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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

Here we present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Application of singular value decomposition to structural dynamics systems with constraints

Singular value decomposition is used to construct a coordinate transformation for a linear dynamic system subject to linear, homogeneous constraint equations. The method is compared with two commonly used methods, namely classical Gaussian elimination and Walton-Steeves approach. Although the classical method requires fewer numerical operations, the singular value decomposition method is more accurate and convenient in eliminating the dependent coordinates. Numerical examples are presented to demonstrate the application of the method.

Juang, J.-N.↗
NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗
NASA NTRS1986

Numerical difficulties associated with using equality constraints to achieve multi-level decomposition in structural optimization

There has been recent interest in multidisciplinary multilevel optimization applied to large engineering systems. The usual approach is to divide the system into a hierarchy of subsystems with ever increasing detail in the analysis focus. Equality constraints are usually placed on various design quantities at every successive level to ensure consistency between levels. In many previous applications these equality constraints were eliminated by reducing the number of design variables. In complex systems this may not be possible and these equality constraints may have to be retained in the optimization process. In this paper the impact of such a retention is examined for a simple portal frame problem. It is shown that the equality constraints introduce numerical difficulties, and that the numerical solution becomes very sensitive to optimization parameters for a wide range of optimization algorithms.

Thareja, R.↗
NASA NTRS1988

On correcting radial orbit errors for altimetric satellites using crossover analysis

A method is proposed for correcting radial orbit error in measurements of sea surface height using a satellite altimeter. Traditionally, the orbit error is modeled in terms of a Fourier series with the Fourier coefficients determined by minimizing the residual crossover difference in a least-squares sense. In this method an a priori constraint must be imposed to obtain a unique solution. It is shown that by using singular value decomposition, no such constraint is needed. This proposed method leaves the geographically dependent errors unchanged and makes only those corrections warranted by the information contained in crossover differences. Thus, the resultant ocean topography is free from any undue distortion which might be incurred by an a priori constraint. It is suggested that the method is useful for application to high-accuracy altimetric mission, because the orbit error can be reduced without compromising the accuracy of the measured mean ocean topography.

Fu, Lee-Lueng↗
NASA NTRS1994

Multidisciplinary Optimization Methods for Aircraft Preliminary Design

This paper describes a research program aimed at improved methods for multidisciplinary design and optimization of large-scale aeronautical systems. The research involves new approaches to system decomposition, interdisciplinary communication, and methods of exploiting coarse-grained parallelism for analysis and optimization. A new architecture, that involves a tight coupling between optimization and analysis, is intended to improve efficiency while simplifying the structure of multidisciplinary, computation-intensive design problems involving many analysis disciplines and perhaps hundreds of design variables. Work in two areas is described here: system decomposition using compatibility constraints to simplify the analysis structure and take advantage of coarse-grained parallelism; and collaborative optimization, a decomposition of the optimization process to permit parallel design and to simplify interdisciplinary communication requirements.

Kroo, Ilan↗
NASA NTRS1993

Forcing function modeling for flow induced vibration

The fundamental forcing function unsteady aerodynamics for application to turbomachine blade row forced response are considered, accomplished through a series of experiments performed in a rotating annular cascade and a research axial flow turbine. In particular, the unsteady periodic flowfields downstream of rotating rows of perforated plates, airfoils and turbine blade rows are measured with a cross hot-wire and an unsteady total pressure probe. The unsteady velocity and static pressure fields were then analyzed harmonically and split into vortical and potential gusts, accomplished by developing a gust splitting analysis which includes both gust unsteady static pressure and velocity data. The perforated plate gusts closely were found to be linear theory vortical gusts, satisfying the vortical gust constraints. The airfoil and turbine blade row generated velocity perturbations did not satisfy the vortical gust constraints. However, the decomposition of the unsteady flow field separated the data into a propagating vortical component which satisfied these vortical gust constraints and a decaying potential component.

