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At least 91 records · Page 5

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NASA NTRS1991

Optimal Control Problems with Switching Points

The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

Seywald, Hans↗

NASA NTRS1990

Artificial intelligence and design: Opportunities, research problems and directions

The issues of industrial productivity and economic competitiveness are of major significance in the U.S. at present. By advancing the science of design, and by creating a broad computer-based methodology for automating the design of artifacts and of industrial processes, we can attain dramatic improvements in productivity. It is our thesis that developments in computer science, especially in Artificial Intelligence (AI) and in related areas of advanced computing, provide us with a unique opportunity to push beyond the present level of computer aided automation technology and to attain substantial advances in the understanding and mechanization of design processes. To attain these goals, we need to build on top of the present state of AI, and to accelerate research and development in areas that are especially relevant to design problems of realistic complexity. We propose an approach to the special challenges in this area, which combines 'core work' in AI with the development of systems for handling significant design tasks. We discuss the general nature of design problems, the scientific issues involved in studying them with the help of AI approaches, and the methodological/technical issues that one must face in developing AI systems for handling advanced design tasks. Looking at basic work in AI from the perspective of design automation, we identify a number of research problems that need special attention. These include finding solution methods for handling multiple interacting goals, formation problems, problem decompositions, and redesign problems; choosing representations for design problems with emphasis on the concept of a design record; and developing approaches for the acquisition and structuring of domain knowledge with emphasis on finding useful approximations to domain theories. Progress in handling these research problems will have major impact both on our understanding of design processes and their automation, and also on several fundamental questions that are of intrinsic concern to AI. We present examples of current AI work on specific design tasks, and discuss new directions of research, both as extensions of current work and in the context of new design tasks where domain knowledge is either intractable or incomplete. The domains discussed include Digital Circuit Design, Mechanical Design of Rotational Transmissions, Design of Computer Architectures, Marine Design, Aircraft Design, and Design of Chemical Processes and Materials. Work in these domains is significant on technical grounds, and it is also important for economic and policy reasons.

Amarel, Saul↗

NASA NTRS1993

Variable-permittivity linear inverse problem for the H(sub z)-polarized case

The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.

Moghaddam, M.↗

NASA NTRS1994

LSENS: A General Chemical Kinetics and Sensitivity Analysis Code for homogeneous gas-phase reactions. Part 3: Illustrative test problems

LSENS, the Lewis General Chemical Kinetics and Sensitivity Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 3 of a series of three reference publications that describe LSENS, provide a detailed guide to its usage, and present many example problems. Part 3 explains the kinetics and kinetics-plus-sensitivity analysis problems supplied with LSENS and presents sample results. These problems illustrate the various capabilities of, and reaction models that can be solved by, the code and may provide a convenient starting point for the user to construct the problem data file required to execute LSENS. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions.

Bittker, David A.↗

NASA NTRS1997

Numerical Boundary Conditions for Computational Aeroacoustics Benchmark Problems

Category 1, Problems 1 and 2, Category 2, Problem 2, and Category 3, Problem 2 are solved computationally using the Dispersion-Relation-Preserving (DRP) scheme. All these problems are governed by the linearized Euler equations. The resolution requirements of the DRP scheme for maintaining low numerical dispersion and dissipation as well as accurate wave speeds in solving the linearized Euler equations are now well understood. As long as 8 or more mesh points per wavelength is employed in the numerical computation, high quality results are assured. For the first three categories of benchmark problems, therefore, the real challenge is to develop high quality numerical boundary conditions. For Category 1, Problems 1 and 2, it is the curved wall boundary conditions. For Category 2, Problem 2, it is the internal radiation boundary conditions inside the duct. For Category 3, Problem 2, they are the inflow and outflow boundary conditions upstream and downstream of the blade row. These are the foci of the present investigation. Special nonhomogeneous radiation boundary conditions that generate the incoming disturbances and at the same time allow the outgoing reflected or scattered acoustic disturbances to leave the computation domain without significant reflection are developed. Numerical results based on these boundary conditions are provided.

