Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Nonlinear optimization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Optimization of Air-Breathing Engine Concept

The design optimization of air-breathing propulsion engine concepts has been accomplished by soft-coupling the NASA Engine Performance Program (NEPP) analyzer with the NASA Lewis multidisciplinary optimization tool COMETBOARDS. Engine problems, with their associated design variables and constraints, were cast as nonlinear optimization problems with thrust as the merit function. Because of the large number of mission points in the flight envelope, the diversity of constraint types, and the overall distortion of the design space; the most reliable optimization algorithm available in COMETBOARDS, when used by itself, could not produce satisfactory, feasible, optimum solutions. However, COMETBOARDS' unique features-which include a cascade strategy, variable and constraint formulations, and scaling devised especially for difficult multidisciplinary applications-successfully optimized the performance of subsonic and supersonic engine concepts. Even when started from different design points, the combined COMETBOARDS and NEPP results converged to the same global optimum solution. This reliable and robust design tool eliminates manual intervention in the design of air-breathing propulsion engines and eases the cycle analysis procedures. It is also much easier to use than other codes, which is an added benefit. This paper describes COMETBOARDS and its cascade strategy and illustrates the capabilities of the combined design tool through the optimization of a high-bypass- turbofan wave-rotor-topped subsonic engine and a mixed-flow-turbofan supersonic engine.

Patnaik, Surya N.↗
NASA NTRS1997

A Disturbance Rejection Approach to Actuator and Sensor Placement

For various reasons as discussed for instance in, the selection of actuator and sensor positions is still ad hoc. This is especially true for flexible structures where many candidate configurations can exist. This study is an attempt to make the selection process more methodical. One approach to actuator and sensor placement is to optimize a closed loop performance metric directly by selecting the actuators, sensors, and controller gains simultaneously. This direct approach makes sense if the desired closed loop performance is well defined. Since the individual actuator and sensor contributions to the closed loop performance metric is complex, the solution strategy usually employs non linear programming with many design and numerical iterations. A second approach is to select actuators and/or sensors based on open loop properties so that closed loop performance is indirectly optimized. Since the individual sensor and actuator contributions to the open loop metric is simple, nonlinear optimization is usually not needed. This approach will suggest efficient actuator and sensor configurations for any type of control law. The method suggested in this study falls into the latter class of approaches.

Lim, K. B.↗
DOE OSTI2021

Physics basis for design of 3D coils in tokamaks

Recent progress in 3D tokamak modeling is now leveraged to create a conceptual design of new external 3D field coils for the DIII-D tokamak. In this work generalized perturbed equilibrium code is used to determine optimally efficient spectrum for driving total, core, and edge neoclassical toroidal viscosity torque. These fundamental modes of 3D control are shown to have consistent outboard structures across a wide variety of plasma scenarios and machines. Given these target spectra, the currents and 3D geometry of multiple coils can be optimized to increase efficient drive for the physics of interest without undesired secondary effects. Here, this nonlinear optimization is demonstrated using the flexible optimized coils using space-curves code. The optimized coils are individually distorted in space, creating toroidal 'arrays' containing a variety of shapes that often wrap around a significant poloidal extent of the machine. Importantly, efficient coupling can be maintained even when enforcing large distances between coils and the plasma during the geometric optimization of coil designs. Finally, the physics-driven optimization presented here thus provides a practical path to utilizing coils built on the exterior of the vacuum chamber in future reactors to obtain the powerful 3D field benefits demonstrated on current machines with close, internal coils.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

DERMS Online: A New Voltage Sensitivity-Enabled Feedback Optimization Framework

This paper proposes a distributed energy resource management system (DERMS) solution by developing a new voltage sensitivity-enabled feedback optimization framework. The key idea is to adopt a measurement feedback scheme to reformulate the original nonlinear optimization into a linear programming (LP) problem via perturb-and-observe-based voltage sensitivity analysis. The proposed solution eliminates the dependence on load knowledge and can be implemented online thanks to an efficient open-source solver for LP problems. Comparison results with other control methods on a real distribution feeder in Southern California highlight the feasibility as well as benefits for the proposed framework.

distributed energy resource management↗
NASA NTRS1989

Optimal three finger grasps

Consideration is given to the problem of optimal force distribution among three point fingers holding a planar object. A scheme that reduces the nonlinear optimization problem to an easily solved generalized eigenvalue problem is proposed. This scheme generalizes and simplifies results of Ji and Roth (1988). The generalizations include all possible geometric arrangements and extensions to three dimensions and to the case of variable coefficients of friction. For the two-dimensional case with constant coefficients of friction, it is proved that, except for some special cases, the optimal grasping forces (in the sense of minimizing the dependence on friction) are those for which the angles with the corresponding normals are all equal (in absolute value).

