A practical polynomial chaos Kalman filter implementation using nonlinear error projection on a reduced polynomial chaos expansion

Abstract

The polynomial chaos Kalman filter (PCKF) has been gaining popularity as a computationally efficient and robust alternative to sampling methods in sequential data assimilation settings. The PCKF's sampling free scheme and attractive structure to represent non-Gaussian uncertainties makes it a promising approach for data filtering techniques in nonlinear and non-Gaussian frameworks. However, the accuracy of PCKF is dependent on the dimension and order of the polynomial chaos expansion used to represent all sources of uncertainty in the system. Thus, when independent sources of errors, like process noise and time independent sensors' errors are incorporated in the system, the curse of dimensionality hinders the efficiency and the applicability of PCKF. This study sheds light on this issue and presents a practical framework to maintain an acceptable accuracy of PCKF without scarifying the computational efficiency of the filter. The robustness and efficiency of the presented implementation is demonstrated on 3 typical numerical examples to illustrate its ability to achieve considerable accuracy at a low computational tax.

A Health Monitoring Framework for Optimal Service Life Predictions of Steel Structures Under Fatigue Loading

“…Sequential data assimilation is based on estimating unknown state variables based on the dynamic response of the structure besides the available observation data. Recently, sequential data assimilation has been popular in many engineering fields especially with the advances in monitoring technique and computer-based simulations [12,13]. A widely used sequential assimilation filters are the Kalman filter family.…”