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DOE OSTI2020

Quantum Spectral Methods for Differential Equations

Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a d-dimensional system of linear equations or linear differential equations with complexity poly(logd). While several of these algorithms approximate the solution to within ϵ with complexity poly(log(1/ϵ)), no such algorithm was previously known for differential equations with time-dependent coefficients. In this work, we develop a quantum algorithm for linear ordinary differential equations based on so-called spectral methods, an alternative to finite difference methods that approximates the solution globally. Using this approach, we give a quantum algorithm for time-dependent initial and boundary value problems with complexity poly(logd, log(1/ϵ)).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data

This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. Furthermore, the results demonstrate the advantage of the algorithm in finding high-precision solutions.

interior point method↗

NASA NTRS1982

Automated preprocessing of spaceborne SAR data

An efficient algorithm has been developed for estimation of the echo phase delay in spaceborne synthetic aperture radar (SAR) data. This algorithm utilizes the spacecraft ephemeris data and the radar echo data to produce estimates of two parameters: (1) the centroid of the Doppler frequency spectrum f(d) and (2) the Doppler frequency rate. Results are presented from tests conducted with Seasat SAR data. The test data indicates that estimation accuracies of 3 Hz for f(d) and 0.3 Hz/sec for the Doppler frequency rate are attainable. The clutterlock and autofocus techniques used for estimation of f(d) and the Doppler frequency rate, respectively are discussed and the algorithm developed for optimal implementation of these techniques is presented.

Curlander, J. C.↗

DOE OSTI2023

Design Considerations of a Coordinative Demand Charge Mitigation Strategy

This paper presents a coordinative demand charge mitigation (DCM) strategy for reducing electricity consumption during system peak periods. Available DCM resources include batteries, diesel generators, controllable loads, and conservation voltage reduction. All resources are directly controlled by load serving entities. A mixed integer linear programming based energy management algorithm is developed to optimally coordinate of DCM resources considering the load payback effect. To better capture system peak periods, two different kinds of load forecast are used: the day-ahead load forecast and the peak-hour probability forecast. Five DCM strategies are compared for reconciling the discrepancy between the two forecasting results. The DCM strategies are tested using actual utility data. Simulation results show that the proposed algorithm can effectively mitigate the demand charge while preventing the system peak from being shifted to the payback hours. We also identify the diminishing return effect, which can help load serving entities optimize the size of their DCM resources.

Hu, Rongxing↗

DOE OSTI2023

Development of window scheduler algorithm exploiting natural ventilation and thermal mass for building energy simulation and smart home controls

Building energy simulations often rely on abstract assumptions when it comes to natural ventilation, such as ‘windows always open [or closed]’ or ‘windows open when outdoor temperature is below a certain threshold.’ However, simulations based on these assumptions fail to fully exploit the cooling potential of natural ventilation, as its effectiveness can be enhanced or diminished by various factors, including the presence of thermal mass. This issue also extends to smart home controls, where determining the window schedule becomes challenging without information about the building's response to outdoor conditions. To address these issues, this study has developed an analytical model for window operation schedules that leverages the passive cooling from natural ventilation. The analytical model was validated against a Modelica simulation. A case study utilizing the BESTEST model of ANSI/ASHRAE Standard 140 underwent validation with EnergyPlus simulations, showing strong concordance. The algorithm provides window schedule recommendations adapted to various airflow rates, thermal masses, and climate variations. Notably, the case study demonstrated that proper window scheduling could reduce indoor temperature by up to 8 °C under the given simulation settings, thereby improving resilience and indicating potential energy savings. Furthermore, the paper explores the potential opportunities and challenges this approach presents, especially for building simulation and smart home applications.

42 ENGINEERING↗

NASA NTRS1976

On the problem of embedding picture elements in regions

A few new algorithms for region growing in pictures were developed. These algorithms are a step toward finding a satisfactory solution to the image segmentation problem, and in-depth understanding of the problems of nonsemantic image segmentation. The algorithms utilize a sequential decision approach for region boundaries detection. The sequential decisions are supported by a stochastic algorithm that maintains local statistics of the region near the boundaries as the region grows. A few illustrations of the algorithm's performance are included.

