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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 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Optimal Allocation of Static Var Compensator via Mixed Integer Conic Programming

Shunt FACTS devices, such as, a Static Var Compensator (SVC), are capable of providing local reactive power compensation. They are widely used in the network to reduce the real power loss and improve the voltage profile. This paper proposes a planning model based on mixed integer conic programming (MICP) to optimally allocate SVCs in the transmission network considering load uncertainty. The load uncertainties are represented by a number of scenarios. Reformulation and linearization techniques are utilized to transform the original non-convex model into a convex second order cone programming (SOCP) model. Numerical case studies based on the IEEE 30-bus system demonstrate the effectiveness of the proposed planning model.

Zhang, Xiaohu↗
DOE OSTI2019

On Holder-Brascamp-Lieb inequalities for torsion-free discrete Abelian groups

H\"older-Brascamp-Lieb inequalities provide upper bounds for a class of multilinear expressions, in terms of $L^p$ norms of the functions involved. They have been extensively studied for functions defined on Euclidean spaces. Bennett-Carbery-Christ-Tao have initiated the study of these inequalities for discrete Abelian groups and, in terms of suitable data, have characterized the set of all tuples of exponents for which such an inequality holds for specified data, as the convex polyhedron defined by a particular finite set of affine inequalities. In this paper we advance the theory of such inequalities for torsion-free discrete Abelian groups in three respects. The optimal constant in any such inequality is shown to equal $1$ whenever it is finite. An algorithm that computes the admissible polyhedron of exponents is developed. It is shown that nonetheless, existence of an algorithm that computes the full list of inequalities in the Bennett-Carbery-Christ-Tao description of the admissible polyhedron for all data, is equivalent to an affirmative solution of Hilbert's Tenth Problem over the rationals. That problem remains open. Applications to computer science will be explored in a forthcoming companion paper.

Christ, Michael↗
DOE OSTI2016

Super-resolution for scanning light stimulation systems

Super-resolution (SR) is a technique used in digital image processing to overcome the resolution limitation of imaging systems. In this process, a single high resolution image is reconstructed from multiple low resolution images. SR is commonly used for CCD and CMOS (Complementary Metal-Oxide-Semiconductor) sensor images, as well as for medical applications, e.g., magnetic resonance imaging. Here, we demonstrate that super-resolution can be applied with scanning light stimulation (LS) systems, which are common to obtain space-resolved electro-optical parameters of a sample. For our purposes, the Projection Onto Convex Sets (POCS) was chosen and modified to suit the needs of LS systems. To demonstrate the SR adaption, an Optical Beam Induced Current (OBIC) LS system was used. The POCS algorithm was optimized by means of OBIC short circuit current measurements on a multicrystalline solar cell, resulting in a mean square error reduction of up to 61% and improved image quality.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1976

Method of constructing dished ion thruster grids to provide hole array spacing compensation

The center-to-center spacings of a photoresist pattern for an array of holes applied to a thin metal sheet are increased by uniformly stretching the thin metal sheet in all directions along the plane of the sheet. The uniform stretching is provided by securely clamping the periphery of the sheet and applying an annular force against the face of the sheet, within the periphery of the sheet and around the photoresist pattern. The technique is used in the construction of ion thruster grid units where the outer or downstream grid is subjected to uniform stretching prior to convex molding. The technique provides alignment of the holes of grid pairs so as to direct the ion beamlets in a direction parallel to the axis of the grid unit and thereby provide optimization of the available thrust.

Banks, B. A.↗
DOE OSTI2016

Multivariate Predictive Analytics of Wind Power Data for Robust Control of Energy Storage

Short-term forecasting is frequently identified as an important tool for the effective management of wind generation. However, forecasting errors, inherent to the point forecasts, increase requirements for energy storage and can affect optimal system operation. Probabilistic forecasts can help tackle this issue by providing a proper characterization of forecasting errors in the optimization process. This paper proposes a multivariate model of forecasting data for wind generation. Predictive uncertainty intervals of wind power can be obtained by sampling from the proposed model. The main goal is to use empirical data models without linear or Gaussian approximations of the distributional or temporal variations. The predictive modeling is utilized within a case study of an energy storage system. Finally, a modified robust convex programming is used to maintain the practical robustness and feasibility of the solution based on the sampled scenarios from the model.

