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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.

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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

A nonlinear programming approach for optimizing two-stage lifting vehicle ascent to orbit

An optimal atmospheric flight branched trajectory-shaping capability is presented based on the Davidon-Fletcher-Powell variable metric parameter optimization technique. Gradient information is generated using finite difference methods. A typical atmospheric flight branched optimization problem is analyzed which requires the determination of 31 parameters. This parameter set includes the three-dimensional description of vehicle attitude control angles for three branches of flight: first-stage ascent, second-stage ascent, and first-stage flyback. The important inflight inequality contraints required to maintain the integrity of the vehicles are considered. Some of the numerical methods employed are discussed, along with several new auxiliary techniques developed to improve the compatibility of the numerical gradient and iterator.

Kamm, J. L.↗
NASA NTRS1984

Post and a random-walk search mode

Multidisciplinary analysis often requires optimization of nonlinear systems that are subject to constraints. Trajectory optimization is one example of this situation. The Program to Optimize Simulated Trajectories (POST) was used successfully for a number of problems. The purpose is to describe POST and a new optimization approach that has been incorporated into it. Typical uses of POST will also be illustrated. The projected-gradient approach to optimization is the preferred option in POST and is discussed. A new approach to optimization, the random-walk approach, is described, and results with the random-walk approach are presented.

Martin, J. A.↗
NASA NTRS1989

Optimizing for minimum weight when two different finite element models and analyses are required

The Finite Element Structural Optimization Program's (FESOP) ability to perform minimum weight optimization using two different finite element analyses and models is discussed. FESOP uses the ADS optimizer developed by Dr. Garret Vanderplaats to solve the nonlinear constrained optimization problem. The design optimization problem requires a response spectrum analysis and model to evaluate the stress and displacement constraints. However, the problem needs a frequency analysis and model to calculate the natural frequencies used to evaluate the frequency range constraints. The results of both the successful and unsuccessful approaches used to solve this difficult weight minimization problem are summarized. The results show that no one ADS optimization algorithm worked in all cases. However, the Sequential Convex Programming and Modified Method of Feasible Directions algorithms were the most successful.

Hall, Jeffrey C.↗
DOE OSTI2011

Numerical Methods for Large-Scale Data Factorization (Final Report (Milestone Date 9/30/11) for Subcontract No. B594099)

The following work has been performed by PI Hans De Sterck and graduate student Manda Winlaw for the required tasks 1-5 (as listed in the Statement of Work). Graduate student Manda Winlaw has visited LLNL January 31-March 11, 2011 and May 23-August 19, 2010, working with Van Henson and Mike O'Hara on non-negative matrix factorizations (NMF). She has investigated the dense subgraph clustering algorithm from 'Finding Dense Subgraphs for Sparse Undirected, Directed, and Bipartite Graphs' by Chen and Saad, testing this method on several term-document matrices and adapting it to cluster based on the rank of the subgraphs instead of the density. Manda Winlaw was awarded a first prize in the annual LLNL summer student poster competition for a poster on her NMF research. PI Hans De Sterck has developed a new adaptive algebraic multigrid algorithm for computing a few dominant or minimal singular triplets of sparse rectangular matrices. This work builds on adaptive algebraic multigrid methods that were further developed by the PI and collaborators (including Sanders and Henson) for Markov chains. The method also combines and extends existing multigrid algorithms for the symmetric eigenproblem. The PI has visited LLNL February 22-25, 2011, and has given a CASC seminar 'Algebraic Multigrid for the Singular Value Problem' on this work on February 23, 2011. During his visit, he has discussed this work and related topics with Van Henson, Geoffrey Sanders, Panayot Vassilevski, and others. He has tested the algorithm on PDE matrices and on a term-document matrix, with promising initial results. Manda Winlaw has also started to work, with O'Hara, on estimating probability distributions over undirected graph edges. The goal is to estimate probabilistic models from sets of undirected graph edges for the purpose of prediction, anomaly detection and support to supervised learning. Graduate student Manda Winlaw is writing a paper on the results obtained with O'Hara which will be submitted some time later in 2011 to a data mining conference. PI Hans De Sterck has developed a new optimization algorithm for canonical tensor approximation, formulating an extension of the nonlinear GMRES method to optimization problems. Numerical results for tensors with up to 8 modes show that this new method is efficient for sparse and dense tensors. He has written a paper on this which has been submitted to the SIAM Journal on Scientific Computing. PI Hans De Sterck has further developed his new optimization algorithm for canonical tensor approximation, formulating an extension in terms of steepest-descent preconditioning, which makes the approach generally applicable for nonlinear optimization. He has written a paper on this extension which has been submitted to Numerical Linear Algebra with Applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A mixed-integer PDE-constrained optimization formulation for constructing electromagnetic cloaks with multiple materials