Tam, Chritsopher K. W.↗

NASA NTRS2000

Algorithmic Perspectives on Problem Formulations in MDO

This work is concerned with an approach to formulating the multidisciplinary optimization (MDO) problem that reflects an algorithmic perspective on MDO problem solution. The algorithmic perspective focuses on formulating the problem in light of the abilities and inabilities of optimization algorithms, so that the resulting nonlinear programming problem can be solved reliably and efficiently by conventional optimization techniques. We propose a modular approach to formulating MDO problems that takes advantage of the problem structure, maximizes the autonomy of implementation, and allows for multiple easily interchangeable problem statements to be used depending on the available resources and the characteristics of the application problem.

Alexandrov, Natalia M.↗

NASA NTRS2006

Enabling the Discovery of Recurring Anomalies in Aerospace System Problem Reports using High-Dimensional Clustering Techniques

This paper describes the results of a significant research and development effort conducted at NASA Ames Research Center to develop new text mining techniques to discover anomalies in free-text reports regarding system health and safety of two aerospace systems. We discuss two problems of significant importance in the aviation industry. The first problem is that of automatic anomaly discovery about an aerospace system through the analysis of tens of thousands of free-text problem reports that are written about the system. The second problem that we address is that of automatic discovery of recurring anomalies, i.e., anomalies that may be described m different ways by different authors, at varying times and under varying conditions, but that are truly about the same part of the system. The intent of recurring anomaly identification is to determine project or system weakness or high-risk issues. The discovery of recurring anomalies is a key goal in building safe, reliable, and cost-effective aerospace systems. We address the anomaly discovery problem on thousands of free-text reports using two strategies: (1) as an unsupervised learning problem where an algorithm takes free-text reports as input and automatically groups them into different bins, where each bin corresponds to a different unknown anomaly category; and (2) as a supervised learning problem where the algorithm classifies the free-text reports into one of a number of known anomaly categories. We then discuss the application of these methods to the problem of discovering recurring anomalies. In fact the special nature of recurring anomalies (very small cluster sizes) requires incorporating new methods and measures to enhance the original approach for anomaly detection. ?& pant 0-

Srivastava, Ashok, N.↗

NASA NTRS2014

Novel Problem Solving - The NASA Solution Mechanism Guide

Over the past five years, the Human Health and Performance (HH&P) Directorate at the NASA Johnson Space Center (JSC) has conducted a number of pilot and ongoing projects in collaboration and open innovation. These projects involved the use of novel open innovation competitions that sought solutions from "the crowd", non-traditional problem solvers. The projects expanded to include virtual collaboration centers such as the NASA Human Health and Performance Center (NHHPC) and more recently a collaborative research project between NASA and the National Science Foundation (NSF). These novel problem-solving tools produced effective results and the HH&P wanted to capture the knowledge from these new tools, to teach the results to the directorate, and to implement new project management tools and coursework. The need to capture and teach the results of these novel problem solving tools, the HH&P decided to create a web-based tool to capture best practices and case studies, to teach novice users how to use new problem solving tools and to change project management training/. This web-based tool was developed with a small, multi-disciplinary group and named the Solution Mechanism Guide (SMG). An alpha version was developed that was tested against several sessions of user groups to get feedback on the SMG and determine a future course for development. The feedback was very positive and the HH&P decided to move to the beta-phase of development. To develop the web-based tool, the HH&P utilized the NASA Tournament Lab (NTL) to develop the software with TopCoder under an existing contract. In this way, the HH&P is using one new tool (the NTL and TopCoder) to develop the next generation tool, the SMG. The beta-phase of the SMG is planed for release in the spring of 2014 and results of the beta-phase testing will be available for the IAC meeting in September. The SMG is intended to disrupt the way problem solvers and project managers approach problem solving and to increase the use of novel and more cost and time effective problem solving tools such as open innovation, collaborative research, and virtual collaborative project centers. The HH&P envisions changing project management coursework by including the SMG in the teaching of project management problem solving tools.

