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Results for “optimization under uncertainty”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.

Newman, Perry A.↗
DOE OSTI2024

Surrogate-assisted optimization under uncertainty for design for remanufacturing considering material price volatility

Remanufacturing is a well-established end-of-life (EOL) strategy that promises significant savings in energy and carbon emissions. However, the current design practices are not remanufacturing-inclusive, i.e., the majority of products are designed for a single life cycle. As a result, potential products that can sustain multiple life cycles are deprived of additional benefits of being designed for remanufacturing, such as reduced material usage, lower cost, and improved environmental impact. Moreover, the uncertainty in design, material selection, and economics are not considered to produce remanufacturable designs. Accordingly, this research proposes a design for remanufacturing (DfRem) framework that accounts for design uncertainty and material price volatility. The framework systematically explores the design space, performs design optimization under uncertainty, followed by topology optimization to provide additional mass savings, and finally, a price volatility analysis for plausible design material choices. The candidate designs are evaluated based on their design mass, material price volatility, failure mode characteristics, carbon footprint, and embodied energy impacts. The proposed framework's utility is demonstrated via the use of an engine cylinder head case study subjected to thermo-mechanical loads along with fatigue and wear failure. Considering grey cast iron and aluminum alloy as the design material choices, it was found that the cast iron design reduced the initial design mass by 6% as opposed to a 5% decrease for aluminum. On the other hand, about 8% area of the cast iron design failed due to fatigue, compared to 3% for aluminum. Here, we further observed that although the aluminum design provided better mechanical performance than the cast iron design, this material was more expensive and volatile in price.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Pareto solutions in multicriteria optimization under uncertainty

We present and analyze several definitions of Pareto optimality for multicriteria optimization or decision problems with uncertainty primarily in their objective function values. In comparison to related notions of Pareto robustness, we first provide a full characterization of an alternative efficient set hierarchy that is based on six different ordering relations both with respect to the multiple objectives and a possibly finite, countably infinite or uncountable number of scenarios. We then establish several scalarization results for the generation of the corresponding efficient points using generalized weighted-sum and epsilon-constraint techniques. Finally, we leverage these scalarization results to also derive more general conditions for the existence of efficient points in each of the corresponding optimality classes, under suitable assumptions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Wake steering optimization under uncertainty

Turbines in wind power plants experience significant power losses when wakes from upstream turbines affect the energy production of downstream turbines. A promising plant-level control strategy to reduce these losses is wake steering, where upstream turbines are yawed to direct wakes away from downstream turbines. However, there are significant uncertainties in many aspects of the wake steering problem. For example, infield sensors do not give perfect information, and inflow to the plant is complex and difficult to forecast with available information, even over short time periods. Here, we formulate and solve an optimization under uncertainty (OUU) problem for determining optimal plant-level wake steering strategies in the presence of independent uncertainties in the direction, speed, turbulence intensity, and shear of the incoming wind, as well as in turbine yaw positions. The OUU wake steering strategy is first examined for a two-turbine test case to explore the impacts of different types of inflow uncertainties, and it is then demonstrated for a more realistic 11-turbine wind power plant. Of the sources of uncertainty considered, we find that wake steering strategies are most sensitive to uncertainties in the wind speed and direction. When maximizing expected power production, the OUU strategy also tends to favor smaller yaw angles, which have been shown in previous work to reduce turbine loading. Ultimately, the plant-level wake steering strategy formulated using an OUU approach yields 0.48?% more expected annual energy production for the 11-turbine wind plant than a strategy that neglects uncertainty when considering stochastic inputs. Thus, not only does the present OUU strategy produce more power in realistic conditions, but it also reduces risk by prescribing strategies that call for less extreme yaw angles.

17 WIND ENERGY↗
DOE OSTI2017

A framework for modeling and optimizing dynamic systems under uncertainty

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming. We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Equation of State Optimization and Uncertainty Quantization: Implementation in the LANL EOS Production Code OpenSesame

We detail the approaches of particle swarm optimization and Bayesian inference through Markov chain Monte Carlo for equation of state development. This work includes formulation of the modeling for the equation of state, numeric optimization of the parametric models via particle swarm optimization, and generation of probability distributions of equations of state from Markov chain Monte Carlo.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Shape optimization under uncertainty for rotor blades of horizontal axis wind turbines

We present a computational framework for the shape optimization of a Horizontal-Axis Wind Turbine (HAWT) rotor blade under uncertainty. Our framework integrates aerodynamic simulations based on the blade element method which utilizes reduced order models of the blade structure and wind load with design sensitivity analysis and nonlinear programming. The wind velocity is modeled as a stochastic process to account for variations in time and space. An additional stochastic process accounts for uncertainties in the structural material properties. The uncertainty propagation is based on a non-intrusive polynomial chaos expansion that allows accurate estimation of stochastic performance metrics such as generated power and structural compliance. Sensitivities of cost and constraint functions with respect to shape parameters namely twist angles are computed with an efficient scheme to enable gradient based optimization. To demonstrate the effect of uncertainty, designs obtained from optimization under uncertainty are compared to those obtained from deterministic optimization.

