Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear optimization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Bi-Level Volt-VAR Optimization to Coordinate Smart Inverters with Voltage Control Devices

Conservation voltage reduction (CVR) uses voltage control to reduce customer power demand and help improve the operational efficiency of the electric power distribution system. With the advent of advanced distribution management systems (ADMS), the underlying data and control-rich platform can be utilized to enable a centralized Volt-VAR optimization (VVO) scheme that includes smart inverter controls along with legacy voltage control devices such as voltage regulators and capacitor banks to ensure a maximum CVR benefit. The objective of this paper to present a VVO approach that controls system’s legacy voltage control devices and coordinates their operation with smart inverter control. An optimal power flow (OPF) formulation is proposed by developing linear and nonlinear power flow approximations for a three-phase unbalanced electric power distribution system. A bi-level VVO approach is proposed where, Level-1 optimizes the control of legacy devices and smart inverters using a linear approximate three-phase power flow. In Level-2, the control parameters for smart inverters are adjusted to obtain an optimal and feasible solution by solving the approximate nonlinear OPF model. Level-1 is modeled as a Mixed Integer Linear Program (MILP) while Level-2 as a Quadratically Constrained Quadratic Program (QCQP). The proposed approach is validated using IEEE test cases and the results demonstrate the applicability of the framework in achieving the CVR objective.

Jha, Rahul Ranjan↗
DOE OSTI2022

Peak Power Minimization for Commercial Thermostatically Controlled Loads in Multi-Unit Grid-Interactive Efficient Buildings

The load profiles of most commercial and industrial consumers are characterized by brief periods of very high power consumption followed by intervals of lower demand. To encourage such consumers to flatten their load profiles, power utilities in and around the world often levy a monthly demand charge (DC) on the peak demand measured over brief intervals. In this work, we consider the joint optimization of energy costs (EC) and the instantaneous peak power of a multi-unit building which uses a hydronic heating, ventilation and cooling (HVAC) system and responds to a demand response (DR) program. Despite the non-linear structure of the problem, we show how optimal solutions can be obtained efficiently using linear programming. Next, we study the power demand patterns resulting from our proposed strategy for thermostatically controlled loads (TCLs), and evaluate the strategy’s performance for various climate zones in the US, under both typical and atypical weather conditions. Finally, the results show that depending on the ambient conditions and the tariff structure, our strategy can result in utility bill savings of up to nearly 19% compared to the baseline. The results also indicate that our power control strategy can significantly reduce the instantaneous peak power consumption in commercial TCLs.

HVAC↗
DOE OSTI2019

Complete Assembly of Circular and Chloroplast Genomes Based on Global Optimization

This paper focuses on the last two stages of genome assembly, namely scaffolding and gap-filling, and shows that they can be solved as part of a single optimization problem. Our approach is based on modeling genome assembly as a problem of finding a simple path in a specific graph that satisfies as many as possible of the distance constraints encoding the insert-size information. We formulate it as a mixed-integer linear programming problem and apply an optimization solver to find the exact solutions on a benchmark of chloroplasts. We show that the presence of repetitions in the set of unitigs is the main reason for the existence of multiple equivalent solutions that are associated to alternative subpaths. We also describe two sufficient conditions and we design efficient algorithms for identifying these subpaths. Comparisons of the results achieved by our tool with the ones obtained with recent assemblers are presented.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Optimized low-depth quantum circuits for molecular electronic structure using a separable-pair approximation

We present a classically tractable model that leads to optimized low-depth quantum circuits leveraging separable-pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the long term, provide significantly improved initial states for quantum algorithms. The associated wave functions can be represented with linear memory requirement, which allows classical optimization of the circuits and naturally defines a minimum benchmark for quantum algorithms. In this work we employ directly determined pair-natural orbitals within a basis-set-free approach. This leads to accurate representation of the one- and many-body parts for weakly correlated systems and we explicitly illustrate how the model can be integrated into other quantum algorithms for stronger correlated systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Development and Implementation of an Optimization Model for Hydropower and Total Dissolved Gas in the Mid-Columbia River System

