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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1962

STABILITY PROBLEMS IN MISSILE STRUCTURES

A number of specific buckling problems relating to missile propellant tanks and transition sections are enumerated. In some cases approximate techniques used by missile designers to determine stability are mentioned. The inadequacies of these approximate methods and the unavailability of appropriate usable information is stressed. Furthermore, the mathematical complexities of nonlinear buckling problems are considered. Some possibly fruitful areas of mathematics to simplify these complexities are discussed with the hope that research in these areas will provide a batter means through which the analyst may supply the designer with more realistic and accurate theoretical data.

MISSILE↗
NASA NTRS1980

Inversion of multiwavelength radiometer measurements by three-dimensional filtering

Remote sensing data from satellites typically have three dimensions: scan position, spacecraft position, and wavelength. Inversion of the radiometric data to infer geophysical parameters is a filtering problem in which the dimension of wavelength (or channel number) is transformed into a dimension of geophysical parameters, and the most general solution is a three-dimensional filter. Linear filters have the advantages of computational speed and easily described transfer functions; but often the measurements are nonlinear functions of the parameters to be inferred. To the extent that the nonlinear inversion problem is overdetermined, it can be modeled by a critically determined linear problem. As an example, inversion of Scanning Multichannel Microwave Radiometer (SMMR) data by means of a three-dimensional Wiener Filter is described. Atmospheric water vapor content, rain liquid water content, surface wind speed and surface temperature are the parameters inferred from the measurements. Nonprecipitating liquid water and water vapor scale height are also modeled but not retrieved. The a priori statistics on which the filter is trained have the effect of governing the selection of a trade-off point of noise as a function of resolution (in all three retrieval dimensions).

Rosenkranz, P. W.↗
NASA NTRS1993

A novel pulse technique for thermal diffusivity determination of high-temperature levitated materials - Inverse analysis and experimental set-up

In order to determine the thermal diffusivity of materials at high temperatures, a two-step extended flash technique, which is applicable to levitated spherical samples, is proposed. The containerless flash method is modeled as an axisymmetric transient conduction heat transfer problem within the sphere subjected to a radiative boundary condition on its surface. The problem of nonlinearity which arises from the radiative heat transfer boundary condition is solved by replacing it with the measured time-dependent surface temperature data, thus giving rise to an 'Inverse Analysis'. Upon obtaining the analytic solution for the temperature field, the determination of the thermal diffusivity turns into a minimization problem, whereby the difference between the actual surface boundary condition and the analytic solution is minimized. In performing the proposed experiments, there is a need to undertake a cool-down experiment which should be governed by the lumped parameter analysis.

Shen, F.↗
NASA NTRS1972

Adaptive control of stochastic linear systems with unknown parameters

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Ku, R. T.↗
NASA NTRS1989

Goertler vortices in growing boundary layers: The leading edge receptivity problem, linear growth and the nonlinear breakdown stage

Goertler vortices are thought to be the cause of transition in many fluid flows of practical importance. A review of the different stages of vortex growth is given. In the linear regime, nonparallel effects completely govern this growth, and parallel flow theories do not capture the essential features of the development of the vortices. A detailed comparison between the parallel and nonparallel theories is given and it is shown that at small vortex wavelengths, the parallel flow theories have some validity; otherwise nonparallel effects are dominant. New results for the receptivity problem for Goertler vortices are given; in particular vortices induced by free stream perturbations impinging on the leading edge of the walls are considered. It is found that the most dangerous mode of this type can be isolated and it's neutral curve is determined. This curve agrees very closely with the available experimental data. A discussion of the different regimes of growth of nonlinear vortices is also given. Again it is shown that, unless the vortex wavelength is small, nonparallel effects are dominant. Some new results for nonlinear vortices of 0(1) wavelengths are given and compared to experimental observations.

