## 6 Conclusions  
Due to inevitable uncertainties from various sources, the concept of robust optimization has been deeply rooted in engineering designs. Compared to traditional probability models, evidence theory may be an alternative to model uncertainties in robustness optimization, especially in the cases of limited samples or conflicting information. In this paper, an effective EBRO method is developed, which can provide a computational tool for engineering problems with epistemic uncertainty. The contribution of this study is summarized as follows. Firstly, the improved EBDO model is formulated by introducing performance threshold as a newly-added design variable, and this model can handle the uncertainties involved in design variables and parameters. Secondly, the original EBRO is transformed into a series of sub-problems to avoid double-objective optimization, and thus the difficulty of solving is reduced greatly. Thirdly, an iterative strategy is proposed to drive the robustness analysis and  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Results** & **Proposed Method** & **Reference Solution** \\ \hline \multirow{5}{*}{\(\mathbf{X}_{j}^{*}\) (mm)} & (9.0661, 8.9042) & (9.0661, 8.9042) \\  & (9.0659, 8.9040) & (9.0660, 8.9040) \\  & (9.0657, 8.9038) & (9.0657, 8.9039) \\  & (9.0653, 8.9035) & (9.0654, 8.9036) \\  & (9.0653, 8.9035) & (9.0648, 8.9031) \\ \hline \multirow{5}{*}{\(\mathbf{v}_{j}^{*},Bel_{j}^{*}\)} & (0.244 \(\upmu\)m, 81.8\%) & (0.244 \(\upmu\)m, 81.8\%) \\  & (0.302 \(\upmu\)m, 86.3\%) & (0.279 \(\upmu\)m, 85.2\%) \\ \cline{1-1}  & (0.350 \(\upmu\)m, 90.8\%) & (0.338 \(\upmu\)m, 90.1\%) \\ \cline{1-1}  & (0.449 \(\upmu\)m, 96.1\%) & (0.424 \(\upmu\)m, 95.5\%) \\ \cline{1-1}  & (0.607 \(\upmu\)m, 99.4\%) & (0.594 \(\upmu\)m, 99.2\%) \\ \cline{1-1}  & (0.776 \(\upmu\)m, 100.0\%) & (0.733 \(\upmu\)m, 99.9\%) \\ \hline \hline \end{tabular}
\end{table}
Table 5: The optimal set of the accelerometer problem.  
the optimization solution alternately, resulting in nested optimization in the sub-problems achieving decoupling. The proposed method is applied to the three MEMS design problems, including a micro-force sensor, an image sensor, and a capacitive accelerometer. In the applications, the finite element simulation models and surrogate models are both given. Numerical results show that the proposed method has good engineering practicality due to comprehensive performance in terms of efficiency, accuracy, and convergence. Also, this work provides targeted engineering examples for peers to develop novel algorithms. In the future, the proposed method may be extended to more complex engineering problems with dynamic characteristics or coupled multiphysics.  
Conceptualization, Z.H. and S.D.; Data curation, J.X.; Formal analysis, J.X.; Funding acquisition, T.Y.; Investigation, Z.H.; Methodology, Z.H.; Project administration, T.Y.; Resources, S.D. and F.L.; Software, J.X.; Validation, S.D. and F.L.; Visualization, J.X.; Writing-original draft, Z.H.; Writing-review & editing, S.D.  
This research was supported by the Major Program of National Natural Science Foundation of China (51490662); the Educational Commission of Hunan Province of China (18A403, 17A036, 17C0044); and the Natural Science Foundation of Hunan Province of China (2016J)2012, 2017J]2022, 2019J]40296, 2019J]40014).  
The authors declare no conflict of interest.