Interval Analysis for System Identification of Linear MDOF Structures in the Presence of Modeling Errors

Abstract

Modeling errors, represented as uncertainty associated with the parameters of a mathematical model, inevitably exist in the process of constructing a theoretical model of real structures and limit the practical application of system identification. They are usually represented either in a deterministic manner or in a probabilistic way. However, if the available information is uncertain but of a nonprobabilistic nature, as it may emerge from a lack of knowledge about the sources and characteristics of model uncertainties, a third type of approach may be useful. Presented in this paper is an approach to treat modeling errors with the aid of intervals, resulting in bounded values for the identified parameters. Compared with the traditional identification procedures where model-based forward dynamic analysis is often involved, computing bounded time history responses from a computational model with interval parameters is avoided. Two required submatrices are firstly extracted from identified state-space models by applying a subspace identification method to the measurements, and then interval analysis is performed upon these two matrices to estimate the bounded uncertainty in the identified parameters. The effectiveness of the proposed methodology is evaluated through numerical simulation of a linear multiple–degree-of-freedom (MDOF) system when modeling errors in the mass and damping parameters are taken into account. The results show the ability of the proposed method to maintain sharp enclosures of the identified stiffness parameters.