Physics-Constrained Bayesian Optimization for Optimal Actuators Placement in Composite Structures Assembly

Abstract

Complex constrained global optimization problems such as optimal actuators placement are extremely challenging. Such challenges, including nonlinearity and nonstationarity of engineering response surfaces, hinder the use of ordinary constrained Bayesian optimization (CBO) techniques with standard Gaussian processes as surrogate models. To overcome those challenges, we propose a physics-constrained Bayesian optimization with multi-layer deep structured Gaussian processes, <i>MGP-CBO</i>. Specifically, we introduce a surrogate model with a multi-layer deep Gaussian process (MGP) mean function. The hierarchical structure of our model enables the applicability of constrained Bayesian optimization to complex nonlinear and nonstationary processes. The deep Gaussian process regression model, <i>MGP</i>, can efficiently and effectively represent the response surface function between actuators and dimensional deformations, thus yielding a better estimated global optimum in a shorter computational time. The proposed <i>MGP-CBO</i> model can realize faster convergence to the global optimum with lower constraint violations. Through extensive evaluations carried out on synthetic problems and a real-world engineering design problem, we show that <i>MGP-CBO</i> outperforms existing benchmarks. Although we use the optimal actuators placement as a demonstration example, the proposed <i>MGP-CBO</i> model can be applied to other complex nonstationary engineering optimization problems. <i>Note to Practitioners</i>&#x2014;Bayesian optimization is a widely used sequential design strategy for engineering optimization because it does not rely on functional forms of response surfaces. This paper helps address two questions in practice: (i) how to incorporate physics constraints into Bayesian optimization. (ii) How to do Bayesian optimization when the systems have hierarchical structures. In practice, the hierarchical system structure is ubiquitous, and the engineering optimization is constrained by physical laws or special requirements. Therefore, the proposed physics-constrained Bayesian optimization with a multi-layer Gaussian process could provide a new tool for engineering design optimization problems. The computational convergence and complexity have been investigated. The proposed method is applicable to broad complex and nonstationary engineering optimization problems.