Fleeter, Sanford↗
NASA NTRS1990

New evidence favoring multilevel decomposition and optimization

The issue of the utility of multilevel decomposition and optimization remains controversial. To date, only the structural optimization community has actively developed and promoted multilevel optimization techniques. However, even this community acknowledges that multilevel optimization is ideally suited for a rather limited set of problems. It is warned that decomposition typically requires eliminating local variables by using global variables and that this in turn causes ill-conditioning of the multilevel optimization by adding equality constraints. The purpose is to suggest a new multilevel optimization technique. This technique uses behavior variables, in addition to design variables and constraints, to decompose the problem. The new technique removes the need for equality constraints, simplifies the decomposition of the design problem, simplifies the programming task, and improves the convergence speed of multilevel optimization compared to conventional optimization.

Padula, Sharon L.↗
NASA NTRS1988

Experimental verification of a large flexible manipulator

A large experimental lightweight manipulator would be useful for material handling, for welding, or for ultrasonic inspection of a large structure, such as an airframe. The flexible parallel link mechanism is designed for high rigidity without increasing weight. This constrained system is analyzed by singular value decomposition of the constraint Jacobian matrix. A verification of the modeling using the assumed mode method is presented. Eigenvalues and eigenvectors of the linearized model are compared to the measured system natural frequencies and their associated mode shapes. The modeling results for large motions are compared to the time response data from the experiments. The hydraulic actuator is verified.

Lee, Jac Won↗
NASA NTRS1990

Dynamic Analysis and Control of Lightweight Manipulators with Flexible Parallel Link Mechanisms

The objective is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equation of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to higher order. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. Elastic motion is expressed by the assumed mode method. Mode shape functions of each link are chosen using the load interfaced component mode synthesis. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model.

Lee, Jeh Won↗
NASA NTRS1991

Dynamic analysis and control of lightweight manipulators with flexible parallel link mechanisms

The flexible parallel link mechanism is designed for increased rigidity to sustain the buckling when it carries a heavy payload. Compared to a one link flexible manipulator, a two link flexible manipulator, especially the flexible parallel mechanism, has more complicated characteristics in dynamics and control. The objective of this research is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model. The step response of the analytical model and the TREETOPS model match each other well. The nonlinear dynamics is studied using a sinusoidal excitation. The actuator dynamic effect on a flexible robot was investigated. The effects are explained by the root loci and the Bode plot theoretically and experimentally. For the base performance for the advanced control scheme, a simple decoupled feedback scheme is applied.

Lee, Jeh Won↗
NASA NTRS1990

Rapid design of aerospace vehicle

This document presents in viewgraph form techniques for the optimal design of aerospace vehicles which take into account vehicle shape, aerodynamic performance, and weight minimization. Methods include multilevel optimization with linear decomposition, multi-constraint optimization, global sensitivity matrix, and calculation of sensitivity derivatives using both first and second order derivatives. The effects of including flexibility in the optimization is discussed.

Abdi, Frank↗
NASA NTRS1991

Large constraint length high speed viterbi decoder based on a modular hierarchial decomposition of the deBruijn graph

A method of formulating and packaging decision-making elements into a long constraint length Viterbi decoder which involves formulating the decision-making processors as individual Viterbi butterfly processors that are interconnected in a deBruijn graph configuration. A fully distributed architecture, which achieves high decoding speeds, is made feasible by novel wiring and partitioning of the state diagram. This partitioning defines universal modules, which can be used to build any size decoder, such that a large number of wires is contained inside each module, and a small number of wires is needed to connect modules. The total system is modular and hierarchical, and it implements a large proportion of the required wiring internally within modules and may include some external wiring to fully complete the deBruijn graph. pg,14.

