Structural Deterioration Modeling Using Variational Inference

Abstract

Integrity and risk assessment of structures and infrastructure systems includes the evaluation of deterioration processes such as corrosion, fatigue, and wear. Future deterioration is often estimated from imprecise inspection data using stochastic deterioration models. Bayesian inference for such models mostly relies on stochastic simulation techniques to generate samples from the posterior probability distributions of the unknown model variables. This paper introduces variational inference as an alternative to simulation methods to make deterioration models more suitable for large inspection data sets. Variational inference treats inference as an optimization problem in which the posterior probability distributions of interest are iteratively determined using an optimization function that is derived from the Kullback–Leibler divergence. The variational solution for a hierarchical stochastic deterioration model is derived based on a homogeneous stochastic gamma process and noisy inspection data. Two numerical examples are provided to demonstrate the accuracy of the results and the scalability of variational inference to large inspection data problems.