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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Design Under Uncertainty with Design-Dependent Uncertain Variables

Uncertainty quantification (UQ) can provide a more robust understanding of a system, leading to better informed decisions earlier in the design process. The additional information that UQ provides can be leveraged during a design optimization process known as design under uncertainty that, when incorporated with multidisciplinary design and optimization, can become computationally infeasible due to the large number of responses required for meaningful results. Previous work addressed reducing the computational expense in design under uncertainty by incorporating analytic derivatives throughout polynomial chaos expansion. Although this allows design under uncertainty to be feasible for more systems, some multidisciplinary systems have design-dependent uncertain variables. This paper details an implementation of design dependent uncertain variables in a manner than preserves derivatives required for efficient gradient-based optimization throughout the process. Two analytic examples of design-dependent uncertain variables are given: the first transforms a uniform uncertain variable with one design variable and the second transforms a normal uncertain variable with two design variables. The polynomial chaos expansion (PCE) results are comparable to both the Monte Carlo (MC) results and the analytic results for the two examples. A case study that maximizes the lift-to-drag ratio with a design-dependence between the wing leading edge sweep angle and uncertain parameter percentage of laminar flow is compared to a MC and alternative optimization formulations. This paper demonstrates that design-dependent uncertain variables are valid and hold throughout PCE.

robust design↗
NASA NTRSDate not supplied

Design Under Uncertainty with Design-Dependent Uncertain Variables

Uncertainty quantification (UQ) can provide a more robust understanding of a system, leading to better informed decisions earlier in the design process. The additional information that UQ provides can be leveraged during a design optimization process known as design under uncertainty that, when incorporated with multidisciplinary design and optimization, can become computationally infeasible due to the large number of responses required for meaningful results. Previous work addressed reducing the computational expense in design under uncertainty by incorporating analytic derivatives throughout polynomial chaos expansion. Although this allows design under uncertainty to be feasible for more systems, some multidisciplinary systems have design-dependent uncertain variables. This paper details an implementation of design dependent uncertain variables in a manner than preserves derivatives required for efficient gradient-based optimization throughout the process. Two analytic examples of design-dependent uncertain variables are given: the first transforms a uniform uncertain variable with one design variable and the second transforms a normal uncertain variable with two design variables. The polynomial chaos expansion (PCE) results are comparable to both the Monte Carlo (MC) results and the analytic results for the two examples. A case study that maximizes the lift-to-drag ratio with a design-dependence between the wing leading edge sweep angle and uncertain parameter percentage of laminar flow is compared to a MC and alternative optimization formulations. This paper demonstrates that design-dependent uncertain variables are valid and hold throughout PCE.

Joanna N Schmidt↗
NASA NTRSDate not supplied

Design Under Uncertainty for Conceptual Aircraft Design Leveraging Analytical Gradients

The purpose of this paper is to extend previously demonstrated methodologies for design under uncertainty, leveraging analytical gradients to higher fidelity analysis for use in conceptual aircraft design. Previous work developed methods to generate analytical derivatives through polynomial chaos expansion, eliminating the need to estimate derivatives via complex step or finite difference. In this research, the authors build upon the methods to include physics-based aircraft design codes for aircraft design under uncertainty. This extends the previous work’s case study, which employed analytical aerodynamics and Breguet range estimations for wing design, to a higher fidelity level. In addition, this work extends previous work on interface development between the Uncertainty Quantification with Polynomial Chaos Expansion (UQPCE) software and Model-Based Systems Analysis and Engineering (MBSA&E) frameworks. This paper will discuss the development work necessary to perform multidisciplinary design under uncertainty as well as demonstrate the mechanics of interfacing UQPCE and conceptual aircraft design tools such as NASA’s Aviary code. In a case study, a conceptual aircraft design under uncertainty was conducted and compared against a traditional deterministic design. When given information about the uncertainty space from UQPCE, the optimizer was able to shape the output distribution and produce a more robust design

UQ↗
NASA NTRSDate not supplied

Design Under Uncertainty for Conceptual Aircraft Design Leveraging Analytical Gradients

The purpose of this paper is to extend previously demonstrated methodologies for design under uncertainty, leveraging analytical gradients to higher fidelity analysis for use in conceptual aircraft design. Previous work developed methods to generate analytical derivatives through polynomial chaos expansion, eliminating the need to estimate derivatives via complex step or finite difference. In this research, the authors build upon the methods to include physics-based aircraft design codes for aircraft design under uncertainty. This extends the previous work’s case study, which employed analytical aerodynamics and Breguet range estimations for wing design, to a higher fidelity level. In addition, this work extends previous work on interface development between the Uncertainty Quantification with Polynomial Chaos Expansion (UQPCE) software and Model-Based Systems Analysis and Engineering (MBSA&E) frameworks. This paper will discuss the development work necessary to perform multidisciplinary design under uncertainty as well as demonstrate the mechanics of interfacing UQPCE and conceptual aircraft design tools such as NASA’s Aviary code. In a case study, a conceptual aircraft design under uncertainty was conducted and compared against a traditional deterministic design. When given information about the uncertainty space from UQPCE, the optimizer was able to shape the output distribution and produce a more robust design.

