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At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Stochastic Analysis for Long Term Capital Structures, Systems, and Components Refurbishment and Replacement

As commercial Nuclear Power Plants (NPPs) pursue extended plant operation in the form of Second License Renewal (SLR), opportunities exist for these plants to provide capital investments to ensure long-term safe and economic performance. At the current time, several utilities have announced an intention to pursue extended operation for one or more of their NPPs via SLR . The goal of this research is to develop a risk-informed approach to evaluate and prioritize plant capital investments made in preparation for, and during the period of, extended plant operations to support decisions for NPP operations. Since the capital investments are influenced by various factors, such as markets, safety and regulatory, the decision-making process of NPP operations should take into account relevant factors for balancing risks, costs and profits. The traditional method of capital budgeting is based on the priority list of candidate projects using economic measures such as benefit-investment ratio, net present value (NPV) and internal rate of return. In the literatures, the problem of capital budgeting or the variant can be represented by an appropriate knapsack problem. The knapsack approach to capital budgeting takes as input as investment, along with the cost and profit of each project. The objective of capital budgeting is to find the combination of the binary decisions for every investment such that the overall profit is as large as possible. The output is a collection of projects to be carried out, and we refer this selected collection of projects as a project portfolio. One limitation of traditional optimization models for capital budgeting is that they do not account for risk/uncertainty in profit and cost streams associated with individual projects, they do not account for risk in resource availability in future years [1,2,3]. Projects can incur cost over-runs, especially when projects are large, performed infrequently, and when there is risk regarding technical viability, external contractors, and/or suppliers of requisite parts and materials. Occasionally, projects are performed ahead of schedule and with cost savings. Planned budgets for capital improvements can be cut and key personnel may be lost. Or, there may be surprise windfalls in budgets for maintenance activities due to decreased costs for “unplanned” maintenance. In these cases, how should we resolve capital budgeting when we have risk forecasts for costs, profits and budgets? One approach we proposed in this summary is to re-solve the optimization models based on assumed statistical distributions of given parameters. If these distributions were not available, a two-stage stochastic optimization approach can be used to provide priority lists to decision-makers to support better risk-informed decisions [4, 5]. In this summary, we will only focus on the first approach.

42 ENGINEERING↗
DOE OSTI2024

Towards optimal sensor placement for inverse problems in spaces of measures

The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in the sensor configuration and robust with respect to the source, yet relatively easy to compute in practice, compared to a direct evaluation of the error by a large number of samples. In particular, we consider the identification of a measure consisting of an unknown linear combination of point sources from a finite number of measurements contaminated by Gaussian noise. The statistical framework for recovery relies on two main ingredients: first, a convex but non-smooth variational Tikhonov point estimator over the space of Radon measures and, second, a suitable mean-squared error based on its Hellinger–Kantorovich distance to the ground truth. To quantify the error, we employ a non-degenerate source condition as well as careful linearization arguments to derive a computable upper bound. This leads to asymptotically sharp error estimates in expectation that are explicit in the sensor configuration. Thus they can be used to estimate the expected reconstruction error for a given sensor configuration and guide the placement of sensors in sparse inverse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Selecting registration schemes in case of interstitial lung disease follow-up in CT

