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At least 307 records · Page 17

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NASA NTRS1987

Tactical missile turbulence problems

Of particular interest is atmospheric turbulence in the atmospheric boundary layer, since this affects both the launch and terminal phase of flight, and the total flight for direct fire systems. Brief discussions are presented on rocket artillery boost wind problems, mean wind correction, turbulent boost wind correction, the Dynamically Aimed Free Flight Rocket (DAFFR) wind filter, the DAFFR test, and rocket wake turbulence problems. It is concluded that many of the turbulence problems of rockets and missiles are common to those of aircraft, such as structural loading and control system design. However, these problems have not been solved at this time.

Dickson, Richard E.↗

NASA NTRS1987

Problem size, parallel architecture and optimal speedup

The communication and synchronization overhead inherent in parallel processing can lead to situations where adding processors to the solution method actually increases execution time. Problem type, problem size, and architecture type all affect the optimal number of processors to employ. The numerical solution of an elliptic partial differential equation is examined in order to study the relationship between problem size and architecture. The equation's domain is discretized into n sup 2 grid points which are divided into partitions and mapped onto the individual processor memories. The relationships between grid size, stencil type, partitioning strategy, processor execution time, and communication network type are analytically quantified. In so doing, the optimal number of processors was determined to assign to the solution, and identified (1) the smallest grid size which fully benefits from using all available processors, (2) the leverage on performance given by increasing processor speed or communication network speed, and (3) the suitability of various architectures for large numerical problems.

Nicol, David M.↗

NASA NTRS1987

Multigrid methods for bifurcation problems: The self adjoint case

This paper deals with multigrid methods for computational problems that arise in the theory of bifurcation and is restricted to the self adjoint case. The basic problem is to solve for arcs of solutions, a task that is done successfully with an arc length continuation method. Other important issues are, for example, detecting and locating singular points as part of the continuation process, switching branches at bifurcation points, etc. Multigrid methods have been applied to continuation problems. These methods work well at regular points and at limit points, while they may encounter difficulties in the vicinity of bifurcation points. A new continuation method that is very efficient also near bifurcation points is presented here. The other issues mentioned above are also treated very efficiently with appropriate multigrid algorithms. For example, it is shown that limit points and bifurcation points can be solved for directly by a multigrid algorithm. Moreover, the algorithms presented here solve the corresponding problems in just a few work units (about 10 or less), where a work unit is the work involved in one local relaxation on the finest grid.

Taasan, Shlomo↗

NASA NTRS1986

Primal and dual formulations of sequential gradient-restoration algorithms for trajectory optimization problems

One of the most effective first-order algorithms for solving trajectory optimization problems is the sequential gradient-restoration algorithm (SGRA). Originally developed in the primal formulation, this algorithm is extended to incorporate a dual formulation. Both the primal formulation and the dual formulation involve a sequence of two-phase cycles, each cycle including a gradient phase and a restoration phase. In turn, each iteration of the gradient phase and the restoration phase requires the solution of an auxiliary minimization problem (AMP). In the primal formulation, the AMP is solved with respect to the variations of the state, the control, and the parameter. In the dual formulation, the AMP is solved with respect to the Lagrange multipliers. A characteristic of the dual formulation is that the AMPs associated with the gradient phase and the restoration phase of SGRA can be reduced to mathematical programming problems involving a finite number of parameters as unknowns. A comparison of the primal formulation and the dual formulation is presented. The comparison is done in terms of several trajectory optimization problems having current aerospace interest.

Miele, A.↗

NASA NTRS1987

Dynamic optimization problems with bounded terminal conditions

Bounded terminal conditions of nonlinear optimization problems are converted to equality terminal conditions via Valentine's device. In so doing, additional unknown parameters are introduced into the problem. The transformed problems can still be easily solved using the sequential gradient-restoration algorithm (SGRA) via a simple augmentation of the unknown parameter vector pi. Three example problems with bounded terminal conditions are solved to verify this technique.