42 ENGINEERING↗
DOE OSTI2019

An Efficient, Globally Convergent Method for Optimization Under Uncertainty Using Adaptive Model Reduction and Sparse Grids

We present a new approach to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed: (1) stochastic collocation based on dimension-adaptive sparse grids (SGs), which approximates the stochastic objective function with a limited number of quadrature nodes, and (2) projection-based reduced-order models (ROMs), which generate efficient approximations to PDE solutions. These two sources of inexactness lead to inexact objective function and gradient evaluations, which are managed by a trust-region method that guarantees global convergence by adaptively refining the SG and ROM until a proposed error indicator drops below a tolerance specified by trust-region convergence theory. A key feature of the proposed method is that the error indicator---which accounts for errors incurred by both the SG and ROM---must be only an asymptotic error bound, i.e., a bound that holds up to an arbitrary constant that need not be computed. This allows the approach to be applicable to a wide range of problems, including those where sharp, computable error bounds are not available; this distinguishes the proposed method from previous works. Numerical experiments performed on a model problem from optimal flow control under uncertainty verify global convergence of the method and demonstrate the method's ability to outperform previously proposed alternatives.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2014

Integrated Arrival and Departure Schedule Optimization Under Uncertainty

In terminal airspace, integrating arrivals and departures with shared waypoints provides the potential of improving operational efficiency by allowing direct routes when possible. Incorporating stochastic evaluation as a post-analysis process of deterministic optimization, and imposing a safety buffer in deterministic optimization, are two ways to learn and alleviate the impact of uncertainty and to avoid unexpected outcomes. This work presents a third and direct way to take uncertainty into consideration during the optimization. The impact of uncertainty was incorporated into cost evaluations when searching for the optimal solutions. The controller intervention count was computed using a heuristic model and served as another stochastic cost besides total delay. Costs under uncertainty were evaluated using Monte Carlo simulations. The Pareto fronts that contain a set of solutions were identified and the trade-off between delays and controller intervention count was shown. Solutions that shared similar delays but had different intervention counts were investigated. The results showed that optimization under uncertainty could identify compromise solutions on Pareto fonts, which is better than deterministic optimization with extra safety buffers. It helps decision-makers reduce controller intervention while achieving low delays.

stochastic optimization↗
NASA NTRS2004

Using High Resolution Design Spaces for Aerodynamic Shape Optimization Under Uncertainty

This paper explains why high resolution design spaces encourage traditional airfoil optimization algorithms to generate noisy shape modifications, which lead to inaccurate linear predictions of aerodynamic coefficients and potential failure of descent methods. By using auxiliary drag constraints for a simultaneous drag reduction at all design points and the least shape distortion to achieve the targeted drag reduction, an improved algorithm generates relatively smooth optimal airfoils with no severe off-design performance degradation over a range of flight conditions, in high resolution design spaces parameterized by cubic B-spline functions. Simulation results using FUN2D in Euler flows are included to show the capability of the robust aerodynamic shape optimization method over a range of flight conditions.

Li, Wu↗
NASA NTRS2000

Parameterization of Model Validating Sets for Uncertainty Bound Optimizations

Given measurement data, a nominal model and a linear fractional transformation uncertainty structure with an allowance on unknown but bounded exogenous disturbances, easily computable tests for the existence of a model validating uncertainty set are given. Under mild conditions, these tests are necessary and sufficient for the case of complex, nonrepeated, block-diagonal structure. For the more general case which includes repeated and/or real scalar uncertainties, the tests are only necessary but become sufficient if a collinearity condition is also satisfied. With the satisfaction of these tests, it is shown that a parameterization of all model validating sets of plant models is possible. The new parameterization is used as a basis for a systematic way to construct or perform uncertainty tradeoff with model validating uncertainty sets which have specific linear fractional transformation structure for use in robust control design and analysis. An illustrative example which includes a comparison of candidate model validating sets is given.