Yakimovsky, Y.↗

NASA NTRS1981

Contextual classification on PASM

The use of N microprocessors in the SIMD mode of parallel processing to do classifications almost N times faster than a single microprocessor is discussed. Examples of contextual classifiers are given, uniprocessor algorithms for performing contextual classifications are presented, and their computational complexity is analyzed. The SIMD mode of parallel processing is defined and PASM is overviewed. The presented uniprocessor algorithms are used as a basis for developing parallel algorithms for performing computationally intensive contextual classifications.

Siegel, H. J.↗

NASA NTRS1994

Design of a walking robot

Carnegie Mellon University's Autonomous Planetary Exploration Program (APEX) is currently building the Daedalus robot; a system capable of performing extended autonomous planetary exploration missions. Extended autonomy is an important capability because the continued exploration of the Moon, Mars and other solid bodies within the solar system will probably be carried out by autonomous robotic systems. There are a number of reasons for this - the most important of which are the high cost of placing a man in space, the high risk associated with human exploration and communication delays that make teleoperation infeasible. The Daedalus robot represents an evolutionary approach to robot mechanism design and software system architecture. Daedalus incorporates key features from a number of predecessor systems. Using previously proven technologies, the Apex project endeavors to encompass all of the capabilities necessary for robust planetary exploration. The Ambler, a six-legged walking machine was developed by CMU for demonstration of technologies required for planetary exploration. In its five years of life, the Ambler project brought major breakthroughs in various areas of robotic technology. Significant progress was made in: mechanism and control, by introducing a novel gait pattern (circulating gait) and use of orthogonal legs; perception, by developing sophisticated algorithms for map building; and planning, by developing and implementing the Task Control Architecture to coordinate tasks and control complex system functions. The APEX project is the successor of the Ambler project.

Whittaker, William↗

NASA NTRS1995

SeaWiFS Technical Report Series. Volume 29: SeaWiFS CZCS-type pigment algorithm

The Sea-viewing Wide Field-of-view Sensor (SeaWiFS) mission will provide operational ocean color that will be superior to the previous Coastal Zone Color Sensor (CZCS) proof-of-concept mission. an algorithm is needed that exploits the full functionality of SeaWiFS whilst remaining compatible in concept with algorithms used for the CZCS. This document describes the theoretical rationale of radiance band-radio methods for determining chlorophyll alpha and other important biogeochemical parameters, and their implementation for the SeaWiFS mission. Pigment interrelationships are examined to explain the success of the CZCS algorithms. In the context where chlorophyll alpha absorbs only weakly at 520 nm, the success of the 520 nm to 550 nm CZCS band ratio needs to be explained. This is explained by showing that in pigment data from a range of oceanic provinces chlorophyll alpha (absorbing at less than 490 nm), carotenoids (absorbing at greater than 460 nm), and total pigment are highly correlated. Correlations within pigment groups particularly photoprotectant and photosynthetic carotenoids are less robust. The sources of variability in optical data re examined using the NIMBUS Experiment Team (NET) bio-optical data set and bio-optical model. In both the model and NET data, the majority of the variance in the optical data is attributed to variability in pigment (chlorophyll alpha, and total particulates, with less than 5% of the variability resulting from pigment assemblage. The relationships between band ratios and chlorophyll is examined analytically, and a new formulation based on a dual hyperbolic model is suggested which gives a better calibration curve than the conventional log-log linear regression fit. The new calibration curve shows that 490:555 ratio is the best single-band ratio and is the recommended CZCS-type pigment algorithm. Using both the model and NET data, a number of multiband algorithms are developed; the best of which is an algorithm based on the 443:555 and 490:555 ratios. From model data, the form of potential algorithms for other products, such as total particulates and dissolved organic matter (DOM), are suggested.

