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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Graphical models for optimal power flow

Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithm for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary tree-structured distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for “smart grid” applications like control of distributed energy resources. In conclusion, numerical evaluations on several benchmark networks show that practical OPF problems can be solved effectively using this approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2006

Algorithms for Maneuvering Spacecraft Around Small Bodies

A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of flyby, descent-to-hover, and ascent-from-hover maneuvers.

Acikmese, A. Bechet↗
DOE OSTI2020

A regression algorithm for accelerated lattice QCD that exploits sparse inference on the D-Wave quantum annealer

We propose a regression algorithm that utilizes a learned dictionary optimized for sparse inference on a D-Wave quantum annealer. In this regression algorithm, we concatenate the independent and dependent variables as a combined vector, and encode the high-order correlations between them into a dictionary optimized for sparse reconstruction. On a test dataset, the dependent variable is initialized to its average value and then a sparse reconstruction of the combined vector is obtained in which the dependent variable is typically shifted closer to its true value, as in a standard inpainting or denoising task. Here, a quantum annealer, which can presumably exploit a fully entangled initial state to better explore the complex energy landscape, is used to solve the highly non-convex sparse coding optimization problem. The regression algorithm is demonstrated for a lattice quantum chromodynamics simulation data using a D-Wave 2000Q quantum annealer and good prediction performance is achieved. The regression test is performed using six different values for the number of fully connected logical qubits, between 20 and 64. The scaling results indicate that a larger number of qubits gives better prediction accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Freeway Loop Detector Data Reconciliation Based on Vehicle Conservation

Loop detector is the most common source of traffic flow measurements on freeways. Though being a mature technology, loop detector is prone to miscounts even when it is properly deployed and adjusted. If a loop detectors systematically over- or under-counts, the estimation based on vehicle conservation leads to results that are not physically plausible such as negative density or density higher than the jam-density. Here we propose an optimization-based method in which plausible values of accumulation is guaranteed through explicit constraints. Compared to similar methods, the proposed method distinct in the following: (i) the optimization problem is convex therefore leads to shorter computational time; (ii) occupancy is also taken into account in order to estimate upper and lower bounds in the accumulation between stations; (iii) no modifications are required when data from one or multiple lanes are missing. The method is first validated using micro-simulation by disturbing the loop-detector from micro-simulation, applying the method and then comparing the results with the ground truth data. The results show the method is able to capture the average counts almost exactly while providing estimate of density with satisfactory accuracy. The method is also successfully applied in a scenario in which field-data is available.

data reconciliation↗
NASA NTRS2017

Computationally Efficient Motion Planning Algorithms for Agile Autonomous Vehicles in Cluttered Environments

Fast, real-time motion planning of an agile, autonomous vehicle in a cluttered environment, with many geometrically-fixed obstacles, is a very complex problem, especially because of the vehicle dynamics constraints and resource constrained computational capabilities onboard the vehicle. In this paper, we present computationally-efficient versions of our novel motion planning algorithm called the Spherical Expansion and Sequential Convex Programming (SE–SCP) algorithm. The SE–SCP algorithm first uses a spherical-expansion-based randomized sampling algorithm to explore the workspace. Oncea path is found from the start position to the goal position, the algorithm computes a locally optimal trajectory, within its homotopy class for a desired cost function, by solving a sequence of convex optimization problems. Thus, the SE–SCP algorithm is anytime locally optimal and the trajectory is globally optimal if the number of samples tends to infinity. In this paper, we further enhance the computational efficiency of the SE–SCP algorithm using uni-directional and bi-directional rewiring techniques. We also present a detailed proof of the local optimality characteristics of the new SE–SCP algorithms for aspecial case of vehicle dynamics. Simulation examples involving quadrotor and spacecraft help demonstrate the effectiveness of our new algorithms.

Bandyopadhyay, Saptarshi↗
DOE OSTI2020

Multi-Commodity Traffic Signal Control and Routing With Connected Vehicles

We report a real-time traffic management policy that integrates traffic signal control and multi-commodity routing of connected vehicles in networks with multiple destinations is developed. The proposed policy is based on a multi-commodity formulation of the store-and-forward model and assumes all vehicles are able to exchange information with the infrastructure. Vehicles share information about their current location and final destination. Based on this information, the strategy determines both optimized signal timings at every intersection and vehicle-specific routing information at every link of the network. The control actions, i.e., signal times and routing information, are updated at every cycle and delivered by a finite horizon optimal control problem cast into a rolling horizon framework. The underlying optimization problem is convex, and thus the method is suitable for real-time operation in large networks. The method is validated via a micro-simulation study in networks with up to twenty intersections and, in all simulations, outperforms a real-time traffic-responsive signal control strategy that is based on a single-commodity store-and-forward model. The scalable computation effort for increasing network sizes and prediction horizon confirms the computational efficiency of the method.

