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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Adaptive Space-Time Methods for Large Scale Optimal Design

When modeling complex physical systems with advanced dynamics, such as shocks and singularities, many classic methods for solving partial differential equations can return inaccurate or unusable results. One way to resolve these complex dynamics is through r-adaptive refinement methods, in which a fixed number of mesh points are shifted to areas of high interest. The mesh refinement map can be found through the solution of the Monge-Ampére equation, a highly nonlinear partial differential equation. Due to its nonlinearity, the numerical solution of the Monge-Ampére equation is nontrivial and has previously required computationally expensive methods. In this report, we detail our novel optimization-based, multigrid-enabled solver for a low-order finite element approximation of the Monge-Ampére equation. This fast and scalable solver makes r-adaptive meshing more readily available for problems related to large-scale optimal design. Beyond mesh adaptivity, our report discusses additional applications where our fast solver for the Monge-Ampére equation could be easily applied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Accelerated basis adaptation in homogeneous chaos spaces

Polynomial chaos expansions (PCE) provide an efficient approach to uncertainty quantification (UQ) and have been adapted to diverse applications across the spectrum of science and engineering. For situations involving large stochastic parameterizations, the curse of dimensionality renders PCE-based methods computationally prohibitive. A basis adaptation approach for PCE was proposed by Tipireddy and Ghanem (2014) which transforms the input random variables through an isometry such that sufficient probabilistic characterization of specific quantities of interest (QoI) is concentrated in an algebraic manifold embedded in the linear span of the dominant transformed variables. While quite versatile, that original version of the PCE basis adaptation exhibited slow convergence for a number of problems of practical significance. In the present paper, we propose two novel methods to accelerate the convergence of the original basis adaptation approach, thus expanding its reach while also providing insight into its performance. In the first method, information gained from a pilot PCE representation is used to correct the mean and Gaussian coefficients in the adapted space. By taking advantages of probabilistic information in higher dimensional adaptation gleaned from an initial adaptation, the second method updates the rotation matrix used to identify the dominant transformed variables. In this manner, the new rotation matrix concentrates even more probabilistic information in its first few dimensions. These two method can be combined to achieve even better performance, the combined method is referred to as sequentially optimized adaptation method. Here, the methods are demonstrated on an analytical test function and a model of a space structure with several sub-components and a non-smooth quantity of interest representing the maximum acceleration over time. Both methods achieve accelerated convergence of the basis adaptation approach with negligible additional costs.

Accelerated convergence↗
DOE OSTI2016

System and method for design and optimization of grid connected photovoltaic power plant with multiple photovoltaic module technologies

A system and method of using one or more DC-DC/DC-AC converters and/or alternative devices allows strings of multiple module technologies to coexist within the same PV power plant. A computing (optimization) framework estimates the percentage allocation of PV power plant capacity to selected PV module technologies. The framework and its supporting components considers irradiation, temperature, spectral profiles, cost and other practical constraints to achieve the lowest levelized cost of electricity, maximum output and minimum system cost. The system and method can function using any device enabling distributed maximum power point tracking at the module, string or combiner level.

14 SOLAR ENERGY↗
DOE OSTI2015

System, methods and apparatus for program optimization for multi-threaded processor architectures

Methods, apparatus and computer software product for source code optimization are provided. In an exemplary embodiment, a first custom computing apparatus is used to optimize the execution of source code on a second computing apparatus. In this embodiment, the first custom computing apparatus contains a memory, a storage medium and at least one processor with at least one multi-stage execution unit. The second computing apparatus contains at least two multi-stage execution units that allow for parallel execution of tasks. The first custom computing apparatus optimizes the code for parallelism, locality of operations and contiguity of memory accesses on the second computing apparatus. This Abstract is provided for the sole purpose of complying with the Abstract requirement rules. This Abstract is submitted with the explicit understanding that it will not be used to interpret or to limit the scope or the meaning of the claims.

42 ENGINEERING↗
DOE OSTI2020

Two dimensional topology optimization of heat exchangers with the volume fraction method

We perform a comparison study of two topology optimizations methods applied to the design of a two fluids heat exchanger modeled with a coupled thermal-flow problem. The flow follows an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation without internal generation and high Peclet number. To keep the two fluid phases separated, we solve two Stokes-Brinkman equations, where the Brinkman term models the other phase as a solid. These two velocity fields are then fed to the heat transfer equation. Our goal is to maximize the enthalpy at the cold outlet while constraining the pressure drop. We first solve the design modeling the solid and fluid phases with a volume fraction variable. A SIMP-like penalization in the Brinkman term drives the optimization to a discrete design. The cost and constraint function derivatives are calculated with the library pyadjoint and the optimization is performed by IPOPT. We present optimized designs in two dimensions and discuss the influence of the parameters.

