# Optimization Design of Coupling Beam Metal Damper in Shear Wall Structures
## 4 Optimization of Pore Parameters Based on the Kriging Surrogate Model
### Optimal Design Results and Discussion  
The optimization results of the dampers, based on four different opening shapes, are shown in Table 1. As shown in the table, maximum hysteresis energy exists in the feasible region for SP1, while the other dampers are shown in the feasible region boundary under the conditions of having the same amount of material and the same length and width in the plane. The result shows that thickness has very little influence on the hysteresis energy for these three types of plates, besides SP1. This table also shows that the larger the hysteresis energy with a smaller opening area is, there is a restriction relationship between the parameters of SP1 and the thickness of the steel plate. The hysteresis energy for the four kinds of coupling beam metal dampers, after optimization, is compared in Figure 7,  
Figure 6: Optimization process.  
which shows that SP1 has the maximum hysteresis energy while SP3 has the minimum capacity of hysteresis energy.  
SP1 is selected to analyze the influence of the numbers of the initial samples on the optimization design efficiency. Four different initial samples (25, 50, 75, 100) were chosen to build the initial Kriging surrogate model, as shown in Figure 8. The shapes and types of all four different initial surrogate models were almost the same except for some minor local differences.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Opening Shapes** & **Design Variables** & \(\mathbf{x_{1}}\) **(mm)** & \(\mathbf{x_{2}}\) **(mm)** & \
\begin{tabular}{c} **Hysteresis Energy** \\ **(N*mm)** \\ \end{tabular} &
\begin{tabular}{c} **Hysteresis Energy** \\ **Improvement** \\ \end{tabular} \\ \hline \multirow{2}{*}{SP1} & SOS & 76,72 & 31,64 & 5,940,777 & \multirow{2}{*}{0.064\%} \\  & OMS & 74,74 & 31,78 & 5,944,571 & \\ \hline \multirow{2}{*}{SP2} & SOS & 58,60 & 26,83 & 4,252,911 & \multirow{2}{*}{5.3\%} \\  & OMS & 53,42 & 26,71 & 4,477,092 & \\ \hline \multirow{2}{*}{SP3} & SOS & 84,66 & 27,03 & 2,141,277 & \multirow{2}{*}{13.7\%} \\  & OMS & 74,67 & 27,27 & 2,436,392 & \\ \hline \multirow{2}{*}{SP4} & SOS & 32,04 & 26,9 & 3,950,700 & \multirow{2}{*}{6\%} \\  & OMS & 30,68 & 27,27 & 4,084,100 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Optimization results for sample optimal solution (SOS) and optimization model solution (OMS).  
Figure 8: _Cont._  
Figure 7: Hysteresis energy of four kinds of optimized coupling beam metal dampers.  
In order to illustrate the optimization design efficiency of the Kriging surrogate model, SP1 was optimized with the SCE optimization design. The calculation times for the different initial samples were compared using the same computer (Intel Core(TM)[EMAIL_ADDRESS] GHz, 16 G RAM, Santa Clara, CA, USA), as shown in Figure 9. The combination of the Kriging surrogate model with the SCE optimization algorithm could highly improve the parameter optimization design efficiency. Meanwhile, the initial sample had an influence on the design optimization efficiency. In general, as the initial samples increased, the surrogate model became more accurate and needed fewer iteration steps. However, the iteration steps of the SCE optimization algorithm may increase due to randomness during the period of searching for the optimum, as well as in the selection of a threshold at the end of the iteration. The dimensions of the optimal problem and the complexity of the engineering conditions, as well as the method of selecting initial samples, could influence the iteration numbers, as well as the calculation time. It should be noted that it also took time to calculate the hysteresis energy and it took longer to calculate the energy when the initial sample was increased. Thus, a larger initial sample is not better for the optimal design case.  
Figure 8: Kriging models with different initial samples for SP1: (**a**) 25 samples; (**b**) 50 samples; (**c**) 75 samples; and (**d**) 100 samples.  
Figure 9: Calculation times.