Metamodels have been proposed in the literature to reduce the time and resources devoted to design space exploration, to learn about design trade-offs, and to find the best solution to the design problem in the context of simulation-based design and optimization. In previous work in engineering design based on multiple performance criteria, we have proposed the use of Multi-response Bayesian Surrogate Models (MR-BSM) to model several response variables simultaneously, instead of modeling them independently. By doing so, it is expected that the correlation among the response variables can be used to achieve better models with smaller data sets. In this work, we extend the capabilities of MR-BSM by developing a multistage formulation with non-stationary covariance functions. This formulation for multi-response metamodeling in successive stages of experimental design, data acquisition and model fitting, enables the integration of different sources of information about system responses, with different levels of accuracy, into a single, global model of the system. The feasibility of the proposed formulation is demonstrated with an example in which two test functions are jointly approximated in two stages. In addition, we demonstrate the potential of the methodology to take advantage of a priori information, expressed as upper and lower bounds on the responses, to improve the accuracy of the metamodels. Results show that the use of bound information can result in order-of-magnitude improvements in metamodel accuracy.

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