Collins, Oliver↗
DOE OSTI2025

SNoGloDe: A Structured Nonlinear Global Decomposition Solver

Large-scale optimization problems often require decomposition strategies and customized algorithms to achieve optimal solutions within a reasonable time. Building on the work of Cao and Zavala (2019) for solving nonlinear two-stage stochastic programs to global optimality, we implement and extend their approach. We generalize to optimization problems reformulated with a block-angular constraint structure (e.g., temporal decomposition). Our framework, written in Python using Pyomo, is highly customizable and enables parallel execution of the decomposition. SNoGloDe allows tailored branching strategies, lower bounding problems, and candidate generators to leverage problem-specific knowledge. To demonstrate effectiveness, we compare SNoGloDe’s performance with Gurobi on a temporally decomposed produced water case study.

algorithms↗
DOE OSTI2024

Electric field effects during disruptions

Tokamak disruptions are associated with breaking magnetic surfaces, which makes magnetic field lines chaotic in large regions of the plasma. The enforcement of quasi-neutrality in a region of chaotic field lines requires an electric potential that has both short and long correlation distances across the magnetic field lines. The short correlation distances produce a Bohm-like diffusion coefficient ∼Te/eB and the long correlation distances aT produce a large scale flow ∼Te/eBaT. This cross-field diffusion and flow are important for sweeping impurities into the core of a disrupting tokamak. The analysis separates the electric field in a plasma into the sum of a divergence-free, E→B, and a curl-free, E→q, part, a Helmholtz decomposition. The divergence-free part of E→ determines the evolution of the magnetic field. The curl-free part enforces quasi-neutrality, E→q=−∇→Φq. Magnetic helicity evolution gives the required boundary condition for a unique Helmholtz decomposition and an unfortunate constraint on steady-state tokamak maintenance.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1995

Structural design using equilibrium programming formulations

Solutions to increasingly larger structural optimization problems are desired. However, computational resources are strained to meet this need. New methods will be required to solve increasingly larger problems. The present approaches to solving large-scale problems involve approximations for the constraints of structural optimization problems and/or decomposition of the problem into multiple subproblems that can be solved in parallel. An area of game theory, equilibrium programming (also known as noncooperative game theory), can be used to unify these existing approaches from a theoretical point of view (considering the existence and optimality of solutions), and be used as a framework for the development of new methods for solving large-scale optimization problems. Equilibrium programming theory is described, and existing design techniques such as fully stressed design and constraint approximations are shown to fit within its framework. Two new structural design formulations are also derived. The first new formulation is another approximation technique which is a general updating scheme for the sensitivity derivatives of design constraints. The second new formulation uses a substructure-based decomposition of the structure for analysis and sensitivity calculations. Significant computational benefits of the new formulations compared with a conventional method are demonstrated.

Scotti, Stephen J.↗
NASA NTRS2013

Antarctica, Greenland and Gulf of Alaska Land-ice Evolution from an Iterated GRACE Global Mascon Solution

We have determined the ice mass evolution of the Antarctica and Greenland ice sheets (AIS and GIS) and Gulf of Alaska (GOA) glaciers from a new GRACE global solution of equal-area surface mass concentration parcels (mascons) in equivalent height of water. The mascons were estimated directly from the reduction of the inter-satellite K-band range-rate (KBRR) observations, taking into account the full noise covariance, and formally iterating the solution. The new solution increases signal recovery while reducing the GRACE KBRR observation residuals. The mascons were estimated with 10 day and 1 arc degree equal-area sampling, applying anisotropic constraints. An ensemble empirical mode decomposition adaptive filter was applied to the mascon time series to compute annual mass balances. The details and causes of the spatial and temporal variability of the land-ice regions studied are discussed. The estimated mass trend over the total GIS, AIS and GOA glaciers for the time period 1 December 2003 to 1 December 2010 is -380 plus or minus 31 Gt a(exp -1), equivalent to -1.05 plus or minus 0.09 mma(exp -1) sea-level rise. Over the same time period we estimate the mass acceleration to be -41 plus or minus 27 Gt a(exp -2), equivalent to a 0.11 plus or minus 0.08 mm a(exp -2) rate of change in sea level. The trends and accelerations are dependent on significant seasonal and annual balance anomalies.

MASCON↗