) & \(3.00\times 10^{-7}\) & \(7.73\times 10^{-6}\) & \(1.52\times 10^{-5}\) & \(2.26\times 10^{-5}\) & \(3.00\times 10^{-5}\) \\ Q \(\geq 100\) Lu rock layer & \(3\) & \(3.00\times 10^{-6}\) & \(7.73\times 10^{-5}\) & \(1.52\times 10^{-4}\) & \(2.26\times 10^{-4}\) & \(3.00\times 10^{-4}\) \\ Fracture zone & \(4\) & \(3.00\times 10^{-6}\) & \(2.73\times 10^{-5}\) & \(5.15\times 10^{-5}\) & \(7.58\times 10^{-5}\) & \(1.00\times 10^{-4}\) \\ Defective grout curtain & \(5\) & \(1.00\times 10^{-7}\) & \(8.25\times 10^{-7}\) & \(1.55\times 10^{-6}\) & \(2.28\times 10^{-6}\) & \(3.00\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Values of each factor based on orthogonal design parameters (m/s).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Seepage Monitoring** & **Measured Hydraulic Head** & **Calculated Hydraulic Head** & **Absolute Error** & **Relative Error** \\
**Points** & **(m)** & **(m)** & **(m)** & **(\%)** \\ \hline RK9 & 2353.15 & 2352.50 & 0.65 & 0.59\% \\ RK11 & 2273.81 & 2275.57 & \(-1.76\) & \(-1.61\%\) \\ RK12 & 2266.68 & 2264.82 & 1.86 & 1.70\% \\ RK17 & 2351.46 & 2352.57 & \(-1.11\) & \(-1.01\%\) \\ RK19 & 2349.40 & 2348.17 & 1.23 & 1.13\% \\ RK20 & 2362.09 & 2360.80 & 1.28 & 1.17\% \\ RK23 & 2265.64 & 2264.28 & 1.36 & 1.24\% \\ RK25 & 2263.08 & 2265.21 & \(-2.13\) & \(-1.94\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Errors between measured and calculated hydraulic heads.  
RK25 having the largest relative error of about 1.94%. The results show high accuracy and good stability of the IWOA-SVR inversion analysis model.