Bayesian Information Fusion of Multmodality Nondestructive Measurements for Probabilistic Mechanical Property Estimation

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Abstract Missing data occur when no data value is available for the variable in an observation. In this research, Bayesian data augmentation method is adopted and implemented for prediction with missing data. The data augmentation process is conducted through Bayesian inference with missing data assuming the multivariate normal distribution. Gibbs sampling is used to draw posterior simulations of the joint distribution of unknown parameters and unobserved quantities. The missing elements of the data are sampled conditional on the observed elements. The distribution of model parameters and variables with missing data can be obtained for reliability analysis. Two examples are given to illustrate the engineering application of Bayesian inference with missing data. The first example is to predict the yield strength of aging pipeline by fusing the incomplete surface information with missing data. The predictive performance is compared among direct surface indentation technique, linear regression with complete data and Bayesian inference with missing data. The second example is to predict the fatigue life of corroded steel reinforcing bar from the incomplete input dataset. The predicted fatigue lives are compared with experimental data. Both examples demonstrate that the Bayesian method can deal with missing data problem properly and show good predictive performance.