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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Average Incremental Cost Pricing for the AC Unit Commitment Problem [Rev. 1]

Unit Commitment (UC) problems that consider the Alternating Current (AC) model of the transmission network have long been considered intractable to solve at scale by the power system community. Recently, the Grid-Optimization (GO) Competition held by the Advanced Research Project Agency-Energy (ARPA-E) has facilitated the development of the first algorithms to solve large-scale ACUC problems. This new capability opens a path towards the explicit consideration of the AC transmission network model in UC problems used to clear day-ahead electricity markets. This calls for the analysis of electricity market structures that accommodate both the continuous non-linearity of the AC transmission network and the discrete non-linearity of the UC problem simultaneously. This paper serves as an initial effort to do so by proposing an Average Incremental Cost (AIC) pricing structure that is designed around the ACUC problem. In particular, an AIC one-pass pricing problem is proposed that represents a continuously constrained variant of the ACUC problem and allows for the computation of Locational Incremental Prices (LIPs) for both real and reactive power as the local optimal Lagrange multipliers of the power balance constraints. To avoid degeneracy, the pricing problem includes a small parameter ϵ > 0. Under certain assumptions market participants are shown to realize profit that converges to a non-negative value as ϵ approaches zero, practically ensuring profitability for small values of ϵ. We additionally provide many simple and important examples that provide intuition and insights into the proposed prices. Examples illustrate the basic concept of AIC pricing, the derived profitability results, the existence of multiple LIPs, the importance of including reactive power in the dispatch and pricing problems, the need for reactive power prices, and the improved incentives exhibited by LIPs as compared to traditional Locational Marginal Prices (LMPs). We additionally indicate many directions for future work including analysis of larger test cases.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1984

Fundamental differences between optimization code test problems in engineering applications

The purpose here is to suggest that there is at least one fundamental difference between the problems used for testing optimization codes and the problems that engineers often need to solve; in particular, the level of precision that can be practically achieved in the numerical evaluation of the objective function, derivatives, and constraints. This difference affects the performance of optimization codes, as illustrated by two examples. Two classes of optimization problem were defined. Class One functions and constraints can be evaluated to a high precision that depends primarily on the word length of the computer. Class Two functions and/or constraints can only be evaluated to a moderate or a low level of precision for economic or modeling reasons, regardless of the computer word length. Optimization codes have not been adequately tested on Class Two problems. There are very few Class Two test problems in the literature, while there are literally hundreds of Class One test problems. The relative performance of two codes may be markedly different for Class One and Class Two problems. Less sophisticated direct search type codes may be less likely to be confused or to waste many function evaluations on Class Two problems. The analysis accuracy and minimization performance are related in a complex way that probably varies from code to code. On a problem where the analysis precision was varied over a range, the simple Hooke and Jeeves code was more efficient at low precision while the Powell code was more efficient at high precision.

Eason, E. D.↗
NASA NTRS1991

AI techniques for a space application scheduling problem

Scheduling is a very complex optimization problem which can be categorized as an NP-complete problem. NP-complete problems are quite diverse, as are the algorithms used in searching for an optimal solution. In most cases, the best solutions that can be derived for these combinatorial explosive problems are near-optimal solutions. Due to the complexity of the scheduling problem, artificial intelligence (AI) can aid in solving these types of problems. Some of the factors are examined which make space application scheduling problems difficult and presents a fairly new AI-based technique called tabu search as applied to a real scheduling application. the specific problem is concerned with scheduling application. The specific problem is concerned with scheduling solar and stellar observations for the SOLar-STellar Irradiance Comparison Experiment (SOLSTICE) instrument in a constrained environment which produces minimum impact on the other instruments and maximizes target observation times. The SOLSTICE instrument will gly on-board the Upper Atmosphere Research Satellite (UARS) in 1991, and a similar instrument will fly on the earth observing system (Eos).

