Search NASA⌕ Search

SEARCH · Search NASA

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 1,063 records · Page 59

Solving Large‐Scale Linear Systems of Equations by a Quantum Hybrid Algorithm

Abstract Today's intermediate‐scale quantum computers, although imperfect, already perform computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, so far, quantum‐enabled large‐scale solutions have been realized only for limited set of problems. Here a hybrid algorithm based on phase estimation and classical optimization of the circuit width and depth is employed for solving a specific class of large linear systems of equations ubiquitous to many areas of science and engineering. A classification of linear systems based on the entanglement properties of the associated phase‐estimation unitary operation is introduced, enabling a highly efficient search for solutions that is facilitated by a straightforward matrix‐to‐circuit map. A 2 17 ‐dimensional problem is implemented on several IBM quantum computer superconducting quantum processors, a record‐breaking result for a linear system solved by a quantum computer. Demonstrated realisation sets a clear benchmark in the quest for the future quantum speedup in the linear systems of equations solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Control algorithms for dynamic attenuators

Purpose: The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator. Methods: The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not requirea priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen. Results: The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current modulation) without increasing peak variance. The 15-element piecewise-linear dynamic attenuator reduces dose by an average of 42%, and the perfect attenuator reduces dose by an average of 50%. Improvements in peak variance are several times larger than improvements in mean variance. Heuristic control eliminates the need for a prescan. For the piecewise-linear attenuator, the cost of heuristic control is an increase in dose of 9%. The proposed iterated WMV minimization produces results that are within a few percent of the true solution. Conclusions: Dynamic attenuators show potential for significant dose reduction. A wide class of dynamic attenuators can be accurately controlled using the described methods.

61 RADIATION PROTECTION AND DOSIMETRY↗

HHL algorithm with mapping function and enhanced sampling for model predictive control in microgrids

Here, this paper presents a refined quantum Harrow Hassidim Lloyd (HHL) algorithm for microgrid control. The first novelty of the developed method is that a mapping shift function enables the original HHL algorithm to handle general linear equations with non-singular and indefinite matrix. Second, a method of Matrix Extension for Amplifying Sampling Probabilities of Intended Solution (ME-ASPI) is proposed to design the reformulated linear algebraic equations, allowing for improved sampling efficiency of the quantum tomography in the refined HHL algorithm. Then, we applied the method to solve the model predictive control (MPC) problem in nonlinear dynamical microgrids. Specifically, with the ME-ASPI method, the refined HHL algorithm can effectively obtain the intended partial optimal control inputs for MPC. The optimization of quadratic programming problem in each time step of MPC is transformed into a linear system problem, which is addressed by the proposed quantum solver through using only partial information, with the time complexity improved from $\mathscr{O}(\mathscr{N}^{2.37286})$ classically to $\mathscr{O}(\mathscr{N}^{2} log \mathscr{N}$ x $p$ log $p)$ in quantum. Numerical examples have validated the effectiveness of the refined HHL algorithm with the proposed mapping function and the ME-ASPI method. By leveraging quantum properties, the proposed method provides a hybrid quantum–classical framework for microgrid control. This generic method can also potentially tackle many other challenges in analyzing and controlling general complex engineered systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Autonomous sputter synthesis of thin film nitrides with composition controlled by Bayesian optimization of optical plasma emission

Autonomous experimentation has emerged as an efficient approach to accelerate the pace of material discovery. Although instruments for autonomous synthesis have become popular in molecular and polymer science, solution processing of hybrid materials, and nanoparticles, examples of autonomous tools for physical vapor deposition are scarce yet important for the semiconductor industry. Here, we report the design and implementation of an autonomous workflow for sputter deposition of thin films with controlled composition, leveraging a highly automated sputtering reactor custom-controlled by Python, optical emission spectroscopy (OES), and a Bayesian optimization algorithm. We modeled film composition, measured by x-ray fluorescence, as a linear function of plasma emission lines monitored during co-sputtering from elemental Zn and Ti targets in an N 2 and Ar atmosphere. A Bayesian control algorithm, informed by OES, navigates the space of sputtering power to fabricate films with user-defined compositions by minimizing the absolute error between desired and measured optical emission signals. We validated our approach by autonomously fabricating Zn x Ti 1-x N y films that deviate from the targeted cation composition by a relative ±3.5%, even for 15 nm thin films, demonstrating that the proposed approach can reliably synthesize thin films with a specific composition and minimal human interference. Moreover, the proposed method can be extended to more difficult synthesis experiments where plasma intensity lines depend non-linearly on pressure, or the elemental sticking coefficients strongly depend on the substrate temperature.