Demmel, J.↗
DOE OSTI2022

DERMS Online: A New Voltage Sensitivity-Enabled Feedback Optimization Framework: Preprint

This paper proposes a distributed energy resource management system (DERMS) solution by developing a new voltage sensitivity enabled feedback optimization framework. The key idea is to adopt a measurement feedback scheme to reformulate the original nonlinear optimization into a linear programming (LP) problem via perturb and observe-based voltage sensitivity analysis. The proposed solution eliminates the dependence on load knowledge and can be implemented online thanks to an efficient open-source solver for LP problems. The proposed DERMS online platform is generalizable to deal with various types of distributed energy resources (DERs), including distributed photovoltaics (PVs), energy storage, electric vehicles, demand response, etc. Comparison results with other control methods on a realistic distribution feeder in Southern California highlight the feasibility as well as benefits for the proposed framework.

distributed energy resources management↗
NASA NTRS1996

Cascade Optimization Strategy for Aircraft and Air-Breathing Propulsion System Concepts

Design optimization for subsonic and supersonic aircraft and for air-breathing propulsion engine concepts has been accomplished by soft-coupling the Flight Optimization System (FLOPS) and the NASA Engine Performance Program analyzer (NEPP), to the NASA Lewis multidisciplinary optimization tool COMETBOARDS. Aircraft and engine design problems, with their associated constraints and design variables, were cast as nonlinear optimization problems with aircraft weight and engine thrust as the respective merit functions. Because of the diversity of constraint types and the overall distortion of the design space, the most reliable single optimization algorithm available in COMETBOARDS could not produce a satisfactory feasible optimum solution. Some of COMETBOARDS' unique features, which include a cascade strategy, variable and constraint formulations, and scaling devised especially for difficult multidisciplinary applications, successfully optimized the performance of both aircraft and engines. The cascade method has two principal steps: In the first, the solution initiates from a user-specified design and optimizer, in the second, the optimum design obtained in the first step with some random perturbation is used to begin the next specified optimizer. The second step is repeated for a specified sequence of optimizers or until a successful solution of the problem is achieved. A successful solution should satisfy the specified convergence criteria and have several active constraints but no violated constraints. The cascade strategy available in the combined COMETBOARDS, FLOPS, and NEPP design tool converges to the same global optimum solution even when it starts from different design points. This reliable and robust design tool eliminates manual intervention in the design of aircraft and of air-breathing propulsion engines where it eases the cycle analysis procedures. The combined code is also much easier to use, which is an added benefit. This paper describes COMETBOARDS and its cascade strategy and illustrates the capability of the combined design tool through the optimization of a subsonic aircraft and a high-bypass-turbofan wave-rotor-topped engine.

Patnaik, Surya N.↗
NASA NTRS2020

Prediction and Evaluation of the Image of the WFIRST Coronagraph Pupil at the Shaped-Pupil Mask

To create a high contrast field of view with a shaped pupil coronagraph (SPC), the telescope pupil is imaged onto the shaped pupil mask, the shaped pupil mask is designed and fabricated through a design optimization based on a given pupil wavefront, and deformable mirrors (DM) in the coronagraph are modulated according to a nonlinear optimization procedure. Both the mask design optimization and the DM optimization require accurate knowledge of the image of the pupil at the shaped pupil plane for the calculation of Jacobians, and the evaluation of alignment tolerances. The shaped pupil coronagraphs demonstrated in the high contrast imaging testbed (HCIT) at JPL has heretofore assumed perfect imaging of the pupil onto the shaped pupil mask. Similarly, the design and performance modeling of the WFIRST CGI instrument makes the same assumption. In this paper we estimate and compare the image of the pupil mask at the shaped pupil plane in the case of the coronagraph testbed, and the image of the telescope pupil at the shaped pupil plane for the WFIRST CGI instrument. The estimated pupil images include field curvature and aberrations resulting from the layout of the parabolic mirror imaging system, which is optimized for the source image, not the image of the pupil. We also show the results of direct measurement of the image of the pupil mask at the shaped pupil plane in the coronagraph testbed.

