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NASA NTRS1988

Robust operative diagnosis as problem solving in a hypothesis space

This paper describes an approach that formulates diagnosis of physical systems in operation as problem solving in a hypothesis space. Such a formulation increases robustness by: (1) incremental hypotheses construction via dynamic inputs, (2) reasoning at a higher level of abstraction to construct hypotheses, and (3) partitioning the space by grouping fault hypotheses according to the type of physical system representation and problem solving techniques used in their construction. It was implemented for a turbofan engine and hydraulic subsystem. Evaluation of the implementation on eight actual aircraft accident cases involving engine faults provided very promising results.

Abbott, Kathy H.↗

NASA NTRS1989

Blackboard system generator (BSG) - An alternative distributed problem-solving paradigm

A status review is presented for a generic blackboard-based distributed problem-solving environment in which multiple-agent cooperation can be effected. This environment is organized into a shared information panel, a chairman control panel, and a metaplanning panel. Each panel contains a number of embedded AI techniques that facilitate its operation and that provide heuristics for solving the underlying team-agent decision problem. The status of these panels and heuristics is described along with a number of robustness considerations. The techniques for each of the three panels and for four sets of paradigm-related advances are described, along with selected results from classroom teaching experiments and from three applications.

Silverman, Barry G.↗

NASA NTRS1990

Neural Network Solves "Traveling-Salesman" Problem

Experimental electronic neural network solves "traveling-salesman" problem. Plans round trip of minimum distance among N cities, visiting every city once and only once (without backtracking). This problem is paradigm of many problems of global optimization (e.g., routing or allocation of resources) occuring in industry, business, and government. Applied to large number of cities (or resources), circuits of this kind expected to solve problem faster and more cheaply.

Thakoor, Anilkumar P.↗

NASA NTRS1990

KIPSE1: A Knowledge-based Interactive Problem Solving Environment for data estimation and pattern classification

A knowledge-based interactive problem solving environment called KIPSE1 is presented. The KIPSE1 is a system built on a commercial expert system shell, the KEE system. This environment gives user capability to carry out exploratory data analysis and pattern classification tasks. A good solution often consists of a sequence of steps with a set of methods used at each step. In KIPSE1, solution is represented in the form of a decision tree and each node of the solution tree represents a partial solution to the problem. Many methodologies are provided at each node to the user such that the user can interactively select the method and data sets to test and subsequently examine the results. Otherwise, users are allowed to make decisions at various stages of problem solving to subdivide the problem into smaller subproblems such that a large problem can be handled and a better solution can be found.

Han, Chia Yung↗

NASA NTRS1990

LANZ: Software solving the large sparse symmetric generalized eigenproblem

A package, LANZ, for solving the large symmetric generalized eigenproblem is described. The package was tested on four different architectures: Convex 200, CRAY Y-MP, Sun-3, and Sun-4. The package uses a Lanczos' method and is based on recent research into solving the generalized eigenproblem.

Jones, Mark T.↗

NASA NTRS1989

Solving sparse triangular linear systems on parallel computers

This paper describes and compares three parallel algorithms for solving sparse triangular systems of equations. These methods involve some preprocessing overhead and are primarily of interest in solving many systems with the same coefficient matrix. The first approach is to use a fixed blocksize and form the inverse of the diagonal blocks. The second approach is to use a variable blocksize and reorder the unknowns so that the diagonal blocks are diagonal matrices. The latter technique is called level scheduling because of how it is represented in the adjacency graph, and both row-wise and jagged diagonal storage for the off-diagonal blocks are considered. These techniques are analyzed for general parallel computers and experiments are presented for the eight-processor Alliant FX/8.

Anderson, Edward↗

NASA NTRS1991

Use of edge-based finite elements for solving three dimensional scattering problems

Edge based finite elements are free from drawbacks associated with node based vectorial finite elements and are, therefore, ideal for solving 3-D scattering problems. The finite element discretization using edge elements is checked by solving for the resonant frequencies of a closed inhomogeneously filled metallic cavity. Great improvements in accuracy are observed when compared to the classical node based approach with no penalty in terms of computational time and with the expected absence of spurious modes. A performance comparison between the edge based tetrahedra and rectangular brick elements is carried out and tetrahedral elements are found to be more accurate than rectangular bricks for a given storage intensity. A detailed formulation for the scattering problem with various approaches for terminating the finite element mesh is also presented.