Keeton, Kathryn E.↗

DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗

NASA NTRS2005

New high performance algorithmic solution for diagnosis problem

In this paper we address the problem of generating the minimal diagnosis from the conflicts. This problem can be formulated as the well-known Hitting Set Problem. Our approach starts by mapping the Hitting Set problem into the Integer Programming Problem that enables us, for the first time, a priori determination of the lower and upper bounds on the size for the solution. Based on these bounds, we introduce a new concept of solution window for the problem. We also propose a new branch-and-bound technique that not only is faster than the current techniques in terms of number of operations (by exploiting the structure of the problem) but also, using the concept of window, allows a massive reduction (pruning) in the number of branches. Furthermore, as the branch-and-bound proceeds, the solution window is dynamically updated and narrowed to enable further pruning.

diagnosis problems↗

NASA NTRSDate not supplied

Designing the Design Process for Early Problem Discovery for a Complex Aeronautics Systems Challenge

The earliest stage in the innovation lifecycle, problem formulation, is crucial for setting direction in an innovation effort. When faced with an interesting problem, engineers commonly assume the approximate solution area and focus on ideating innovative solutions. However, in this project, NASA and their contracted partner, Accenture, collaboratively conducted problem discovery to ensure that solutioning efforts were focused on the right problems, for the right users, and addressing the most critical needs—in this case, exploring weather tolerant operations (WTO) to further urban air mobility (UAM) – known as UAM WTO. The project team leveraged generative, qualitative methods to understand the ecosystem, players, and where challenges in the industry are inhibiting development. The complexity of the problem area required that the team constantly observe and iterate on problem discovery, effectively “designing the design process.” This report discusses the approach, methodologies, and selected results, including insights on the application of early-stage design methodologies to a complex, system-level problem.

Problem formulation↗

NASA NTRSDate not supplied

MAGE: Alleviating Uncertainty in Real-Time Decision-Making as a Function of Problem Complexity

In this paper, we discuss a critical aspect of uncertainty in the operation of complex systems, such as the future air traffic: the ability of agents in the system to arrive at satisfactory decisions and the attendant actions as a function of problem complexity. Intuitively, when the problem complexity is manageable, given an appropriate decision problem formulation and solution tools, an agent (computational or human) has no trouble arriving at a solution that yields good outcomes for the agent and the system. Growing problem complexity results in progressively larger computational problems that may yield suboptimal solutions or even be intractable within required time limits or at all. We propose a measurable representation of complexity in terms of problem tractability and quality of solutions. We also propose a computational scheme, MAGE (Monitor, Anticipate, Guide, Evolve), for detecting approaching transitions from efficient decision-making states to inefficient to unsafe ones, so that operations based on decision-making can be reconfigured to forestall unfavorable transitions, returning to efficient modes when complexity diminishes. Maintaining tractable complexity reduces the uncertainty in the outcomes of decision-making. We describe the general scheme, an outline of MAGE applied to managing airspace complexity, and initial examples of investigating the tractability of problem-solving schemes.

complexity management↗

DOE OSTI2024

Alternating Direction Decomposition with Strong Bounding and Convexification (ADDSBC) for Solving Security Constrained AC Unit Commitment Problems

This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1973

An application of a linear programing technique to nonlinear minimax problems

A differential correction technique for solving nonlinear minimax problems is presented. The basis of the technique is a linear programing algorithm which solves the linear minimax problem. By linearizing the original nonlinear equations about a nominal solution, both nonlinear approximation and estimation problems using the minimax norm may be solved iteratively. Some consideration is also given to improving convergence and to the treatment of problems with more than one measured quantity. A sample problem is treated with this technique and with the least-squares differential correction method to illustrate the properties of the minimax solution. The results indicate that for the sample approximation problem, the minimax technique provides better estimates than the least-squares method if a sufficient amount of data is used. For the sample estimation problem, the minimax estimates are better if the mathematical model is incomplete.

