Probabilistic model updating via variational Bayesian inference and adaptive Gaussian process modeling

Abstract

The estimation of the posterior probability distribution of unknown parameters remains a challenging issue for model updating with uncertainties. Most current studies are based on stochastic simulation techniques. This paper proposes a novel variational Bayesian inference approach to estimate posterior probability distributions by using the vibration responses of civil engineering structures. An adaptive Gaussian process modeling technique is used to represent the “expensive-to-evaluate” likelihood function, and the unknown posterior probability distribution is represented using a Gaussian mixture model. The evidence lower bound (ELBO) and its gradients can be computed analytically using the built Gaussian process and mixture models. The unknown parameters in the Gaussian mixture model can be identified by maximizing the value of ELBO. The stochastic gradient descent method is applied to perform the optimization. Numerical studies on an eight-story shear-type building and a simply supported beam are conducted to verify the accuracy and efficiency of using the proposed approach for probabilistic model updating and damage identification. Experimental studies on a laboratory steel frame structure are also conducted to validate the proposed approach. Results demonstrate that the posterior probability distributions of the unknown structural parameters can be successfully identified, and reliable probabilistic model updating and damage identification can be achieved.