36 MATERIALS SCIENCE↗

SU-E-T-793: Validation of COMPASS 3D Dosimetry as Pre Treatment Verification with Commercial TPS Algorithms

Purpose: The purpose of this study was to validate the advent of COMPASS 3D dosimetry as a routine pre treatment verification tool with commercially available CMS Monaco and Oncentra Masterplan planning system. Methods: Twenty esophagus patients were selected for this study. All these patients underwent radical VMAT treatment in Elekta Linac and plans were generated in Monaco v5.0 with MonteCarlo(MC) dose calculation algorithm. COMPASS 3D dosimetry comprises an advanced dose calculation algorithm of collapsed cone convolution(CCC). To validate CCC algorithm in COMPASS, The DICOM RT Plans generated using Monaco MC algorithm were transferred to Oncentra Masterplan v4.3 TPS. Only final dose calculations were performed using CCC algorithm with out optimization in Masterplan planning system. It is proven that MC algorithm is an accurate algorithm and obvious that there will be a difference with MC and CCC algorithms. Hence CCC in COMPASS should be validated with other commercially available CCC algorithm. To use the CCC as pretreatment verification tool with reference to MC generated treatment plans, CCC in OMP and CCC in COMPASS were validated using dose volume based indices such as D98, D95 for target volumes and OAR doses. Results: The point doses for open beams were observed <1% with reference to Monaco MC algorithms. Comparisons of CCC(OMP) Vs CCC(COMPASS) showed a mean difference of 1.82%±1.12SD and 1.65%±0.67SD for D98 and D95 respectively for Target coverage. Maximum point dose of −2.15%±0.60SD difference was observed in target volume. The mean lung dose of −2.68%±1.67SD was noticed between OMP and COMPASS. The maximum point doses for spinal cord were −1.82%±0.287SD. Conclusion: In this study, the accuracy of CCC algorithm in COMPASS 3D dosimetry was validated by compared with CCC algorithm in OMP TPS. Dose calculation in COMPASS is feasible within < 2% in comparison with commercially available TPS algorithms.

60 APPLIED LIFE SCIENCES↗

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗

Visualization of Porphyrin-Based Photosensitizer Distribution from Fluorescence Images In Vivo Using an Optimized RGB Camera

A handheld RGB camera was developed to monitor the in vivo distribution of porphyrin-based photosensitizer (PS) hematoporphyrin monomethyl ether (HMME) in blood vessels during photodynamic therapy (PDT). The focal length, f-number, International Standardization Organization (ISO) sensitivity, and shutter speed of the camera were optimized for the solution sample with various HMME concentrations. After the parameter optimization, it was found that the red intensity value of the fluorescence image was linearly related to the fluorescence intensity under investigated conditions. The RGB camera was then used to monitor the in vivo distribution of HMME in blood vessels in a skin-fold window chamber model. The red intensity value of the recorded RGB fluorescence image was found to be linearly correlated to HMME concentrations in the range 0–24 μM. Significant differences in the red to green intensity ratios were observed between the blood vessels and the surrounding tissue.

