## 5 Conclusions  
Based on the experimental data and finite element analysis results, the ultimate strength and stiffness of electric wheel dump truck frame at interval can be obtained through blind number theory. The stresses under dynamic horizontal bending, unexpected braking (fracturing) and torsion as well as the stiffness under bending and torsion were estimated. The thickness of main bearing beams in frame was considered as a design variable, and the material properties were regarded as uncertain variables caused by manufacturing process. Based on the response surface method, the interval multi-objectives optimization function was obtained. Finally, the non-dominated sorting genetic algorithm was used to search for the optimal solution. The specific conclusions are listed as follows:  
1. Based on the blind number theory, the ultimate strength of electric wheel dump truck welded frame at interval was \([439.11,792.52]\) MPa. The bending and torsional stiffness were \([3.28\times 10^{9},20.28\times 10^{9}]\) N\(\cdot\)m\({}^{2}\) and \([0.84\times 10^{9},2.91\times 10^{9}]\) N\(\cdot\)m\({}^{2}\)/rad. Using Latin Hypercube method to acquire sample data, the stresses due to dynamic horizontal bending under horizontal bending, braking and torsional conditions were \([211.11,357.10]\) MPa, \([343.31,461.20]\) MPa and \([222.60,374.54]\) MPa, The stiffness under bending and torsion was \([9.65\times 10^{9},10.50\times 10^{9}]\) N\(\cdot\)m\({}^{2}\) and \([1.35\times 10^{9},1.64\times 10^{9}]\) N\(\cdot\)m\({}^{2}\)/rad. 2. In full consideration of the uncertain factors caused by the manufacturing process, Young's modulus and Poisson's ratio were considered as uncertain variables. The thickness of four main bearing beams was regarded as a design variable. Based on the non-dominated sorting genetic algorithm, the stresses due to dynamic horizontal bending in horizontal bending, unexpected braking (fracturing) and torsion were decreased by 19.18%, 17.25% and 9.06%, respectively. The bending and torsional stiffness were improved by 21.53% and 15.88%. In the meantime, all design variables were increased by approximately 15%. Conceptualization, C.M. and J.L. ([PERSON]); Methodology, C.M. ; Software, W.L. ; Validation, W.L., X.X. and J.L. ([PERSON]); Formal analysis, C.M. ; Investigation, C.M. ; Resources, R.M. ; Data Curadian, X.X. ; Writing--Original Draft Preparation, C.M. ; Writing--Review & Editing, Q.Y. ; Visualization, X.X. ; Supervision, Q.Y. ; Project Administration, C.M. ; Funding Acquisition, C.M. and W.L. This research was funded by Excellent Youth Project of Hunan Education Department (Grant No. : 18B301) and Postgraduate Research Innovation Project of Hunan Education Department (Grant No. : CX20190846) and National Natural Science Foundation of China (Grant No. : 51975192). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & **\(\mathbf{y_{1}}\) (MPa)** & **\(\mathbf{y_{2}}\) (MPa)** & **\(\mathbf{y_{3}}\) (MPa)** & **\(\mathbf{y_{4}}\) (N-m\({}^{2}\))** & **\(\mathbf{y_{5}}\) (N-m\({}^{2}\)/rad)** \\ \hline Initial value & 253.4 & 404.7 & 300.2 & \(9.96\times 10^{9}\) & \(1.599\times 10^{9}\) \\ Optimized value & 204.8 & 334.9 & 273.0 & \(1.210\times 10^{10}\) & \(1.853\times 10^{9}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of the initial and optimized certain objective values. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Design Variables** & **Initial Value** & **Optimized Value** \\ \hline \(x_{1}\) (mm) & 45 & 54 \\ \(x_{2}\) (mm) & 16 & 19 \\ \(x_{3}\) (mm) & 25 & 30 \\ \(x_{4}\) (mm) & 45 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of the initial and optimized design variables. **Acknowledgments:** The authors gratefully thank for the support of Excellent Youth Project of Hunan Education Department (Grant No. : 18B301) and Postgraduate Research Innovation Project of Hunan Education Department (Grant No. : CX20190846) and National Natural Science Foundation of China (Grant No. : 51975192).