## 4 Structural Design Optimization
### Example Verification  
The four variables which were optimized simultaneously were \(\alpha\), \(\beta\), \(l_{1}\) and \(l_{3}\). Additionally, the optimization results are shown in Table 2. At the same time, each of the four variables were individually optimized according to the results. The errors of the spine load of all five optimizations between the test and the simulation did not exceed 10%. Thus, the simulation result is acceptable. Before the improvement, the peak spine load during the crash was 8578 N. After optimizing the variable \(\alpha\) independently, the maximum load at the spine of the ATD was 6948 N (see Figure 9(a) for the comparison). The optimization of the variable \(\beta\) changed the peak spine load from 8578 N to 7850 N (see Figure 9(b)). If the optimized variable was \(l_{1}\), the load would be reduced from 8578 N to 7615 N (see Figure 10c). Optimizing \(l_{3}\) independently made the maximum load 8180 N (see Figure 10d). Compared with the previous four cases, optimizing all four parameters at the same time had the best effect and the peak spine load was 6292 N (see Figure 10e). The corresponding peak spine load for the above five cases decreased by 19%, 8.5%, 11.2%, 4.6% and 26.6%, respectively.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Before the Optimization** & **After the Optimization** \\ \hline \(\alpha\) & 14\({}^{\circ}\) & 31\({}^{\circ}\) \\ \(\beta\) & 57\({}^{\circ}\) & 64\({}^{\circ}\) \\ \(l_{1}\) & 303 mm & 335 mm \\ \(l_{3}\) & 103 mm & 122 mm \\ \hline \multicolumn{3}{c}{The peak spine load of the ATD} & 8578 N & 6292 N \\ \multicolumn{3}{c}{The mass of the system} & 90.9 kg & 91.3 kg \\ \hline \hline \end{tabular}
\end{table}
Table 2: Optimization results.  
Figure 10: Comparison of the spine load before and after the optimization. (**a**) The optimized variable is \(\alpha\). (**b**) The optimized variable is \(\beta\). (**c**) The optimized variable is \(l_{1}\). (**d**) The optimized variable is \(l_{3}\). (**e**) The optimized variables are \(\alpha\), \(\beta\), \(l_{1}\) and \(l_{3}\).  
According to the description of the results provided above, the four structural parameters of the key energy-absorbing structure of the seat (\(\alpha\), \(\beta\), \(l_{1}\) and \(l_{3}\)) have a significant impact on the ability to absorb energy when the rear-facing seat is tested for vertical impact. Compared with the other three variables, the change of the single variable \(\alpha\) plays a more important role in the energy absorption improvement under the constraints. When the four variables were simultaneously changed, the structure of this helicopter seat was greatly optimized. In the human-seat coupling system, the optimized seat can effectively reduce its impact on the spine of the occupant during collision and it also improves the crashworthiness of the helicopter. According to the AIS (Abbreviated Injury Scale), which was proposed by AAAM (Association for the Advancement of Automotive Medicine) in 1969, the condition is severe but the passenger can be saved from death. This condition corresponds to AIS level 4 [40]. At the same time, the result meets the following regulations of the CCAR-27-R2 on the dynamics of landing.  
1. The seating system must withstand the intended separation, while the rest of the system must remain intact.
2. The connection within the main structures of the seating system must not be destroyed, even though the load on the seating system may have exceeded its limit.
3. The peak spine load of the ATD should be less than 6668 N (1500 pounds).