42 ENGINEERING↗
DOE OSTI2020

Batch Measurement Extremum Seeking Control of Distributed Energy Resources to Account for Communication Delays and Information Loss

Distributed Energy Resources (DER) have great potential to enhance the operation of electric power distribution systems. Previously, we explored the use of 2 Dimensional Extremum Seeking (2D-ES) control algorithms to enable model-free optimal control of DER to provide grid services to both the distribution and transmissions systems. Motivated by preliminary deployments of DER managed by 2D-ES algorithms in hardware-in-the-loop tests and in operational distribution grids, in this work, we extend the control scheme to accommodate communication delays and information loss. We propose a modification to the 2D-ES scheme to allow for the processing of batches of possibly noncontiguous objective function measurements at unknown and possibly uneven intervals. We provide a proof of the convergence of the batch 2D-ES (2D-BES) scheme when optimizing a generic convex objective function, as well as simulation results that demonstrate the suitability of the approach for substation active and reactive power target tracking.

Sankur, Michael↗
NASA NTRS2017

Distributed Spatiotemporal Motion Planning for Spacecraft Swarms in Cluttered Environments

This paper focuses on trajectory planning for spacecraft swarms in cluttered environments, like debris fields or the asteroid belt. Our objective is to reconfigure the spacecraft swarm to a desired formation in a distributed manner while minimizing fuel and avoiding collisions among themselves and with obstacles. In our prior work we proposed a novel distributed guidance algorithm for spacecraft swarms in static environments. In this paper, we present the Multi-Agent Moving-Obstacles Spherical Expansion and Sequential Convex Programming (MAMO SE-SCP) algorithm that extends our prior work to include spatiotemporal constraints such as time-varying, moving obstacles and desired time-varying terminal positions. In the MAMO SE-SCP algorithm, each agent uses a spherical-expansion-based sampling algorithm to cooperatively explore the time-varying environment, a distributed assignment algorithm to agree on the terminal position for each agent, and a sequential-convex-programming-based optimization step to compute the locally-optimal trajectories from the current location to the assigned time-varying terminal position while avoiding collision with other agents and moving obstacles. Simulation results demonstrate that the proposed distributed algorithm can be used by a spacecraft swarm to achieve a time-varying, desired formation around an object of interest in a dynamic environment with many moving and tumbling obstacles.

Bandyopadhyay, Saptarshi↗
NASA NTRS2017

Distributed Spatiotemporal Motion Planning for Spacecraft Swarms in Cluttered Environments

This paper focuses on trajectory planning for spacecraft swarms in cluttered environments, like debris fields or the asteroid belt. Our objective is to reconfigure the spacecraft swarm to a desired formation in a distributed manner while minimizing fuel and avoiding collisions among themselves and with the obstacles. In our prior work we proposed a novel distributed guidance algorithm for spacecraft swarms in static environments.1 In this paper, we present the Multi-Agent Moving-Obstacles Spherical Expansion and Sequential Convex Programming (MAMO SE–SCP) algorithm that extends our prior work to include spatiotemporal constraints such as time-varying, moving obstacles and desired time-varying terminal positions. In the MAMO SE–SCP algorithm, each agent uses a spherical-expansion-based sampling algorithm to cooperatively explore the time-varying environment, a distributed assignment algorithm to agree on the terminal position for each agent, and a sequential-convex-programming-based optimization step to compute the locally-optimal trajectories from the current location to the assigned time-varying terminal position while avoiding collision with other agent and the moving obstacles. Simulations results demonstrate that the proposed distributed algorithm can be used by a spacecraft swarm to achieve a time-varying, desired formation around an object of interest in a dynamic environment with many moving and tumbling obstacles.

Hadaegh, Fred Y.↗
DOE OSTI2014

Poster — Thur Eve — 69: Computational Study of DVH-guided Cancer Treatment Planning Optimization Methods

Purpose: To compare methods to incorporate the Dose Volume Histogram (DVH) curves into the treatment planning optimization. Method: The performance of three methods, namely, the conventional Mixed Integer Programming (MIP) model, a convex moment-based constrained optimization approach, and an unconstrained convex moment-based penalty approach, is compared using anonymized data of a prostate cancer patient. Three plans we generated using the corresponding optimization models. Four Organs at Risk (OARs) and one Tumor were involved in the treatment planning. The OARs and Tumor were discretized into total of 50,221 voxels. The number of beamlets was 943. We used commercially available optimization software Gurobi and Matlab to solve the models. Plan comparison was done by recording the model runtime followed by visual inspection of the resulting dose volume histograms. Conclusion: We demonstrate the effectiveness of the moment-based approaches to replicate the set of prescribed DVH curves. The unconstrained convex moment-based penalty approach is concluded to have the greatest potential to reduce the computational effort and holds a promise of substantial computational speed up.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Multidimensional sum-up rounding for integer programming in optimal experimental design