UQ↗
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.↗
NASA NTRSDate not supplied

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Uncertainty quantification (UQ) is a rapidly growing and evolving discipline, especially within the aerospace community. Performing analysis with UQ can provide decision makers with a wealth of information about a candidate design. However, the value of UQ is fully realized when the information gained during UQ analysis is leveraged in a feedback loop of a design optimization process, often referred to as design under uncertainty. Although design under uncertainty can be a powerful risk mitigation technique, there are a number of roadblocks that prevent its implementation. Two primary factors are computational costs and added complexity of the analysis. High fidelity simulations on the order tens of uncertain variables quickly become computationally infeasible. Also, implementing UQ into an existing multidisciplinary design and optimization (MDO) process often requires extensive knowledge of the UQ methods and careful treatment of the problem formulation. The objective of this work is to address these two primary roadblocks and enable practitioners to efficiently perform design under uncertainty with limited knowledge of the UQ discipline. Methods outlined in this paper demonstrate MDO incorporating UQ into the design process, leveraging an analytic derivative tool chain through the entire optimization. The proposed approach leverages machine learning techniques to generate a differentiable confidence interval output from polynomial chaos models. This technique, coupled with the incorporation of analytical derivatives through the Polynomial Chaos Expansion (PCE) process, eliminates the need to estimate derivatives which are usually obtained from finite difference, complex step, or similar methods. Developing a differentiable confidence interval allows mixed uncertainty problems (both epistemic and aleatory) to be modeled. Without such modeling, these problems cannot accurately predict objective functions containing statistical quantities such as mean and variance. The addition of analytic derivatives to a polynomial chaos-based UQ method decreases the computational costs of performing design under uncertainty by orders of magnitude in comparison with methods such as complex step. The method and codes developed are modular in nature and are a drop-in solution for design under uncertainty within existing MDO problems. A low-fidelity analytical multidisciplinary optimization under uncertainty for a wing design in OpenMDAO is detailed in this paper. This demonstration case will include both objective functions and constraints which are influenced by uncertain parameters.

Ben D Phillips↗
NASA NTRSDate not supplied

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Uncertainty quantification (UQ) is a rapidly growing and evolving discipline, especially within the aerospace community. Performing analysis with UQ can provide decision makers with a wealth of information about a candidate design. However, the value of UQ is fully realized when the information gained during UQ analysis is leveraged in a feedback loop of a design optimization process, often referred to as design under uncertainty. Although design under uncertainty can be a powerful risk mitigation technique, there are a number of roadblocks that prevent its implementation. Two primary factors are computational costs and added complexity of the analysis. High fidelity simulations on the order tens of uncertain variables quickly become computationally infeasible. Also, implementing UQ into an existing multidisciplinary design and optimization (MDO) process often requires extensive knowledge of the UQ methods and careful treatment of the problem formulation. The objective of this work is to address these two primary roadblocks and enable practitioners to efficiently perform design under uncertainty with limited knowledge of the UQ discipline. Methods outlined in this paper demonstrate MDO incorporating UQ into the design process, leveraging an analytic derivative tool chain through the entire optimization. The proposed approach leverages machine learning techniques to generate a differentiable confidence interval output from polynomial chaos models. This technique, coupled with the incorporation of analytical derivatives through the Polynomial Chaos Expansion (PCE) process, eliminates the need to estimate derivatives which are usually obtained from finite difference, complex step, or similar methods. Developing a differentiable confidence interval allows mixed uncertainty problems (both epistemic and aleatory) to be modeled. Without such modeling, these problems cannot accurately predict objective functions containing statistical quantities such as mean and variance. The addition of analytic derivatives to a polynomial chaos-based UQ method decreases the computational costs of performing design under uncertainty by orders of magnitude in comparison with methods such as complex step. The method and codes developed are modular in nature and are a drop-in solution for design under uncertainty within existing MDO problems. A low-fidelity analytical multidisciplinary optimization under uncertainty for a wing design in OpenMDAO is detailed in this paper. This demonstration case will include both objective functions and constraints which are influenced by uncertain parameters.

Ben Phillips↗
NASA NTRSDate not supplied

Efficient Global Optimization with Gradient Finish for Design Under Uncertainty

The Efficient Global Optimization (EGO) algorithm is extended to include a gradient-descent-based finish upon reaching a threshold value of the expected improvement function. Emphasis is placed on efficient evaluation of local gradients using Kriging models during the gradient-based finish to enable application to design under uncertainty (DUU) problems. The modified algorithm is applied to both the well-known Rosenbrock function and a more challenging hypersonic inlet design under uncertainty problem. Results demonstrate improvement in locating the global optimum compared to the classical implementation of EGO, as well as a reduced number of true function evaluations compared to pure gradient-based algorithms. For the Rosenbrock function, a global optimum is returned using an average of 12% fewer function calls than a gradient-based optimizer with comparable tolerances. For the design under uncertainty problem, a global optimum is found using an average of 75% fewer function calls than a gradient-based optimizer. Global Pareto fronts of multiobjective DUU problems are obtained at little additional cost after a single optimization is complete.