Managing energy, water, and environmental priorities and constraints within a cascade hydropower system is a challenging multiobjective optimization effort that requires advanced modeling and forecasting tools. Within the mid-Columbia River system, there is currently a lack of specific solutions for predicting how coordinated operational decisions can mitigate the impacts of total dissolved gas (TDG) supersaturation while satisfying multiple additional policy and hydropower generation objectives. In this study, a reduced-order TDG uptake equation is developed that predicts tailrace TDG at seven hydropower facilities on the mid-Columbia River. The equation is incorporated into a general multiobjective river, reservoir, and hydropower optimization tool as a prioritized operating goal within a broader set of system-level objectives and constraints. A test case is presented to assess the response of TDG and hydropower generation when TDG supersaturation is optimized to remain under state water-quality standards. Satisfaction of TDG as an operating goal is highly dependent on whether constraints that limit TDG uptake are implemented at a higher priority than generation requests. According to the model, an opportunity exists to reduce TDG supersaturation and meet hydropower generation requirements by shifting spillway flows to different time periods. In conclusion, a coordinated effort between all project owners is required to implement systemwide optimized solutions that satisfy the operating policies of all stakeholders.

13 HYDRO ENERGY↗
DOE OSTI2021

Peak Power Reduction for HVAC Operations in Multi-unit Commercial Buildings

The load profiles of most commercial consumers are characterized by brief periods of very high power consumption followed by intervals of relatively lower demand. In order to flatten commercial load profiles, several power utilities in addition to billing energy consumption, levy a demand charge (DC) on the monthly peak demand. In this work, we consider the problem of joint optimization of energy costs (EC) and DC incurred by a multi-unit building which follows a demand response (DR) program. Despite the non-linear structure of the problem, we show how the optimal solutions can be obtained efficiently using linear programming. We evaluate the performance of the proposed power control scheme for various climate zones in the US. We show that depending on the ambient conditions and the prescribed tariff structure, our strategy can result in savings of up to nearly 19% compared to the baseline.

Raza Naqvi, Syed A.↗
DOE OSTI2024

Hydrothermal solubility of Dy hydroxide as a function of pH and stability of Dy hydroxyl aqueous complexes from 25 to 250 °C

The rare earth elements (REE) have important applications in green energy technologies. The formation of mineral deposits in geologic systems commonly involves hydrothermal fluids which can mobilize the REE. However, the REE speciation is not well known as a function of pH. The thermodynamic properties of REE hydroxyl complexes used in geochemical models are based on the Helgeson-Kirkham-Flowers (HKF) equation of state parameters which were derived by extrapolation of low temperature experimental and estimated data. In this study, Dy hydroxide solubility experiments are combined with available literature data to improve these models from 25 to 250 °C and optimize the thermodynamic properties of Dy 3+ and Dy hydroxyl complexes using GEMSFITS. Batch-type solubility experiments were conducted from 150 to 250 °C and at saturated water vapor pressure in perchloric acid solutions with initial pH values of 2 to 5 in 0.5 pH unit increments. The measured solubility of Dy hydroxide is retrograde with temperature and decreases with pH. The logarithm of total dissolved Dy molality ranges from –2.3 to –5.3 at 150 °C (pH 4.7–5.5), from –2.4 to –5.6 at 200 °C (pH 3.9–5.1), and from –3.7 to –6.9 at 250 °C (pH of 3.4 and 5.0). The optimized standard partial molal Gibbs energies of formation (Δ f G° T ) derived for Dy 3+ and DyOH 2+ display a close to linear relationship with temperature, fitting with previous optimizations based on DyPO 4 solubility data in the literature. A comparison of the optimized ΔfG°T values for aqueous Dy species with predictions from available HKF parameters indicates significant differences ranging from +11 to –26 kJ/mol between 25 and 250 °C. The experimental fits are used to derive the Dy hydroxide solubility products (K s0 ) and formation constants for the hydrolysis of Dy (β n with n = 1 to 3; Dy 3+ + nOH – = DyOH n 3-n ) as a function of temperature. The optimization method presented yields accurate thermodynamic properties for the Dy 3+ aqua ions and the DyOH 2+ species at the acidic to mildly acidic pH studied whereas more experimental work is needed at near-neutral and alkaline conditions to better constrain the other hydroxyl complexes. Furthermore, the optimized thermodynamic data have a significant impact on geochemical modeling of the mobility and solubility of REE minerals in acidic hydrothermal fluids.

