A surrogate model based active interval densifying method for nonlinear inverse problems

Abstract

A surrogate model based active interval densifying method is proposed to solve the uncertain nonlinear inverse problem providing an efficient tool for the unknown inputs identifications by using limited information of uncertain outputs. The active interval is first defined to determine the key input interval whose bounds would strongly influence the upper and lower bounds of the outputs, and then an active vertex densifying strategy is proposed by combining the active interval and vertex method to further reduce the number of densifying samples. A novel iterative mechanism is developed to sequentially densify the active interval vector to construct a more precise surrogate model. Therefore, the interval inverse problem is transformed into a series of surrogate model based interval inverse problems and densifies the sample set that is sequentially solved, which could improve the computational efficiency and expand the application area of existing surrogate model based methods for nonlinear inverse problems. Moreover, it is hopeful to be applied to heat conduction, structural parameters and dynamic load identifications. A numerical example and two practical engineering applications are used to verify its feasibility, computational accuracy and efficiency.