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At least 307 records · Page 17

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NASA NTRS2004

Adjoint Formulation for an Embedded-Boundary Cartesian Method

Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation.

Nemec, Marian↗

NASA NTRS1993

Construction and parameterization of all static and dynamic H2-optimal state feedback solutions, optimal fixed modes, and fixed decoupling zeros

This paper considers an H2 optimization problem via state feedback. The class of problems dealt with here are general singular type which have a left invertible transfer matrix function from the control input to the controlled output. This class subsumes the regular H2 optimization problems. The paper constructs and parameterizes all the static and dynamic H2 optimal state feedback solutions. Moreover, all the eigenvalues of an optimal closed-loop system are characterized. All optimal closed-loop systems share a set of eigenvalues which are termed here as the optimal fixed modes. Every H2 optimal controller must assign among the closed-loop eigenvalues the set of optimal fixed modes. This set of optimal fixed modes includes a set of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and locations of pole-zero cancellations present in any H2 optimal design. It is shown that both the sets of optimal fixed modes and optimal fixed decoupling zeros do not vary depending upon whether the static or the dynamic controllers are used.

Chen, Ben M.↗

NASA NTRS1965

Combined optimal control and estimation.

Combined optimization problem, equivalent to dual control problem, considering determination of optimal control policies for plant under random disturbances, using iterative equations

CONTROL SYSTEM↗

DOE OSTI2026

Adaptive Sampling-Based Bi-Fidelity Stochastic Trust Region Method for Stochastic Derivative-Free Optimization

Bi-fidelity stochastic optimization has gained increasing attention as an efficient approach to reduce computational costs by leveraging a low-fidelity (LF) model to optimize an expensive high-fidelity (HF) objective. In this paper, we propose ASTRO-BFDF, an adaptive sampling trust-region method specifically designed for unconstrained bi-fidelity stochastic derivative-free optimization problems. In ASTRO-BFDF, the LF function serves two purposes: (i) to identify better iterates for the HF function when the optimization process indicates a high correlation between them and (ii) to reduce the variance of the HF function estimates using bi-fidelity Monte Carlo (BFMC). The algorithm dynamically determines sample sizes while adaptively choosing between crude Monte Carlo and BFMC to balance the trade-off between optimization and sampling errors. We prove that the iterates generated by ASTRO-BFDF converge to a first-order stationary point almost surely. Additionally, we demonstrate the effectiveness of the proposed algorithm through numerical experiments on synthetic benchmarks and simulation optimization problems involving discrete event systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Modeling plasticity-mediated void growth at the single crystal scale: A physics-informed machine learning approach

Modeling the evolution of voids during plastic flow as well as their effects on plastic dissipation is critical for both component manufacturing and lifetime estimation purposes. To this end, we propose a rate-dependent constitutive model to homogenize the effects of semi-randomly distributed voids on single crystal plasticity whilst capturing void interaction and plastic anisotropy. Here, this present work focuses on the case of face centered cubic crystals to introduce an anisotropic gauge function applicable within the crystal plasticity formalism. The approach combines analytical methods to describe the micromechanics of the system in combination with symbolic regression to capture analytically intractable mechanisms from data. The hybrid framework uses a physics-informed genetic programming-based symbolic regression algorithm to solve a multiform optimization problem simultaneously producing a new gauge function and a new strain rate equation. This is also a multi-objective optimization problem with many competing objectives. A new search and selection step is introduced to the genetic algorithm that promotes convergence toward a global solution that better satisfies all the objectives. Overall, the symbolic equations produced leverage data-driven methods to achieve greater accuracy than comparable alternatives on an analytically intractable problem while maintaining model transparency.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Integrated Transmission-Distribution Multi-Period Switching for Wildfire Risk Mitigation: Improving Speed and Scalability with Distributed Optimization: Preprint

With increasingly severe wildfire conditions driven by climate change, utilities must manage the risk of wildfire ignitions from electric power lines. During "public safety power shutoff'" events, utilities de-energize power lines to reduce wildfire ignition risk, which may result in load shedding. Distributed energy resources provide flexibility that can help support the system to reduce load shedding when lines are de-energized. We investigate a coordinated transmission-distribution optimization problem that balances wildfire risk mitigation and load shedding. We model distribution systems that include battery energy storage systems which may support loads when transmission lines are de-energized. This multi-period integrated transmission-distribution optimal switching problem jointly optimizes line switching decisions, the generators' setpoints, load shedding, and the batteries' states of charge, resulting in significant computational challenges. To improve scalability, we decompose the problem over both space and time and apply a distributed optimization algorithm. Using a large-scale synthetic California test case with realistic distribution models and real wildfire risk data, we show that distributed optimization can solve large-scale multi-period switching problems that are otherwise intractable for centralized solvers. We also discuss challenges and future directions for improving the distributed algorithm's convergence performance as the number of time periods increases.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1972

Rapid optimization of multiple-burn rocket flights.