Beck, VictorA.↗
DOE OSTI2016

WE-AB-209-01: A Monte Carlo-Based Method to Include Random Errors in Robust Optimization

Purpose: To develop an efficient method to implement random set-up errors and organ motion in robust optimization for proton therapy treatment planning. Methods: The plans were created with an in-house robust optimizer, coupled with a super-fast Monte Carlo (MC) engine (less than 1 minute for final dose). MC simulates random errors by shifting randomly the starting point of each particle, according to their probability distribution. Such strategy assumes a sufficient number of treatment fractions. Two strategies are presented: 1) Full robust optimization with beamlets that already include the effect of random errors and 2) Mixed robust optimization, where the nominal beamlets are involved but a correction term C modifies the prescription. Starting from C=0, the method alternates optimization of the spot weights with the nominal beamlets and updates of C, with C=Drandom-Dnominal and where Drandom results from a regular MC computation (without pre-computed beamlets) that simulates random errors. Updates of C can be triggered as often as necessary by running the MC engine with the last corrected values for the spot weights as input. The method was applied to lung and prostate cases. For both patients the range error was set to 3%, systematic setup error to 5mm and standard deviation for random errors to 5 mm. Comparison between full robust optimization and the mixed strategy (with 3 updates of C) is presented. Results: Target coverage was far below the clinical constraints (D{sub 95} > 95% of the prescribed dose) for plans where random errors were not simulated, especially for lung case. However, by using the proposed strategies the plans achieved a target coverage above clinical constraints. Conclusion: Full robust optimization gives better results than the mixed strategy, but the latter can be useful in cases where a MC engine is not available or too computationally intensive for beamlets calculation.

60 APPLIED LIFE SCIENCES↗
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↗
DOE OSTI2018

Advanced trust region optimization strategies for glass box / black box models

We present an improved trust region filter (TRF) method for optimization of combined glass box/black box systems. Glass box systems refer to models that are easily expressed in an algebraic modeling language, providing cheap and accurate derivative information. By contrast, black box systems may be computationally expensive and derivatives are unavailable. The TRF method, as first introduced in our previous work (Eason and Biegler, AIChE J . 2016; 62:3124–3136), is able to handle hybrid systems containing both glass and black box components, which can frequently arise in chemical engineering, for example, when a multiphase reactor model is included in a flow sheet optimization problem. We discuss several recent modifications in the algorithm such as the sampling region, which maintains the algorithm's global convergence properties without requiring the trust region to shrink to zero in the limit. To benchmark the development of this optimization method, a test set of problems is generated based on modified problems from the CUTEr and COPS sets. The modified algorithm demonstrates improved performance using the test problem set. Finally, the algorithm is implemented within the Pyomo environment and demonstrated on a rigorous process optimization case study for carbon capture. © 2018 American Institute of Chemical Engineers AIChE J , 64: 3934–3943, 2018

Eason, John P.↗
DOE OSTI2015

Scenario generation for stochastic optimization problems via the sparse grid method

We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid method can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. As a result, it is indicated that the method scales well with the dimension of the distribution--especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A log-barrier Newton-CG method for bound constrained optimization with complexity guarantees

Abstract We describe an algorithm based on a logarithmic barrier function, Newton’s method and linear conjugate gradients that seeks an approximate minimizer of a smooth function over the non-negative orthant. We develop a bound on the complexity of the approach, stated in terms of the required accuracy and the cost of a single gradient evaluation of the objective function and/or a matrix-vector multiplication involving the Hessian of the objective. The approach can be implemented without explicit calculation or storage of the Hessian.

O’Neill, Michael↗
DOE OSTI2024

Floating Wind Farm Layout Optimization Considering Moorings and Seabed Variations

This paper presents a method for optimizing the layout of floating wind farms that accounts for realistic seabed variations and the consequent adjustments to the mooring systems required for different turbine positions. The mooring lines of floating wind farms create large spatial constraints that are depth-dependent, since mooring designs must adapt to variations in seabed conditions over the array area. We develop a layout optimization methodology that addresses this, adjusting mooring system designs based on the local seabed characteristics as the layout changes and using steady-state models for the wake effects and mooring lines. The approach includes design algorithms that adjust the anchor positions and line length to achieve the desired mooring line profile for different water depths, and a layout optimization framework that implements spatial constraints between the turbines, mooring lines, and lease area boundaries. Demonstrating the method on several cases shows the effect of the seabed and spatial-constraint factors, as well as their interactions, on the optimal array layout. This demonstration paves the way for scaling up the method, using more powerful optimization algorithms to handle larger farm sizes and situations with more intensely varied seabed conditions.

17 WIND ENERGY↗
DOE OSTI2014

Metabolic Network Discovery by Top-Down and Bottom-Up Approaches and Paths for Reconciliation

The primary focus in the network-centric analysis of cellular metabolism by systems biology approaches is to identify the active metabolic network for the condition of interest. Two major approaches are available for the discovery of the condition-specific metabolic networks. One approach starts from genome-scale metabolic networks, which cover all possible reactions known to occur in the related organism in a condition-independent manner, and applies methods such as the optimization-based Flux-Balance Analysis to elucidate the active network. The other approach starts from the condition-specific metabolome data, and processes the data with statistical or optimization-based methods to extract information content of the data such that the active network is inferred. These approaches, termed bottom-up and top-down, respectively, are currently employed independently. However, considering that both approaches have the same goal, they can both benefit from each other paving the way for the novel integrative analysis methods of metabolome data- and flux-analysis approaches in the post-genomic era. This study reviews the strengths of constraint-based analysis and network inference methods reported in the metabolic systems biology field; then elaborates on the potential paths to reconcile the two approaches to shed better light on how the metabolism functions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Effectively using multifidelity optimization for wind turbine design

