Particle filtering and marginalization for parameter identification in structural systems

Summary In structural health monitoring, one wishes to use available measurements from a structure to assess structural condition, localize damage if present, and quantify remaining life. Nonlinear system identification methods are considered that use a parametric, nonlinear, physics-based model of the system, cast in the state-space framework. Various nonlinear filters and parameter learning algorithms can then be used to recover the parameters and quantify uncertainty. This paper focuses on the particle filter (PF), which shows the advantage of not assuming Gaussianity of the posterior densities. However, the PF is known to behave poorly in high dimensional spaces, especially when static parameters are added to the state vector. To improve the efficiency of the PF, the concept of Rao–Blackwellisation is applied, that is, we use conditional linearities present in the equations to marginalize out some of the states/parameters and infer their conditional posterior pdf using the Kalman filtering equations. This method has been studied extensively in the particle filtering literature, and we start our discussion by improving upon and applying two well-known algorithms on a benchmark structural system. Then, noticing that in structural systems, high nonlinearities are often localized while the remaining equations are bilinear in the states and parameters, a novel algorithm is proposed, which combines this marginalization approach with a second-order extended Kalman filter. This new approach enables us to marginalize out all the states/parameters, which do not contribute to any high nonlinearity in the equations and, thus, improve identification of the unknown parameters. Copyright © 2016 John Wiley & Sons, Ltd.