Different formulations of the fuel optimization problem for multiple burn trajectories are considered. It is shown that certain customary idealizing assumptions lead to an ill-posed optimization problem for which no solution exists. Several ways are discussed for avoiding such difficulties by more realistic problem statements. An iterative solution of the boundary value problem is presented together with efficient coast arc computations, the right end conditions for various orbital missions, and some test results.

Brown, K. R.↗

NASA NTRS2005

Distributed Optimization

We demonstrate a new framework for analyzing and controlling distributed systems, by solving constrained optimization problems with an algorithm based on that framework. The framework is ar. information-theoretic extension of conventional full-rationality game theory to allow bounded rational agents. The associated optimization algorithm is a game in which agents control the variables of the optimization problem. They do this by jointly minimizing a Lagrangian of (the probability distribution of) their joint state. The updating of the Lagrange parameters in that Lagrangian is a form of automated annealing, one that focuses the multi-agent system on the optimal pure strategy. We present computer experiments for the k-sat constraint satisfaction problem and for unconstrained minimization of NK functions.

Macready, William↗

NASA NTRS2002

Overall Traveling-Wave-Tube Efficiency Improved By Optimized Multistage Depressed Collector Design

Depressed Collector Design The microwave traveling wave tube (TWT) is used widely for space communications and high-power airborne transmitting sources. One of the most important features in designing a TWT is overall efficiency. Yet, overall TWT efficiency is strongly dependent on the efficiency of the electron beam collector, particularly for high values of collector efficiency. For these reasons, the NASA Glenn Research Center developed an optimization algorithm based on simulated annealing to quickly design highly efficient multistage depressed collectors (MDC's). Simulated annealing is a strategy for solving highly nonlinear combinatorial optimization problems. Its major advantage over other methods is its ability to avoid becoming trapped in local minima. Simulated annealing is based on an analogy to statistical thermodynamics, specifically the physical process of annealing: heating a material to a temperature that permits many atomic rearrangements and then cooling it carefully and slowly, until it freezes into a strong, minimum-energy crystalline structure. This minimum energy crystal corresponds to the optimal solution of a mathematical optimization problem. The TWT used as a baseline for optimization was the 32-GHz, 10-W, helical TWT developed for the Cassini mission to Saturn. The method of collector analysis and design used was a 2-1/2-dimensional computational procedure that employs two types of codes, a large signal analysis code and an electron trajectory code. The large signal analysis code produces the spatial, energetic, and temporal distributions of the spent beam entering the MDC. An electron trajectory code uses the resultant data to perform the actual collector analysis. The MDC was optimized for maximum MDC efficiency and minimum final kinetic energy of all collected electrons (to reduce heat transfer). The preceding figure shows the geometric and electrical configuration of an optimized collector with an efficiency of 93.8 percent. The results show the improvement in collector efficiency from 89.7 to 93.8 percent, resulting in an increase of three overall efficiency points. In addition, the time to design a highly efficient MDC was reduced from a month to a few days. All work was done in-house at Glenn for the High Rate Data Delivery Program. Future plans include optimizing the MDC and TWT interaction circuit in tandem to further improve overall TWT efficiency.

Vaden, Karl R.↗

NASA NTRS2016

Automated Generation of Finite-Element Meshes for Aircraft Conceptual Design

This paper presents a novel approach for automated generation of fully connected finite-element meshes for all internal structural components and skins of a given wing-body geometry model, controlled by a few conceptual-level structural layout parameters. Internal structural components include spars, ribs, frames, and bulkheads. Structural layout parameters include spar/rib locations in wing chordwise/spanwise direction and frame/bulkhead locations in longitudinal direction. A simple shell thickness optimization problem with two load conditions is used to verify versatility and robustness of the automated meshing process. The automation process is implemented in ModelCenter starting from an OpenVSP geometry and ending with a NASTRAN 200 solution. One subsonic configuration and one supersonic configuration are used for numerical verification. Two different structural layouts are constructed for each configuration and five finite-element meshes of different sizes are generated for each layout. The paper includes various comparisons of solutions of 20 thickness optimization problems, as well as discussions on how the optimal solutions are affected by the stress constraint bound and the initial guess of design variables.

Li, Wu↗

NASA NTRS1985

Constrained optimization for image restoration using nonlinear programming

The constrained optimization problem for image restoration, utilizing incomplete information and partial constraints, is formulated using nonlinear proramming techniques. This method restores a distorted image by optimizing a chosen object function subject to available constraints. The penalty function method of nonlinear programming is used. Both linear or nonlinear object function, and linear or nonlinear constraint functions can be incorporated in the formulation. This formulation provides a generalized approach to solve constrained optimization problems for image restoration. Experiments using this scheme have been performed. The results are compared with those obtained from other restoration methods and the comparative study is presented.

