An efficient new PDEM-COM based approach for time-variant reliability assessment of structures with monotonically deteriorating materials

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.