We study the design of an electromagnetic cloak from multiple materials with an additional constraint on the mass of the cloak. Our problem is an example of a topology optimization problem, and we formulate this problem as a mixed-integer partial-differential equation constrained optimization (MIPDECO) problem, where Maxwell’s equation models the propagation of the wave through the cloak and surrounding medium. We use binary variables to model the assignment of the different materials, and their relevant properties (permittivity and density). The mass constraint adds a nontrivial constraint to this problem. We propose a two-phase strategy to solve this problem. In the first phase, we solve a continuous relaxation, and then propose a new variant of the feasibility pump that exploits the structure of the PDE to obtain an initial integral solution candidate. In the second phase, we use a trust-region approach to improve this incumbent. We also consider a continuation or mesh-sequencing approach to find better solutions faster on consecutively finer meshes. We present detailed numerical results to illustrate the effectiveness of our approaches for constructing multi-material cloaks with a mass constraint.

Calculus of Variations and Optimization↗
DOE OSTI2016

A multi-objective optimization approach to optimal sensor location problem in $\mathrm{IGCC}$ power plants

Integrated Gasification Combined Cycle (IGCC) power plants provide a cleaner and more efficient way to obtain energy from coal. In order to operate an IGCC power plant in a safe and stable manner, several input and output process parameters need to be monitored. However, due to economic and operational constraints, it is infeasible to place sensors at every input and output process parameter location. Hence, it becomes important to select the most effective sensor locations which lead to maximum information gain about the plant conditions. Practical issues present in an IGCC power plant, such as harsh physical conditions and variability in process parameters, make the optimal sensor location problem an especially complicated one. Further, sensors can have multiple objectives and they can produce uncertainties due to measurement errors. Here this work considers hybrid hardware and virtual sensing for advanced power systems with multiple objectives. In order to solve this real world large scale problem, we use a novel algorithm called Better Optimization of Nonlinear Uncertain Systems (BONUS). BONUS works in probability distribution space and avoids sampling for each optimization and derivative calculations iterations. A new algorithm for multi-objective optimization is also developed specifically for problem. The result of this nonlinear stochastic multi-objective problem is the non-dominated, or Pareto set, which provides trade-offs between various objectives like observability, cost, and thermal efficiency. This is the first attempt at solving the problem of optimal sensor deployment in advanced power plants, with consideration of hybrid hardware and virtual sensing and incorporation of uncertainty with multiple objectives.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2016

Analysis of Nonlinear Dynamics by Square Matrix Method

The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.

43 PARTICLE ACCELERATORS↗
NASA NTRS1992

Neural network based adaptive control of nonlinear plants using random search optimization algorithms

This paper presents a method for utilizing artificial neural networks for direct adaptive control of dynamic systems with poorly known dynamics. The neural network weights (controller gains) are adapted in real time using state measurements and a random search optimization algorithm. The results are demonstrated via simulation using two highly nonlinear systems.

Boussalis, Dhemetrios↗
DOE OSTI2021

Data-driven Chaos Indicator for Nonlinear Dynamics and Applications on Storage Ring Lattice Design

A data-driven chaos indicator concept is introduced to characterize the degree of chaos for nonlinear dynamical systems. The indicator is represented by the prediction accuracy of surrogate models established purely from data. It provides a metric for the predictability of nonlinear motions in a given system. When using the indicator to implement a tune-scan for a quadratic Hénon map, the main resonances and their asymmetric stop-band widths can be identified. When applied to particle transportation in a storage ring, as particle motion becomes more chaotic, its surrogate model prediction accuracy decreases correspondingly. Therefore, the prediction accuracy, acting as a chaos indicator, can be used directly as the objective for nonlinear beam dynamics optimization. This method provides a different perspective on nonlinear beam dynamics and an efficient method for nonlinear lattice optimization. Applications in dynamic aperture optimization are demonstrated as real world examples.

43 PARTICLE ACCELERATORS↗