Particle filter-based hybrid damage prognosis considering bias

Hybrid prognosis combining both the physical knowledge and data-driven techniques has shown great potential for damage prognosis in structural health monitoring (SHM). Current practices consider the physics-based process and data-driven measurement equations to describe the damage evolution and the mapping between the damage state and the SHM signal (or the feature extracted from SHM signal), respectively. However, the bias between the measurements predicted by data-driven equation and the actual SHM measurements, arising from uncertainties like damage geometries and sensor placement or noise, can lead to inaccurate prognosis results. To account for this problem, this paper adopts a methodology typically applied for sensor fault diagnosis, and develops a new hybrid state space model with a bias parameter included into the state vector and the measurement equation. Particle filter (PF) serves as the estimation technique to identify the state and parameters relating to the damage as well as the bias parameter, and RUL can be predicted by the PF estimates and physics-based process equation. The numerical study about the fatigue crack growth shows the new model together with PF can provide satisfactory estimation and prediction results in case of bias in the measurement model.