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 estimator is developed to accurately predict the true error for facilitating 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 efficiency and accuracy of the suggest method are verified by 2D and 3D dynamic structure studies.

中文翻译：

---

动态拓扑优化伴随灵敏度分析的新型简化基方法

在基于梯度的时域拓扑优化中，动态响应的设计灵敏度分析（DSA）至关重要，并且需要很高的计算成本来直接微分，特别是对于高阶动态系统。针对这一问题，本研究提出了一种高效的基于简化基法（RBM）的离散伴随敏感性分析方法，一方面显着提高了敏感性分析的效率，另一方面避免了连续统方法带来的一致性误差。在该算法中，基于贪婪POD方法在离线阶段构建伴随问题的基函数，并开发了一种新颖的基于模型的估计器来准确预测真实误差以促进这一过程。基于这些基函数，然后通过伽辽金投影建立快速且相当准确的模型，用于每次动态拓扑优化迭代中的灵敏度分析。最后，通过2D和3D动态结构研究验证了该建议方法的效率和准确性。