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Department of Statistics

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https://hdl.handle.net/10919/24213

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Browsing Department of Statistics by Author "AlBahar, Areej"

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    Physics-Constrained Bayesian Optimization for Optimal Actuators Placement in Composite Structures Assembly
    AlBahar, Areej; Kim, Inyoung; Wang, Xing; Yue, Xiaowei (IEEE, 2022-08)
    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.
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    A Robust Asymmetric Kernel Function for Bayesian Optimization, With Application to Image Defect Detection in Manufacturing Systems
    AlBahar, Areej; Kim, Inyoung; Yue, Xiaowei (IEEE, 2021-09-29)
    Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive to evaluate. To tackle this challenge, Bayesian optimization (BO), which conducts sequential design via a posterior distribution over the objective function, is a critical method used to find the global optimum of black-box functions. Kernel functions play an important role in shaping the posterior distribution of the estimated function. The widely used kernel function, e.g., radial basis function (RBF), is very vulnerable and susceptible to outliers; the existence of outliers is causing its Gaussian process (GP) surrogate model to be sporadic. In this article, we propose a robust kernel function, asymmetric elastic net radial basis function (AEN-RBF). Its validity as a kernel function and computational complexity are evaluated. When compared with the baseline RBF kernel, we prove theoretically that AEN-RBF can realize smaller mean squared prediction error under mild conditions. The proposed AEN-RBF kernel function can also realize faster convergence to the global optimum. We also show that the AEN-RBF kernel function is less sensitive to outliers, and hence improves the robustness of the corresponding BO with GPs. Through extensive evaluations carried out on synthetic and real-world optimization problems, we show that AEN-RBF outperforms the existing benchmark kernel functions.