Physics-Constrained Bayesian Optimization for Optimal Actuators Placement in Composite Structures Assembly
Physics-Constrained Bayesian Optimization for Optimal Actuators Placement in Composite Structures Assembly
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DOI：
10.1109/tase.2022.3200376
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发表时间：
2023-10
影响因子：
5.6
通讯作者：
Areej AlBahar;Inyoung Kim;Xingang Wang;Xiaowei Yue
中科院分区：
文献类型：
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作者：
Areej AlBahar;Inyoung Kim;Xingang Wang;Xiaowei Yue
复杂的约束全局优化问题（例如最佳执行器放置）极具挑战性。这些挑战，包括工程响应面的非线性和非平稳性，阻碍了以标准高斯过程作为替代模型的普通约束贝叶斯优化 (CBO) 技术的使用。为了克服这些挑战，我们提出了一种具有多层深层结构高斯过程的物理约束贝叶斯优化，MGP-CBO。具体来说，我们引入了具有多层深度高斯过程（MGP）均值函数的代理模型。我们模型的层次结构使得约束贝叶斯优化适用于复杂的非线性和非平稳过程。深度高斯过程回归模型 MGP 可以高效地表示执行器和尺寸变形之间的响应面函数，从而在更短的计算时间内产生更好的估计全局最优值。所提出的MGP-CBO模型可以以较低的约束违规实现更快地收敛到全局最优值。通过对综合问题和实际工程设计问题进行广泛评估，我们表明 MGP-CBO 优于现有基准。尽管我们使用最佳执行器放置作为演示示例，但所提出的 MGP-CBO 模型可以应用于其他复杂的非平稳工程优化问题。从业者注意事项——贝叶斯优化是一种广泛使用的工程优化顺序设计策略，因为它不依赖于响应面的函数形式。本文有助于解决实践中的两个问题：（i）如何将物理约束纳入贝叶斯优化。 (ii) 当系统具有层次结构时如何进行贝叶斯优化。实践中，递阶系统结构普遍存在，工程优化受到物理定律或特殊要求的约束。因此，所提出的具有多层高斯过程的物理约束贝叶斯优化可以为工程设计优化问题提供新的工具。研究了计算收敛性和复杂性。所提出的方法适用于广泛的复杂和非平稳工程优化问题。
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, MGP-CBO. 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, MGP, 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 MGP-CBO 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 MGP-CBO outperforms existing benchmarks. Although we use the optimal actuators placement as a demonstration example, the proposed MGP-CBO model can be applied to other complex nonstationary engineering optimization problems. Note to Practitioners—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.