Abstract. Wind turbines are complex multidisciplinary systems that are challenging to design because of the tightly coupled interactions between different subsystems. Computational modeling attempts to resolve these couplings so we can efficiently explore new wind turbine systems early in the design process. Low-fidelity models are computationally efficient but make assumptions and simplifications that limit the accuracy of design studies, whereas high-fidelity models capture more of the actual physics but with increased computational cost. This paper details the use of multifidelity methods for optimizing wind turbine designs by using information from both low- and high-fidelity models to find an optimal solution at reduced cost. Specifically, a trust-region approach is used with a novel corrective function built from a nonlinear surrogate model. We find that for a diverse set of design problems – with examples given in rotor blade geometry design, wind turbine controller design, and wind power plant layout optimization – the multifidelity method finds the optimal design using 38 %–58 % of the computational cost of the high-fidelity-only optimization. The success of the multifidelity method in disparate applications suggests that it could be more broadly applied to other wind energy or otherwise generic applications.

17 WIND ENERGY↗
DOE OSTI2015

A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by three steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Optimal operation and sizing of pumped thermal energy storage for net benefits maximization

Abstract Current trends in the modern grid are leading to the development and deployment of energy storage to help integrate increasing variable renewable energy sources into the grid. This paper studies a pumped thermal energy storage (PTES) system for multiple grid services including energy arbitrage, frequency regulation, spinning and non‐spinning reserve, and resource adequacy. Optimal dispatch methods are proposed for individual services as well as value stacking from multiple services to maximize the economic benefits. Assessment results demonstrate the superiority of value stacking. Specifically, the study shows the maximum revenue from an individual grid service with a 30‐MWh PTES system was $522,520, while the value stacking could increase the benefits to $678,477. In addition, sensitivity analyses were conducted to explore the cost‐effectiveness of a PTES system with different combinations of power transfer limits and energy capacity. It was found that the power transfer limit had a greater impact than the energy capacity on the benefits. The proposed method could help determine the optimal duration of a future PTES system.

25 ENERGY STORAGE↗
DOE OSTI2014

A multicriteria framework with voxel-dependent parameters for radiotherapy treatment plan optimization

Purpose: To establish a new mathematical framework for radiotherapy treatment optimization with voxel-dependent optimization parameters. Methods: In the treatment plan optimization problem for radiotherapy, a clinically acceptable plan is usually generated by an optimization process with weighting factors or reference doses adjusted for a set of the objective functions associated to the organs. Recent discoveries indicate that adjusting parameters associated with each voxel may lead to better plan quality. However, it is still unclear regarding the mathematical reasons behind it. Furthermore, questions about the objective function selection and parameter adjustment to assure Pareto optimality as well as the relationship between the optimal solutions obtained from the organ-based and voxel-based models remain unanswered. To answer these questions, the authors establish in this work a new mathematical framework equipped with two theorems. Results: The new framework clarifies the different consequences of adjusting organ-dependent and voxel-dependent parameters for the treatment plan optimization of radiation therapy, as well as the impact of using different objective functions on plan qualities and Pareto surfaces. The main discoveries are threefold: (1) While in the organ-based model the selection of the objective function has an impact on the quality of the optimized plans, this is no longer an issue for the voxel-based model since the Pareto surface is independent of the objective function selection and the entire Pareto surface could be generated as long as the objective function satisfies certain mathematical conditions; (2) All Pareto solutions generated by the organ-based model with different objective functions are parts of a unique Pareto surface generated by the voxel-based model with any appropriate objective function; (3) A much larger Pareto surface is explored by adjusting voxel-dependent parameters than by adjusting organ-dependent parameters, possibly allowing for the generation of plans with better trade-offs among different clinical objectives. Conclusions: The authors have developed a mathematical framework for radiotherapy treatment optimization using voxel-based parameters. The authors can improve the plan quality by adjusting voxel-based weighting factors and exploring the unique and large Pareto surface which include all the Pareto surfaces that can be generated by organ-based model using different objective functions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2017

Coordinated distribution network control of tap changer transformers, capacitors and PV inverters

A power distribution system operates most efficiently with voltage deviations along a feeder kept to a minimum and must ensure all voltages remain within specified limits. Recently with the increased integration of photovoltaics, the variable power output has led to increased voltage fluctuations and violation of operating limits. This study proposes an optimization model based on a recently developed heuristic search method, grey wolf optimization, to coordinate the various distribution controllers. Several different case studies on IEEE 33 and 69 bus test systems modified by including tap changing transformers, capacitors and photovoltaic solar panels are performed. Simulation results are compared to two other heuristic-based optimization methods: harmony search and differential evolution. Finally, the simulation results show the effectiveness of the method and indicate the usage of reactive power outputs of PVs facilitates better voltage magnitude profile.

24 POWER TRANSMISSION AND DISTRIBUTION↗