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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8

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NASA NTRS1979

Mathematic modeling of the Earth's surface and the process of remote sensing

It is shown that real data from remote sensing of the Earth from outer space are not best suited to the search for optimal procedures with which to process such data. To work out the procedures, it was proposed that data synthesized with the help of mathematical modeling be used. A criterion for simularity to reality was formulated. The basic principles for constructing methods for modeling the data from remote sensing are recommended. A concrete method is formulated for modeling a complete cycle of radiation transformations in remote sensing. A computer program is described which realizes the proposed method. Some results from calculations are presented which show that the method satisfies the requirements imposed on it.

Balter, B. M.↗

NASA NTRS2005

Transonic-Small-Disturbance and Linear Analyses for the Active Aeroelastic Wing Program

Analysis serves many roles in the Active Aeroelastic Wing (AAW) program. It has been employed to ensure safe testing of both a flight vehicle and wind tunnel model, has formulated models for control law design, has provided comparison data for validation of experimental methods and has addressed several analytical research topics. Aeroelastic analyses using mathematical models of both the flight vehicle and the wind tunnel model configurations have been conducted. Static aeroelastic characterizations of the flight vehicle and wind tunnel model have been produced in the transonic regime and at low supersonic Mach numbers. The flight vehicle has been analyzed using linear aerodynamic theory and transonic small disturbance theory. Analyses of the wind-tunnel model were performed using only linear methods. Research efforts conducted through these analyses include defining regions of the test space where transonic effects play an important role and investigating transonic similarity. A comparison of these aeroelastic analyses for the AAW flight vehicle is presented in this paper. Results from a study of transonic similarity are also presented. Data sets from these analyses include pressure distributions, stability and control derivatives, control surface effectiveness, and vehicle deflections.

Wiesman, Carol D.↗

NASA NTRS2011

Systems, methods and apparatus for generation and verification of policies in autonomic computing systems

Described herein is a method that produces fully (mathematically) tractable development of policies for autonomic systems from requirements through to code generation. This method is illustrated through an example showing how user formulated policies can be translated into a formal mode which can then be converted to code. The requirements-based programming method described provides faster, higher quality development and maintenance of autonomic systems based on user formulation of policies.Further, the systems, methods and apparatus described herein provide a way of analyzing policies for autonomic systems and facilities the generation of provably correct implementations automatically, which in turn provides reduced development time, reduced testing requirements, guarantees of correctness of the implementation with respect to the policies specified at the outset, and provides a higher degree of confidence that the policies are both complete and reasonable. The ability to specify the policy for the management of a system and then automatically generate an equivalent implementation greatly improves the quality of software, the survivability of future missions, in particular when the system will operate untended in very remote environments, and greatly reduces development lead times and costs.

Hinchey, Michael G.↗

DOE OSTI2020

Distributionally robust facility location problem under decision-dependent stochastic demand

While the traditional facility location problem considers exogenous demand, in some applications, locations of facilities could affect the willingness of customers to use certain types of services, e.g., carsharing, and therefore they also affect realizations of random demand. Moreover, a decision maker may not know the exact distribution of such endogenous demand and how it is affected by location choices. In this paper, we consider a distributionally robust facility location problem, in which we interpret the moments of stochastic demand as functions of facility-location decisions. We reformulate a two-stage decision-dependent distributionally robust optimization model as a monolithic formulation, and then derive exact mixed-integer linear programming reformulation as well as valid inequalities when the means and variances of demand are piecewise linear functions of location solutions. We conduct extensive computational studies, in which we compare our model with a decision-dependent deterministic model, as well as stochastic programming and distributionally robust models without the decision-dependent assumption. Here, the results show superior performance of our approach with remarkable improvement in profit and quality of service under various settings, in addition to computational speed-ups given by formulation enhancements. These results draw attention to the need of considering the impact of location decisions on customer demand within this strategic-level planning problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Multiparametric Programming in Process Systems Engineering: Recent Developments and Path Forward

The inevitable presence of uncertain parameters in critical applications of process optimization can lead to undesirable or infeasible solutions. For this reason, optimization under parametric uncertainty was, and continues to be a core area of research within Process Systems Engineering. Multiparametric programming is a strategy that offers a holistic perspective for the solution of this class of mathematical programming problems. Specifically, multiparametric programming theory enables the derivation of the optimal solution as a function of the uncertain parameters, explicitly revealing the impact of uncertainty in optimal decision-making. By taking advantage of such a relationship, new breakthroughs in the solution of challenging formulations with uncertainty have been created. Apart from that, researchers have utilized multiparametric programming techniques to solve deterministic classes of problems, by treating specific elements of the optimization program as uncertain parameters. In the past years, there has been a significant number of publications in the literature involving multiparametric programming. The present review article covers recent theoretical, algorithmic, and application developments in multiparametric programming. Additionally, several areas for potential contributions in this field are discussed, highlighting the benefits of multiparametric programming in future research efforts.

