Multifidelity Gaussian Process Model Integrating Low- and High-Fidelity Data Considering Censoring

To investigate the behavior of engineering systems in the context of uncertainty propagation, sensitivity analysis, and design optimization, where large numbers of system model evaluations are needed, direct adoption of high-fidelity system models (such as physical experiments or detailed simulations) is impractical. Efficient surrogate models built based on a small number of high-fidelity data have been proposed. However, for many engineering applications, the outputs of high-fidelity models are not always the exact values of the output of interest; rather, censored data, which only provide bounds for the interested output, are given. Surrogate models that can address censored data and make best use of a limited number of high-fidelity data and leverage the information from data with different levels of accuracy are needed. This paper proposes a general multifidelity Gaussian process model integrating low-fidelity data and high-fidelity data considering censoring in high-fidelity data. To alleviate the cost associated with establishing high-fidelity data, the proposed model integrates information from a small number of expensive high-fidelity data and information provided by a large number of cheap low-fidelity data to efficiently inform a more accurate surrogate model. Censored data are explicitly considered in the calibration of the multifidelity Gaussian process model. Posterior distributions of the model parameters are established in the context of Bayesian updating to explicitly take into account the uncertainties in the model parameters and the measurement errors in the data. To address the computational challenges in estimating the likelihood function of model parameters when considering censored data, a data augmentation algorithm is adopted where the censored data are treated as additional uncertain model parameters and closed-form conditional posterior distributions are derived for the model parameters. Gibbs sampling is then used to efficiently generate samples from the posterior distributions for the model parameters, which are used to establish the posterior statistics for the output predictions at new inputs. The effectiveness of the proposed model is illustrated in an example to establish a predictive model for the deformation capacity of reinforced concrete (RC) columns using a limited number of high-fidelity experimental data (the majority of which are censored data) and a large number of low-fidelity data established from analytical and numerical modeling.