Robust Optimization for Micromachine Design Problems Involving Multimodal Distributions

The conventional robust optimization methods usually focus on problems with unimodal random variables. In real applications, input random variables may follow multimodal distributions with multiple peaks in their probability density. When multimodal random variables are involved, the conventional methods, such as the mean-variance-based methods, will be not accurate. This paper presents an efficient robust optimization method, which provides a potential computational tool for engineering problems involving multimodal random variables. A robustness metric is formulated by introducing the concept of accepting/rejecting the limit to calculate the failure probability of the performance response, which can directly capture the multimodal characteristics of the performance. A second-order higher moment method is presented to efficiently conduct the probability calculation in the inner loop of design optimization. The proposed decoupling strategy drives the probability calculation and the design optimization sequentially and alternately. This method is applied to the three micromachine design problems, including a sweat-rate sensor, a piezoelectric sensor, and an image sensing module. The numerical results show that the method has excellent engineering practicality due to the comprehensive performance in terms of efficiency, accuracy, and convergence.