Time‐varying reliability analysis based on hybrid Kalman filtering and probability density evolution

Abstract

AbstractThe study introduces a novel approach for time‐varying reliability analysis of structures called “hybrid UKF‐PDEM” by integrating the unscented Kalman filter (UKF) and the probability density evolution method (PDEM). The UKF estimates the displacement, velocity, stiffness, and damping parameters of a structure at each time step subjected to dynamic loading for structural damage quantification. The estimated parameters at each time step are then input into the PDEM to calculate the time‐varying probability density function (PDF) of the estimated states. The estimated PDF is used to update the uncertainty matrix of the estimated states in each iteration and to determine the time‐varying reliability curves of the structure. To demonstrate the effectiveness of the proposed method, we applied it to a numerical model of a three‐degree‐of‐freedom system and a full‐scale seven‐story building with different damage scenarios. The method is used to estimate the level of damage and calculate the corresponding reliability curve of the system over time for each damage scenario, utilizing the estimated structural responses and stiffness values. The extracted reliability values for each damage scenario follow the level of damage over time. This study shows that the newly developed method is computationally efficient for building a digital twin and enables real‐time damage identification and reliability analysis in various structural systems. The method's applicability to different types of structures highlights its versatility and potential for widespread use in assessing the integrity of buildings and infrastructure.