Abstract
Life-cycle time-variant reliability of engineering structures with material deterioration is of paramount importance but still a great challenge. Generally, the computational costs due to embedded structural analyses tracing the life-cycle performance process with monotonically deteriorating material, are prohibitively large. In the present paper, a new method by synthesizing the probability density evolution method (PDEM) and the change of probability measure (COM) is proposed for this purpose. Besides, a functional perspective is provided. The theoretical basis is established by involving the Frobenius-Perron operator, which characterizes the change of random variables, and the Radon-Nikodym operator, which characterizes the change of probability measure of the original source random variables. The material deterioration characterized by time-variant random variables can then be equivalently captured by the time-variant change of probability measure of the basic random variables. Thereby the deterministic analyses at different time instances can be shared in the process of capturing the time-variant probability density of the performance function, and thus the efficiency can be improved considerably. Numerical algorithms are elaborated. Three examples in terms of time-variant reliability evaluation of structures with monotonically deteriorating material and parametric stochastic loading are illustrated, showing the effectiveness of the proposed method. Problems to be further studied are also outlined.
Published Version
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