## 6 Conclusions  
In order to improve the mechanical properties of an irregularly-shaped bridge, a typical irregularly-shaped bridge is selected and its static and dynamic characteristics are optimized by the proposed comprehensive weight analysis method. According to the orthogonal analysis results, the influence of parameters, including ramp radius, bifurcation diaphragm stiffness, box girder height, and supporting conditions on maximum stress, stress variation coefficient, and torsion vibration fundamental frequency are investigated. Combining with AHP, the comprehensive weight analysis method is proposed to determine the influence order and preferred values of parameters for the mechanical properties of an irregularly-shaped bridge. Based on the test results, the following conclusions are obtained:  
1. Bifurcation diaphragm stiffness and box girder height are the main factors that affect the maximum stress and stress variation coefficient relative to the ramp radius and supporting condition. The increasing bifurcation diaphragm thickness decreases the maximum stress and stress variation coefficient. As box girder height increases, the maximum stress decreases and uneven stress distribution becomes serious.
2. The supporting condition plays the most important role in the influence on torsion vibration fundamental frequency. Double torsional supports set at the end of an irregularly-shaped bridge can improve the ability of the irregularly-shaped bridge to resist torsional vibration, which is more beneficial to driving safety.
3. Based on the influence weights of factors to the mechanical properties of an irregularly-shaped bridge, the influence order of parameters is: supporting condition > bifurcation diaphragm stiffness > box girder height > ramp radius. According to the influence weights of levels in each factor, the best parameters for an irregularly-shaped bridge design are obtained when the ramp radius, bifurcation diaphragm thickness, box girder height, and supporting conditions are \(R\) = 50 m, \(D\) = 2.0 m, \(H\) = 2.0 m, and 1, respectively.
4. Comparative analysis with test results of optimal parameters obtained from the overall balance method reveals that the comprehensive weight analysis method is superior to the overall balance method. The comprehensive weight analysis method possesses more favorable accuracy and validity in the sensitivity analysis and design optimization of parameters for the mechanical properties of irregularly-shaped bridges.  
**Acknowledgments:** The authors express their appreciation for the financial supports of National Natural Science Foundation of China (Nos. 51378236, 51408258); China Postdoctoral Science Foundation funded project (2014 MS60237, 2015T80305); Fundamental Research Funds for the Central Universities (JCKY-QKJC06); Science & Technology Development Program of Jilin Province.  
**Author Contributions:** [PERSON] conceived and proposed the optimization algorithm; [PERSON] designed the orthogonal test and wrote the manuscript; [PERSON] performed the finite element simulations and analyzed the results; [PERSON] edited and audited the content; [PERSON] contributed to the revisions and discussion of the results. All authors have read and approved the final manuscript.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Analysis Method**} & \multicolumn{4}{c}{**Factor**} & \multicolumn{4}{c}{**Index**} \\ \cline{2-7}  & \(R\) **(m)** & \(D\) **(m)** & \(H\) **(m)** & \(U\) & \(\sigma_{\text{max (MPa)}}\) & \(\lambda\) & \(f_{d}\) **(Hz)** \\ \hline Overall balance method & 50 & 2.0 & 1.8 & 1 & 2.24 & 1.51 & 8.4667 \\ \hline Comprehensive weight analysis method & 50 & 2.0 & 2.0 & 1 & 1.94 & 1.54 & 8.5642 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Mechanical properties with different optimal parameters.