Review of Nonlinear Filtering for SHM with an Exploration of Novel Higher-Order Kalman Filtering Algorithms for Uncertainty Quantification

Abstract

Recent work has shown the applicability of Bayesian inference techniques, which use a physics-based representation of the structure of interest, to structural health monitoring (SHM) tasks, such as damage identification. This paper focuses on Bayesian filtering algorithms that provide a way to detect, localize, and identify damage in an online fashion. These algorithms aim to identify the states and parameters of the structure, and take into account noise in the system and measurements, and are thus well fitted to quantify uncertainties. In this paper, a thorough review of these algorithms is provided, primarily the particle filter and the unscented Kalman filter. Estimates of the posterior probability-density functions (PDFs) obtained with these filters are compared for three nonlinear mechanical systems, thus providing an insight into the filters’ behavior and their ability to quantify uncertainties. Furthermore, novel techniques are introduced to take into account non-Gaussian noise and non-Gaussian posterior PDFs by means of a novel framework that expands the nonlinear Kalman filtering theory to non-Gaussian baseline distributions.