60 APPLIED LIFE SCIENCES↗

TU-AB-303-12: Towards Inter and Intra Fraction Plan Adaptation for the MR-Linac

Purpose: To develop a new sequencer for IMRT that during treatment can account for anatomy changes provided by online and real-time MRI. This sequencer employs a novel inter and intra fraction scheme that converges to the prescribed dose without a final segment weight optimization (SWO) and enables immediate optimization and delivery of radiation adapted to the deformed anatomy. Methods: The sequencer is initially supplied with a voxel-based dose prescription and during the optimization iteratively generates segments that provide this prescribed dose. Every iteration selects the best segment for the current anatomy state, calculates the dose it will deliver, warps it back to the reference prescription grid and subtracts it from the remaining prescribed dose. This process continues until a certain percentage of dose or a number of segments has been delivered. The anatomy changes that occur during treatment require that convergence is achieved without a final SWO. This is resolved by adding the difference between the prescribed and delivered dose up to this fraction to the prescription of the subsequent fraction. This process is repeated for all fractions of the treatment. Results: Two breast cases were selected to stress test the pipeline by producing artificial inter and intra fraction anatomy deformations using a combination of incrementally applied rigid transformations. The dose convergence of the adaptive scheme over the entire treatment, relative to the prescribed dose, was on average 8.6% higher than the static plans delivered to the respective deformed anatomies and only 1.6% less than the static segment weighted plans on the static anatomy. Conclusion: This new adaptive sequencing strategy enables dose convergence without the need of SWO while adapting the plan to intermediate anatomies, which is a prerequisite for online plan adaptation. We are now testing our pipeline on prostate cases using clinical anatomy deformation data from our department. This work is financially supported by Elekta AB, Stockholm, Sweden.

60 APPLIED LIFE SCIENCES↗

SU-F-T-540: Comprehensive Fluence Delivery Optimization with Multileaf Collimation

Purpose: Multileaf collimator (MLC) leaf sequencing is performed via commercial black-box implementations, on which a user has limited to no access. We have developed an explicit, generic MLC sequencing model to serve as a tool for future investigations of fluence map optimization, fluence delivery optimization, and rotational collimator delivery methods. Methods: We have developed a novel, comprehensive model to effectively account for a variety of transmission and penumbra effects previously treated on an ad hoc basis in the literature. As the model is capable of quantifying a variety of effects, we utilize the asymmetric leakage intensity across each leaf to deliver fluence maps with pixel size smaller than the narrowest leaf width. Developed using linear programming and mixed integer programming formulations, the model is implemented using state of the art open-source solvers. To demonstrate the versatility of the algorithm, a graphical user interface (GUI) was developed in MATLAB capable of accepting custom leaf specifications and transmission parameters. As a preliminary proof-ofconcept, we have sequenced the leaves of a Varian 120 Leaf Millennium MLC for five prostate cancer patient fields and one head and neck field. Predetermined fluence maps have been processed by data smoothing methods to obtain pixel sizes of 2.5 cm{sup 2}. The quality of output was analyzed using computer simulations. Results: For the prostate fields, an average root mean squared error (RMSE) of 0.82 and gamma (0.5mm/0.5%) of 91.4% were observed compared to RMSE and gamma (0.5mm/0.5%) values of 7.04 and 34.0% when the leakage considerations were omitted. Similar results were observed for the head and neck case. Conclusion: A model to sequence MLC leaves to optimality has been proposed. Future work will involve extensive testing and evaluation of the method on clinical MLCs and comparison with black-box leaf sequencing algorithms currently used by commercial treatment planning systems.

60 APPLIED LIFE SCIENCES↗

Feedback Optimization of Incentives for Distribution Grid Services

Energy prices and net power injection limitations regulate the operations in distribution grids and typically ensure that operational constraints are met. Nevertheless, unexpected or prolonged abnormal events could undermine the grid's functioning. During contingencies, customers could contribute effectively to sustaining the network by providing services. Herein this paper proposes an incentive mechanism that promotes users' active participation by essentially altering the energy pricing rule. The incentives are modeled via a linear function whose parameters can be computed by the system operator (SO) by solving an optimization problem. Feedback-based optimization algorithms are then proposed to seek optimal incentives by leveraging measurements from the grid, even in the case when the SO does not have a full grid and customer information. Numerical simulations on a standard testbed validate the proposed approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity

Mathematical models for flow through porous media typically enjoy the so-called maximum principles, which place bounds on the pressure field. It is highly desirable to preserve these bounds on the pressure field in predictive numerical simulations, that is, one needs to satisfy discrete maximum principles (DMP). Unfortunately, many of the existing formulations for flow through porous media models do not satisfy DMP. This paper presents a robust, scalable numerical formulation based on variational inequalities (VI), to model non-linear flows through heterogeneous, anisotropic porous media without violating DMP. VI is an optimization technique that places bounds on the numerical solutions of partial differential equations. To crystallize the ideas, a modification to Darcy equations by taking into account pressure-dependent viscosity will be discretized using the lowest-order Raviart–Thomas (RT0) and Variational Multi-scale (VMS) finite element formulations. It will be shown that these formulations violate DMP, and, in fact, these violations increase with an increase in anisotropy. It will be shown that the proposed VI-based formulation provides a viable route to enforce DMP. Moreover, it will be shown that the proposed formulation is scalable, and can work with any numerical discretization and weak form. Aseriesof numerical benchmark problems are solved to demonstrate the effects of heterogeneity, anisotropy and non-linearity on DMP violations under the two chosen formulations (RT0 and VMS), and that of non-linearity on solver convergence for the proposed VI-based formulation. Parallel scalability on modern computational platforms will be illustrated through strong-scaling studies, which will prove the efficiency of the proposed formulation in a parallel setting. Algorithmic scalability as the problem size is scaled up will be demonstrated through novel static-scaling studies. The performed static-scaling studies can serve as a guide for users to be able to select an appropriate discretization for a given problem size.

42 ENGINEERING↗

Overall chilled water system energy consumption modeling and optimization

The emergence of increasingly affordable variable-speed drive technology has changed the approach used to control chilled water systems equipped with these drives. The purpose of this research was to develop an integrated chilled water modeling technique that can determine the optimal system setpoints and estimate the energy saving potential of chiller system. The chiller system equipped with Variable Frequency Drives (VFDs) on cooling tower fans and condenser water pumps. To accomplish the objective, physical component models of the centrifugal chiller, cooling tower and condenser water pump were established with the goal of incorporating the system’s condenser water flow rate and cooling tower fan speeds as optimization variables. Furthermore, a cooling load prediction algorithm was developed using a multiple non-linear regression model to approximate the building’s cooling load subject to a range of environmental conditions. The inputs and outputs of the individual component models were linked to estimate how adjusting the cooling tower fan and condenser water pump speed would influence the system’s comprehensive performance. Here, the overall system model was then optimized using a generalized reduced gradient optimization algorithm to determine the potential energy savings through speed control with VFDs and to ascertain a control logic strategy for the building automation system to operate the heating and cooling system. A case-study was performed on a single chiller system at a museum and the model was calibrated according to logged data collected over four months. Results showed that for the system analyzed, the energy saving of optimizing the cooling tower fan system was found to be 12–15%, while the energy saving potential of optimizing the condenser water pump with the cooling tower fan was negligible. Additionally, comparing different cooling tower fan control strategies showed that a wet-bulb approach-based cooling tower control strategy was shown to have the highest correlation to the optimized fan speed with an R 2 of 0.924.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Design and analysis of optimal pre-cooling in residential buildings

Existing pre-cooling strategies provide a means of shifting or reducing the peak demand and/or energy cost in residential buildings. However, majority of them are rule-based and therefore may not be optimal in terms of cost saving, leaving room for improvement. In this paper, an integer linear programming problem that accounts for the thermal properties of a specific home, HVAC system capacity, utility rate structure, and weather conditions and makes use of a home thermal model is formulated. This problem determines the HVAC on/off control signal that minimizes the 24-h energy cost while maintaining thermal comfort and calculates the corresponding optimal indoor air temperature. The model is constructed using home thermal properties identified via data training in real-time. Through simulation, the energy performance of the proposed optimal pre-cooling strategy is investigated and compared with three rule-based operation strategies from the literature. It is found that the optimal strategy requires the least energy consumption without sacrificing thermal comfort. The superb energy performance of the optimal strategy is attributed to a longer runtime of the HVAC system in cool outdoor air conditions and to the elimination of deadband in HVAC operation, which is required by the rule-based strategies, to allow the indoor air temperature to stay near the thermal comfort upper bound as much as possible. In terms of energy cost, the rule-based operation strategies require 3.52, 1.90, and 2.79, respectively, while the optimal strategy only requires 1.52. These figures represent a saving of 56.82%, 20.00%, and 45.52%, respectively. The results suggest that the optimal strategy is indeed significantly more effective than the existing rule-based operation strategies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Co-optimized trading of hybrid wind power plant with retired EV batteries in energy and reserve markets under uncertainties

