Robust Structural Health Monitoring Using a Polynomial Chaos Based Sequential Data Assimilation Technique

Abstract

With the recent technological advances and the evolution of advanced smart systems for damage detection and signal processing, Structural Health Monitoring (SHM) emerged as a multidisciplinary field with wide applicability throughout the various branches of engineering, mathematics and physical sciences. However, significant challenges associated with modeling the physical complexity of systems comprising these structures remain. This is mainly due to the fact that numerous uncertainties associated with modeling, parametric and measurement errors could be introduced. In cases where these uncertainties are significant, standard identification and damage detection techniques are either unsuitable or inefficient. This study presents a robust data assimilation approach based on a stochastic variation of the Kalman Filter where polynomial functions of random variables are used to represent the inherent process uncertainties. The presented methodology is combined with a non-parametric modeling technique to tackle structural health monitoring of a four-story shear building. The structure is subject to a base motion specified by a time series consistent with the El-Centro earthquake and undergoes a preset damage in the first floor. The purpose of the problem is localizing the damage in both space and time, and tracking the state of the system throughout and subsequent to the damage time. The application of the introduced data assimilation technique to SHM enhances the latter’s applicability to a wider range of structural problems with strongly nonlinear dynamical behavior and with uncertain and complex governing laws.