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Summary: A challenge in engineering design is to choose suitable objectives and constraints from many quantities of interest, while ensuring an optimization is both meaningful and computationally tractable. We propose an optimization formulation that can take account of more quantities of interest than existing formulations, without reducing the tractability of the problem. This formulation searches for designs that are optimal with respect to a binary relation within the set of designs that are optimal with respect to another binary relation. We then propose a method of finding such designs in a single optimization by defining an overall ranking function to use in optimizers, reducing the cost required to solve this formulation. In a design under uncertainty problem, our method obtains the most robust design that is not stochastically dominated faster than a multiobjective optimization. In a car suspension design problem, our method obtains superior designs according to a k‐optimality condition than previously suggested multiobjective approaches to this problem. In an airfoil design problem, our method obtains designs closer to the true lift/drag Pareto front using the same computational budget as a multiobjective optimization. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the challenge of design optimization under uncertainty when the designer only has limited data to characterize uncertain variables. We demonstrate that the error incurred when estimating a probability distribution from limited data affects the out‐of‐sample performance (ie, performance under the true distribution) of optimized designs. We demonstrate how this can be mitigated by reformulating the engineering design problem as a distributionally robust optimization (DRO) problem. We present computationally efficient algorithms for solving the resulting DRO problem. The performance of the DRO approach is explored in a practical setting by applying it to an acoustic horn design problem. The DRO approach is compared against traditional approaches to optimization under uncertainty, namely, sample‐average approximation and multiobjective optimization incorporating a risk reduction objective. In contrast with the multiobjective approach, the proposed DRO approach does not use an explicit risk reduction objective but rather specifies a so‐called ambiguity set of possible distributions and optimizes against the worst‐case distribution in this set. Our results show that the DRO designs, in some cases, significantly outperform those designs found using the sample‐average or the multiobjective approach. [ABSTRACT FROM AUTHOR]

Summary: In optimization under uncertainty for engineering design, the behavior of the system outputs due to uncertain inputs needs to be quantified at each optimization iteration, but this can be computationally expensive. Multifidelity techniques can significantly reduce the computational cost of Monte Carlo sampling methods for quantifying the effect of uncertain inputs, but existing multifidelity techniques in this context apply only to Monte Carlo estimators that can be expressed as a sample average, such as estimators of statistical moments. Information reuse is a particular multifidelity method that treats previous optimization iterations as lower fidelity models. This work generalizes information reuse to be applicable to quantities whose estimators are not sample averages. The extension makes use of bootstrapping to estimate the error of estimators and the covariance between estimators at different fidelities. Specifically, the horsetail matching metric and quantile function are considered as quantities whose estimators are not sample averages. In an optimization under uncertainty for an acoustic horn design problem, generalized information reuse demonstrated computational savings of over 60% compared with regular Monte Carlo sampling. [ABSTRACT FROM AUTHOR]

Abstract: For many engineering systems, current design methodologies do not adequately quantify and manage uncertainty as it arises during the design process, which can lead to unacceptable risks, increases in programmatic cost, and schedule overruns. This paper develops new sensitivity analysis methods that can be used to better understand and mitigate the effects of uncertainty in system design. In particular, a new entropy‐based sensitivity analysis methodology is introduced, which apportions output uncertainty into contributions due to not only the variance of input factors and their interactions, but also to features of the underlying probability distributions that are related to distribution shape and extent. Local sensitivity analysis techniques are also presented, which provide computationally inexpensive estimates of the change in output uncertainty resulting from design modifications. The proposed methods are demonstrated on an engineering example to show how they can be used in the design context to systematically manage uncertainty budgets—which specify the allowable level of uncertainty for a system—by helping to identify design alternatives, evaluate trade‐offs between available options, and guide decisions regarding the allocation of resources. [ABSTRACT FROM AUTHOR]