To be competitive in the electricity markets, various technologies have been reported to increase profits of wind farm owners. Combining battery storage system, wind farms can be operated as conventional power plants which promotes the integration of wind power into the power grid. However, high expenses on batteries keep investors away. Retired EV batteries, fortunately, still have enough capacity to be reused and could be obtained at a low price. In this work, a two-stage optimization of a wind energy retired EV battery-storage system is proposed. The economic performance of the proposed system is examined concerning its participation in the frequency containment normal operation reserve (FCR-N) market and the spot market simultaneously. To account uncertainties in the wind farm output, various electricity market prices, and up/down regulation status, a scenario-based stochastic programming method is used. The sizing of the equipment is optimized on top of daily operations of the hybrid system which formulates a mixed-integer linear programming (MILP) problem. Scenarios are generated with the Monte Carlo simulation (MCS) and Roulette Wheel Mechanism (RWM), which are further reduced with the simultaneous backward method (SBM) to increase computational efficiency. A 21 MW wind farm is selected as a case study. Here, the optimization results show that by integrating with a retired EV battery-storage system (RESS) and a bi-directional inverter, the wind farm can increase its profits significantly when forwarding bids in both of the aforementioned electricity markets.

17 WIND ENERGY↗

Mathematical Models for Optimization of Grid-Integrated Energy Storage Systems

Energy storage has been proven to yield positive effects on planning, operation and control of electric grids. It has become a crucial task to properly model the energy storage systems (ESS) under the framework of grid optimization on transmission and distribution networks including microgrids. This paper presents a review on mathematical models and test cases of ESSs used for grid optimization studies, where the network constraints of power systems are included. The existing ESS models are mainly classified into two categories – linear and nonlinear models. The two main categories are further divided into several subcategories respectively; such as mixed-integer linear and convex nonlinear sub-categories. Based on the review and discussions, this paper aims at providing suggestions for choosing proper ESS models for specific grid optimization studies considering the chosen power network model.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Integration of graphical approaches into optimization-based design of multistage liquid extraction

We propose two optimization models for designing two liquid extraction systems: simple multistage liquid extractors and extractors with extract reflux. Both models are motivated by the concepts of the modified McCabe-Thiele graphical method for multistage extractor design. The operating and equilibrium curves in the McCabe-Thiele method are represented by material balances and piece-wise linearized thermodynamics properties. The use of piece-wise approximations improves computational tractability of both optimization models. In addition, we consider some extensions such as dilute systems, insoluble solvents, and non-ideal stages. In conclusion, the applicability of the proposed models is demonstrated with four illustrative examples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Risk-averse optimization for resilience enhancement of complex engineering systems under uncertainties

With the growth of complexity and extent, large scale interconnected network systems, e.g., transportation networks or infrastructure networks, become more vulnerable to external disturbances. Hence, managing potential disruptive events during the design, operating, and recovery phase of an engineered system and therefore improving the system’s resilience is an important yet challenging task. Here, to ensure system resilience after the occurrence of failure events, this study proposes a mixed-integer linear programming (MILP) based restoration framework using heterogeneous dispatchable agents. The scenario-based stochastic optimization (SO) technique is adopted to deal with the inherent uncertainties imposed on the recovery process from nature. Moreover, different from conventional SO using deterministic equivalent formulations, the CVaR risk measure is implemented for this study because of the temporal sparsity of the decision making in applications such as the recovery from extreme events. The resulting restoration framework involves a large-scale MILP problem and thus an adequate decomposition technique i.e. modified Lagrangian dual decomposition, is also employed to achieve tractable computational complexity. Case study results based on the IEEE 37-bus test feeder demonstrate the benefits of using the proposed framework for resilience improvement as well as the advantages of adopting SO formulations.

42 ENGINEERING↗

CORN (Crop Optimization Realized through Neuralnets)

Traditional models of predicting plant traits are limited because they often rely on linear assumptions that do not fully capture the complexity of biological interactions and DNA-based markers which are static across environments. This project generated a set of RNA-based data from large multi-environment field trials and combined it with advanced machine learning techniques to account for these complex interactions and improve the accuracy of predictions.

59 BASIC BIOLOGICAL SCIENCES↗