58 GEOSCIENCES↗
DOE OSTI2015

Mean-Variance Problems for Finite Horizon Semi-Markov Decision Processes

This paper deals with a mean-variance problem for finite horizon semi-Markov decision processes. The state and action spaces are Borel spaces, while the reward function may be unbounded. The goal is to seek an optimal policy with minimal finite horizon reward variance over the set of policies with a given mean. Using the theory of N-step contraction, we give a characterization of policies with a given mean and convert the second order moment of the finite horizon reward to a mean of an infinite horizon reward/cost generated by a discrete-time Markov decision processes (MDP) with a two dimension state space and a new one-step reward/cost under suitable conditions. We then establish the optimality equation and the existence of mean-variance optimal policies by employing the existing results of discrete-time MDPs. We also provide a value iteration and a policy improvement algorithms for computing the value function and mean-variance optimal policies, respectively. In addition, a linear program and the dual program are developed for solving the mean-variance problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Stochastic Waveform Estimation at the Fundamental Quantum Limit

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well understood despite it being a widespread task at the frontier of experimental physics. State-of-the-art precision sensors of random forces must account for the underlying quantum nature of the measurement but the optimal quantum protocol for interrogating such linear sensors is not known. We derive the fundamental precision limit: the extended-channel quantum Cramér-Rao bound. In the experimentally relevant regime in which losses dominate, we prove that non-Gaussian-state preparation and measurement are required to achieve this fundamental limit and we determine numerically the optimal non-Gaussian protocol. We discuss how this scheme could accelerate searches for signatures of quantum gravity, stochastic gravitational waves, and axionic dark matter.

Axions↗
DOE OSTI2013

Comparison of open-source linear programming solvers.

When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.

Gearhart, Jared Lee↗
DOE OSTI2015

A two-phase investment model for optimal allocation of phasor measurement units considering transmission switching

Ensuring the reliability of an electrical power system requires a wide-area monitoring and full observability of the state variables. Phasor measurement units (PMUs) collect in real time synchronized phasors of voltages and currents which are used for the observability of the power grid. Due to the considerable cost of installing PMUs, it is not possible to equip all buses with PMUs. In this paper, we propose an integer linear programming model to determine the optimal PMU placement plan in two investment phases. In the first phase, PMUs are installed to achieve full observability of the power grid whereas additional PMUs are installed in the second phase to guarantee the N - 1 observability of the power grid. The proposed model also accounts for transmission switching and single contingencies such as failure of a PMU or a transmission line. Results are provided on several IEEE test systems which show that our proposed approach is a promising enhancement to the methods available for the optimal placement of PMUs.

Phasor measurement unit↗
DOE OSTI2013

4π Non-Coplanar Liver SBRT: A Novel Delivery Technique

Purpose: To improve the quality of liver stereotactic body radiation therapy (SBRT) treatments, a novel 4π framework was developed with accompanying algorithms to optimize non-coplanar beam orientations and fluences. The dose optimization is performed on a patient-specific deliverable beam geometry solution space, parameterized with patient and linear accelerator gantry orientations. Methods and Materials: Beams causing collision between the gantry and the couch or patient were eliminated by simulating all beam orientations using a precise computer assisted design model of the linear accelerator and a human subject. Integrated beam orientation and fluence map optimizations were performed on remaining beams using a greedy column generation method. Testing of the new method was performed on 10 liver SBRT cases previously treated with 50 to 60 Gy in 5 fractions using volumetric modulated arc therapy (VMAT). For each patient, both 14 and 22 non-coplanar fields were selected and optimized to meet the objective of ≥95% of the planning target volume (PTV) covered by 100% of the prescription dose. Doses to organs at risk, normal liver volumes receiving <15 Gy, integral dose, and 50% dose spillage volumes were compared against the delivered clinical VMAT plans. Results: Compared with the VMAT plans, the 4π plans yielded reduced 50% dose spillage volume and integral dose by 22% (range 10%-40%) and 19% (range 13%-26%), respectively. The mean normal liver volume receiving <15 Gy was increased by 51 cc (range 21-107 cc) with a 31% reduction of the mean normal liver dose. Mean doses to the left kidney and right kidney and maximum doses to the stomach and spinal cord were on average reduced by 70%, 51%, 67%, and 64% (P≤.05). Conclusions: This novel 4π non-coplanar radiation delivery technique significantly improved dose gradient, reduced high dose spillage, and improved organ at risk sparing compared with state of the art VMAT plans.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2026

