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NASA NTRS1993

Extending substructure based iterative solvers to multiple load and repeated analyses

Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.

Farhat, Charbel↗

NASA NTRS1981

Mathematical specifications of the Onboard Navigation Package (ONPAC) simulator (revision 1)

The mathematical theory of the computational algorithms employed in the onboard navigation package system is described. This system, which simulates an onboard navigation processor, was developed to aid in the design and evaluation of onboard navigation software. The mathematical formulations presented include the factorized UDU(T) form of the extended Kalman filter, the equations of motion of the user satellite, the user clock equations, the observation equations and their partial derivatives, the coodinate transformations, and the matrix decomposition algorithms.

Dunham, J. B.↗

DOE OSTI2021

Data-Driven Adaptive Damping Controller for Wind Power Plants with Doubly-Fed Induction Generators

This paper presents an adaptive damping controller for wind power plants in which the turbines are equipped with doubly-fed induction generators. The controller is designed to respond to an input control signal that is triggered according to the system operating conditions. A processing unit continuously estimates the electromechanical modes of oscillation based on real-time streaming data acquired from a phasor measurement unit that is strategically positioned on the grid. The decision to trigger (or not trigger) the control signal is automatic, based on the relative damping of the dominant mode. The modes are estimated using the dynamic mode decomposition algorithm with time-delay embedding. Numerical simulations performed on the two-area system demonstrate that the proposed controller enhances the rotor angle stability for both small-signal and large disturbances, and is adaptive to changing grid conditions.

damping controller↗

NASA NTRS2014

Distributed Prognostics based on Structural Model Decomposition

Within systems health management, prognostics focuses on predicting the remaining useful life of a system. In the model-based prognostics paradigm, physics-based models are constructed that describe the operation of a system and how it fails. Such approaches consist of an estimation phase, in which the health state of the system is first identified, and a prediction phase, in which the health state is projected forward in time to determine the end of life. Centralized solutions to these problems are often computationally expensive, do not scale well as the size of the system grows, and introduce a single point of failure. In this paper, we propose a novel distributed model-based prognostics scheme that formally describes how to decompose both the estimation and prediction problems into independent local subproblems whose solutions may be easily composed into a global solution. The decomposition of the prognostics problem is achieved through structural decomposition of the underlying models. The decomposition algorithm creates from the global system model a set of local submodels suitable for prognostics. Independent local estimation and prediction problems are formed based on these local submodels, resulting in a scalable distributed prognostics approach that allows the local subproblems to be solved in parallel, thus offering increases in computational efficiency. Using a centrifugal pump as a case study, we perform a number of simulation-based experiments to demonstrate the distributed approach, compare the performance with a centralized approach, and establish its scalability. Index Terms-model-based prognostics, distributed prognostics, structural model decomposition ABBREVIATIONS

centrifugal pump↗

DOE OSTI2020

Joint Planning of EV Fast Charging Stations and Power Distribution Systems With Balanced Traffic Flow Assignment

To tackle the challenges introduced by the fast-growing charging demand of electric vehicles (EVs), the power distribution systems (PDSs) and fast charging stations (FCSs) of EVs should be planned and operated in a more coordinated fashion. However, existing planning approaches generally aim to minimize investment costs in PDSs while ignoring the risk of worsening traffic conditions. To overcome this research gap, this article integrates the interests of traffic networks into PDS and FCS joint planning model to mitigate negative impacts on traffic conditions caused by installing FCSs. First, a novel microscopic method that is different from traditional assignment methods is proposed to simulate the influences of FCSs on traffic flows and EV charging loads. Then, a multiobjective joint planning model is developed to minimize both the planning costs and unbalanced traffic flows. A new bilayer Benders decomposition algorithm is designed to solve the proposed joint planning model. Numerical results on two practical systems in China validate the feasibility of our microscopic method by comparing the simulated results with real data. Compared with existing approaches, it is also demonstrated that the proposed joint planning approach helps to balance traffic flow assignments and relieve traffic congestion.

bilayer expanded Benders decomposition↗

DOE OSTI2021

Data-Driven Adaptive Damping Controller for Wind Power Plants with Doubly-Fed Induction Generators: Preprint

