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.

翻译：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，但直接微分需要高昂计算成本，尤其对于高阶动态系统。针对此问题，本研究发展了一种基于降阶基方法（RBM）的高效离散伴随灵敏度分析方法，该方法一方面显著提升了灵敏度分析效率，另一方面避免了连续方法导致的一致性误差。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，并开发了新型模型估计以加速这一过程。基于这些基函数，通过伽辽金投影建立快速且具有合理精度的模型，用于每次动态拓扑优化迭代中的灵敏度分析。最后，通过二维和三维动态结构研究验证了误差准则的有效性、以及所提降阶方法的效率与精度。