Pappas, Iosif↗

NASA NTRS1989

A vectorized algorithm for 3D dynamics of a tethered satellite

Equations of motion characterizing the three dimensional motion of a tethered satellite during the retrieval phase are studied. The mathematical model involves an arbitrary number of point masses connected by weightless cords. Motion occurs in a gravity gradient field. The formulation presented accounts for general functions describing support point motion, rate of tether retrieval, and arbitrary forces applied to the point masses. The matrix oriented program language MATLAB is used to produce an efficient vectorized formulation for computing natural frequencies and mode shapes for small oscillations about the static equilibrium configuration; and for integrating the nonlinear differential equations governing large amplitude motions. An example of time response pertaining to the skip rope effect is investigated.

Wilson, Howard B.↗

NASA NTRS1987

Optimal cure cycle design of a resin-fiber composite laminate

A unified computed aided design method was studied for the cure cycle design that incorporates an optimal design technique with the analytical model of a composite cure process. The preliminary results of using this proposed method for optimal cure cycle design are reported and discussed. The cure process of interest is the compression molding of a polyester which is described by a diffusion reaction system. The finite element method is employed to convert the initial boundary value problem into a set of first order differential equations which are solved simultaneously by the DE program. The equations for thermal design sensitivities are derived by using the direct differentiation method and are solved by the DE program. A recursive quadratic programming algorithm with an active set strategy called a linearization method is used to optimally design the cure cycle, subjected to the given design performance requirements. The difficulty of casting the cure cycle design process into a proper mathematical form is recognized. Various optimal design problems are formulated to address theses aspects. The optimal solutions of these formulations are compared and discussed.

Hou, Jean W.↗

NASA NTRS1991

Spatial-Operator Algebra For Robotic Manipulators

Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.

Rodriguez, Guillermo↗

DOE OSTI2017

Exploiting Identical Generators in Unit Commitment

Here, we present sufficient conditions under which thermal generators can be aggregated in mixed-integer linear programming (MILP) formulations of the unit commitment (UC) problem, while maintaining feasibility and optimality for the original disaggregated problem. Aggregating thermal generators with identical characteristics (e.g., minimum/maximum power output, minimum up/down-time, and cost curves) into a single unit reduces redundancy in the search space induced by both exact symmetry (permutations of generator schedules) and certain classes of mutually non-dominated solutions. We study the impact of aggregation on two large-scale UC instances, one from the academic literature and another based on real-world operator data. Our computational tests demonstrate that when present, identical generators can negatively affect the performance of modern MILP solvers on UC formulations. Further, we show that our reformation of the UC MILP through aggregation is an effective method for mitigating this source of computational difficulty.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Stochastic Simulation of Complex Fluid Flows (Progress Report for period 07/01/2016 - 06/30/2018)

At a microscopic scale, fluids are composed of molecules whose positions and velocities are random. This gives rise to thermal fluctuations that span the whole range of scales from the microscopic through the mesoscopic, and even the macroscopic. The inclusion of thermal fluctuations is crucial in multi-scale models, which are an important theme in the research program of the DOE Office of Science, and in particular the ASCR Applied Mathematics program's priority focus area on modeling of complex systems involving processes that span vastly different time and/or length scales. In this five-year Early Career project, the PI Aleksandar Donev and collaborators developed computational algorithms for modeling complex fluid mixtures at small scales using a formulation based on fluctuating hydrodynamics. Novel computational methods were developed to model complex fluids with increasing physical complexity, starting from binary miscible and immiscible mixtures, going through multispecies non-reactive and reactive mixtures, and culminating with reactive electrolytes mixtures of neutral molecules and ions. In close collaboration with the group of John Bell at Lawrence Berkeley National Laboratory, the methods were implemented in a scalable computational framework suitable for modern parallel supercomputers, and made publicly available on github. A number of physical examples in which giant nonequilibrium fluctuations are improtant were studied, with a special focus on instabilities at a liquid-liquid interface driven by gravity, diffusion, reactions, and/or electric fields. The methods and codes developed in this project are expected to enable other novel applications in the DOE Basic Energy Sciences program, and engineering sciences more broadly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1973

A study of the dynamics of rotating space stations with elastically connected counterweight and attached flexible appendages. Volume 1: Theory

The formulation of a mathematical model for predicting the dynamic behavior of rotating flexible space station configurations was conducted. The overall objectives of the study were: (1) to develop the theoretical techniques for determining the behavior of a realistically modeled rotating space station, (2) to provide a versatile computer program for the numerical analysis, and (3) to present practical concepts for experimental verification of the analytical results. The mathematical model and its associated computer program are described.

Austin, F.↗

NASA NTRS1975

New control concept of anthropomorphic manipulators

The control of active articulated mechanisms involves the construction of trajectories and corresponding forces (torques). Two procedures for developing mathematical models of manipulator dynamics are explored. The control task can be formulated as follows: define the dynamic control parameters of the basic manipulator configuration with three degrees of freedom, which should perform movements at N points of the working space. The task can be solved by forming programmed coordinated motion which have to realize the adopted tip trajectory.