Crowther, Blake↗
NASA NTRS2000

Improved Speech Coding Based on Open-Loop Parameter Estimation

A nonlinear optimization algorithm for linear predictive speech coding was developed early that not only optimizes the linear model coefficients for the open loop predictor, but does the optimization including the effects of quantization of the transmitted residual. It also simultaneously optimizes the quantization levels used for each speech segment. In this paper, we present an improved method for initialization of this nonlinear algorithm, and demonstrate substantial improvements in performance. In addition, the new procedure produces monotonically improving speech quality with increasing numbers of bits used in the transmitted error residual. Examples of speech encoding and decoding are given for 8 speech segments and signal to noise levels as high as 47 dB are produced. As in typical linear predictive coding, the optimization is done on the open loop speech analysis model. Here we demonstrate that minimizing the error of the closed loop speech reconstruction, instead of the simpler open loop optimization, is likely to produce negligible improvement in speech quality. The examples suggest that the algorithm here is close to giving the best performance obtainable from a linear model, for the chosen order with the chosen number of bits for the codebook.

Juang, Jer-Nan↗
DOE OSTI2022

Automatic Calibration of a Geomechanical Model from Sparse Data for Estimating Stress in Deep Geological Formations

Summary In this study, we demonstrate geomechanical modeling with fully automatic parameter calibration to estimate the full geomechanical stress fields of a prospective US carbon dioxide (CO2) storage site, based on sparse measurement data. The goal is to compute full stress tensor field estimates (principal stresses and orientations) that are maximally compatible with observations within the constraints of the model assumptions, thereby extending pointwise, incomplete partial stress measurement to a simulated full formation stress field, as well as a rough assessment of the associated error. We use the Perch site, located in Otsego County, Michigan, USA, as our case study. The input data consist of partial stress tensor information inferred from in-situ borehole tests, geophysical well logs, and processing of seismic data. A static earth model (SEM) of the site was developed, and geomechanical simulation functionality of the open-source MATLAB Reservoir Simulation Toolbox (MRST) was used to model the stress field. Adjoint-based nonlinear optimization was used to adjust boundary conditions and material properties to calibrate simulated results of observations. Results were interpreted through a Bayesian framework. The focus of this paper is to demonstrate how the fully automatic calibration procedure works and discuss the results obtained; it does not attempt a detailed analysis of the stress field in the context of the proposed CO2 storage initiatives. Our work is part of a larger effort to noninvasively determine in-situ stresses in deep formations considered for CO2 storage. Guided by previously published research on geomechanical model calibration, our work presents a novel calibration approach supporting a potentially large number of linear or nonlinear calibration parameters to produce results optimally agreeing with available measurements and thus extend partial pointwise estimates to full tensor fields compatible with the physics of the site.

Engineering↗
NASA NTRS1976

Operations research investigations of satellite power stations

A systems model reflecting the design concepts of Satellite Power Stations (SPS) was developed. The model is of sufficient scope to include the interrelationships of the following major design parameters: the transportation to and between orbits; assembly of the SPS; and maintenance of the SPS. The systems model is composed of a set of equations that are nonlinear with respect to the system parameters and decision variables. The model determines a figure of merit from which alternative concepts concerning transportation, assembly, and maintenance of satellite power stations are studied. A hybrid optimization model was developed to optimize the system's decision variables. The optimization model consists of a random search procedure and the optimal-steepest descent method. A FORTRAN computer program was developed to enable the user to optimize nonlinear functions using the model. Specifically, the computer program was used to optimize Satellite Power Station system components.

Cole, J. W.↗
DOE OSTI2022

Protection settings optimizer

SAND2023-06672O The Protection Settings Optimizer (PSO) uses system and fault data as inputs to formulate the problem of calculating relay settings as a mixed integer, nonlinear optimization problem (MINLP). The MINLP is solved using a genetic algorithm-based optimizer that attempts to find settings to reduce the relay operating times. The PSO protects the power system by using the steady-state fault voltages and currents, which then calculates the optimal device setting to protect the power system. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Patel, Trupal↗
DOE OSTI2025

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) (iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. As a result, the symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

Al Daas, Hussam [Rutherford Appleton Laboratory, D↗
NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗
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↗
DOE OSTI2025

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1985

Optimal landing of a helicopter in autorotation

Gliding descent in autorotation is a maneuver used by helicopter pilots in case of engine failure. The landing of a helicopter in autorotation is formulated as a nonlinear optimal control problem. The OH-58A helicopter was used. Helicopter vertical and horizontal velocities, vertical and horizontal displacement, and the rotor angle speed were modeled. An empirical approximation for the induced veloctiy in the vortex-ring state were provided. The cost function of the optimal control problem is a weighted sum of the squared horizontal and vertical components of the helicopter velocity at touchdown. Optimal trajectories are calculated for entry conditions well within the horizontal-vertical restriction curve, with the helicopter initially in hover or forwared flight. The resultant two-point boundary value problem with path equality constraints was successfully solved using the Sequential Gradient Restoration Technique.

Lee, A. Y. N.↗
DOE OSTI2023

Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. Here, we demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.

97 MATHEMATICS AND COMPUTING↗