Yeh, C.-L.↗

NASA NTRS1993

Real-time trajectory optimization on parallel processors

A parallel algorithm has been developed for rapidly solving trajectory optimization problems. The goal of the work has been to develop an algorithm that is suitable to do real-time, on-line optimal guidance through repeated solution of a trajectory optimization problem. The algorithm has been developed on an INTEL iPSC/860 message passing parallel processor. It uses a zero-order-hold discretization of a continuous-time problem and solves the resulting nonlinear programming problem using a custom-designed augmented Lagrangian nonlinear programming algorithm. The algorithm achieves parallelism of function, derivative, and search direction calculations through the principle of domain decomposition applied along the time axis. It has been encoded and tested on 3 example problems, the Goddard problem, the acceleration-limited, planar minimum-time to the origin problem, and a National Aerospace Plane minimum-fuel ascent guidance problem. Execution times as fast as 118 sec of wall clock time have been achieved for a 128-stage Goddard problem solved on 32 processors. A 32-stage minimum-time problem has been solved in 151 sec on 32 processors. A 32-stage National Aerospace Plane problem required 2 hours when solved on 32 processors. A speed-up factor of 7.2 has been achieved by using 32-nodes instead of 1-node to solve a 64-stage Goddard problem.

Psiaki, Mark L.↗

NASA NTRS2002

Quadratic Optimization in the Problems of Active Control of Sound

We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

Loncaric, J.↗

DOE OSTI2024

Enhancing quantum annealing accuracy through replication-based error mitigation *

Abstract Quantum annealers like those manufactured by D-Wave Systems are designed to find high quality solutions to optimization problems that are typically hard for classical computers. They utilize quantum effects like tunneling to evolve toward low-energy states representing solutions to optimization problems. However, their analog nature and limited control functionalities present challenges to correcting or mitigating hardware errors. As quantum computing advances towards applications, effective error suppression is an important research goal. We propose a new approach called replication based mitigation (RBM) based on parallel quantum annealing (QA). In RBM, physical qubits representing the same logical qubit are dispersed across different copies of the problem embedded in the hardware. This mitigates hardware biases, is compatible with limited qubit connectivity in current annealers, and is well-suited for currently available noisy intermediate-scale quantum annealers. Our experimental analysis shows that RBM provides solution quality on par with previous methods while being more flexible and compatible with a wider range of hardware connectivity patterns. In comparisons against standard QA without error mitigation on larger problem instances that could not be handled by previous methods, RBM consistently gets better energies and ground state probabilities across parameterized problem sets.

Djidjev, Hristo N. (ORCID:0000000192868824)↗

NASA NTRS2008

Morphing Wing Weight Predictors and Their Application in a Template-Based Morphing Aircraft Sizing Environment II: Morphing Aircraft Sizing via Multi-level Optimization - Part 2

This report presents an approach for sizing of a morphing aircraft based upon a multi-level design optimization approach. For this effort, a morphing wing is one whose planform can make significant shape changes in flight - increasing wing area by 50% or more from the lowest possible area, changing sweep 30 or more, and/or increasing aspect ratio by as much as 200% from the lowest possible value. The top-level optimization problem seeks to minimize the gross weight of the aircraft by determining a set of "baseline" variables - these are common aircraft sizing variables, along with a set of "morphing limit" variables - these describe the maximum shape change for a particular morphing strategy. The sub-level optimization problems represent each segment in the morphing aircraft's design mission; here, each sub-level optimizer minimizes fuel consumed during each mission segment by changing the wing planform within the bounds set by the baseline and morphing limit variables from the top-level problem.

Skillen, Michael D.↗

NASA NTRS1987

Passive stabilization for large space systems

The optimal tuning of multiple tuned-mass dampers for the transient vibration damping of large space structures is investigated. A multidisciplinary approach is used. Structural dynamic techniques are applied to gain physical insight into absorber/structure interaction and to optimize specific cases. Modern control theory and parameter optimization techniques are applied to the general optimization problem. A design procedure for multi-absorber multi-DOF vibration damping problems is presented. Classical dynamic models are extended to investigate the effects of absorber placement, existing structural damping, and absorber cross-coupling on the optimal design synthesis. The control design process for the general optimization problem is formulated as a linear output feedback control problem via the development of a feedback control canonical form. The techniques are applied to sample micro-g and pointing problems on the NASA dual keel space station.

Sesak, J. R.↗

NASA NTRS1995

Practical aspects of variable reduction formulations and reduced basis algorithms in multidisciplinary design optimization

This paper discusses certain connections between nonlinear programming algorithms and the formulation of optimization problems for systems governed by state constraints. The major points of this paper are the detailed calculation of the sensitivities associated with different formulations of optimization problems and the identification of some useful relationships between different formulations. These relationships have practical consequences; if one uses a reduced basis nonlinear programming algorithm, then the implementations for the different formulations need only differ in a single step.

Lewis, Robert Michael↗

NASA NTRS1975

Design of low-speed airfoils by numerical optimization

A practical procedure for the optimum design of low-speed airfoils is demonstrated. The procedure uses an optimization program based on a gradient algorithm coupled with an aerodynamic analysis program that uses a relaxation solution of the inviscid, full-potential equation. The analysis program is valid for both incompressible and compressible flow, thereby making optimum design of high-speed, shock-free airfoils possible. Results are presented for the following three constrained optimization problems at fixed angle of attack and Mach number: (1) adverse pressure-gradient minimization, (2) pitching-moment minimization; and (3) lift maximization. All three optimization problems were studied with various aerodynamic and geometric constraints.

Hicks, R. M.↗