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

Valladares, Homero; Tovar, Andrés

doi:10.4271/2022-01-0790

Cited by 3 publications

References 24 publications

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Multi-Objective Bayesian Optimization Supported by an Expected Pareto Distance Change

Valladares

Tovar

2023

Journal of Mechanical Design

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The solution to global (a posteriori) multi-objective optimization problems traditionally relies on population-based algorithms, which are very effective in generating a Pareto front. Unfortunately, due to the high number of function evaluations, these methods are of limited use in problems that involve expensive black-box functions. In recent years, multi-objective Bayesian optimization has emerged as a powerful alternative; however, in many applications, these methods fail to generate a diverse and well-spread Pareto front. To address this limitation, our work introduces a novel acquisition function (AF) for multi-objective Bayesian optimization that produces more informative acquisition landscapes. The proposed AF comprises two terms, namely, a distance-based metric and a diversity index. The distance-based metric, referred to as the expected Pareto distance change, promotes the evaluation of high-performing designs and repels low-performing design zones. The diversity term prevents the evaluation of designs that are similar to the ones contained in the current sampling plan. The proposed AF is studied using seven analytical problems and in the design optimization of sandwich composite armors for blast mitigation, which involves expensive finite element simulations. The results show that the proposed AF generates high-quality Pareto sets outperforming well-established methods such as the Euclidean-based expected improvement function. The proposed AF is also compared with respect to a recently proposed multi-objective approach. The difference in their performance is problem dependent.

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Multi-Objective Bayesian Optimization Supported by an Expected Pareto Distance Change

Valladares

Tovar

2023

Journal of Mechanical Design

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

Valladares¹,

Tovar²

2022

SAE Int. J. Adv. & Curr. Prac. in Mobility

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<div class="section abstract"><div class="htmlview paragraph">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.</div></div>

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Multi-Objective Bayesian Optimization Supported by Deep Gaussian Processes

Valladares¹,

Tovar²

2023

SAE Technical Paper Series

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<div class="section abstract"><div class="htmlview paragraph">A common scenario in engineering design is the evaluation of expensive black-box functions: simulation codes or physical experiments that require long evaluation times and/or significant resources, which results in lengthy and costly design cycles. In the last years, Bayesian optimization has emerged as an efficient alternative to solve expensive black-box function design problems. Bayesian optimization has two main components: a probabilistic surrogate model of the black-box function and an acquisition functions that drives the design process. Successful Bayesian optimization strategies are characterized by accurate surrogate models and well-balanced acquisition functions. The Gaussian process (GP) regression model is arguably the most popular surrogate model in Bayesian optimization due to its flexibility and mathematical tractability. GP regression models are defined by two elements: the mean and covariance functions. In some modeling scenarios, the prescription of proper mean and covariance functions can be a difficult task, e.g., when modeling non-stationary functions and heteroscedastic noise. Motivated by recent advancements in the deep learning community, this study explores the implementation of deep Gaussian processes (DGPs) as surrogate models for Bayesian optimization in order to build flexible predictive models from simple mean and covariance functions. The proposed methodology employs DGPs as the surrogate models and the Euclidean-based expected improvement as the acquisition function. This approach is compared with a strategy that employs GP regression models. These methodologies solve two analytical problems and one engineering problem: the design of sandwich composite armors for blast mitigation. The analytical problems involve non-convex and segmented Pareto fronts. The engineering problem involves expensive finite element simulations, three design variables, and two expensive black-box function objectives. The results show that the architecture of the DGP model plays an important role in the performance of the optimization approach. If the DGP architecture is adequate, the implementation of DGPs produces satisfactory results; otherwise, the use of GP regression models is preferable.</div></div>

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

Cited by 3 publications

References 24 publications

Multi-Objective Bayesian Optimization Supported by an Expected Pareto Distance Change

Multi-Objective Bayesian Optimization Supported by an Expected Pareto Distance Change

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

Multi-Objective Bayesian Optimization Supported by Deep Gaussian Processes

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