Schiess, J. R.↗

NASA NTRS1976

The Crack-contact and the Free End Problem for a Strip Under Residual Stress

The plane problem for an infinite strip with two edge cracks under a given state of residual stress is considered. The residual stress is compressive near and at the surfaces and tensile in the interior of the strip. If the crack is deep enough to penetrate into the tensile zone, then the problem is one of crack-contact problem in which the depth of the contact area is an unknown which depends on the crack depth and the residual stress profile. The problem has applications to the static fatigue of glass plates and is solved for three typical residual stress profiles. In the limiting case of the crack crossing the entire plate thickness, the problem becomes a stress-free end problem for a semi-infinite strip under a given residual stress state away from the end. This is a typical stress diffusion problem in which decay behavior of the residual stress near and the nature of the normal displacement at the end of the semi-infinite strip are of special interest. For two typical residual stress states the solution is obtained, and some numerical results are given.

Bakioglu, M.↗

NASA NTRS1978

Human problem solving performance in a fault diagnosis task

It is proposed that humans in automated systems will be asked to assume the role of troubleshooter or problem solver and that the problems which they will be asked to solve in such systems will not be amenable to rote solution. The design of visual displays for problem solving in such situations is considered, and the results of two experimental investigations of human problem solving performance in the diagnosis of faults in graphically displayed network problems are discussed. The effects of problem size, forced-pacing, computer aiding, and training are considered. Results indicate that human performance deviates from optimality as problem size increases. Forced-pacing appears to cause the human to adopt fairly brute force strategies, as compared to those adopted in self-paced situations. Computer aiding substantially lessens the number of mistaken diagnoses by performing the bookkeeping portions of the task.

Rouse, W. B.↗

NASA NTRS1983

Formulation and solution of rotary-wing aeroelastic stability and response problems

The state of the art in the formulation and solution of rotary-wing aeroelastic stability and response problems is reviewed in detail. The approximations used in the structural, inertia and aerodynamic operators are discussed. The important role of geometric nonlinearities, due to moderate deflections, and aerodynamic stall in the aeroelastic stability and response problem are identified. It is also shown that geometric nonlinearities are of primary importance in aeroelastic stability calculations, and have a more limited, though important, role in response calculations. Next, formulation of coupled rotor/fuselage problems is described, for both air and ground resonance type problems. Both topics, the isolated blade problem and the coupled rotor/fuselage problem, are treated for both hover and forward flight. Solution of aeroelastic stability and response problems proceeds in two stages. First, the spatial dependence is eliminated by using Galerkin's method, or by using the finite element method. Next the nonlinear, or linear, ordinary differential equation with periodic coefficients have to be solved for stability or response. Efficient numerical methods for accomplishing these objectives are presented in a comprehensive manner. The paper contains a number of illustrative numerical results which are intended to clarify various aspects of the modeling process and serve as representative results for both aeroelastic stability and response calculations for a variety of blade and rotor configurations.

Friedmann, P. P.↗

NASA NTRS1984

Numerical solutions of acoustic wave propagation problems using Euler computations

This paper reports solution procedures for problems arising from the study of engine inlet wave propagation. The first problem is the study of sound waves radiated from cylindrical inlets. The second one is a quasi-one-dimensional problem to study the effect of nonlinearities and the third one is the study of nonlinearities in two dimensions. In all three problems Euler computations are done with a fourth-order explicit scheme. For the first problem results are shown in agreement with experimental data and for the second problem comparisons are made with an existing asymptotic theory. The third problem is part of an ongoing work and preliminary results are presented for this case.

Hariharan, S. I.↗