Chatterjee, A.↗

NASA NTRS1991

Solving constrained minimum-time robot problems using the sequential gradient restoration algorithm

Three constrained minimum-time control problems of a two-link manipulator are solved using the Sequential Gradient and Restoration Algorithm (SGRA). The inequality constraints considered are reduced via Valentine-type transformations to nondifferential path equality constraints. The SGRA is then used to solve these transformed problems with equality constraints. The results obtained indicate that at least one of the two controls is at its limits at any instant in time. The remaining control then adjusts itself so that none of the system constraints is violated. Hence, the minimum-time control is either a pure bang-bang control or a combined bang-bang/singular control.

Lee, Allan Y.↗

NASA NTRS1992

High order parallel numerical schemes for solving incompressible flows

The use of parallel computers for numerically solving flow fields has gained much importance in recent years. This paper introduces a new high order numerical scheme for computational fluid dynamics (CFD) specifically designed for parallel computational environments. A distributed MIMD system gives the flexibility of treating different elements of the governing equations with totally different numerical schemes in different regions of the flow field. The parallel decomposition of the governing operator to be solved is the primary parallel split. The primary parallel split was studied using a hypercube like architecture having clusters of shared memory processors at each node. The approach is demonstrated using examples of simple steady state incompressible flows. Future studies should investigate the secondary split because, depending on the numerical scheme that each of the processors applies and the nature of the flow in the specific subdomain, it may be possible for a processor to seek better, or higher order, schemes for its particular subcase.

Lin, Avi↗

NASA NTRS1990

Solving unstructured grid problems on massively parallel computers

A highly parallel graph mapping technique that enables one to efficiently solve unstructured grid problems on massively parallel computers is presented. Many implicit and explicit methods for solving discretized partial differential equations require each point in the discretization to exchange data with its neighboring points every time step or iteration. The cost of this communication can negate the high performance promised by massively parallel computing. To eliminate this bottleneck, the graph of the irregular problem is mapped into the graph representing the interconnection topology of the computer such that the sum of the distances that the messages travel is minimized. It is shown that using the heuristic mapping algorithm significantly reduces the communication time compared to a naive assignment of processes to processors.

Hammond, Steven W.↗

NASA NTRS1991

Problem solving with genetic algorithms and Splicer

Genetic algorithms are highly parallel, adaptive search procedures (i.e., problem-solving methods) loosely based on the processes of population genetics and Darwinian survival of the fittest. Genetic algorithms have proven useful in domains where other optimization techniques perform poorly. The main purpose of the paper is to discuss a NASA-sponsored software development project to develop a general-purpose tool for using genetic algorithms. The tool, called Splicer, can be used to solve a wide variety of optimization problems and is currently available from NASA and COSMIC. This discussion is preceded by an introduction to basic genetic algorithm concepts and a discussion of genetic algorithm applications.

Bayer, Steven E.↗

NASA NTRS1990

Solving inversion problems with neural networks

A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.

Kamgar-Parsi, Behzad↗

NASA NTRS1992

Improved method for solving the viscous shock layer equations

An improved method for solving the viscous shock layer equations for supersonic/hypersonic flows past blunt-nosed bodies is presented. The method is capable of handling slender to thick bodies. The solution is obtained by solving a coupled set of five equations, built of the four basic viscous shock layer equations and an additional equation for the standoff distance. The coupling of the equations prevents the local iterations divergence problems encountered by previous methods of solution far downstream on slender bodies. It also eliminates the need for local iterations, which were required by previous methods of solution, for a first-order scheme in the streamwise direction. A new global iteration procedure is employed to impose the shock boundary conditions. The procedure prevents the global iteration instability encountered by the basic method of solution and improves the convergence rate of the global iteration procedure of later methods devised to overcome this difficulty. The new technique reduces the computation time by 65-95 percent as compared to previous methods of solution. The method can efficiently be implemented in vector/parallel computers.

