Multimodel Fusion Based Sequential Optimization

Simulation models with different levels of fidelity have been widely used in engineering design. Even though the nonhierarchical multimodel fusion approach has been developed for integrating data from multiple competing low-fidelity models and a high-fidelity model, how to allocate samples from multifidelity models for the purpose of design optimization still remains challenging. In this work, a new multimodel fusion-based sequential optimization approach is proposed to address the issues of 1) where in the design space to allocate more samples, and 2) which model to evaluate at the chosen infilling sample sites. First, an objective-oriented sampling criterion that balances global exploration and local exploitation is employed to identify the infilling sample location to address the first question. To address the second question, an improved preposterior analysis is developed to determine which simulation model to evaluate, considering both predictive accuracy and computational cost. The improved preposterior analysis not only eliminates the time-consuming Monte Carlo loop in the conventional method but also adopts an analytical model updating formula to further improve the efficiency. To demonstrate the merits of the current proposed multimodel fusion-based sequential optimization approach, two numerical examples and a vehicle engine piston design example are tested. It is shown that the proposed multimodel fusion-based sequential optimization approach is capable of allocating samples from multifidelity models to sequentially update the predictive model for optimization at less computational cost compared to the conventional kriging-based sequential optimization approach.