Modeling time and spatial variability of degradation through gamma processes for structural reliability assessment

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.

A Perturbed Markovian process with state‐dependent increments and measurement uncertainty in degradation modeling

“…Finally, an interesting extension of the model that incorporates either the heterogeneity or the spatial variability in the modeling (Oumouni et al, 2019) will be the topic of further studies.…”

“…Due © 2021 Computer-Aided Civil and Infrastructure Engineering to the mathematical benefits of the Gamma process, many deterioration phenomena are modeled with a smaller computational cost. Further, failure probabilities are provided with analytic forms (Oumouni, Schoefs, & Castanier, 2019;Van Noortwijk, 2009;Wenocur, 1989). However, in many deterioration phenomena (corrosion of reinforced concrete with chloride propagation, crack growth process in materials due to fatigue), increments of the degradation are not independent, but each one depends on the current state and the increment of time (El Hajj, Schoefs, Castanier, & Yeung, 2017;Giorgio, Guida, & Pulcini, 2015;, so the degradation growth statistically depends on the current state.…”

Probabilistic Modelling of Spatio-Temporal Uncertainties in Degradation

“…Another well-established method in spatio-temporal modelling is the use of separable fields. Oumouni et. al.…”

A data-driven probabilistic model for well integrity management: case study and model calibration for the Danish sector of North Sea

“…The choice of the probabilistic distribution used to model time to failure and degradation process has large influence on the resulting reliability (Quesenberry, 1982, Rausand, 1998. The use of Leví process (especially Gamma) to simulate deterioration of components has been largely suggested (Williams et al, 1985, Pandey et al, 2005, Noortwijk et al, 2007, Amaya-Gómez et al, 2019, Oumouni et al, 2019. Main advantage of using Gamma distribution lays in the easier inclusion of time variation though the shape parameter, while keeping constant the scale parameter.…”

“…Main advantage of using Gamma distribution lays in the easier inclusion of time variation though the shape parameter, while keeping constant the scale parameter. However, a Gamma process has independent positive increments, which makes realizations monotonic and linearly increasing, thus a dataset of progressive increments of defect size is needed to model the degradation process where any non-linearity of corrosion processes, , any variation of the degradation rate and any dependency over operational parameters can be introduced by Bayesian updating whenever new observations are available (Pandey et al, 2005, Straub et al, 2007, Oumouni et al, 2019. The dataset available for this study does not provides increments of defect size in between inspections, but only pit sizes at failure, leading to the choice of a shock load type of distribution, as highlighted in the following sections.…”