## 3 Parameter Identification Method and Process
### Particle Swarm Optimization Algorithm Based on Random Perturbation
#### 4.2.4 Steam Generator Module Parameter Identification  
The input variables are \(T_{\text{HL}}\) and \(Q_{\text{sg}}\). Besides some other intermediate variables, \(T_{\text{CL}}\) and \(P_{\text{s}}\) are the main output variables. The steam generator parameters are mainly related to design parameters with different order magnitudes large to a 7 order of magnitude. Supposing that \(Q_{\text{sg}}\) was constant at 1, it gave \(T_{\text{HL}}\) a step change of 10 \({}^{\circ}\)C from the rated value of 321.1 \({}^{\circ}\)C at 1 s. Both the simulation and  
Figure 10: Reactor power control module simulation comparison.  
Figure 9: Core fuel and coolant temperature module simulation comparison. (**a**) Change of \(T_{\text{F}}\); (**b**) change of \(T_{\text{62}}\); and (**c**) change of \(T_{\text{av}}\).  
tested deviation values of \(T_{\text{CL}}\) and \(P_{\text{s}}\) were used in the fitness function. Figure 8 shows the input \(T_{\text{HL}}\) change and output variable simulation comparison.  
The simulation result could basically fit with the tested curve (see Figure 11). The variable curves of another condition with \(Q_{\text{sg}}\) that were given a step change from 1 to 0.9 were more complex. The identification result using single variable deviation (i.e., the deviation of \(T_{\text{CL}}\) or \(P_{\text{s}}\)) as the fitness function could not match multiple output variable curves. Thus, the identified parameters might only fit several output variables or parts of the tested curves, if the output variables and tested curves chosen for identification are unable to completely reflect the variable transition process.  
Moreover, the parameters of the turbine bypass control system module and the time constants of the cold line, hot line and primary loop average temperature module were easy to be identified, which were omitted in details due to space limitations. Besides the designed parameters, Table 1 lists the main sub-module parameters. Table 2 lists partial parameters with their actual and identified values. The index of relative error was applied to judge the identified results that deviated from their true values. Through the caculation of relative error given in Table 2, the identification precision is basically higher than 95%.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \(l\) & Average neutron lifetime \\  & \(\beta\) & Total share of delayed neutron group group \\ Core neutron dynamic module & \(\lambda\) & Time delay of equivalent delayed neutron group \\  & \(\alpha_{\text{F}}\) & Reactivity coefficient of fuel temperature \\  & \(\alpha_{\text{C}}\) & Reactivity coefficient of coolant temperature \\ \hline Reactor control system module & \(K_{\text{C}}\) & Position coefficient of control rods \\  & \(\tau_{1}\), \(\tau_{2}\), \(\tau_{3}\), \(\tau_{4}\) and \(\tau_{5}\) & Time constants of compensator and filter \\ \hline Cold line, hot line and primary loop & \(T_{\text{HL}}\) and \(T_{\text{CL}}\) & Hot and cold line time constants \\  & \(\tau_{\text{C}}\) & Temperature sensor time constant \\ \hline Core fuel and coolant temperature module & \(a_{1}=P_{0}\times F_{\text{F}}/\mu_{\text{F}},a_{2}=P_{0}\times(1-F_{\text{F}})/ \mu_{\text{F}},a_{3}=\Omega/\mu_{\text{F}},a_{4}=\Omega/\mu_{\text{F}},a_{5}=M/ \mu_{\text{F}}\) \\ \hline \multirow{3}{*}{Steam generator module} & \(K_{P_{\text{LS}}}\) & Steam pressure time constant \\ \cline{2-2}  & \(K_{P_{\text{LS}},T_{\text{L}}}\) & Conversion coefficient between pressure and \\ \cline{1-1} \cline{2-2}  & \(c_{1}=M/\mu_{\text{F}},c_{2}=\Omega_{\text{F}}/\mu_{\text{F}},c_{3}=\Omega_{ \text{F}}/\mu_{\text{F}},c_{4}=\Omega_{\text{S}}/\mu_{\text{F}},c_{5}=\Omega_{ \text{S}},c_{6}=(h_{\text{s}}-h_{\text{br}})\times G_{\text{sn}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Sub-module parameters.  
Figure 11: Steam generator module simulation comparison. (**a**) Input change of \(T_{\text{HL}}\); (**b**) output change of \(T_{\text{CL}}\); and (**c**) output change of \(P_{\text{s}}\).