# Two-Phase Approach for Fast Topology Optimization of Multi-Resonant MEMS Involving Model Order Reduction

## TL;DR

This paper introduces a two-phase optimization method to speed up the design of multi-resonant MEMS devices using model order reduction.

## Contribution

A novel two-phase optimization approach combining BESO and density-based methods with model order reduction for faster MEMS design.

## Key findings

- The two-phase approach achieves optimal MEMS designs within 200 iterations.
- Model order reduction reduces computation time by 50% in the examples tested.

## Abstract

In this work, we propose a two-phase approach for a fast topology optimization of multi-resonant MEMSs. The approach minimizes the computation effort required to achieve an optimal design. In the first step, we perform a pre-optimization using bi-directional evolutionary structural optimization (BESO). We found in previous research that BESO can achieve optimal MEMS designs in a significantly lower number of iterations when compared to classical density-based methods. However, we encountered convergence issues with BESO towards the end of the optimization. Therefore, we introduced a second, density-based optimization phase to circumvent this issue. Finally, we introduced model order reduction to reduce the optimization time further. The novel approach is benchmarked with the design task of two common multi-resonant MEMS devices: a linear gyroscope and a micromirror. We show that the two-phase approach can achieve an optimal design within 200 iterations. With the addition of MOR, the computation of the goal function can be further reduced by 50% in our examples.