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2018

An Algorithm for Enhancing the Image Contrast of Electron Tomography

Abstract Three-dimensional (3D) reconstruction of a single protein molecule is essential for understanding the relationship between the structural dynamics and functions of the protein. Electron tomography (ET) provides a tool for imaging an individual particle of protein from a series of tilted angles. Individual-particle electron tomography (IPET) provides an approach for reconstructing a 3D density map from a single targeted protein particle (without averaging from different particles of this type of protein), in which the target particle was imaged from a series of tilting angles. However, owing to radiation damage limitations, low-dose images (high noise, and low image contrast) are often challenging to be aligned for 3D reconstruction at intermediate resolution (1–3 nm). Here, we propose a computational method to enhance the image contrast, without increasing any experimental dose, for IPET 3D reconstruction. Using an edge-preserving smoothing-based multi-scale image decomposition algorithm, this method can detect the object against a high-noise background and enhance the object image contrast without increasing the noise level or significantly decreasing the image resolution. The method was validated by using both negative staining (NS) ET and cryo-ET images. The successful 3D reconstruction of a small molecule (<100 kDa) indicated that this method can be used as a supporting tool to current ET 3D reconstruction methods for studying protein dynamics via structure determination from each individual particle of the same type of protein.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

Resilient NdFeB magnet recycling under the impacts of COVID-19 pandemic: Stochastic programming and Benders decomposition

Neodymium-iron-boron (NdFeB) magnets are the most powerful magnets per unit volume sold in the commercial market. Despite the increasing demand for clean energy applications such as electric vehicles and wind turbines, disruptive events including the COVID-19 pandemic have caused significant uncertainties in the supply and demand for NdFeB magnets. Therefore, this study aims to alleviate the risk of supply shortage for NdFeB magnets and the containing critical materials, rare-earth elements (REEs), through the development of a resilient reverse supply chain and logistics network design. We develop scenarios to model the unique impact of the COVID-19 pandemic on the proposed business, incorporating both disruption intensity and recovery rate. We formulate a chance-constrained two-stage stochastic programming model to maximize the profit while guaranteeing the network resiliency against disruption risks. To solve the problem in large-scale instances, we develop an efficient Benders decomposition algorithm that reduces the computational time by 98.5% on average compared to the default CPLEX algorithm. When applied to the United States, the model suggests the optimal facility locations, processing capacities, inventory levels, and material flows for NdFeB magnet recyclers that could meet 99.7% of the demand. To the best of our knowledge, this study is the first to incorporate the impacts of the COVID-19 pandemic to design a resilient NdFeB magnet recycling supply chain and logistics network, leveraging risk-averse stochastic programming.

42 ENGINEERING↗

DOE OSTI2014

Phosphine-stabilised Au{sub 9} clusters interacting with titania and silica surfaces: The first evidence for the density of states signature of the support-immobilised cluster

Chemically made, atomically precise phosphine-stabilized clusters Au{sub 9}(PPh{sub 3}){sub 8}(NO{sub 3}){sub 3} were deposited on titania and silica from solutions at various concentrations and the samples heated under vacuum to remove the ligands. Metastable induced electron spectroscopy was used to determine the density of states at the surface, and X-ray photoelectron spectroscopy for analysing the composition of the surface. It was found for the Au{sub 9} cluster deposited on titania that the ligands react with the titania substrate. Based on analysis using the singular value decomposition algorithm, the series of MIE spectra can be described as a linear combination of 3 base spectra that are assigned to the spectra of the substrate, the phosphine ligands on the substrate, and the Au clusters anchored to titania after removal of the ligands. On silica, the Au clusters show significant agglomeration after heat treatment and no interaction of the ligands with the substrate can be identified.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Final Report, DE-FG01-06ER25718 Domain Decomposition and Parallel Computing

The goal of this project is to develop and improve domain decomposition algorithms for a variety of partial differential equations such as those of linear elasticity and electro-magnetics.These iterative methods are designed for massively parallel computing systems and allow the fast solution of the very large systems of algebraic equations that arise in large scale and complicated simulations. A special emphasis is placed on problems arising from Maxwell's equation. The approximate solvers, the preconditioners, are combined with the conjugate gradient method and must always include a solver of a coarse model in order to have a performance which is independent of the number of processors used in the computer simulation. A recent development allows for an adaptive construction of this coarse component of the preconditioner.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A multistage distributionally robust optimization approach to water allocation under climate uncertainty