Gordon, Rachel↗

NASA NTRS1992

Analyzing the path of responding in maze-solving and other tasks

Response time and accuracy are sensitive measures of overall performance but may mask underlying response strategies. For example, analysis of latency and accuracy measures produced in a computerized-maze task does not reveal whether rhesus monkeys really 'solve a maze' or simply move as much as is possible toward the target, negotiating barriers through trial and error as they encounter them. Regression procedures are described for analyzing response path against several hypothetical response curves, and analyses of response path for rhesus monkeys' performance on the computerized MAZE task are presented as an illustration. The data suggest that rhesus monkeys do invoke a response strategy of solving the maze, because the observed response topography is significantly associated with the optimal path of responding. Many experimental paradigms should similarly benefit from analysis of the response paths that subjects exhibit.

Washburn, David A.↗

NASA NTRS1993

Criteria for assessing problem solving and decision making in complex environments

Training crews to cope with unanticipated problems in high-risk, high-stress environments requires models of effective problem solving and decision making. Existing decision theories use the criteria of logical consistency and mathematical optimality to evaluate decision quality. While these approaches are useful under some circumstances, the assumptions underlying these models frequently are not met in dynamic time-pressured operational environments. Also, applying formal decision models is both labor and time intensive, a luxury often lacking in operational environments. Alternate approaches and criteria are needed. Given that operational problem solving and decision making are embedded in ongoing tasks, evaluation criteria must address the relation between those activities and satisfaction of broader task goals. Effectiveness and efficiency become relevant for judging reasoning performance in operational environments. New questions must be addressed: What is the relation between the quality of decisions and overall performance by crews engaged in critical high risk tasks? Are different strategies most effective for different types of decisions? How can various decision types be characterized? A preliminary model of decision types found in air transport environments will be described along with a preliminary performance model based on an analysis of 30 flight crews. The performance analysis examined behaviors that distinguish more and less effective crews (based on performance errors). Implications for training and system design will be discussed.

Orasanu, Judith↗

NASA NTRS1993

An upwind multigrid method for solving viscous flows on unstructured triangular meshes

A multigrid algorithm is combined with an upwind scheme for solving the two dimensional Reynolds averaged Navier-Stokes equations on triangular meshes resulting in an efficient, accurate code for solving complex flows around multiple bodies. The relaxation scheme uses a backward-Euler time difference and relaxes the resulting linear system using a red-black procedure. Roe's flux-splitting scheme is used to discretize convective and pressure terms, while a central difference is used for the diffusive terms. The multigrid scheme is demonstrated for several flows around single and multi-element airfoils, including inviscid, laminar, and turbulent flows. The results show an appreciable speed up of the scheme for inviscid and laminar flows, and dramatic increases in efficiency for turbulent cases, especially those on increasingly refined grids.

Bonhaus, Daryl Lawrence↗

NASA NTRS1993

Electronic neural network for solving traveling salesman and similar global optimization problems

This invention is a novel high-speed neural network based processor for solving the 'traveling salesman' and other global optimization problems. It comprises a novel hybrid architecture employing a binary synaptic array whose embodiment incorporates the fixed rules of the problem, such as the number of cities to be visited. The array is prompted by analog voltages representing variables such as distances. The processor incorporates two interconnected feedback networks, each of which solves part of the problem independently and simultaneously, yet which exchange information dynamically.

Thakoor, Anilkumar P.↗

NASA NTRS1993

A multilevel cost-space approach to solving the balanced long transportation problem

We develop a multilevel scheme for solving the balanced long transportation problem, that is, given a set (c(sub kj)) of shipping costs from a set of M supply nodes S(sub k) to a set of N demand nodes D(sub j), we seek to find a set of flows, (x(sub kj)), that minimizes the total cost Sigma(sub k=1)(exp M) Sigma(sub j=1)(exp N) x(sub kj)c(sub kj). We require that the problem be balanced, that is, the total demand must equal the total supply. Solution techniques for this problem are well known from optimization and linear programming. We examine this problem, however, in order to develop principles that can then be applied to more intractible problems of optimization. We develop a multigrid scheme for solving the problem, defining the grids, relaxation, and intergrid operators. Numerical experimentation shows that this line of research may prove fruitful. Further research directions are suggested.

Cavanaugh, Kevin J.↗