Vukobratovic, M.↗

NASA NTRS1997

Error Analysis System for Spacecraft Navigation Using the Global Positioning System (GPS)

The Flight Dynamics Division (FDD) at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) is currently developing improved space-navigation filtering algorithms to use the Global Positioning System (GPS) for autonomous real-time onboard orbit determination. In connection with a GPS technology demonstration on the Small Satellite Technology Initiative (SSTI)/Lewis spacecraft, FDD analysts and programmers have teamed with the GSFC Guidance, Navigation, and Control Branch to develop the GPS Enhanced Orbit Determination Experiment (GEODE) system. The GEODE system consists of a Kalman filter operating as a navigation tool for estimating the position, velocity, and additional states required to accurately navigate the orbiting Lewis spacecraft by using astrodynamic modeling and GPS measurements from the receiver. A parallel effort at the FDD is the development of a GPS Error Analysis System (GEAS) that will be used to analyze and improve navigation filtering algorithms during development phases and during in-flight calibration. For GEAS, the Kalman filter theory is extended to estimate the errors in position, velocity, and other error states of interest. The estimation of errors in physical variables at regular intervals will allow the time, cause, and effect of navigation system weaknesses to be identified. In addition, by modeling a sufficient set of navigation system errors, a system failure that causes an observed error anomaly can be traced and accounted for. The GEAS software is formulated using Object Oriented Design (OOD) techniques implemented in the C++ programming language on a Sun SPARC workstation. The Phase 1 of this effort is the development of a basic system to be used to evaluate navigation algorithms implemented in the GEODE system. This paper presents the GEAS mathematical methodology, systems and operations concepts, and software design and implementation. Results from the use of the basic system to evaluate navigation algorithms implemented on GEODE are also discussed. In addition, recommendations for generalization of GEAS functions and for new techniques to optimize the accuracy and control of the GPS autonomous onboard navigation are presented.

Truong, S. H.↗

DOE OSTI2016

Coherent states, quantum gravity, and the Born- Oppenheimer approximation. II. Compact Lie groups

In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall “coherent state” transform for compact Lie groups G, which we prove for G = U(1){sup n} and support by numerical evidence for G = SU(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups G. But, as Weyl and Berezin quantisation for ℝ{sup 2d} are intimately related by heat kernel evolution, it is natural to ask whether a similar connection exists for compact Lie groups as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann-Hall transform, can serve as basis of the former.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. III.: Applications to loop quantum gravity

In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space structure of loop quantum gravity-type models. Thus, the proposed Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1987

Use of an implicit formulation based on quasilinearization for the aeroelastic response and stability of rotor blades in forward flight

This paper describes a new methodology for the formulation of the aeroelastic stability and response problem for helicopter rotor blades. The mathematical expressions for the aerodynamic loads need not be explicit functions of the blade displacement quantities. This methodology is combined with a finite element model of the blade, and a quasilinearization solution technique. The resulting computer program is used to study the behavior of blades with noncoincident elastic axis, aerodynamic centers, and centers of mass.

Celi, R.↗

NASA NTRSDate not supplied

Rolling Horizon with K-Position Search Method for Strategic Deconfliction of Package Delivery UAS

In this research, the strategic deconfliction of unmanned aircraft systems for an urban package delivery environment with two depots and multiple drop-off locations is studied. This research aims to formulate a mathematical model to compute both the departure sequence and scheduled time of departure for each unmanned aircraft system at a depot, considering temporal constraints at en-route crossing waypoints and depots for strategic deconfliction. However, the problem formulation results in an NP-hard mixed-integer nonlinear programming problem for the global optimal solution, so instead, a "rolling horizon with𝑘-position search"heuristic method is developed. The simulation studies show that an increase in the value of𝑘(the parameter used to determine the size of the local neighborhood) reduces the average ground delay at the cost of an increase in the computation time for a given problem size. The study also shows an order of magnitude increase in the maximum number of flights scheduled with the integration of rolling horizon (time decomposition) compared to those without the integration of rolling horizon in the heuristic algorithm for a given computation time cut off.

UTM↗

DOE OSTI2015

Unit Commitment With Continuous-Time Generation and Ramping Trajectory Models

There is increasing evidence of shortage of ramping resources in the real-time operation of power systems. To explain and remedy this problem systematically, we take a novel look at the way the day-ahead unit commitment (UC) problem represents the information about load, generation and ramping constraints. We specifically investigate the approximation error made in mapping of the original problem, that would decide the continuous-time generation and ramping trajectories of the committed generating units, onto the discrete-time problem that is solved in practice. We first show that current practice amounts to approximating the trajectories with linear splines. We then offer a different representation through cubic splines that provides physically feasible schedules and increases the accuracy of the continuous-time generation and ramping trajectories by capturing sub-hourly variations and ramping of load in the day-ahead power system operation. The corresponding day-ahead UC model is formulated as an instance of mixed-integer linear programming (MILP), with the same number of binary variables as the traditional UC formulation. Numerical simulation over real load data from the California ISO demonstrate that the proposed UC model reduces the total day-ahead and real-time operation cost, and the number of events of ramping scarcity in the real-time operations.

24 POWER TRANSMISSION AND DISTRIBUTION↗