Algebraic Multigrid with Filtering: An Efficient Preconditioner for Interior Point Methods in Large-Scale Contact Mechanics Optimization

Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are often nonlinear, nonconvex, and increasingly difficult to solve as mesh resolution increases. In this work, we employ a Newton-based interior-point (IP) filter line-search method, an effective approach for large-scale constrained optimization. While this method converges rapidly, each iteration requires solving a large saddle-point linear system that becomes ill-conditioned as the optimization process converges, largely due to IP treatment of the contact constraints. Such ill-conditioning can hinder solver scalability and increase iteration counts with mesh refinement. Here, to address this, we introduce a novel preconditioner, algebraic multigrid with filtering (AMGF), tailored to the Schur complement of the saddle-point system. Building on the classical AMG solver, commonly used for elasticity, we augment it with a specialized subspace correction that filters near null space components introduced by contact interface constraints. Through theoretical analysis and numerical experiments on a range of linear and nonlinear contact problems, we demonstrate that the proposed solver achieves mesh independent convergence and maintains robustness against the ill-conditioning that notoriously plagues IP methods. These results indicate that AMGF makes contact mechanics simulations more tractable and broadens the applicability of Newton-based IP methods in challenging engineering scenarios. More broadly, AMGF is well suited for problems, optimization or otherwise, where solver performance is limited by a low-dimensional subspace, such as those arising from localized constraints, interface conditions, or model heterogeneities. This makes the method widely applicable beyond contact mechanics and constrained optimization.

Mathematics and Computing↗
DOE OSTI2024

MULTI-LEADER: MULTI-source LEarning-Accelerated Design of high-Efficiency multi-stage compRessor (Final Technical Report)

The objective of MULTI-LEADER is to cut design costs by 80% while generating more energy-efficient designs of multi-stage compressors by developing and implementing novel machine learning (ML) techniques, which enable faster and fewer design iterations, improved solver performance, and concurrent multi-disciplinary design. Current industrial practices for the design of multi-stage compressors involve simulation-based design optimization with successive levels of model fidelity, iteratively evaluated between distinct disciplines, one stage at a time to tackle the high dimensional design variations. This project addresses these key design challenges: (1) concurrent optimization of multiple stages under many non-linear constraints; (2) multitude of evaluation of high-fidelity and expensive solvers and their gradients during optimization convergence in high-dimensional design; (3) multi-disciplinary design to maximize aerodynamic performance while guaranteeing structural integrity and additive manufacturability; (4) utilization of multiple fidelity of solvers with disparate parameterization and modeling assumptions. MULTI-LEADER achieved more than 5x speed up in detailed design of more energy-efficient compressors via these machine learning (ML) innovations: (i) rapid design surrogates by multi-source learning from diverse fidelities across multiple disciplines, (ii) physics-constrained data-augmented modeling for improved empiricism, (iii) generative manifold embedding for high dimensional concurrent design without gradient information; (iv) budget-constrained fidelity-adaptive sampling towards fewer design iterations.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Holistic fleet optimization incorporating system design considerations

