# Safety Design of Rotary Drilling Rig Mast Based on Multi-Condition Analysis
## 5 Engineering Application
### Optimization Results  
The parameters for the optimization algorithm are set as follows: the maximum number of iterations is 100, the population size is 100, and the standard plate thickness dataset is \(T=\)[6; 8; 10; 12]. The range of variation for the optimization variables is presented in Table 14.  
The results are presented in the Table 15 below.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Calculated Values** & **Limit Value** & **Unit** \\ \hline Strength & 289 & 495 & MPa \\ Stiffness & 354 & 180 & \\ Fatigue Strength & 234 & 313 & MPa \\ Nominal Euler Critical Load & & 4245 & kN \\ Overall Stability & 434 & 495 & MPa \\ Safety Score & 89.4 & 80 & \\ \hline \hline \end{tabular}
\end{table}
Table 13: Load-bearing capacity and safety assessment.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(\mathbf{k_{1}^{g}}\) & \(\mathbf{k_{2}^{g}}\) & \(\mathbf{b_{3}^{g}}\) & \(\mathbf{b_{4}^{g}}\) \\ \hline Static Strength & 345 & 395 & 445 & 495 \\ Stiffness & 60 & 100 & 140 & 180 \\ Overall Stability & 345 & 395 & 445 & 495 \\ Fatigue Strength & 223 & 253 & 283 & 313 \\ \hline \hline \end{tabular}
\end{table}
Table 12: The evaluation range boundaries.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(\mathbf{x_{1}}\) & \(\mathbf{x_{2}}\) & \(\mathbf{x_{3}}\) & \(\mathbf{x_{4}}\) & **Objective Function** & **Safety Score** \\ \hline Original design & 750 & 750 & 24 & 24 & 45,056 & 89.4 \\ Optimized design & 750 & 750 & 16 & 24 & 39,248 & 72.6 \\ Safety-optimized design & 749 & 749 & 20 & 24 & 42,108 & 83.3 \\ \hline \hline \end{tabular}
\end{table}
Table 14: The range of variation for the optimization variables.  
From the table above, it can be observed that both ordinary optimization design and safety optimization design successfully reduced the cross-sectional dimensions, achieving a certain degree of structural lightweighting. However, compared to ordinary optimization design, safety optimization design resulted in a slight increase in self-weight, approximately 7.3%, but its safety score significantly improved by nearly 14.74%. This difference reflects the significant advantage of safety optimization design in balancing both lightweighting and structural safety.  
Although ordinary optimization design can reduce self-weight, it may lead to higher risks due to insufficient consideration of the structural safety performance. In extreme working conditions, this could potentially pose safety hazards. On the other hand, safety optimization design, by incorporating safety assessment constraints, effectively enhances the structural safety performance, significantly reducing the potential failure risk, and provides higher reliability and practicality for the design outcome.  
From the perspective of feasibility and engineering practice, safety optimization design not only achieves the lightweighting goal but also significantly improves safety performance, demonstrating exceptional potential in meeting modern engineering demands. This design approach offers valuable reference for achieving the optimization goals of rotary drilling rig masts and sets a good example for the optimization design of other structural components.