Thalman, N.↗
NASA NTRS1991

Balancing antagonistic time and resource utilization constraints in over-subscribed scheduling problems

In this paper, we report work aimed at applying concepts of constraint-based problem structuring and multi-perspective scheduling to an over-subscribed scheduling problem. Previous research has demonstrated the utility of these concepts as a means for effectively balancing conflicting objectives in constraint-relaxable scheduling problems, and our goal here is to provide evidence of their similar potential in the context of HST observation scheduling. To this end, we define and experimentally assess the performance of two time-bounded heuristic scheduling strategies in balancing the tradeoff between resource setup time minimization and satisfaction of absolute time constraints. The first strategy considered is motivated by dispatch-based manufacturing scheduling research, and employs a problem decomposition that concentrates local search on minimizing resource idle time due to setup activities. The second is motivated by research in opportunistic scheduling and advocates a problem decomposition that focuses attention on the goal activities that have the tightest temporal constraints. Analysis of experimental results gives evidence of differential superiority on the part of each strategy in different problem solving circumstances. A composite strategy based on recognition of characteristics of the current problem solving state is then defined and tested to illustrate the potential benefits of constraint-based problem structuring and multi-perspective scheduling in over-subscribe scheduling problems.

Smith, Stephen F.↗
NASA NTRS1995

Developmental problems and their solution for the Space Shuttle main engine alternate liquid oxygen high-pressure turbopump: Anomaly or failure investigation the key

The Space Shuttle main engine (SSME) alternate high-pressure liquid oxygen pump experienced synchronous vibration and ball bearing life problems that were program threatening. The success of the program hinged on the ability to solve these development problems. The design and solutions to these problems are engirded in the lessons learned and experiences from prior programs, technology programs, and the ability to properly conduct failure or anomaly investigations. The failure investigation determines the problem cause and is the basis for recommending design solutions. For a complex problem, a comprehensive solution requires that formal investigation procedures be used, including fault trees, resolution logic, and action items worked through a concurrent engineering-multidiscipline team. The normal tendency to use an intuitive, cut-and-try approach will usually prove to be costly, both in money and time and will reach a less than optimum, poorly understood answer. The SSME alternate high-pressure oxidizer turbopump development has had two complex problems critical to program success: (1) high synchronous vibrations and (2) excessive ball bearing wear. This paper will use these two problems as examples of this formal failure investigation approach. The results of the team's investigation provides insight into the complexity of the turbomachinery technical discipline interacting/sensitivities and the fine balance of competing investigations required to solve problems and guarantee program success. It is very important to the solution process that maximum use be made of the resources that both the contractor and Government can bring to the problem in a supporting and noncompeting way. There is no place for the not-invented-here attitude. The resources include, but are not limited to: (1) specially skilled professionals; (2) supporting technologies; (3) computational codes and capabilities; and (4) test and manufacturing facilities.

Ryan, R.↗
NASA NTRS1999

Known TCP Implementation Problems

This memo catalogs a number of known TCP implementation problems. The goal in doing so is to improve conditions in the existing Internet by enhancing the quality of current TCP/IP implementations. It is hoped that both performance and correctness issues can be resolved by making implementors aware of the problems and their solutions. In the long term, it is hoped that this will provide a reduction in unnecessary traffic on the network, the rate of connection failures due to protocol errors, and load on network servers due to time spent processing both unsuccessful connections and retransmitted data. This will help to ensure the stability of the global Internet. Each problem is defined as follows: Name of Problem The name associated with the problem. In this memo, the name is given as a subsection heading. Classification one or more problem categories for which the problem is classified: "congestion control", "performance", "reliability", "resource management". Description A definition of the problem, succinct but including necessary background material. Significance A brief summary of the sorts of environments for which the problem is significant.

Paxson, Vern↗
NASA NTRS1997

Regularization for Atmospheric Temperature Retrieval Problems

Passive remote sensing of the atmosphere is used to determine the atmospheric state. A radiometer measures microwave emissions from earth's atmosphere and surface. The radiance measured by the radiometer is proportional to the brightness temperature. This brightness temperature can be used to estimate atmospheric parameters such as temperature and water vapor content. These quantities are of primary importance for different applications in meteorology, oceanography, and geophysical sciences. Depending on the range in the electromagnetic spectrum being measured by the radiometer and the atmospheric quantities to be estimated, the retrieval or inverse problem of determining atmospheric parameters from brightness temperature might be linear or nonlinear. In most applications, the retrieval problem requires the inversion of a Fredholm integral equation of the first kind making this an ill-posed problem. The numerical solution of the retrieval problem requires the transformation of the continuous problem into a discrete problem. The ill-posedness of the continuous problem translates into ill-conditioning or ill-posedness of the discrete problem. Regularization methods are used to convert the ill-posed problem into a well-posed one. In this paper, we present some results of our work in applying different regularization techniques to atmospheric temperature retrievals using brightness temperatures measured with the SSM/T-1 sensor. Simulation results are presented which show the potential of these techniques to improve temperature retrievals. In particular, no statistical assumptions are needed and the algorithms were capable of correctly estimating the temperature profile corner at the tropopause independent of the initial guess.

