Hierarchical Surrogate Modeling With Multiple Order Partially Observed Information

Abstract

Understanding the input and output relationship of a complex engineering system is an essential task that attracts widespread interests in engineering design fields. To investigate the system performance, surrogate models can be developed based upon a finite set of input-output sample points, and then used to replace expensive black box type performance function and reduce the cost on function evaluations for system design optimization. The finite set of sample points could be obtained from multiple information sources such as experiments with different tests or simulation using different order of computer models. There is a pressing need for an efficient surrogate modeling method that can comprehensively utilize all available information, both fully and partially observed information (POI) collected from sources with different fidelities and dimensionalities. This paper proposes a multi-order system modeling method for partially observed information (MOSM-POI), which takes account of the POI structure and sparseness and uses multiple reduced order models to assist the understanding of the high-dimensional complex system. The Bayesian Gaussian process latent variable model (BGP-LVM) was employed to incorporate POI and a new framework was developed to cope with the high sparseness POI. The numerical experiments demonstrated that the proposed MOSM-POI method provides an accurate solution to take advantage of partially observed information from the multi-order system in developing surrogate models for complex systems.