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1. Early-Stage Uncertainty: Effects of Robust Convex Optimization on Design Exploration

   https://doi.org/10.1115/DETC2020-22626  

   Pillai, P.; Burnell, E.; Wang, X.; Yang, M. C. (August 2020, Proceedings of the ASME Design Engineering Technical Conferences)

   null (Ed.)

   Engineers design for an inherently uncertain world. In the early stages of design processes, they commonly account for such uncertainty either by manually choosing a specific worstcase and multiplying uncertain parameters with safety factors, or by using Monte Carlo simulations to estimate the probabilistic boundaries in which their design is feasible. The safety factors of this first practice are determined by industry and organizational standards, providing an inexpressive account of uncertainty; the second practice is time intensive, requiring the development of separate testing infrastructure. In theory, robust optimization provides an alternative, allowing set based conceptualizations of uncertainty to be represented during model development as optimizable design parameters. How these theoretical benefits translate to design practice has not previously been studied. In this work, we analyzed present use of geometric programs as design models in the aerospace industry to determine the current state-of-the-art, then conducted a human-subjects experiment to investigate how various mathematical representations of uncertainty affect design space exploration. We found that robust optimization led to far more efficient explorations of possible designs with only small differences in experimental participant’s understandings of their model. Specifically, the Pareto frontier of a typical participant using robust optimization left less performance “on the table” across various levels of risk than the very best frontiers of participants using industry-standard practices. 

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2. A Data-Driven Approach for Process Optimization of Metallic Additive Manufacturing Under Uncertainty

   https://doi.org/10.1115/1.4043798  

   Wang, Zhuo; Liu, Pengwei; Xiao, Yaohong; Cui, Xiangyang; Hu, Zhen; Chen, Lei (August 2019, Journal of Manufacturing Science and Engineering)

   The presence of various uncertainty sources in metal-based additive manufacturing (AM) process prevents producing AM products with consistently high quality. Using electron beam melting (EBM) of Ti-6Al-4V as an example, this paper presents a data-driven framework for process parameters optimization using physics-informed computer simulation models. The goal is to identify a robust manufacturing condition that allows us to constantly obtain equiaxed materials microstructures under uncertainty. To overcome the computational challenge in the robust design optimization under uncertainty, a two-level data-driven surrogate model is constructed based on the simulation data of a validated high-fidelity multiphysics AM simulation model. The robust design result, indicating a combination of low preheating temperature, low beam power, and intermediate scanning speed, was acquired enabling the repetitive production of equiaxed structure products as demonstrated by physics-based simulations. Global sensitivity analysis at the optimal design point indicates that among the studied six noise factors, specific heat capacity and grain growth activation energy have the largest impact on the microstructure variation. Through this exemplar process optimization, the current study also demonstrates the promising potential of the presented approach in facilitating other complicate AM process optimizations, such as robust designs in terms of porosity control or direct mechanical property control. 

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3. Conserving Biodiversity via Adjustable Robust Optimization

   Ye, Yingxiao; Doehring, Christopher; Georghiou, Angelos; Robinson, H.; Vayanos, P. (January 2022, Proceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2022), Workshop on Autonomous Agents for Social Good)

   Human development is a threat to biodiversity and conservation organizations (COs) are purchasing land to protect areas for biodiversity preservation. COs have limited budgets and cannot purchase all the land necessary to perfectly preserve biodiversity, and human activities are uncertain, so exact developments are unpredictable. We propose a multistage, robust optimization problem with a data-driven hierarchical-structured uncertainty set which captures the endogenous nature of the binary (0-1) human land use uncertain parameters to help COs choose land parcels to purchase to minimize the worst-case human impact on biodiversity. In the proposed approach, the problem is formulated as a game between COs, which choose parcels to protect with limited budgets, and the human development, which will maximize the loss to the unprotected parcels. We leverage the cellular automata model to simulate the development based on climate data, land characteristics, and human land use data. We use the simulation to build data-driven uncertainty sets. We demonstrate that an equivalent formulation of the problem can be obtained that presents exogenous uncertainty only and where uncertain parameters only appear in the objective. We leverage this reformulation to propose a conservative $$K$$-adaptability reformulation of our problem that can be solved routinely by off-the-shelf solvers like Gurobi or CPLEX. The numerical results based on real data show that the proposed method reduces conservation loss by 19.46% on average compared to standard approaches used in practice for biodiversity conservation. 

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4. Inferring the basal sliding coefficient field for the Stokes ice sheet model under rheological uncertainty

   https://doi.org/10.5194/tc-15-1731-2021  

   Babaniyi, Olalekan; Nicholson, Ruanui; Villa, Umberto; Petra, Noémi (January 2021, The Cryosphere)

   null (Ed.)

   Abstract. We consider the problem of inferring the basal sliding coefficientfield for an uncertain Stokes ice sheet forward model from syntheticsurface velocity measurements. The uncertainty in the forward modelstems from unknown (or uncertain) auxiliary parameters (e.g., rheologyparameters). This inverse problem is posed within the Bayesianframework, which provides a systematic means of quantifyinguncertainty in the solution. To account for the associated modeluncertainty (error), we employ the Bayesian approximation error (BAE)approach to approximately premarginalize simultaneously over both thenoise in measurements and uncertainty in the forward model. We alsocarry out approximative posterior uncertainty quantification based ona linearization of the parameter-to-observable map centered at themaximum a posteriori (MAP) basal sliding coefficient estimate, i.e.,by taking the Laplace approximation. The MAP estimate is found byminimizing the negative log posterior using an inexact Newtonconjugate gradient method. The gradient and Hessian actions to vectorsare efficiently computed using adjoints. Sampling from theapproximate covariance is made tractable by invoking a low-rankapproximation of the data misfit component of the Hessian. We studythe performance of the BAE approach in the context of three numericalexamples in two and three dimensions. For each example, the basalsliding coefficient field is the parameter of primary interest whichwe seek to infer, and the rheology parameters (e.g., the flow ratefactor or the Glen's flow law exponent coefficient field) representso-called nuisance (secondary uncertain) parameters. Our resultsindicate that accounting for model uncertainty stemming from thepresence of nuisance parameters is crucial. Namely our findingssuggest that using nominal values for these parameters, as is oftendone in practice, without taking into account the resulting modelingerror, can lead to overconfident and heavily biased results. We alsoshow that the BAE approach can be used to account for the additionalmodel uncertainty at no additional cost at the online stage. 

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5. Optimization Under Uncertainty Versus Algebraic Heuristics: A Research Method for Comparing Computational Design Methods

   Binder, William R.; Paredis, Christiaan J.J. (August 2017, Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   In this paper, we introduce a research method for comparing computational design methods. This research method addresses the challenge of measuring the difference in performance of different design methods in a way that is fair and unbiased with respect to differences in modeling abstraction, accuracy and uncertainty representation. The method can be used to identify the conditions under which each design method is most beneficial. To illustrate the research method, we compare two design methods for the design of a pressure vessel: 1) an algebraic approach, based on the ASME pressure vessel code, which accounts for uncertainty implicitly through safety factors, and 2) an optimization-based, expected-utility maximization approach which accounts for uncertainty explicitly. The computational experiments initially show that under some conditions the algebraic heuristic surprisingly outperforms the optimization-based approach. Further analysis reveals that an optimization-based approach does perform best as long as the designer applies good judgment during uncertainty elicitation. An ignorant or overly confident designer is better off using safety factors. 

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