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

Abstract eng:
Modeling errors, represented as uncertainty associated with the parameters of a mathematicalmodel, inevitably exist in the process of constructing a theoreticalmodel 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 non-probabilistic nature, as it may emerge from a lack of knowledge about the sources and characteristics of model uncertainties, a third type of approach unfolds its usefulness. Presented in the paper is an approach to treat modeling errors with the aid of intervals, resulting in bounded values for the identified parameters. Compared with “traditional” identification procedures where the model-based forward dynamic analysis is often involved, computing bounded time history responses from a computational model with interval parameters is avoided. The required sub-matrices are firstly extracted from identified state space models by applying subspace identification method to the measurements, and then interval analysis is performed upon these matrices to estimate the interval bounds for the parameters to be identified. As an interesting extension of the interval analysis to damage detection, a damage index with the concept of Hausdorff distance is proposed to quantify the structural damage based on the interval bounds of the identified stiffness parameters in both undamaged and damaged states. A numerical study of a linear MDOF system with interval-valued mass properties shows that the proposedmethodology ensures the effects ofmodeling errors to be fully captured in the results with high efficiency and accuracy.

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