Dynamic Reliability Assessment of Structures and Machines Using the Probability Density Evolution Method

Afshari, Sajad Saraygord; Zuo, Ming J.; Liang, Xiaodong

doi:10.1007/978-3-030-79519-1_5

Cited by 2 publications

(1 citation statement)

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“…In this regard, a time history of structural responses (i.e., displacement and velocity responses) and dynamic structural properties (stiffness and damping) are first estimated using the UKF and a measured acceleration input. Then, having estimated the desired states over time together with a proper definition of the failure criteria (from case studies, standards, or risk and safety analyses 44 ), we used the PDEM to estimate the time‐varying PDF of the structural response to be used for calculating the probability of crossing the limit state (i.e., structural failure probability). The joint PDF of the displacement ( X ), uncertainty vector ( θ ) of the physical parameters, and time ( t ) were estimated by solving the partial differential equation of PDEM (Equation ) 42 .…”

Section: Methodsmentioning

confidence: 99%

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

Ghorbani,

Afshari,

Svecova

et al. 2023

Earthq Engng Struct Dyn

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The 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.

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Section: Methodsmentioning

confidence: 99%