Stochastic Definition of State-Space Equation for Particle Filtering Algorithms

Abstract

Particle Filtering is a nonlinear and non-Gaussian model-based Bayesian Filtering algorithm based on Monte Carlo Sampling techniques. This filtering methodology can be used to increase the reliability and the availability of the monitored system combining the measurements on the system itself and the analytical model of the observed phenomena. Inside this context, the basic idea of Particle Filtering is the estimation of the system degradation through a series of weighted particles simulating the dynamic evolution of a time process. Two different mathematical models are needed in order to implement it: firstly, the stochastic observation equation linking the measures (and their uncertainties) with the current state of the system, and secondly the stochastic degradation equation linking the present state to the prior state, or the Dynamic State Space (DSS) model. The DSS model is usually based on deterministic parameters plus an artificial noise added through Monte Carlo Sampling in order to produce a stochastic process. The simple deterministic model with added noise is not able to account for all the uncertainties occurring in a real environment in many cases, producing poor results. Thus, the definition of a Stochastic Dynamic State Space (SDSS) model is proposed here. The SDSS merge the deterministic equation of the observed phenomenon with the statistical definition of the parameters available in literature (or mathematically extrapolated from historical data). It is inserted in a Particle Filtering algorithm and applied to crack growth estimation in metallic structures. The results of the algorithm with the Stochastic Dynamic State Space model are compared with a Particle Filtering based on traditional DSS in terms of crack length estimation and remaining lifetime evaluation performances.