This paper presents a quantitative risk assessment for design and development of a renewable energy system to support decision-making among design alternatives. Throughout the decision-making phases, resources are allocated among exploration and exploitation tasks to manage the uncertainties in design parameters and to adapt designs to new information for enhanced performance. The resource allocation problem is formulated as a sequential decision feedback loop for a quantitative analysis of exploration and exploitation trade-offs. We support decision-making by tracking the evolution of uncertainties, the sensitivity of design alternatives to the uncertainties, and the performance, reliability, and robustness of each design. This is achieved by analyzing the uncertainties in the wind resource, the turbine performance and operation, and the models that define the power curve and wake deficiency. Comparison of the performance, reliability, and robustness of aligned and staggered turbine layouts before and after wind assessment experiments aids in improving micro-siting decisions. The results demonstrate that design decisions can be supported by efficiently allocating resources towards improved estimates of achievable design objectives and by quantitatively assessing the risk in meeting those objectives. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. This paper proposes a data-driven projection-based model reduction technique to reduce this computational cost. The proposed technique has two distinctive features. First, the model reduction strategy is tailored to inverse problems: the snapshots used to construct the reduced-order model are computed adaptively from the posterior distribution. Posterior exploration and model reduction are thus pursued simultaneously. Second, to avoid repeated evaluations of the full-scale numerical model as in a standard MCMC method, we couple the full-scale model and the reduced-order model together in the MCMC algorithm. This maintains accurate inference while reducing its overall computational cost. In numerical experiments considering steady-state flow in a porous medium, the data-driven reduced-order model achieves better accuracy than a reduced-order model constructed using the classical approach. It also improves posterior sampling efficiency by several orders of magnitude compared with a standard MCMC method. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY To support effective decision making, engineers should comprehend and manage various uncertainties throughout the design process. Unfortunately, in today's modern systems, uncertainty analysis can become cumbersome and computationally intractable for one individual or group to manage. This is particularly true for systems comprised of a large number of components. In many cases, these components may be developed by different groups and even run on different computational platforms. This paper proposes an approach for decomposing the uncertainty analysis task among the various components comprising a feed-forward system and synthesizing the local uncertainty analyses into a system uncertainty analysis. Our proposed decomposition-based multicomponent uncertainty analysis approach is shown to be provably convergent in distribution under certain conditions. The proposed method is illustrated on quantification of uncertainty for a multidisciplinary gas turbine system and is compared to a traditional system-level Monte Carlo uncertainty analysis approach. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY It is important to design robust and reliable systems by accounting for uncertainty and variability in the design process. However, performing optimization in this setting can be computationally expensive, requiring many evaluations of the numerical model to compute statistics of the system performance at every optimization iteration. This paper proposes a multifidelity approach to optimization under uncertainty that makes use of inexpensive, low-fidelity models to provide approximate information about the expensive, high-fidelity model. The multifidelity estimator is developed based on the control variate method to reduce the computational cost of achieving a specified mean square error in the statistic estimate. The method optimally allocates the computational load between the two models based on their relative evaluation cost and the strength of the correlation between them. This paper also develops an information reuse estimator that exploits the autocorrelation structure of the high-fidelity model in the design space to reduce the cost of repeatedly estimating statistics during the course of optimization. Finally, a combined estimator incorporates the features of both the multifidelity estimator and the information reuse estimator. The methods demonstrate 90% computational savings in an acoustic horn robust optimization example and practical design turnaround time in a robust wing optimization problem. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

There are many 'compelling possibilities' for computational fluid dynamics (CFD) in architecture, as demonstrated by its successful adoption in the aerospace, automotive and product manufacturing industries. Sawako Kaijima, Roland Bouffanais, Karen Willcox and Suresh Naidu of ARCH-CFD, a research initiative at the International Design Centre established by the Singapore University of Technology and Design (SUTD) and the Massachusetts Institute of Technology (MIT), explore CFD's potential. [ABSTRACT FROM AUTHOR]