An efficient solution method for inverse problems with high-dimensional model uncertainty parameters

Inverse problems involving high-dimensional uncertain variables may encounter the challenge of the 'curse of dimensionality' during the solution process. In addition, the current uncertainty inverse algorithms may encounter insufficient prior information on the parameters to be inversely solved, leading to difficulty in determining the search interval for inverse problem modeling and optimization. In light of this, this study introduces an inverse solution algorithm that considers model uncertainty based on a high-dimensional model representation (HDMR) approach. The algorithm utilizes the HDMR method to construct models of system input parameters and uncertain model parameters. Subsequently, by enhancing the traditional CV-Voronoi sequential sampling method, the algorithm ensures that the sequential sampling points in the modeling process satisfy both model prediction accuracy and the distribution forms of uncertain variables. Finally, through a stepwise modeling process based on the HDMR, efficient modeling and solution are achieved in scenarios where prior information on the parameters to be determined inversely is insufficient. The effectiveness of the proposed method is validated through several numerical and engineering examples. The method presented in this study provides an effective tool for solving inverse problems with high-dimensional model uncertainty in the field of structural design.