Velez-Reyes, Miguel↗
NASA NTRS2000

Applications of the Space-Time Conservation Element and Solution Element (CE/SE) Method to Computational Aeroacoustic Benchmark Problems

The Internal Propagation problems, Fan Noise problem, and Turbomachinery Noise problems are solved using the space-time conservation element and solution element (CE/SE) method. The problems in internal propagation problems address the propagation of sound waves through a nozzle. Both the nonlinear and linear quasi 1D Euler equations are solved. Numerical solutions are presented and compared with the analytical solution. The fan noise problem concerns the effect of the sweep angle on the acoustic field generated by the interaction of a convected gust with a cascade of 3D flat plates. A parallel version of the 3D CE/SE Euler solver is developed and employed to obtain numerical solutions for a family of swept flat plates. Numerical solutions for sweep angles of 0, 5, 10, and 15 deg are presented. The turbomachinery problems describe the interaction of a 2D vortical gust with a cascade of flat-plate airfoils with/without a downstream moving grid. The 2D nonlinear Euler Equations are solved and the converged numerical solutions are presented and compared with the corresponding analytical solution. All the comparisons demonstrate that the CE/SE method is capable of solving aeroacoustic problems with/without shock waves in a simple and efficient manner. Furthermore, the simple non-reflecting boundary condition used in the CE/SE method which is not based on the characteristic theory works very well in 1D, 2D and 3D problems.

Wang, Xiao-Yen↗
NASA NTRS2004

Reconfigurability in MDO Problem Synthesis

Integrating autonomous disciplines into a problem amenable to solution presents a major challenge in realistic multidisciplinary design optimization (MDO). We propose a linguistic approach to MDO problem description, formulation, and solution we call reconfigurable multidisciplinary synthesis (REMS). With assistance from computer science techniques, REMS comprises an abstract language and a collection of processes that provide a means for dynamic reasoning about MDO problems in a range of contexts. The approach may be summarized as follows. Description of disciplinary data according to the rules of a grammar, followed by lexical analysis and compilation, yields basic computational components that can be assembled into various MDO problem formulations and solution algorithms, including hybrid strategies, with relative ease. The ability to re-use the computational components is due to the special structure of the MDO problem. The range of contexts for reasoning about MDO spans tasks from error checking and derivative computation to formulation and reformulation of optimization problem statements. In highly structured contexts, reconfigurability can mean a straightforward transformation among problem formulations with a single operation. We hope that REMS will enable experimentation with a variety of problem formulations in research environments, assist in the assembly of MDO test problems, and serve as a pre-processor in computational frameworks in production environments. This paper, Part 1 of two companion papers, discusses the fundamentals of REMS. Part 2 illustrates the methodology in more detail.

Alexandrov, Natalia M.↗
NASA NTRS2004

Reconfigurability in MDO Problem Synthesis

Integrating autonomous disciplines into a problem amenable to solution presents a major challenge in realistic multidisciplinary design optimization (MDO). We propose a linguistic approach to MDO problem description, formulation, and solution we call reconfigurable multidisciplinary synthesis (REMS). With assistance from computer science techniques, REMS comprises an abstract language and a collection of processes that provide a means for dynamic reasoning about MDO problems in a range of contexts. The approach may be summarized as follows. Description of disciplinary data according to the rules of a grammar, followed by lexical analysis and compilation, yields basic computational components that can be assembled into various MDO problem formulations and solution algorithms, including hybrid strategies, with relative ease. The ability to re-use the computational components is due to the special structure of the MDO problem. The range of contexts for reasoning about MDO spans tasks from error checking and derivative computation to formulation and reformulation of optimization problem statements. In highly structured contexts, reconfigurability can mean a straightforward transformation among problem formulations with a single operation. We hope that REMS will enable experimentation with a variety of problem formulations in research environments, assist in the assembly of MDO test problems, and serve as a pre-processor in computational frameworks in production environments. Part 1 of two companion papers, discusses the fundamentals of REMS. This paper, Part 2 illustrates the methodology in more detail.