Hooker, Stanford B.↗

NASA NTRS1995

SeaWiFS Technical Report Series: The SeaWiFS CZCS-Type Pigment Algorithm - Volume 29

The Sea-viewing Wide Field-of-view Sensor (SeaWiFS) mission will provide operational ocean color that will be superior to the previous Coastal Zone Color Sensor (CZCS) proof-of-concept mission. An algorithm is needed that exploits the full functionality of SeaWiFS whilst remaining compatible in concept with algorithms used for the CZCS. This document describes the theoretical rationale of radiance band-ratio methods for determining chlorophyll-a and other important biogeochemical parameters, and their implementation for the SeaWIFS mission. Pigment interrelationships are examined to explain the success of the CZCS algorithms. In the context where chlorophyll-a absorbs only weakly at 520 nm, the success of the 520 nm to 550 nm CZCS band ratio needs to be explained. This is explained by showing that in pigment data from a range of oceanic provinces chlorophyll-a (absorbing at less than 490 nm), carotenoids (absorbing at greater than 460 nm), and total pigment are highly correlated. Correlations within pigment groups particularly photoprotectant and photosynthetic carotenoids are less robust. The sources of variability in optical data are examined using the NIMBUS Experiment Team (NET) bio-optical data set and bio-optical model. In both the model and NET data, the majority of the variance in the optical data is attributed to variability in pigment (chlorophyll-a), and total particulates, with less than 5% of the variability resulting from pigment assemblage. The relationships between band ratios and chlorophyll is examined analytically, and a new formulation based on a dual hyperbolic model is suggested which gives a better calibration curve than the conventional log-log linear regression fit. The new calibration curve shows the 490:555 ratio is the best single-band ratio and is the recommended CZCS-type pigment algorithm. Using both the model and NET data, a number of multiband algorithms are developed; the best of which is an algorithm based on the 443:555 and 490:555 ratios. From model data, the form of potential algorithms for other products, such as total particulates and dissolved organic matter (DOM), are suggested.

Hooker, Stanford B.↗

NASA NTRS2002

Atmospheric Ascent Guidance for Rocket-Powered Launch Vehicles

An advanced ascent guidance algorithm for rocket- powered launch vehicles is developed. This algorithm cyclically solves the calculus-of-variations two-point boundary-value problem starting at vertical rise completion through main engine cutoff. This is different from traditional ascent guidance algorithms which operate in a simple open-loop mode until high dynamic pressure (including the critical max-Q) portion of the trajectory is over, at which time guidance operates under the assumption of negligible aerodynamic acceleration (i.e., vacuum dynamics). The initial costate guess is corrected based on errors in the terminal state constraints and the transversality conditions. Judicious approximations are made to reduce the order and complexity of the state/costate system. Results comparing guided launch vehicle trajectories with POST open-loop trajectories are given verifying the basic formulation of the algorithm. Multiple shooting is shown to be a very effective numerical technique for this application. In particular, just one intermediate shooting point, in addition to the initial shooting point, is sufficient to significantly reduce sensitivity to the guessed initial costates. Simulation results from a high-fidelity trajectory simulation are given for the case of launch to sub-orbital cutoff conditions as well as launch to orbit conditions. An abort to downrange landing site formulation of the algorithm is presented.

Dukeman, Greg A.↗

NASA NTRS2009

Tactical Synthesis Of Efficient Global Search Algorithms

Algorithm synthesis transforms a formal specification into an efficient algorithm to solve a problem. Algorithm synthesis in Specware combines the formal specification of a problem with a high-level algorithm strategy. To derive an efficient algorithm, a developer must define operators that refine the algorithm by combining the generic operators in the algorithm with the details of the problem specification. This derivation requires skill and a deep understanding of the problem and the algorithmic strategy. In this paper we introduce two tactics to ease this process. The tactics serve a similar purpose to tactics used for determining indefinite integrals in calculus, that is suggesting possible ways to attack the problem.