This paper investigates a Multistage Distributionally Robust Optimization (MDRO) approach to water allocation under climate uncertainty. The MDRO is formed by creating sets of conditional distributions (called conditional ambiguity sets) on a finite scenario tree. The distributions in the conditional ambiguity sets remain close to a nominal conditional distribution according a ø-divergence (e.g., Kullback-Leibler divergence, Hellinger distance, Burg entropy, etc.). Here, the paper discusses a decomposition algorithm to solve the resulting MDRO with ø-divergences, which uses the dual formulation and solves only linear subproblems instead of convex ones. Some properties of the algorithm such as generating feasible policies and valid upper/lower bounds are established. The paper then applies the modeling and solution techniques to allocate water in a rapidly-developing area of Tucson, Arizona. Tucson, like many arid and semi-arid regions around the world, faces considerable uncertainty in its ability to provide water for its citizens in the future. The primary sources of uncertainty in the Tucson region include (1) unpredictable population growth, (2) the availability of water from the Colorado River, and (3) the effects of climate variability on water consumption. This paper integrates forecasts for all these sources of uncertainty into a single optimization model for robust and sustainable water allocation. Then, it uses this model to analyze the value of constructing additional treatment facilities to reduce future water shortages. The results indicate that the MDRO approach can be very valuable for water managers by providing insights to minimize their risks and help them plan for the future.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

WE-FG-207B-01: BEST IN PHYSICS (IMAGING): Abdominal CT with Three K-Edge Contrast Materials Using a Whole-Body Photon-Counting Scanner: Initial Results of a Large Animal Experiment

Purpose: To demonstrate the feasibility of in vivo three-material decomposition techniques using photon-counting CT (PCCT) with possible advantage of resolving arterial and venous flow of an organ simultaneously. Methods: Abdominal PCCT scans were acquired using a prototype whole-body PCCT with four energy thresholds (25/50/75/90keV) in a canine. Bismuth subsalicylate (60 mg) was administered orally one day prior to scanning. Immediately prior to CT scan, gadoteric acid (60 ml, Dotarem, Guerbet) was intravenously injected, followed in ten minutes by a 20mL injection of iodinated contrast (iopamidol 370 mg/mL, Bracco). Scans were acquired every ∼20 seconds, starting from the time of iodine injection. Linear material decomposition was performed using the least mean squares method to create concentration maps of iodine, gadolinium, and bismuth. The method was calibrated to vials with known concentrations of materials placed next to the animal. The accuracy of this method was tested on vials with known concentrations. Results: The material decomposition algorithm’s accuracy was confirmed to be within ±4mM in the test vials. In the animal, we could estimate the concentration of gadolinium in delayed-enhanced phase (10 minutes post-injection) in the abdomen. We could follow the wash-in and wash-out of iodine in arterial, venous, and excretory flow of the kidneys (20s, 80s, and 120s post-iodine injection) while gadolinium was present in the delayed-enhanced phase. Bismuth, which was used as a contrast agent for the gastro-intestinal tract, was easily differentiable from the other two contrast agents in the small intestine. Conclusion: This study shows the feasibility of using photon-counting CT with four energy thresholds to differentiate three k-edge contrast agents in vivo. This can potentially reduce radiation dose to patients by combining arterial and venous phases into a single acquisition.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

A New LMP-Sensitivity-Based Heterogeneous Decomposition for Transmission and Distribution Coordinated Economic Dispatch

Transmission and distribution coordinated economic dispatch (TDCED) will be necessary to settle the problems caused by high penetrations of distributed generators in future grids. An efficient heterogeneous decomposition algorithm (HGD) was proposed to solve the TDCED, but it may diverge occasionally. To overcome this shortcoming, a new HGD (N-HGD) with enhanced convergency is proposed and studied in this paper. Compared with the previous HGD, the N-HGD similarly decomposes the TDCED into transmission ED and distribution ED subproblems, but it considers the sensitivity of the boundary locational marginal price to load injections to enhance convergency and avoid divergence. Two kinds of sensitivity computing methods, M-c and M-p, are studied. M-c is based on a centralized sensitivity equation, executed on the transmission side. M-p is based on a probing mechanism and can be executed distributedly on the distribution side. The reason for the N-HGD's improved convergency is theoretically analyzed, and the optimality is proven. Numerical tests show that N-HGD performs better than the original HGD, as well as a penalty-based modified HGD that needs a careful parametertuning process. Furthermore, compared with M-c, an M-p-based N-HGD is preferable because it has a much lower computational cost and no additional communicational cost.