Hall, Philip↗
NASA NTRS1975

Implicit approximate-factorization schemes for the low-frequency transonic equation

Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

Ballhaus, W. F.↗
NASA NTRS1972

The Backup-Gilbert method and its application to the electrical conductivity problem

The theory of Backus and Gilbert gives a technique for solving the general linear inverse problem. Observational error and lack of data are shown to reduce the reliability of the solution in different ways: the former introduces statistical uncertainties in the model, while the latter smooths out the detail. Precision can be improved by sacrificing resolving power, and vice versa, so that some compromise may be made between the two in choosing the best model. Nonlinear inverse problems can be brought into the domain of the theory by linearizing about a typical solution. The inverse problem of electrical conductivity in the mantle is used to illustrate the Backus-Gilbert technique; an example of the tradeoff diagram is given.

Parker, R. L.↗
NASA NTRS1987

Mathematical programming formulations for satellite synthesis

The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

Bhasin, Puneet↗
NASA NTRS1997

Efficient Evaluation and Optimization of Structural Reliability

Use of approximations for calculating the structural failure probability under uncertainties is a necessary aspect. But efficient use of suitable approximations at different stages of reliability prediction and design makes this valuable tool practical for many large scale structures. This research addresses the modern approximation concepts and their utility in structural reliability estimation. Emphasis is placed on building higher order approximations using intervening variables to closely represent the nonlinear limit state functions. Several test problems with highly nonlinear performance functions are used to demonstrate the accuracy of the proposed method. Many of the structural problems are modeled and simulated using the finite element methods (FEM) for obtaining a detailed structural response. FEM is a computationally intensive numerical procedure with a large number of degrees of freedom. With an increase in the complexity of the structural model and the multidisciplinary nature of analyses, the number of limit states and their computation increases very significantly. The requirement of frequent repetitive analysis of the structure hinders the utility of any tool and discourages that approach from being used. One particular tool which faces this difficulty is the computation of the structural reliability under parametric uncertainties.

Grandhi, Ramana V.↗
NASA NTRS2000

Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-capturing Methods

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these scheme are compared with spectral, TVD and fifth- order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

Yee, H. C.↗
NASA NTRS1973

Test of statistical models for gases with and without internal energy states.

The problem of nonlinear rarefied Couette flow with heat transfer has been studied for both monatomic and diatomic gases using the Boltzmann equation with the Bhatnagar-Gross-Krook type models as the governing equation and the method of discrete ordinates as a tool. The calculated results have been compared with the existing experimental data in order to test the accuracy and the applicability of the statistical models for this one-dimensional problem. The calculated density results are found to be in good agreement with available experimental data; the calculated heat flux solution for the linear case is found to always be lower than the experimental data of Teagan and Springer. The comparisons made here indicate that the statistical models are indeed reasonably accurate so that their use is justified in the type of problems investigated.

Huang, A. B.↗
NASA NTRS1994

The Accuracy of Parameter Estimation in System Identification of Noisy Aircraft Load Measurement

This thesis focuses on the subject of the accuracy of parameter estimation and system identification techniques. Motivated by a complicated load measurement from NASA Dryden Flight Research Center, advanced system identification techniques are needed. The objective of this problem is to accurately predict the load experienced by the aircraft wing structure during flight determined from a set of calibrated load and gage response relationship. We can then model the problem as a black box input-output system identification from which the system parameter has to be estimated. Traditional LS (Least Square) techniques and the issues of noisy data and model accuracy are addressed. A statistical bound reflecting the change in residual is derived in order to understand the effects of the perturbations on the data. Due to the intrinsic nature of the LS problem, LS solution faces the dilemma of the trade off between model accuracy and noise sensitivity. A method of conflicting performance indices is presented, thus allowing us to improve the noise sensitivity while at the same time configuring the degredation of the model accuracy. SVD techniques for data reduction are studied and the equivalence of the Correspondence Analysis (CA) and Total Least Squares Criteria are proved. We also looked at nonlinear LS problems with NASA F-111 data set as an example. Conventional methods are neither easily applicable nor suitable for the specific load problem since the exact model of the system is unknown. Neural Network (NN) does not require prior information on the model of the system. This robustness motivated us to apply the NN techniques on our load problem. Simulation results for the NN methods used in both the single load and the 'warning signal' problems are both useful and encouraging. The performance of the NN (for single load estimate) is better than the LS approach, whereas no conventional approach was tried for the 'warning signals' problems. The NN design methodology is also presented. The use of SVD, CA and Collinearity Index methods are used to reduce the number of neurons in a layer.