Lee, A. Y.↗

NASA NTRS1987

On high-continuity transfinite element formulations for linear-nonlinear transient thermal problems

This paper describes recent developments in the applicability of a hybrid transfinite element methodology with emphasis on high-continuity formulations for linear/nonlinear transient thermal problems. The proposed concepts furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom; and the methodology is applicable to linear/nonlinear thermal problems. Characteristic features of the formulations are described in technical detail as the proposed hybrid approach combines the major advantages and modeling features of high-continuity thermal finite elements in conjunction with transform methods and classical Galerkin schemes. Several numerical test problems are evaluated and the results obtained validate the proposed concepts for linear/nonlinear thermal problems.

Tamma, Kumar K.↗

NASA NTRS1988

Estimates of green tensors for certain boundary value problems

Consider the first boundary value problem for a stationary Navier-Stokes system in a bounded three-dimensional region Omega with the boundary S: delta v = grad p+f, div v=0, v/s=0. Odqvist (1930) developed the potential theory and formulated the Green tensor for the above problem. The basic singular solution used by Odqvist to express the Green tensor is given. A theorem generalizing his results is presented along with four associated theorems. A specific problem associated with the study of the differential properties of the solution of stationary problems of magnetohydrodynamics is examined.

Solonnikov, V.↗

NASA NTRS1987

The surface crack problem in an orthotropic plate under bending and tension

The elasticity problem for an infinite orthotropic flat plate containing a series of through and part through cracks and subjected to bending and tension loads is considered. The problem is formulated by using Reissner's plate bending theory and considering three-dimensional material orthotropy. The Line-spring model developed by Rice and Levy is used to formulate the surface crack problem in which a total of nine material constants were used. The effects of material orthotropy on the stress intensity factors was determined, the interaction between two asymmetrically arranged collinear cracks was investigated, and extensive numerical results regarding the stress intensity factors are provided. The problem is reduced to a system of singular integral equations which is solved by using the Gauss-Chebyshev quadrature formulas. The calculated results show that the material orthotropy does have a significant effect on the stress intensity factor.

Wu, Bing-Hua↗

NASA NTRS1988

Implementing direct, spatially isolated problems on transputer networks

Parametric studies were performed on transputer networks of up to 40 processors to determine how to implement and maximize the performance of the solution of problems where no processor-to-processor data transfer is required for the problem solution (spatially isolated). Two types of problems are investigated a computationally intensive problem where the solution required the transmission of 160 bytes of data through the parallel network, and a communication intensive example that required the transmission of 3 Mbytes of data through the network. This data consists of solutions being sent back to the host processor and not intermediate results for another processor to work on. Studies were performed on both integer and floating-point transputers. The latter features an on-chip floating-point math unit and offers approximately an order of magnitude performance increase over the integer transputer on real valued computations. The results indicate that a minimum amount of work is required on each node per communication to achieve high network speedups (efficiencies). The floating-point processor requires approximately an order of magnitude more work per communication than the integer processor because of the floating-point unit's increased computing capacity.

Ellis, Graham K.↗

NASA NTRS1987

Spectral methods and their implementation to solution of aerodynamic and fluid mechanic problems

Fundamental concepts underlying spectral collocation methods, especially pertaining to their use in the solution of partial differential equations, are outlined. Theoretical accuracy results are reviewed and compared with results from test problems. A number of practical aspects of the construction and use of spectral methods are detailed, along with several solution schemes which have found utility in applications of spectral methods to practical problems. Results from a few of the successful applications of spectral methods to problems of aerodynamic and fluid mechanic interest are then outlined, followed by a discussion of the problem areas in spectral methods and the current research under way to overcome these difficulties.

Streett, C. L.↗

NASA NTRS1988

Problem size, parallel architecture, and optimal speedup

Nicol, David M.↗

NASA NTRS1988

Application of fuzzy theories to formulation of multi-objective design problems

Much of the decision making in real world takes place in an environment in which the goals, the constraints, and the consequences of possible actions are not known precisely. In order to deal with imprecision quantitatively, the tools of fuzzy set theory can by used. This paper demonstrates the effectiveness of fuzzy theories in the formulation and solution of two types of helicopter design problems involving multiple objectives. The first problem deals with the determination of optimal flight parameters to accomplish a specified mission in the presence of three competing objectives. The second problem addresses the optimal design of the main rotor of a helicopter involving eight objective functions. A method of solving these multi-objective problems using nonlinear programming techniques is presented. Results obtained using fuzzy formulation are compared with those obtained using crisp optimization techniques. The outlined procedures are expected to be useful in situations where doubt arises about the exactness of permissible values, degree of credibility, and correctness of statements and judgements.