17 WIND ENERGY↗
DOE OSTI2026

Memory-efficient nonsmooth dynamic optimization using adaptive randomized compression

Dynamic optimization problems arise in many applications including flow control, full waveform inversion, and medical imaging. These problems are plagued by significant computational challenges. One such challenge — and the focus of this work — is the memory limitation induced by the size of the underlying dynamical system. In particular, the entire dynamic trajectory is required for derivative computation and therefore must be stored or recomputed using, e.g., checkpointing. Although recent work demonstrated the use of adaptive randomized sketching to overcome the memory challenge, that work only applies to smooth unconstrained problems, prohibiting its use for nonsmooth regularized and constrained problems. The inclusion of nonsmooth regularizers and constraints is critical as they often arise in an attempt to preserve certain physical properties or to promote sparsity. To solve these problems, we introduce a trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function that leverages randomized sketching to compress the dynamical system trajectories and adaptively adjust the sketch rank to satisfy a gradient inexactness condition. We prove convergence of this algorithm and demonstrate that it achieves substantial memory reduction on three discretized PDE-constrained optimization applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Formulations and Valid Inequalities for Optimal Black Start Allocation in Power Systems

The restoration of a power system after a blackout starts around units with enhanced technical capabilities, referred to as black start units (BSUs). We examine the planning problem of optimally allocating these units on the grid subject to a budget constraint. We present a mixed integer programming model based on current literature in power systems. Binary variables are associated with the allocation of BSUs and with the energization state of buses, branches, and generators of the power system over a time horizon. We extract a substructure of the feasible region which imposes the requirement that each island that appears during the restoration process must have at least one operational generator. We discuss three equivalent reformulations for this requirement. We introduce a family of exponentially many, polynomially separable, valid inequalities to strengthen the formulation. Under simplifying assumptions, we show that the convex hull of the feasible region is a full-dimensional polyhedron, and prove that some of the constraints we introduced are facet-defining. We perform experiments to examine the difference in strength between the formulations as well as the computational times to solve the problem to near optimality for synthetic instances of the IEEE-39, IEEE-118, Illinois-200, WECC-225, IEEE-300, South Carolina-500, and Texas-2000 power systems. We illustrate a use case of the model. We conclude by suggesting extensions of the current work for future research.

Black Start Allocation↗
DOE OSTI2024

Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Here, our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto-Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.

Chaotic dynamical systems↗
DOE OSTI2018

Predictively Coordinated Vehicle Acceleration and Lane Selection Using Mixed Integer Programming

Autonomous vehicle technology provides the means to optimize motion planning beyond human capacity. In particular, the problem of navigating multi-lane traffic optimally for trip time, energy efficiency, and collision avoidance presents challenges beyond those of single-lane roadways. For example, the host vehicle must simultaneously track multiple obstacles, the drivable region is non-convex, and automated vehicles must obey social expectations. Furthermore, reactive decision-making may result in becoming stuck in an undesirable traffic position. This paper presents a fundamental approach to these problems using model predictive control with a mixed integer quadratic program at its core. Lateral and longitudinal movements are coordinated to avoid collisions, track a velocity and lane, and minimize acceleration. Vehicle-to-vehicle connectivity provides a preview of surrounding vehicles’ motion. Simulation results show a 79% reduction in congestion-induced travel time and an 80% decrease in congestion-induced fuel consumption compared to a rule-based approach.

