Nonlinear Multi-Fidelity Bayesian Optimization: An Application in the Design of Blast Mitigating Structures

A common scenario in engineering design is the availability of several black-box functions that describe an event with different levels of accuracy and evaluation cost. Solely employing the highest fidelity, often the most expensive, black-box function leads to lengthy and costly design cycles. Multi-fidelity modeling improves the efficiency of the design cycle by combining information from a small set of observations of the high-fidelity function and large sets of observations of the low-fidelity, fast-to-evaluate functions. In the context of Bayesian optimization, the most popular multi-fidelity model is the auto-regressive (AR) model, also known as the co-kriging surrogate. The main building block of the AR model is a weighted sum of two Gaussian processes (GPs). Therefore, the AR model is well suited to exploit information generated by sources that present strong linear correlations. Recently, the non-linear auto-regressive Gaussian process (NARGP) model has appeared as an alternative to integrate information generated by non-linearly correlated black-box functions. The performance of the NARGP model in structural optimization has remained largely unexplored. This investigation presents a Bayesian optimization approach that implements the NARGP model as the multi-fidelity surrogate model. The optimization strategy is utilized in the design sandwich composite armors for blast mitigation. The armors are made of four layers: steel, carbon fiber reinforced polymer (CFRP), aluminum honeycomb (HC), and CFRP. The optimization problem has three design variables, which are the thickness of the CFRP and aluminum HC layers. Two objectives are minimized: the armor’s penetrations and the reaction force at the armor’s supports. The black-box functions are two finite element models with different levels of fidelity. The low-fidelity model assumes elastic behavior of the sandwich composite. The high-fidelity model considers the nonlinear behavior of each layer of the armor. The results show that the proposed non-linear multi-fidelity Bayesian optimization approach produces a more stable expansion of the Pareto front than an optimization strategy that employs the AR model. This outcome suggests that the NARGP model is an appealing alternative in design problems with a limited number of function evaluations of the high-fidelity source.