A Robust Polynomial Chaos Kalman Filter Framework for Corrosion Detection in Reinforced Concrete Structures

Abstract

A main reason behind reinforced concrete structural deterioration is chlorideinduced corrosion. Once the critical chloride concentration is exceeded at the rebar level, the structure becomes susceptible to corrosion initiation. Corrosion propagates progressively, degrades the resistance capacity of the structure and decreases the design safety margin. To mitigate this risk, a stochastic sequential data assimilation technique based on chloride concentration measurements and the Polynomial Chaos Kalman Filter (PCKF) is presented. The Power of PCKF lies in its sampling free scheme and polynomial structure to represent uncertainty. In modeling chloride ingress mechanism, different independent sources of uncertainty should be incorporated in the system including, mathematical model simplification errors, parametric errors, boundary condition errors, and time independent sensors errors. In such circumstances, the curse of dimensionality hinders the efficiency and the applicability of PCKF, due to the exponential growth of the required bases to account for the added uncertainties. This study presents a practical framework to maintain an acceptable accuracy of PCKF without scarifying the computational efficiency of the filter. A one dimensional synthetic numerical example is presented to verify the efficiency of the proposed implementation scheme.

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

“…Although the efficiency of these filters has been demonstrated in different applications, this solution is not favorable in practice especially in highly nonlinear and complex systems . Recently the use of Polynomial chaos expansion in conjunction with Kalman filter gained attention as a potential and robust alternative . The PCKF is a sampling‐free technique that uses a polynomial chaos expansion (PCE) to represent the uncertainty in the parameters and measurements.…”