Dollar, Robert Austin↗
DOE OSTI2025

Efficient proximal subproblem solvers for a nonsmooth trust-region method

In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. Finally, we compare algorithm performance on examples from data science and PDE-constrained optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A Chaos Theoretic Approach to Animal Activity Recognition

Animal activity is a descriptor that can be potentially used to track the health and well-being, which is obviously very important to improve the management process and productivity of farms. This paper deals with an animal behavior recognition problem using a chaos theory approach where we adopt such a technique for automatic classification of calves behavioral states. Two main mutually exclusive behaviors are of interest, namely, lying and standing/walking with six possible activities: feeding, drinking water, drinking milk, playing, rumination, and neutral. The time series generated by ear-tags with a 3D-accelerometer after a wavelet denoising transformation and frequency stabilization are treated as representations of the nonlinear dynamical system. The dynamical system of a certain animal state exhibits specific strange attractor in a phase space. A characterization of such an attractor is performed through metric, dynamic, and topological invariants including Lyapunov exponent, correlation dimension, length of a phase trajectory, sum of edges forming a convex hull and others. These measures are used as a feature vector for the subsequent classification. In a cross validation scheme, six classifiers are built on each training set, and the hyper-parameters are optimized using an inner validation set. The classifier that reaches the highest accuracy on the inner validation set is used to classify the outer validation set. It is shown that this approach can be useful at predicting activity states as an alternative methodology for the animal behavior state recognition problem with acceptable classification accuracy. Furthermore it is possible to include this procedure as part of an ensemble method in machine learning where a combination of different models is used.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

Semilinear (topological) spaces and applications

Semivector spaces are defined and some of their algebraic aspects are developed including some structure theory. These spaces are then topologized to obtain semilinear topological spaces for which a hierarchy of local convexity axioms is identified. A number of fixed point and minmax theorems for spaces with various local convexity properties are established. The spaces of concern arise naturally as various hyperspaces of linear and semilinear (topological) spaces. It is indicated briefly how all this can be applied in socio-economic analysis and optimization.

Prakash, P.↗
NASA NTRS1990

A vectorized Lanczos eigensolver for high-performance computers

The computational strategies used to implement a Lanczos-based-method eigensolver on the latest generation of supercomputers are described. Several examples of structural vibration and buckling problems are presented that show the effects of using optimization techniques to increase the vectorization of the computational steps. The data storage and access schemes and the tools and strategies that best exploit the computer resources are presented. The method is implemented on the Convex C220, the Cray 2, and the Cray Y-MP computers. Results show that very good computation rates are achieved for the most computationally intensive steps of the Lanczos algorithm and that the Lanczos algorithm is many times faster than other methods extensively used in the past.

Bostic, Susan W.↗
DOE OSTI2021

Efficient Automated Driving Strategies Leveraging Anticipation and Optimal Control

Automated vehicles and advanced driver assistance systems bring computation, sensing, and communication technologies that exceed human abilities in some ways. For example, automated vehicles may sense a panorama all at once, do not suffer from human impairments and distractions, and could wirelessly communicate precise data with neighboring vehicles. Prototype and commercial deployments have demonstrated the capability to relieve human operators of some driving tasks up to and including fully autonomous taxi rides in some areas. The ultimate impact of this technology’s large-scale market penetration on energy efficiency remains unclear, with potential negative factors like road use by empty vehicles competing with positive ones like automatic eco-driving. Fundamentally enabled by historic and look-ahead data, this dissertation addresses the use of automated driving and driver assistance to optimize vehicle motion for energy efficiency. Facets of this problem include car following, co-optimized acceleration and lane change planning, and collaborative multi-agent guidance. Optimal control, especially model predictive control, is used extensively to improve energy efficiency while maintaining safe and timely driving via constraints. Techniques including chance constraints and mixed integer programming help overcome uncertainty and non-convexity challenges. Extensions of these techniques to tractor trailers on sloping roads are provided by making use of linear parameter-varying models. To approach the wheel-input energy eco-driving problem over generally shaped sloping roads with the computational potential for closed-loop implementation, a linear programming formulation is constructed. Distributed and collaborative techniques that enable connected and automated vehicles to accommodate their neighbors in traffic are also explored and compared to centralized control. Using simulations and vehicle-in-the-loop car following experiments, the proposed algorithms are benchmarked against others that do not make use of look-ahead information.

