An interval inverse method based on high dimensional model representation and affine arithmetic

This paper proposes an interval inverse method through a high dimensional model representation and affine arithmetic, which can effectively solve inverse problems with interval uncertainty. Firstly, when only the bounds of responses can be obtained from a limited number of experimental measurements, an interval model can be employed to describe the uncertainty of the measured responses and identified parameters. Secondly, in order to reasonably estimate the degree of the closeness between the measured and calculated responses, an error interval and corresponding optimization model are constructed for the interval inverse problem. Thirdly, a high dimensional model representation is utilized to approximate the original system model, and an affine arithmetic is adopted to efficiently calculate the response bounds. Finally, the optimization model for interval inverse problem is solved using genetic algorithm to identify the upper and lower bounds of the system parameters. Three examples are studied to demonstrate the correctness and effectiveness of the proposed method.