Modeling time and spatial variability of degradation through gamma processes for structural reliability assessment. (January 2019) - Oumouni, M.; Schoefs, F.; Castanier, B.
Highlights: The paper addresses the problem of spatial variability in the degradation process. A spatio-temporal random field model is proposed to address this problem with the details of its construction and simulation. Inference procedure is developed for such spatio-temporal model Estimation of quantities of interest used in the reliability analysis and maintenance. The model is applied to numerical examples in one and two dimensional case. The results show that the uncertainties are reduced, the inference procedure is improved. Abstract: The objective of this work is to propose a spatio-temporal random field for assessing the effect of spatial variability on the degradation process in structural reliability assessment. Our model extends the classical Gamma process which is usually developed for degradation temporal variability concerns to integrate spatial variability and heterogeneity issues. A log-normal distributed spatial random scale is then introduced in the Gamma process. Mathematical models for a structure degradation in space and time and estimation procedures are developed in this paper. Approximations and simulations are given to evaluate the failure time distribution and to characterize the residual lifetime after inspection. Simulation results are performed using pseudo-random data based on Monte-Carlo simulations to fit the model and the inference of their parameters. The two proposed estimation method – Method of Moments and Pseudo Maximum Likelihood – are numerically compared according to statistical measures. The accuracy of the methods are also discussed by numerical examples given the approximations of quantities of interests.