Dollar, Robert Austin↗
DOE OSTI2023

Certifiably Correct Range-Aided SLAM

We present the first algorithm capable of efficiently computing certifiably optimal solutions to range-aided simultaneous localization and mapping (RA-SLAM) problems. Robotic navigation systems are increasingly incorporating point-to-point ranging sensors, leading state estimation which takes the form of RA-SLAM. However, the RA-SLAM problem is more difficult to solve than traditional pose-graph SLAM; ranging sensor models introduce additional non-convexity, unlike pose-pose or pose-landmark measurements, a single range measurement does not uniquely determine the relative transform between the involved sensors, and RA-SLAM inference is highly sensitive to initial estimates. Our approach relaxes the RA-SLAM problem to a semidefinite program (SDP), which we show how to solve efficiently using the Riemannian staircase methodology. The solution of this SDP provides a high-quality initialization for our original RA-SLAM problem, which is subsequently refined via local optimization, as well as a lower-bound on the RA-SLAM problem's optimal value. Our algorithm, named certifiably correct RA-SLAM (CORA), applies to problems comprised of arbitrary pose-pose, pose-landmark, and ranging measurements. Evaluation on simulated and real-world marine examples shows that our algorithm frequently produces certifiably optimal RA-SLAM solutions; moreover, even suboptimal estimates are typically within 1-2\% of the optimal value.

Papalia, Alan↗
NASA NTRS1976

Structural optimization via a design space hierarchy

Mathematical programming techniques provide a general approach to automated structural design. An iterative method is proposed in which design is treated as a hierarchy of subproblems, one being locally constrained and the other being locally unconstrained. It is assumed that the design space is locally convex in the case of good initial designs and that the objective and constraint functions are continuous, with continuous first derivatives. A general design algorithm is outlined for finding a move direction which will decrease the value of the objective function while maintaining a feasible design. The case of one-dimensional search in a two-variable design space is discussed. Possible applications are discussed. A major feature of the proposed algorithm is its application to problems which are inherently ill-conditioned, such as design of structures for optimum geometry.

Vanderplaats, G. N.↗
DOE OSTI2016

A two-level approach to large mixed-integer programs with application to cogeneration in energy-efficient buildings

We study a two-stage mixed-integer linear program (MILP) with more than 1 million binary variables in the second stage. We develop a two-level approach by constructing a semi-coarse model that coarsens with respect to variables and a coarse model that coarsens with respect to both variables and constraints. We coarsen binary variables by selecting a small number of prespecified on/off profiles. We aggregate constraints by partitioning them into groups and taking convex combination over each group. With an appropriate choice of coarsened profiles, the semi-coarse model is guaranteed to find a feasible solution of the original problem and hence provides an upper bound on the optimal solution. We show that solving a sequence of coarse models converges to the same upper bound with proven finite steps. This is achieved by adding violated constraints to coarse models until all constraints in the semi-coarse model are satisfied. We demonstrate the effectiveness of our approach in cogeneration for buildings. Here, the coarsened models allow us to obtain good approximate solutions at a fraction of the time required by solving the original problem. Extensive numerical experiments show that the two-level approach scales to large problems that are beyond the capacity of state-of-the-art commercial MILP solvers.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2016

Relating Lexicographic Smoothness and Directed Subdifferentiability

Lexicographic derivatives developed by Nesterov and directed subdifferentials developed by Baier, Farkhi, and Roshchina are both essentially nonconvex generalized derivatives for nonsmooth nonconvex functions and satisfy strict calculus rules and mean-value theorems. This article aims to clarify the relationship between the two generalized derivatives. In particular, for scalar-valued functions that are locally Lipschitz continuous, lexicographic smoothness and directed subdifferentiability are shown to be equivalent, along with the necessary optimality conditions corresponding to each. For such functions, the visualization of the directed subdifferential-the Rubinov subdifferential-is shown to include the lexicographic subdifferential, and is also shown to be included in its closed convex hull. As a result, various implications of these results are discussed.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