Random Fields in Bayesian Inference: Effects of the Random Field Discretization

Probabilistic analysis of engineering systems often requires models that account for the random spatial variability of their parameters. Information about a target set of parameters can be obtained using mathematical models in combination with observational data. Bayesian inference handles this task by computing a posterior probability distribution that quantifies the combined effects of prior knowledge and observations. However, the complexity of the inference process is increased when the spatial variation of the parameters is considered. Spatially variable quantities are usually modeled by random fields that are discretized with a high number of random variables. In this paper, the challenge is addressed by representing the random field with the Karhunen-Loève expansion with the purpose of evaluating its effects on the outcome of the Bayesian inference. To this end, the influence of the number of terms in the expansion and the correlation length of the prior random field are assessed. The analytical study is carried out on a cantilever beam with spatially variable flexibility. We show that it requires more terms in the series expansion to identify the flexibility random field with the same accuracy as the deflection solution. Furthermore, the decay of the variance error when estimating the posterior flexibility is slower than in the posterior deflection.      «

Probabilistic analysis of engineering systems often requires models that account for the random spatial variability of their parameters. Information about a target set of parameters can be obtained using mathematical models in combination with observational data. Bayesian inference handles this task by computing a posterior probability distribution that quantifies the combined effects of prior knowledge and observations. However, the complexity of the inference process is increased when th...     »