Dhingra, A. K.↗

NASA NTRS1989

An evidential approach to problem solving when a large number of knowledge systems is available

Some recent problems are no longer formulated in terms of imprecise facts, missing data or inadequate measuring devices. Instead, questions pertaining to knowledge and information itself arise and can be phrased independently of any particular area of knowledge. The problem considered in the present work is how to model a problem solver that is trying to find the answer to some query. The problem solver has access to a large number of knowledge systems that specialize in diverse features. In this context, feature means an indicator of what the possibilities for the answer are. The knowledge systems should not be accessed more than once, in order to have truly independent sources of information. Moreover, these systems are allowed to run in parallel. Since access might be expensive, it is necessary to construct a management policy for accessing these knowledge systems. To help in the access policy, some control knowledge systems are available. Control knowledge systems have knowledge about the performance parameters status of the knowledge systems. In order to carry out the double goal of estimating what units to access and to answer the given query, diverse pieces of evidence must be fused. The Dempster-Shafer Theory of Evidence is used to pool the knowledge bases.

Dekorvin, Andre↗

NASA NTRS1989

Parallel solution of sparse one-dimensional dynamic programming problems

Parallel computation offers the potential for quickly solving large computational problems. However, it is often a non-trivial task to effectively use parallel computers. Solution methods must sometimes be reformulated to exploit parallelism; the reformulations are often more complex than their slower serial counterparts. We illustrate these points by studying the parallelization of sparse one-dimensional dynamic programming problems, those which do not obviously admit substantial parallelization. We propose a new method for parallelizing such problems, develop analytic models which help us to identify problems which parallelize well, and compare the performance of our algorithm with existing algorithms on a multiprocessor.

Nicol, David M.↗

NASA NTRS1989

A numerical analysis of Stefan problems for generalized multi-dimensional phase-change structures using the enthalpy transforming model

An enthalpy transforming scheme is proposed to convert the energy equation into a nonlinear equation with the enthalpy, E, being the single dependent variable. The existing control-volume finite-difference approach is modified so it can be applied to the numerical performance of Stefan problems. The model is tested by applying it to a three-dimensional freezing problem. The numerical results are in agreement with those existing in the literature. The model and its algorithm are further applied to a three-dimensional moving heat source problem showing that the methodology is capable of handling complicated phase-change problems with fixed grids.

Cao, Yiding↗

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 NTRS1989

The problem of automation: Inappropriate feedback and interaction, not overautomation

As automation increasingly takes its place in industry, especially high-risk industry, it is often blamed for causing harm and increasing the chance of human error when failures occur. It is proposed that the problem is not the presence of automation, but rather its inappropriate design. The problem is that the operations are performed appropriately under normal conditions, but there is inadequate feedback and interaction with the humans who must control the overall conduct of the task. When the situations exceed the capabilities of the automatic equipment, then the inadequate feedback leads to difficulties for the human controllers. The problem is that the automation is at an intermediate level of intelligence, powerful enough to take over control that which used to be done by people, but not powerful enough to handle all abnormalities. Moreover, its level of intelligence is insufficient to provide the continual, appropriate feedback that occurs naturally among human operators. To solve this problem, the automation should either be made less intelligent or more so, but the current level is quite inappropriate. The overall message is that it is possible to reduce error through appropriate design considerations.

Norman, Donald A.↗

NASA NTRS1989

Guidance analysis of the aeroglide plane change maneuver as a turning point problem

The development of guidance approximations for the atmospheric (aeroglide) portion of the minimum fuel, orbital plane change, trajectory optimization problem is described. Asymptotic methods are used to reduce the two point, boundary value, optimization problem to a turning point problem from the bank angle control. The turning point problem solution, which yields an approximate optimal control policy, is given in terms of parabolic cylinder functions, which are tabulated, and integral expressions, which must be numerically computed. Comparisons of the former, over their region of validity, with optimal control solutions show good qualitative agreement. Additional work and analysis is needed to compute the guidance approximation work.

Gracey, Christopher↗