Alexandrov, Natalia M.↗
NASA NTRS2004

Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems

This publication contains the proceedings of the Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems. In this workshop, as in previous workshops, the problems were devised to gauge the technological advancement of computational techniques to calculate all aspects of sound generation and propagation in air directly from the fundamental governing equations. A variety of benchmark problems have been previously solved ranging from simple geometries with idealized acoustic conditions to test the accuracy and effectiveness of computational algorithms and numerical boundary conditions; to sound radiation from a duct; to gust interaction with a cascade of airfoils; to the sound generated by a separating, turbulent viscous flow. By solving these and similar problems, workshop participants have shown the technical progress from the basic challenges to accurate CAA calculations to the solution of CAA problems of increasing complexity and difficulty. The fourth CAA workshop emphasized the application of CAA methods to the solution of realistic problems. The workshop was held at the Ohio Aerospace Institute in Cleveland, Ohio, on October 20 to 22, 2003. At that time, workshop participants presented their solutions to problems in one or more of five categories. Their solutions are presented in this proceedings along with the comparisons of their solutions to the benchmark solutions or experimental data. The five categories for the benchmark problems were as follows: Category 1:Basic Methods. The numerical computation of sound is affected by, among other issues, the choice of grid used and by the boundary conditions. Category 2:Complex Geometry. The ability to compute the sound in the presence of complex geometric surfaces is important in practical applications of CAA. Category 3:Sound Generation by Interacting With a Gust. The practical application of CAA for computing noise generated by turbomachinery involves the modeling of the noise source mechanism as a vortical gust interacting with an airfoil. Category 4:Sound Transmission and Radiation. Category 5:Sound Generation in Viscous Problems. Sound is generated under certain conditions by a viscous flow as the flow passes an object or a cavity.

Dahl, Milo D.↗
NASA NTRS2005

Benchmark Problems Used to Assess Computational Aeroacoustics Codes

The field of computational aeroacoustics (CAA) encompasses numerical techniques for calculating all aspects of sound generation and propagation in air directly from fundamental governing equations. Aeroacoustic problems typically involve flow-generated noise, with and without the presence of a solid surface, and the propagation of the sound to a receiver far away from the noise source. It is a challenge to obtain accurate numerical solutions to these problems. The NASA Glenn Research Center has been at the forefront in developing and promoting the development of CAA techniques and methodologies for computing the noise generated by aircraft propulsion systems. To assess the technological advancement of CAA, Glenn, in cooperation with the Ohio Aerospace Institute and the AeroAcoustics Research Consortium, organized and hosted the Fourth CAA Workshop on Benchmark Problems. Participants from industry and academia from both the United States and abroad joined to present and discuss solutions to benchmark problems. These demonstrated technical progress ranging from the basic challenges to accurate CAA calculations to the solution of CAA problems of increasing complexity and difficulty. The results are documented in the proceedings of the workshop. Problems were solved in five categories. In three of the five categories, exact solutions were available for comparison with CAA results. A fourth category of problems representing sound generation from either a single airfoil or a blade row interacting with a gust (i.e., problems relevant to fan noise) had approximate analytical or completely numerical solutions. The fifth category of problems involved sound generation in a viscous flow. In this case, the CAA results were compared with experimental data.