Optimization↗
NASA NTRSDate not supplied

Robust Design Under Uncertainty of Hypersonic Inlets

The objective of this work is to optimize scramjet inlet designs under uncertainty at multiple fidelity levels. Optimizations are performed for both deterministic and stochastic conditions. For stochastic conditions, robust design is used to minimize the variance in system performance in addition to optimizing mean system performance. Uncertainty quantification is performed using non-intrusive polynomial chaos. Comparisons are made between low-fidelity analysis and high-fidelity analysis, as well as deterministic optimization and robust optimization. Results indicate that the general design trend of previous inlet optimization techniques is recovered for the external compression portion of an inlet. For the internal compression portion of an inlet, when viscous effects become more significant and boundary layer separation becomes more likely, the optimal trend departs from previous results. Multifidelity uncertainty quantification methods are found to substantially reduce the computation time of robust design while obtaining results that nearly match those of high-fidelity analysis. Robust optimization is found to decrease the standard deviation of throat Mach number by up to 40% compared to deterministic optimization. Changes in the design variables and total turning that lead to robust scramjet inlets are identified and linked back to fundamental physical principles through the theta-beta-Mach function.

Hypersonic↗
NASA NTRS2017

Multifidelity, Multidisciplinary Design Under Uncertainty with Non-Intrusive Polynomial Chaos

The primary objective of this work is to develop an approach for multifidelity uncertainty quantification and to lay the framework for future design under uncertainty efforts. In this study, multifidelity is used to describe both the fidelity of the modeling of the physical systems, as well as the difference in the uncertainty in each of the models. For computational efficiency, a multifidelity surrogate modeling approach based on non-intrusive polynomial chaos using the point-collocation technique is developed for the treatment of both multifidelity modeling and multifidelity uncertainty modeling. Two stochastic model problems are used to demonstrate the developed methodologies: a transonic airfoil model and multidisciplinary aircraft analysis model. The results of both showed the multifidelity modeling approach was able to predict the output uncertainty predicted by the high-fidelity model as a significant reduction in computational cost.

West, Thomas K., IV↗
NASA NTRS2003

Reliability Assessment of a Robust Design Under Uncertainty for a 3-D Flexible Wing

The paper presents reliability assessment results for the robust designs under uncertainty of a 3-D flexible wing previously reported by the authors. Reliability assessments (additional optimization problems) of the active constraints at the various probabilistic robust design points are obtained and compared with the constraint values or target constraint probabilities specified in the robust design. In addition, reliability-based sensitivity derivatives with respect to design variable mean values are also obtained and shown to agree with finite difference values. These derivatives allow one to perform reliability based design without having to obtain second-order sensitivity derivatives. However, an inner-loop optimization problem must be solved for each active constraint to find the most probable point on that constraint failure surface.

Gumbert, Clyde R.↗
NASA NTRS2018

Trim Flight Conditions for a Low-Boom Aircraft Design Under Uncertainty

The purpose of this paper is to investigate the noise generation of a low-boom aircraft design in flight trim conditions under uncertainty. The deflection of control surfaces to maintain a trimmed flight state has the potential to change the perceived loudness at the ground. Furthermore, the uncertainties associated with the control surface deflections can complicate the overall uncertainty quantification. Incorporation of the uncertainties in the prediction of perceived sound levels during the design phase can lead to improved robustness. In this paper, a brief review of low-boom flight trim research is presented. Realistic flight trim conditions requiring control surface deflection are integrated into the current research efforts for uncertainty quantification and vehicle design. In addition, a generalized set of procedures for the characterization of uncertainties in flight trim conditions are introduced. In a case study of the application of these procedures, a 5 decibel average difference in the perceived level of loudness was found between clean (no deflections) and trimmed configurations. Also, uncertainties attributable to control surface deflection were found to account for, on average, over 50% of the total near field uncertainty. Uncertainty discretization methods implemented were able to give more insight into the overall global variances.

Phillips, Ben D↗
NASA NTRS1994

System Design under Uncertainty: Evolutionary Optimization of the Gravity Probe-B Spacecraft

This paper discusses the application of evolutionary random-search algorithms (Simulated Annealing and Genetic Algorithms) to the problem of spacecraft design under performance uncertainty. Traditionally, spacecraft performance uncertainty has been measured by reliability. Published algorithms for reliability optimization are seldom used in practice because they oversimplify reality. The algorithm developed here uses random-search optimization to allow us to model the problem more realistically. Monte Carlo simulations are used to evaluate the objective function for each trial design solution. These methods have been applied to the Gravity Probe-B (GP-B) spacecraft being developed at Stanford University for launch in 1999, Results of the algorithm developed here for GP-13 are shown, and their implications for design optimization by evolutionary algorithms are discussed.

Pullen, Samuel P.↗