Purpose: Primary goal of this study is to select optimal registration schemes in the framework of interstitial lung disease (ILD) follow-up analysis in CT. Methods: A set of 128 multiresolution schemes composed of multiresolution nonrigid and combinations of rigid and nonrigid registration schemes are evaluated, utilizing ten artificially warped ILD follow-up volumes, originating from ten clinical volumetric CT scans of ILD affected patients, to select candidate optimal schemes. Specifically, all combinations of four transformation models (three rigid: rigid, similarity, affine and one nonrigid: third order B-spline), four cost functions (sum-of-square distances, normalized correlation coefficient, mutual information, and normalized mutual information), four gradient descent optimizers (standard, regular step, adaptive stochastic, and finite difference), and two types of pyramids (recursive and Gaussian-smoothing) were considered. The selection process involves two stages. The first stage involves identification of schemes with deformation field singularities, according to the determinant of the Jacobian matrix. In the second stage, evaluation methodology is based on distance between corresponding landmark points in both normal lung parenchyma (NLP) and ILD affected regions. Statistical analysis was performed in order to select near optimal registration schemes per evaluation metric. Performance of the candidate registration schemes was verified on a case sample of ten clinical follow-up CT scans to obtain the selected registration schemes. Results: By considering near optimal schemes common to all ranking lists, 16 out of 128 registration schemes were initially selected. These schemes obtained submillimeter registration accuracies in terms of average distance errors 0.18 ± 0.01 mm for NLP and 0.20 ± 0.01 mm for ILD, in case of artificially generated follow-up data. Registration accuracy in terms of average distance error in clinical follow-up data was in the range of 1.985–2.156 mm and 1.966–2.234 mm, for NLP and ILD affected regions, respectively, excluding schemes with statistically significant lower performance (Wilcoxon signed-ranks test, p < 0.05), resulting in 13 finally selected registration schemes. Conclusions: Selected registration schemes in case of ILD CT follow-up analysis indicate the significance of adaptive stochastic gradient descent optimizer, as well as the importance of combined rigid and nonrigid schemes providing high accuracy and time efficiency. The selected optimal deformable registration schemes are equivalent in terms of their accuracy and thus compatible in terms of their clinical outcome.

60 APPLIED LIFE SCIENCES↗
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 OSTI2015

CALIBRATION OF SEMI-ANALYTIC MODELS OF GALAXY FORMATION USING PARTICLE SWARM OPTIMIZATION

We present a fast and accurate method to select an optimal set of parameters in semi-analytic models of galaxy formation and evolution (SAMs). Our approach compares the results of a model against a set of observables applying a stochastic technique called Particle Swarm Optimization (PSO), a self-learning algorithm for localizing regions of maximum likelihood in multidimensional spaces that outperforms traditional sampling methods in terms of computational cost. We apply the PSO technique to the SAG semi-analytic model combined with merger trees extracted from a standard Lambda Cold Dark Matter N-body simulation. The calibration is performed using a combination of observed galaxy properties as constraints, including the local stellar mass function and the black hole to bulge mass relation. We test the ability of the PSO algorithm to find the best set of free parameters of the model by comparing the results with those obtained using a MCMC exploration. Both methods find the same maximum likelihood region, however, the PSO method requires one order of magnitude fewer evaluations. This new approach allows a fast estimation of the best-fitting parameter set in multidimensional spaces, providing a practical tool to test the consequences of including other astrophysical processes in SAMs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Some Results of Multicriterial and Robust Optimization of Nuclear Power Systems Structure

The possibility of applying multicriterial and robust optimization methods as well as stochastic methods of determining the effect of uncertainties in the parameters of a system to structural optimization of nuclear power is discussed for the example of a hypothetical nuclear-power system consisting of thermal and fast reactors. It is shown that the optimal structures of nuclear power systems obtained by such methods are balanced in terms of conflicting criteria and technologically more diversified than those determined by single-criterion deterministic optimization. Cost-based innovative technologies, which can be adopted only by imposing additional external limitations in a single-criterion problem, appear in such structures. The examined methods make it possible to determine on a systematic basis the structures of nuclear power that are balanced in terms of a set of conflicting criteria, since factors having both positive and negative effects on the development of nuclear-power systems are included in the calculations, and to find economically efficient directions of structural changes in the system in order to improve stability and efficiency.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1992

Finite element structural analysis and optimization of space frames and trusses in a massively parallel environment

A set of massively parallel computational procedures are formulated to make finite element method based space frame and truss structural response analyses and stochastic method based structural optimization solution superefficient. Several example frame structural analysis and truss optimization problems are presented for demonstration purposes. All calculations are made on the massively parallel environment of CM-2 computer.

