A novel reduced basis method for adjoint sensitivity analysis of dynamic topology optimization

TL;DR

This paper introduces an efficient reduced basis method for adjoint sensitivity analysis in dynamic topology optimization, significantly reducing computational costs and avoiding errors of continuum methods.

Contribution

It develops a novel RBM-based discrete adjoint sensitivity analysis approach with offline basis construction and model-based acceleration, improving efficiency and accuracy.

Findings

Significant reduction in sensitivity analysis computational cost.

Effective error measures and validation on 2D and 3D structures.

Improved accuracy over traditional continuum methods.

Abstract

In gradient-based time domain topology optimization, design sensitivity analysis (DSA) of the dynamic response is essential, and requires high computational cost to directly differentiate, especially for high-order dynamic system. To address this issue, this study develops an efficient reduced basis method (RBM)-based discrete adjoint sensitivity analysis method, which on the one hand significantly improves the efficiency of sensitivity analysis and on the other hand avoids the consistency errors caused by the continuum method. In this algorithm, the basis functions of the adjoint problem are constructed in the offline phase based on the greedy-POD method, and a novel model-based estimation is developed to facilitate the acceleration of this process. Based on these basis functions, a fast and reasonably accurate model is then built by Galerkin projection for sensitivity analysis in each dynamic topology optimization iteration. Finally, the effectiveness of the error measures, the efficiency and the accuracy of the presented reduced-order method are verified by 2D and 3D dynamic structure studies.