The methodology described in this article enables a type of holistic fleet optimization that simultaneously considers the composition and activity of a fleet through time as well as the design of individual systems within the fleet. Often, real-world system design optimization and fleet-level acquisition optimization are treated separately due to the prohibitive scale and complexity of each problem. Importantly, this means that fleet-level schedules are typically limited to the inclusion of predefined system configurations and are blind to a rich spectrum of system design alternatives. Similarly, system design optimization often considers a system in isolation from the fleet and is blind to numerous, complex portfolio-level considerations. In reality, these two problems are highly interconnected. To properly address this system-fleet design interdependence, we present a general method for efficiently incorporating multi-objective system design trade-off information into a mixed-integer linear programming (MILP) fleet-level optimization. This work is motivated by the authors' experience with large-scale DOD acquisition portfolios. However, the methodology is general to any application where the fleet-level problem is a MILP and there exists at least one system having a design trade space in which two or more design objectives are parameters in the fleet-level MILP.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Optimizing design and dispatch of a renewable energy system with combined heat and power

We embellish a mixed-integer program that prescribes a set of renewable energy, conventional generation, and storage technologies to procure, along with a corresponding dispatch strategy. Specifically, we add combined heat and power to this set. The model minimizes fixed and operational costs less incentives for the use of various technologies, subject to a series of component interoperability and system-wide constraints. The resulting mixed-integer linear program contains hundreds of thousands of variables and constraints. We demonstrate how to efficiently formulate and solve the corresponding instances such that we produce near-optimal solutions in minutes. A previous rendition of the model required hours of solution time for the same instances.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2015

On helium 1083 nm line polarization during the impulsive phase of an X1 flare

We analyze spectropolarimetric data of the He i 1083 nm multiplet (1s2s{sup 3}S{sub 1}−1s2p{sup 3}P{sub 2,1,0}{sup o}) during the X1 flare SOL2014-03-29T17:48, obtained with the Facility Infrared Spectrometer (FIRS) at the Dunn Solar Telescope. While scanning active region NOAA 12017, the FIRS slit crossed a flare ribbon during the impulsive phase, when the helium line intensities turned into emission at ≲twice the continuum intensity. Their linear polarization profiles are of the same sign across the multiplet including 1082.9 nm, intensity-like, at ≲5% of the continuum intensity. Weaker Zeeman-induced linear polarization is also observed. Only the strongest linear polarization coincides with hard X-ray (HXR) emission at 30–70 keV observed by RHESSI. The polarization is generally more extended and lasts longer than the HXR emission. The upper J = 0 level of the 1082.9 nm component is unpolarizable; thus, lower-level polarization is the culprit. We make non-LTE radiative transfer calculations in thermal slabs optimized to fit only intensities. The linear polarizations are naturally reproduced, through a systematic change of sign with wavelength of the radiation anisotropy when slab optical depths of the 1082.9 component are ≲1. Neither are collisions with beams of particles needed, nor can they produce the same sign of polarization of the 1082.9 and 1083.0 nm components. The He i line polarization merely requires heating sufficient to produce slabs of the required thickness. Widely different polarizations of Hα, reported previously, are explained by different radiative anisotropies arising from slabs of different optical depths.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Implicit and Implicit–Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order

Strong stability preserving (SSP) time discretizations preserve the monotonicity properties satisfied by the spatial discretization when coupled with the first order forward Euler, under a certain time-step restriction. The search for high order strong stability preserving time-stepping methods with high order and large allowable time-step has been an active area of research. It is known that implicit SSP Runge–Kutta methods exist only up to sixth order; however, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and we can find implicit SSP Runge–Kutta methods of any linear order. In the current work we find implicit SSP Runge–Kutta methods with high linear order p lin ≤ 9 and nonlinear orders p = 2,3,4, that are optimal in terms of allowable SSP time-step. Next, we formulate a novel optimization problem for implicit–explicit (IMEX) SSP Runge–Kutta methods and find optimized IMEX SSP Runge–Kutta pairs that have high linear order p lin ≤ 7 and nonlinear orders up to p = 4. Here, we also find implicit methods with large linear stability regions that pair with known explicit SSP Runge–Kutta methods. These methods are then tested on sample problems to demonstrate the sharpness of the SSP coefficient and the typical behavior of these methods on test problems.

97 MATHEMATICS AND COMPUTING↗