## 5 Results and Discussion
### Core Neutron Dynamic Module Parameter Sensitivity Analysis  
#### 5.1.1 Parameter Sensitivity Analysis without Temperature Feedback  
The typical values of \(l_{0}\), \(\lambda_{0}\) and \(\beta_{0}\) were 2.1 \(\times\) 10\({}^{-5}\), 0.0767 and 4.4 \(\times\) 10\({}^{-3}\), respectively. The initial output of \(N_{\rm r}\) was 0.9. This gave changes of \(\pm 10\%\) to \(l_{0}\), \(\lambda_{0}\) and \(\beta_{0}\), then the trajectory curve of \(N_{\rm r}\) with a step change of \(\rho\) from 0 to 0.001 at 1 s was recorded. Figure 13a shows the trajectory sensitivity analysis.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Parameter** & **Value** & **Identified** & **Relative Error** & **Parameter** & **Value** & **Identified** & **Relative Error** \\ \hline \(l\) & 2.1 \(\times\) 10\({}^{-5}\) s & 1.99 \(\times\) 10\({}^{-5}\) s & 5.238\% & \(\tau_{2}\) & 56.3514 s & 56.1513 s & 0.355\% \\ \(\beta\) & 4.4 \(\times\) 10\({}^{-3}\) & 0.004417 & 0.386\% & \(\tau_{3}\) & 12.1755 s & 12.1525 s & 0.189\% \\ \(\lambda\) & 0.0767 s\({}^{-1}\) & 0.0784 s\({}^{-1}\) & 2.216\% & \(\tau_{4}\) & 3.9368 s & 3.9496 s & 0.325\% \\ \(a_{1}\) & 144.1409 & 144.14007 & 5.76 \(\times\) 10\({}^{-4}\)\% & \(\tau_{5}\) & 0.7275 s & 0.7157 s & 1.622\% \\ \(a_{2}\) & 0.2043 & 0.20359 & 3.047\% & \(c_{1}\) & 0.4529 & 0.4282 & 5.454\% \\ \(a_{3}\) & 0.1760 & 0.17601 & \(5.68\times\) 10\({}^{-3}\)\% & \(c_{2}\) & 0.8007 & 0.8082 & 0.937\% \\ \(a_{4}\) & 0.0093 & 0.009357 & 0.613\% & \(c_{3}/c_{4}\) & 0.8094 & 0.8754 & \(-8.151\%\) \\ \(a_{5}\) & 0.1945 & 0.19457 & 3.60 \(\times\) 10\({}^{-2}\)\% & \(c_{5}\) & 185,800 & 181,267,446 & 2.439\% \\ \(\tau_{1}\) & 19.4949 s & 19.3830 s & 0.574\% & \(c_{6}\) & 1,717,989.6 & 1,698,615,318 & 1.128\% \\ \hline \end{tabular}
\end{table}
Table 2: Model parameter values.  
Figure 12: Sensitivity of parameter change to the output variables under two different cases. (**a**) Sensitivity analysis of \(\Omega/\mu_{c}\) under input change of \(N_{\rm r}\); and (**b**) sensitivity analysis of \(\Omega/\mu_{c}\) under input change of \(T_{\theta 1}\).  
For a time period longer than 0.04 s, the trajectory sensitivity of \(\beta\) could be expressed by the trajectory sensitivity of \(\lambda\) as follows:  
\[\beta=-0.9451\lambda-0.02044 \tag{20}\]  
Figure 13b shows the trajectory sensitivity curves and the fitting relationship. There was a strong linear correlation between the trajectory sensitivity curves of \(\beta\) and \(\lambda\) for a time slightly longer than 0 s. \(\beta\) had a larger trajectory sensitivity during the entire time, meaning that \(\lambda\) was more difficult identify: Furthermore, \(l\), \(\lambda\) and \(\beta\) were changed by \(\pm 10\%\), \(\pm 20\%\) and \(\pm 30\%\) at the rated working condition. Figure 13b to Figure 13e show the trajectory sensitivity curves.  
From Figure 13a-e, \(l\) and \(\lambda\) had greater impact on the initial time with a sudden change of \(\rho\), but \(l\) did not affect the dynamic simulation of \(N_{\mathrm{r}}\) when the time was slightly over 0 s. \(\lambda\) and \(\beta\) had a continuous opposite influence on the dynamic simulation of \(N_{\mathrm{r}}\). The trajectory sensitivity had little relation to the initial working conditions due to a lack of a non-linear link in the core neutron dynamic module. In addition, the impact of \(l\) and \(\lambda\) on \(N_{\mathrm{r}}\) did not change with the parameter disturbance depths, but \(\beta\) had a larger effect on the simulation result with a bigger parameter disturbance depth.  
Figure 13: Sensitivity analysis of parameter change without temperature feedback. (**a**) Trajectory sensitivity with parameter disturbances of \(\pm 10\%\); (**b**) fitting relationship between the trajectory sensitivity of \(\beta\) and \(\lambda\); (**c**) trajectory sensitivity with different disturbance depths for \(l\); (**d**) trajectory sensitivity with different disturbance depths for \(\lambda\); and (**e**) trajectory sensitivity with different disturbance depths for \(\beta\).