distribution↗

DOE OSTI2018

Stochastic Programming Approach for Resource Selection under Demand Uncertainty

Cost-efficient selection and scheduling of a subset of geographically distributed resources to meet the demands of a scientific workflow is a challenging problem. The problem is exacerbated by uncertainties in demand and availability of resources. In this paper, we present a stochastic optimization based framework for robust decision making in the selection of distributed resources over a planning horizon under demand uncertainty. We present a novel two-stage stochastic programming model for resource selection, and implement an L-shaped decomposition algorithm to solve this model. A Sample Average Approximation algorithm is integrated to enable stochastic optimization to solve problems with a large number of scenarios. Using the metric of stochastic solution, we demonstrate up to 30% cost reduction relative to solutions without explicit consideration of demand uncertainty for a 24-month problem. We also demonstrate up to 54% cost reduction relative to a previously developed solution for a 36-month problem. We further argue that the composition of resources selected is superior to solutions computed without explicit consideration of uncertainties. Given the importance of resource selection and scheduling of complex scientific workflows, especially in the context of commercial cloud computing, we believe that our novel stochastic programming framework will benefit many researchers as well as users of distributed computing resources.

scientific workflows, task scheduling, optimizatio↗

DOE OSTI2018

Finding Maximum Cliques on the D-Wave Quantum Annealer

This work assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, and compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Sustainable network design for multi-purpose pellet processing depots under biomass supply uncertainty

This work develops a two-stage stochastic mixed-integer programming model to manage multi- purpose pellet processing depots under feedstock supply uncertainty. The proposed optimization model would help to minimize cost and to mitigate emissions from the supply chain network. We consider three alternative Biomass Processing and Densi cation Depot (BPDD) technologies; namely, conventional pellet processing, high moisture pellet processing, and ammonia ber expansion. These three technologies pre-process/pre-treat and densify different types of biomass into more highly densi ed intermediate products for different markets in order to improve movability and overall supply network performance in terms of costs and emissions. A hybrid decomposition algorithm was developed that combines sample average approximation with an enhanced Progressive Hedging (PH) algorithm to solve this challenging NP -hard problem. Some heuristics such as Rolling Horizon (RH) heuristic, variable xing technique were later applied to further enhance the PH algorithm. Mississippi and Alabama were selected as a testing ground and ArcGIS was employed to visualize and validate the modeling results. The results of the analysis reveal promising insights that could lead to recommendations to help decision makers achieve a more cost-effective environmentally-friendly supply chain network.

09 BIOMASS FUELS↗

DOE OSTI2024

Multistage Stochastic optimization for mid-term integrated generation and maintenance scheduling of cascaded hydroelectric system with renewable energy uncertainty

The uncertainties resulting from the escalating penetration of renewable energy resources pose severe challenges to the efficient operation of modern power systems. Hydroelectricity is characterized by its flexibility, controllability, and reliability, and thus becomes one of the most ideal energy resources to hedge against such uncertainties. This paper studies the mid-term integrated generation and maintenance scheduling of a cascaded hydroelectric system (CHS) consisting of multiple cascaded reservoirs and hydroelectric units. To precisely describe the mid-term water regulation policies, the hydraulic coupling relationship and water-energy nexus of CHS are incorporated into the proposed optimization model. The uncertainties of natural water inflow and the power outputs of wind/solar energy generation are taken into consideration and captured via a stochastic process modeled by a scenario tree. A multistage stochastic optimization (MSO) approach is developed to coordinate the complementary operations of multiple energy resources, by optimizing the mid-term water resource management, generation scheduling, and maintenance scheduling of CHS. The proposed MSO model is formulated as a large-scale mixed-integer linear program that presents significant computational intractability. To address this issue, a tailored Benders decomposition algorithm is developed. Two real-world case studies are conducted to demonstrate the capability and characteristics of the proposed model and algorithm. The computational results show that the proposed MSO model can exploit the flexibility of hydroelectricity to efficiently respond to variable wind and solar power, and reserve water resources for the generation in peak months to reduce the consumption of fossil fuel. Furthermore, the proposed solution approach also exhibits promising computational efficiency when handling large-scale models.

13 HYDRO ENERGY↗

DOE OSTI2015

Modeling laser-driven electron acceleration using WARP with Fourier decomposition

WARP is used with the recent implementation of the Fourier decomposition algorithm to model laser-driven electron acceleration in plasmas. Simulations were carried out to analyze the experimental results obtained on ionization-induced injection in a gas cell. The simulated results are in good agreement with the experimental ones, confirming the ability of the code to take into account the physics of electron injection and reduce calculation time. We present a detailed analysis of the laser propagation, the plasma wave generation and the electron beam dynamics.

43 PARTICLE ACCELERATORS↗