An online reduced-order method for dynamic sensitivity analysis

Abstract

This study introduces an online reduced-order methodology designed to avoid the need for generating additional samples during the offline phase, a requirement typically associated with the classical reduced basis method. The proposed methodology is implemented for accelerating the sensitivity analysis in the dynamic topology optimization. The dominant Proper Orthogonal Mode (POM) of the adjoint sensitivity solution is initialized by Proper Orthogonal Decomposition (POD). Sequentially, in the incremental Singular Value Decomposition (SVD) approach, the truncated strategy is utilized to enable the algorithm to efficiently update the basis functions. Furthermore, a novel self-learning Temporal Convolutional Neural Network (TCN)-based error predictive model has been built for the presented reduced-order method, aimed at predicting the true error. This advancement facilitates the adaptive construction of the reduced basis functions. Finally, the effectiveness of the algorithm in terms of computational efficiency and accuracy is demonstrated by means of numerical results, and the proposed error estimation is also verified.