Here we present a numerical method for approximating the solution of convex integer programs stemming from optimal experimental design. The statistical setup consists of a Bayesian framework for linear inverse problems for which the direct relationship is described by a discretized integral equation. Specifically, we aim to find the optimal sensor placement from a set of candidate locations where data are collected with measurement error. The convex objective function is a measure of the uncertainty, described here by the trace or log-determinant of the posterior covariance matrix, for the discretized linear inverse problem solution. The resulting convex integer program is relaxed, producing a lower bound. An upper bound is obtained by extending the sum-up rounding approach to multiple dimensions. For this extension, we analyze its accuracy as a function of the discretization mesh size for a rectangular domain. We show asymptotic optimality of the integer solution defining the upper bound for different experimental design criteria (A- and D-optimal), by proving the convergence to zero of the gap between the upper and lower bounds as the mesh size goes to zero. The technique is illustrated on a two-dimensional gravity surveying problem for both A-optimal and D-optimal sensor placement where our designs yield better results compared with a thresholding rounding approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [Zhang et al., Enabling long-range exploration in minimization of multimodal functions, UAI 2021], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by deterministic oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. Here, we also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justifying the advantage of using moderate or large smoothing radii with the method. Furthermore, if the noise level decays to zero when approaching the global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based methods in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

Tran, Hoang [Oak Ridge National Laboratory (ORNL),↗
NASA NTRS2002

Multidimensional indexing structure for use with linear optimization queries

Linear optimization queries, which usually arise in various decision support and resource planning applications, are queries that retrieve top N data records (where N is an integer greater than zero) which satisfy a specific optimization criterion. The optimization criterion is to either maximize or minimize a linear equation. The coefficients of the linear equation are given at query time. Methods and apparatus are disclosed for constructing, maintaining and utilizing a multidimensional indexing structure of database records to improve the execution speed of linear optimization queries. Database records with numerical attributes are organized into a number of layers and each layer represents a geometric structure called convex hull. Such linear optimization queries are processed by searching from the outer-most layer of this multi-layer indexing structure inwards. At least one record per layer will satisfy the query criterion and the number of layers needed to be searched depends on the spatial distribution of records, the query-issued linear coefficients, and N, the number of records to be returned. When N is small compared to the total size of the database, answering the query typically requires searching only a small fraction of all relevant records, resulting in a tremendous speedup as compared to linearly scanning the entire dataset.

Bergman, Lawrence David↗
DOE OSTI2024

Flexible dynamic boundary microgrid operation considering network and load unbalances

Flexible microgrids with dynamic boundaries have recently been introduced in the literature. With the ability to reconfigure the topology of the microgrids dynamically through remotely controlled switches, flexible microgrids with dynamic boundaries can further improve the resiliency and energy efficiency of microgrids with distributed energy resources (DERs). This paper focuses on the optimal operation considering one of the predominant characteristics of microgrids and distribution systems – unbalanced networks and loads. In existing literature, balanced modeling of microgrids is more common due to its attractive simplicity. The three-phase power unbalance has not been considered as a constraint on the generation units in a microgrid. Further, negative sequence constraints have also been neglected. In this article, we propose a set of constraints that is specifically related to the capabilities of inverter interfaced resources to supply unbalanced current/power when the microgrid is islanded from the main distribution grid. We incorporate the new set of constraints into two optimization formulations leveraging two convex relaxations of the three-phase power flow equations: mixed-integer linear programming (MILP) and mixed-integer semidefinite programming (MISDP) that optimize the dispatch of controllable switches and DERs in the microgrid. The algorithms are then extended to networked microgrids with grid-forming sources. We test the algorithms on a realistic community microgrid model in Puerto Rico as well as standardized IEEE distribution test feeders. The testing results demonstrate the performance of the proposed algorithms. The MILP is fast and scalable, and the MISDP enforces the negative sequence voltage constraints.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Strong stability of linear parabolic time-optimal control problems

Sufficient conditions for strong stability of a class of linear time-optimal control problems with general convex terminal set are derived. Strong stability in turn guarantees qualified optimality conditions. The theory is based on a characterization of weak invariance of the target set under the controlled equation. An appropriate strengthening of the resulting Hamiltonian condition ensures strong stability and yields a priori bounds on the size of multipliers, independent of, e.g. , the initial point or the running cost. In particular, the results are applied to the control of the heat equation into an L 2 -ball around a desired state.

Automation & Control Systems↗
DOE OSTI2024

Measure this, not that: Optimizing the cost and model-based information content of measurements

Model-based design of experiments (MBDoE) is a powerful framework for selecting and calibrating science-based mathematical models from data. Here, this work extends popular MBDoE workflows by proposing a convex mixed integer (non)linear programming (MINLP) to optimize the selection of measurements. The solver MindtPy is modified to support calculating the D-optimality objective and its gradient via an external package, scipy, using the grey-box module in Pyomo. The new approach is demonstrated in two case studies: estimating highly correlated kinetics from a batch reactor and estimating transport parameters in a large-scale rotary packed bed for CO 2 capture. Both case studies show how examining the Pareto optimal trade-offs between information content measured by A- and D-optimality versus measurement budget offers practical guidance for selecting measurements for scientific experiments.

97 MATHEMATICS AND COMPUTING↗