Shieh, Rong C.↗
NASA NTRS1979

Aircraft adaptive learning control

The optimal control theory of stochastic linear systems is discussed in terms of the advantages of distributed-control systems, and the control of randomly-sampled systems. An optimal solution to longitudinal control is derived and applied to the F-8 DFBW aircraft. A randomly-sampled linear process model with additive process and noise is developed.

Lee, P. S. T.↗
DOE OSTI2017

Systematic parameter inference in stochastic mesoscopic modeling

We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving dissipative particle dynamics (eDPD). The response surfaces of various target properties (viscosity, diffusivity, pressure, etc.) with respect to model parameters are constructed based on the generalized polynomial chaos (gPC) expansion using simulation results on sampling points (e.g., individual parameter sets). To alleviate the computational cost to evaluate the target properties, we employ the compressive sensing method to compute the coefficients of the dominant gPC terms given the prior knowledge that the coefficients are “sparse”. The proposed method shows comparable accuracy with the standard probabilistic collocation method (PCM) while it imposes a much weaker restriction on the number of the simulation samples especially for systems with high dimensional parametric space. Fully access to the response surfaces within the confidence range enables us to infer the optimal force parameters given the desirable values of target properties at the macroscopic scale. Moreover, it enables us to investigate the intrinsic relationship between the model parameters, identify possible degeneracies in the parameter space, and optimize the model by eliminating model redundancies. The proposed method provides an efficient alternative approach for constructing mesoscopic models by inferring model parameters to recover target properties of the physics systems (e.g., from experimental measurements), where those force field parameters and formulation cannot be derived from the microscopic level in a straight forward way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2006

Stochastic Evolutionary Algorithms for Planning Robot Paths

A computer program implements stochastic evolutionary algorithms for planning and optimizing collision-free paths for robots and their jointed limbs. Stochastic evolutionary algorithms can be made to produce acceptably close approximations to exact, optimal solutions for path-planning problems while often demanding much less computation than do exhaustive-search and deterministic inverse-kinematics algorithms that have been used previously for this purpose. Hence, the present software is better suited for application aboard robots having limited computing capabilities (see figure). The stochastic aspect lies in the use of simulated annealing to (1) prevent trapping of an optimization algorithm in local minima of an energy-like error measure by which the fitness of a trial solution is evaluated while (2) ensuring that the entire multidimensional configuration and parameter space of the path-planning problem is sampled efficiently with respect to both robot joint angles and computation time. Simulated annealing is an established technique for avoiding local minima in multidimensional optimization problems, but has not, until now, been applied to planning collision-free robot paths by use of low-power computers.

Fink, Wolfgang↗
NASA NTRS1972

Control system estimation and design for aerospace vehicles with time delay

The problems of estimation and control of discrete, linear, time-varying systems are considered. Previous solutions to these problems involved either approximate techniques, open-loop control solutions, or results which required excessive computation. The estimation problem is solved by two different methods, both of which yield the identical algorithm for determining the optimal filter. The partitioned results achieve a substantial reduction in computation time and storage requirements over the expanded solution, however. The results reduce to the Kalman filter when no delays are present in the system. The control problem is also solved by two different methods, both of which yield identical algorithms for determining the optimal control gains. The stochastic control is shown to be identical to the deterministic control, thus extending the separation principle to time delay systems. The results obtained reduce to the familiar optimal control solution when no time delays are present in the system.