Nedunuri, Srinivas↗

NASA NTRS2010

Concepts and Challenges for Environmentally Friendly En Route Operations

A flight trajectory optimization algorithm with fuel and contrails models, which develops alternative flight paths, provides policy makers the necessary data to make tradeoffs between persistent contrails mitigation and aircraft fuel consumption. This study develops an algorithm that calculates wind-optimal trajectories for cruising aircraft while avoiding the regions of airspace prone to persistent contrails formation. The optimal trajectory is derived using Singular Perturbation Method. The regions of airspace favorable to persistent contrails formation are modeled as high-risk areas that aircraft should avoid and are adjustable. The tradeoffs between persistent contrails formation and additional travel time are investigated for wind-optimal trajectories and various contrails-avoidance trajectories at 10 different cruising altitudes for flights departing from Chicago and San Diego to New York. The additional travel times required for avoiding 100% persistent contrails formation at various flight altitudes ranged from approximately 0% to 4.3% for flights from Chicago to New York. For flights between San Diego and New York, additional traveling times vary between 1.3% and 5% depending on the cruise altitude and the percentage of contrail avoidance. Talk will present the results of aircraft fuel consumptions that are proportional to the travel time for cruising aircraft.

Sridhar, Banavar↗

NASA NTRS2013

Integrated Model Reduction and Control of Aircraft with Flexible Wings

This paper presents an integrated approach to the modeling and control of aircraft with exible wings. The coupled aircraft rigid body dynamics with a high-order elastic wing model can be represented in a nite dimensional state-space form. Given a set of desired output covariance, a model reduction process is performed by using the weighted Modal Cost Analysis (MCA). A dynamic output feedback controller, which is designed based on the reduced-order model, is developed by utilizing output covariance constraint (OCC) algorithm, and the resulting OCC design weighting matrix is used for the next iteration of the weighted cost analysis. This controller is then validated for full-order evaluation model to ensure that the aircraft's handling qualities are met and the uttering motion of the wings suppressed. An iterative algorithm is developed in CONDUIT environment to realize the integration of model reduction and controller design. The proposed integrated approach is applied to NASA Generic Transport Model (GTM) for demonstration.

AEROELASTIC↗

DOE OSTI2022

Prevalence and scalable control of localized networks

The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast with network size. Here, we introduce a notion of network locality that can be exploited to make the control of networks scalable, even when the dynamics are nonlinear. We show that network locality is captured by an information metric and is almost universally observed across real and model networks. In localized networks, the optimal control actions and system responses are both shown to be necessarily concentrated in small neighborhoods induced by the information metric. This allows us to develop localized algorithms for determining network controllability and optimizing the placement of driver nodes. This also allows us to develop a localized algorithm for designing local feedback controllers that approach the performance of the corresponding best global controllers, while incurring a computational cost orders-of-magnitude lower. Here, we validate the locality, performance, and efficiency of the algorithms in Kuramoto oscillator networks, as well as three large empirical networks: synchronization dynamics in the Eastern US power grid, epidemic spreading mediated by the global air-transportation network, and Alzheimer’s disease dynamics in a human brain network. Taken together, our results establish that large networks can be controlled with computation and communication costs comparable to those for small networks.

42 ENGINEERING↗

NASA NTRS2001

Development of an Innovative Algorithm for Aerodynamics-Structure Interaction Using Lattice Boltzmann Method

The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is developed for inviscid compressible flows.

Mei, Ren-Wei↗

NASA NTRS1984

Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings

A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.

Ehlers, F. E.↗

NASA NTRS2003

Formation Flying Design and Applications in Weak Stability Boundary Regions

Weak Stability regions serve as superior locations for interferometric scientific investigations. These regions are often selected to minimize environmental disturbances and maximize observing efficiency. Design of formations in these regions are becoming ever more challenging as more complex missions are envisioned. The development of algorithms to enable the capability for formation design must be further enabled to incorporate better understanding of WSB solution space. This development will improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple formation missions in WSB regions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes both algorithm and software development. The Constellation-X, Maxim, and Stellar Imager missions are examples of the use of improved numerical methods for attaining constrained formation geometries and controlling their dynamical evolution. This paper presents a survey of formation missions in the WSB regions and a brief description of the formation design using numerical and dynamical techniques.

Folta, David↗