Dahl, Milo D.↗
NASA NTRS2009

High-Performance Algorithm for Solving the Diagnosis Problem

An improved method of model-based diagnosis of a complex engineering system is embodied in an algorithm that involves considerably less computation than do prior such algorithms. This method and algorithm are based largely on developments reported in several NASA Tech Briefs articles: The Complexity of the Diagnosis Problem (NPO-30315), Vol. 26, No. 4 (April 2002), page 20; Fast Algorithms for Model-Based Diagnosis (NPO-30582), Vol. 29, No. 3 (March 2005), page 69; Two Methods of Efficient Solution of the Hitting-Set Problem (NPO-30584), Vol. 29, No. 3 (March 2005), page 73; and Efficient Model-Based Diagnosis Engine (NPO-40544), on the following page. Some background information from the cited articles is prerequisite to a meaningful summary of the innovative aspects of the present method and algorithm. In model-based diagnosis, the function of each component and the relationships among all the components of the engineering system to be diagnosed are represented as a logical system denoted the system description (SD). Hence, the expected normal behavior of the engineering system is the set of logical consequences of the SD. Faulty components lead to inconsistencies between the observed behaviors of the system and the SD. Diagnosis the task of finding faulty components is reduced to finding those components, the abnormalities of which could explain all the inconsistencies. The solution of the diagnosis problem should be a minimal diagnosis, which is a minimal set of faulty components. The calculation of a minimal diagnosis is inherently a hard problem, the solution of which requires amounts of computation time and memory that increase exponentially with the number of components of the engineering system. Among the developments to reduce the computational burden, as reported in the cited articles, is the mapping of the diagnosis problem onto the integer-programming (IP) problem. This mapping makes it possible to utilize a variety of algorithms developed previously for IP to solve the diagnosis problem. In the IP approach, the diagnosis problem can be formulated as a linear integer optimization problem, which can be solved by use of well-developed integer-programming algorithms. This concludes the background information.

Fijany, Amir↗
NASA NTRS2005

Two Methods for Efficient Solution of the Hitting-Set Problem

A paper addresses much of the same subject matter as that of Fast Algorithms for Model-Based Diagnosis (NPO-30582), which appears elsewhere in this issue of NASA Tech Briefs. However, in the paper, the emphasis is more on the hitting-set problem (also known as the transversal problem), which is well known among experts in combinatorics. The authors primary interest in the hitting-set problem lies in its connection to the diagnosis problem: it is a theorem of model-based diagnosis that in the set-theory representation of the components of a system, the minimal diagnoses of a system are the minimal hitting sets of the system. In the paper, the hitting-set problem (and, hence, the diagnosis problem) is translated from a combinatorial to a computational problem by mapping it onto the Boolean satisfiability and integer- programming problems. The paper goes on to describe developments nearly identical to those summarized in the cited companion NASA Tech Briefs article, including the utilization of Boolean-satisfiability and integer- programming techniques to reduce the computation time and/or memory needed to solve the hitting-set problem.

Vatan, Farrokh↗
NASA NTRS2007

Improve Problem Solving Skills through Adapting Programming Tools

There are numerous ways for engineers and students to become better problem-solvers. The use of command line and visual programming tools can help to model a problem and formulate a solution through visualization. The analysis of problem attributes and constraints provide insight into the scope and complexity of the problem. The visualization aspect of the problem-solving approach tends to make students and engineers more systematic in their thought process and help them catch errors before proceeding too far in the wrong direction. The problem-solver identifies and defines important terms, variables, rules, and procedures required for solving a problem. Every step required to construct the problem solution can be defined in program commands that produce intermediate output. This paper advocates improved problem solving skills through using a programming tool. MatLab created by MathWorks, is an interactive numerical computing environment and programming language. It is a matrix-based system that easily lends itself to matrix manipulation, and plotting of functions and data. MatLab can be used as an interactive command line or a sequence of commands that can be saved in a file as a script or named functions. Prior programming experience is not required to use MatLab commands. The GNU Octave, part of the GNU project, a free computer program for performing numerical computations, is comparable to MatLab. MatLab visual and command programming are presented here.

Shaykhian, Linda H.↗
NASA NTRS2017

Applying Graph Theory to Problems in Air Traffic Management

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it is shown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

precision arrival scheduling↗
NASA NTRS2017

Applying Graph Theory to Problems in Air Traffic Management

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it isshown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

computational complexity↗
DOE OSTI2023

Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization

Obtaining lightweight and accurate approximations of discretized objective functional Hessians in inverse problems governed by partial differential equations (PDEs) is essential to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The cubic computational complexity of dense linear algebraic tasks, such as Cholesky factorization, that provide a means to sample Gaussian distributions and determine solutions of Newton linear systems is a computational bottleneck at large-scale. These tasks can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. Here, we demonstrate the use of HODLR Hessian approximation to efficiently sample the Laplace approximation of the posterior distribution with covariance further approximated by HODLR matrix compression. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss–Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global LR approximations, for large-scale problems by studying the data-misfit Hessian associated with inverse problems governed by the first-order Stokes flow model on the Humboldt glacier and Greenland ice sheet.

97 MATHEMATICS AND COMPUTING↗