Kong, Jeffrey↗
NASA NTRS1985

A minimum time control algorithm for linear and nonlinear systems

The minimum time control problem with bounded control has long been of interest to control engineers. Much of the theoretical study of this problem has been limited to linear systems and the results are usually problem-specific. This paper presents a new computational method for solving the minimum-time control problem when the control action is assumed to be bang-bang. A gradient-based algorithm is developed where the switching times are updated to minimize the final state missed distance. The algorithm is applicable to linear and nonlinear problems, including multi-input systems.

Wen, J.↗
NASA NTRS1982

Exact triple integrals of beam functions

Definite triple integrals encountered in applying the Galerkin method to the problem of heat and mass transfer across rectangular enclosures are discussed. Rather than evaluating them numerically, the technique described by Reid and Harris (1958) was extended to obtain the exact solution of the integrals. In the process, four linear simultaneous equations with triple integrals as unknowns were obtained. These equations were then solved exactly to obtain the closed form solution. Since closed form representations of this type have been shown to be useful in solving nonlinear hydrodynamic problems by series expansion, the integrals are presented here in general form.

Jhaveri, B. S.↗
NASA NTRS1974

Estimation and detection of signals in multiplicative noise

We define a class of detection-estimation problems on matrix Lie groups in which the observation noise is multiplicative in nature. By examining the differential versions of the hypotheses, which are bilinear, we are able to derive the relevant likelihood ratio formula and the associated optimal estimation equations for the signal given the observations and the assumption that the signal is present. These estimation equations are of interest in their own right, in that they represent a finite-dimensional optimal solution to a nonlinear estimation problem and consist of a Kalman-Bucy filter along with the on-line computation of the solution of the associated Riccati equation, which is driven by the observations. The usefulness of these results is illustrated via an example concerning the detection of an actuator failure in a rigid-body rotational control system.

Willsky, A. S.↗
NASA NTRS1973

Estimation and detection of signals in multiplicative noise

A class of detection-estimation problems on matrix Lie groups is defined in which the observation noise is multiplicative in nature. By examining the differential versions of the hypotheses, which are bilinear in nature, it is possible to derive the relevant likelihood ratio formula and the associated optimal estimation equations for the signal given the observations and the assumption that the signal is present. These estimation equations are of interest in their own right, in that they represent a finite dimensional optimal solution to a nonlinear estimation problem and can be viewed as consisting of a Kalman-Bucy filter along with the on-line computation of the solution of the associated Riccati equation, which is driven by the observations. The usefulness of these results is illustrated via an example concerning the detection of an actuator failure in a rigid body rotational control system.

Willsky, A. S.↗
NASA NTRS1977

Variational Algorithms for Nonlinear Smoothing Applications

A variational approach is presented for solving a nonlinear, fixed-interval smoothing problem with application to offline processing of noisy data for trajectory reconstruction and parameter estimation. The nonlinear problem is solved as a sequence of linear two-point boundary value problems. Second-order convergence properties are demonstrated. Algorithms for both continuous and discrete versions of the problem are given, and example solutions are provided.

Bach, Ralph E. Jr.↗
NASA NTRS1971

Some heuristic procedures for analyzing random vibration of nonlinear oscillators.

The stationary response of a lightly damped nonlinear oscillator subjected to wideband random excitation can be examined as an example of thermal equilibrium. It may be assumed that the response consists of a series of free-vibration cycles with small random fluctuations in phase and amplitude. Certain statistical properties of the response can be estimated by averaging corresponding properties of the free vibration with respect to cycle amplitude distributions. Such heuristic procedures for determining the expected frequency and the autocorrelation function of the stationary response are outlined. Some additional results concerning first-passage problems for nonlinear oscillators are included.

Crandall, S. H.↗