Allgaier, G. R.↗
DOE OSTI2021

A Data-Driven Multi-Period Importance Sampling Strategy for Stochastic Economic Dispatch

Power systems with high penetrations of renewable energy (e.g., wind power) require sophisticated approaches to optimize system performance due to uncertainty in short-term system generation capacity. In this paper, we combine a data-driven analog scenario selection method with importance sampling to create a novel scenario construction approach for two-stage stochastic economic dispatch problems with a large number of wind farms on a network. The proposed method produces scenarios with realistic physics by finding high-fidelity analogs that can describe future states of the system. We show how to extend this method to multi-period operations and demonstrate the effectiveness of this technique by simulating economic dispatch operations on a synthetic test system over the course of a week.

data-driven forecasting↗
DOE OSTI2017

Efficient relaxations for joint chance constrained AC optimal power flow

Evolving power systems with increasing levels of stochasticity call for a need to solve optimal power flow problems with large quantities of random variables. Weather forecasts, electricity prices, and shifting load patterns introduce higher levels of uncertainty and can yield optimization problems that are difficult to solve in an efficient manner. Solution methods for single chance constraints in optimal power flow problems have been considered in the literature, ensuring single constraints are satisfied with a prescribed probability; however, joint chance constraints, ensuring multiple constraints are simultaneously satisfied, have predominantly been solved via scenario-based approaches or by utilizing Boole's inequality as an upper bound. In this paper, joint chance constraints are used to solve an AC optimal power flow problem while preventing overvoltages in distribution grids under high penetrations of photovoltaic systems. A tighter version of Boole's inequality is derived and used to provide a new upper bound on the joint chance constraint, and simulation results are shown demonstrating the benefit of the proposed upper bound. The new framework allows for a less conservative and more computationally efficient solution to considering joint chance constraints, specifically regarding preventing overvoltages.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1975

The effects of stability augmentation on the gust response of a STOL aircraft during a curved manual approach

The task of investigating the effect of SAS was formulated as two optimal control problems for stochastic systems: (1) to compute SAS gains with a rate model in the performance index algorithm; and (2) to calculate the pilot gains and system gust response using an optimal pilot model. Both problems were solved to yield reasonable low gains for the pilot and SAS, and the lateral directional mode poles and the longitudinal short period poles could be placed accurately by the model matching algorithm. Of the longitudinal (SAS) poles achieved, the vertical rms path error was least for the unaugmented poles. The lateral rms path error was an order of magnitude larger than the vertical error and showed a plus or minus 50 percent variation with SAS. It increased with dutch roll frequency and damping, and it decreased most significantly with increased roll stability. The variation in lateral error with bank angle for curved flight was also a significant function of the augmented poles.

Porter, M. B., Jr.↗
DOE OSTI2024

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.

Derivative-free Optimization↗
NASA NTRS1987

Stochastic control of infinite dimensional systems in Hilbert space: A factorization perspective

A factorization perspective on problems of optimal causal estimation and optimal causal control of linear stochastic systems defined on an infinite-dimensional Hilbert space is presented. A separation principle is derived for the case in which the system input/output map is generated by an abstract evolution operator. The factorization formalism allows for an essentially algebraic approach to these problems.

Milman, Mark M.↗
DOE OSTI2015

A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Stochastic Strategic Participation of Active Distribution Networks With High-Penetration DERs in Wholesale Electricity Markets

With the increasing penetration of distributed energy resources (DERs), traditional distribution networks as load-serving entities in wholesale electricity markets, now evolve towards active distribution networks (ADNs) which can proactively participate in wholesale markets by optimally controlling the DERs in their networks. A stochastic bilevel optimization model is proposed in this paper for the strategic participation of ADNs and DERs to provide energy and grid services in wholesale electricity markets. The bilevel optimization model can capture the interactions between the ADN and the wholesale energy and ancillary service markets, considering the uncertainties of DERs in the ADN. In the upper-level model, the ADN makes optimal decisions on energy and reserve bidding considering the availability, uncertainties, and flexibility of DERs. The joint energy and reserve market-clearing of the independent system operator (ISO) is modeled as the lower-level problem. Using strong duality theory and Karush-Kuhn Tucker (KKT) conditions, the proposed bilevel optimization problem is reformulated as mathematical programming with equilibrium constraints (MPEC) problem and further converted into a computationally-solvable mixed-integer second-order-cone programming (MISOCP) model. The simulation results demonstrate the effectiveness of the model and the interactions between an ADN and wholesale electricity markets.

active distribution network↗