Lim, K. B.↗
DOE OSTI2023

Optimization under uncertainty of a hybrid waste tire and natural gas feedstock flexible polygeneration system using a decomposition algorithm

Market uncertainties motivate the development of flexible polygeneration systems that are able to adjust operating conditions to favor production of the most profitable product portfolio. However, this operational flexibility comes at the cost of higher capital expenditure. A scenario-based two-stage stochastic nonconvex Mixed-Integer Nonlinear Programming (MINLP) approach lends itself naturally to optimizing these trade-offs. This work studies the optimal design and operation under uncertainty of a hybrid feedstock flexible polygeneration system producing electricity, methanol, dimethyl ether, olefins or liquefied (synthetic) natural gas. A recently developed C++ based software framework (named GOSSIP) is used for modeling the optimization problem as well as its efficient solution using the Nonconvex Generalized Benders Decomposition (NGBD) algorithm. Two different cases are studied: The first uses estimates of the means and variances of the uncertain parameters from historical data, whereas the second assesses the impact of increased uncertain parameter volatility. The value of implementing flexible designs characterized by the value of the stochastic solution (VSS) is in the range of 260–405 M$ for a scale of approximately 893 MW of thermal input. Increased price volatility around the same mean results in higher expected net present value and VSS as operational flexibility allows for asymmetric exploitation of price peaks.

42 ENGINEERING↗
DOE OSTI2025

Surrogate-driven design optimization with uncertainty constraints in Monte Carlo simulations

In multi-objective design tasks, the computational cost increases rapidly when high-fidelity simulations are used to evaluate objective functions. Surrogate models help mitigate this cost by approximating the simulation output, simplifying the design process. However, under high uncertainty, surrogate models trained on noisy data can produce inaccurate predictions, as their performance depends heavily on the quality of training data. This study investigates the impact of data uncertainty on two multi-objective design problems modelled using Monte Carlo transport simulations: a neutron moderator and an ion-to-neutron converter. For each, a grid search was performed using five different tally uncertainty levels to generate training data for neural network surrogate models. These models were then optimized using NSGA-III. The recovered Pareto-fronts were analyzed across uncertainty levels: in the moderator problem, normalized hypervolume dropped from 0.886 at 1.0% uncertainty to 0.748 at 10% uncertainty, while in the converter problem it remained near 0.50 for all cases. Average simulation times were also compared to evaluate the trade-off between accuracy and computational cost. Results show that the influence of simulation uncertainty is strongly problem-dependent. In the neutron moderator case, higher uncertainties led to exaggerated objective sensitivities and distorted Pareto-fronts, reducing normalized hypervolume. In contrast, the ion-to-neutron converter task was less affected—low-fidelity simulations produced results similar to those from high-fidelity data. These findings suggest that a fixed-fidelity approach is not optimal. Surrogate models can recover the Pareto-front under noisy conditions, and multi-fidelity studies help identify suitable uncertainty levels for each problem to balance efficiency and accuracy.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS2003

Design Optimization of Composite Structures under Uncertainty

Design optimization under uncertainty is computationally expensive and is also challenging in terms of alternative formulation. The work under the grant focused on developing methods for design against uncertainty that are applicable to composite structural design with emphasis on response surface techniques. Applications included design of stiffened composite plates for improved damage tolerance, the use of response surfaces for fitting weights obtained by structural optimization, and simultaneous design of structure and inspection periods for fail-safe structures.

Haftka, Raphael T.↗
DOE OSTI2020

Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation

A methodology for nonintrusive projection-based nonlinear model reduction originally presented by Renganathan et al. is further extended here toward parametric systems with a focus on application to aerospace design. Specifically, the method is extended to address static systems with parametric geometry (that deforms the mesh) in addition to parametric freestream boundary conditions. The main idea is to first perform a transformation on the governing equations such that it is lifted to a higher-dimensional but linear underdetermined system. This enables one to extract the system matrices easily as compared to that of the original nonlinear system. The underdetermined system is closed with a set of model-dependent nonlinear constraints upon which the model reduction is finally performed. The methodology is validated on the subsonic and transonic inviscid flows past the NACA0012 and the RAE2822 airfoils with parametrized shapes. The utility of the approach is further demonstrated by applying it to two common problems in aerospace design, namely, derivative-free global optimization and parametric uncertainty quantification with Monte Carlo sampling. Overall, the methodology is shown to achieve accuracy up to 5% and computational speedup of two to three orders of magnitude relative to the full order model. Comparison against another nonintrusive model reduction method revealed that the proposed approach is more robust, accurate, and retains the consistency between the state variables.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1998

Parameterization of Model Validating Sets for Uncertainty Bound Optimizations

Given experimental data and a priori assumptions on nominal model and a linear fractional transformation uncertainty structure, feasible conditions for model validation is given. All unknown but bounded exogenous inputs are assumed to occur at the plant outputs. With the satisfaction of the feasible conditions for model validation, it is shown that a parameterization of all model validating sets of plant models is possible. The new parameterization can be used as a basis for the development of a systematic way to construct model validating uncertainty models which have specific linear fractional transformation structure for use in robust control design and analysis. The proposed feasible condition (existence) test and the parameterization is computationally attractive as compared to similar tests currently available.

Lim, K. B.↗