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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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At least 109 records · Page 6
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NASA NTRS1984

Nonlinear displacement analysis of advanced propeller structures using NASTRAN

The steady state displacements of a rotating advanced turboprop are computed using the geometrically nonlinear capabilities of COSMIC NASTRAN Rigid Format 4 and MSC NASTRAN Solution 64. A description of the modified Newton-Raphson algorithm used by Solution 64 and the iterative scheme used by Rigid Format 4 is provided. A representative advanced turboprop, SR3, was used for the study. Displacements for SR3 are computed for rotational speeds up to 10,000 rpm. The results show Solution 64 to be superior for computating displacements of flexible rotating structures. This is attributed to its ability to update the displacement dependent centrifugal force during the solution process.

Lawrence, C.↗
NASA NTRS1984

Large deflections of circular isotropic membranes subjected to arbitrary axisymmetric loading

Circular membranes with fixed peripheral edges, subjected to arbitrary axisymmetric loading are analyzed. A single governing differential equation in terms of radial stress is used. This nonlinear governing equation is solved using the finite difference method in conjunction with Newton-Raphson method. Three loading cases, namely (1) uniformly loaded membrane, (2) a membrane with uniform load over an inner portion, and (3) a membrane with ring load, are analyzed. Calculated central displacement and the central and edge radial stresses for uniformly loaded membrane, agree extremely well with the classical solution.

Kelkar, A.↗
NASA NTRS1984

Modeling clear-air turbulence with vortices using parameter-identification techniques

A vortex model of winds associated with clear-air turbulence (CAT) is shown to be useful for characterizing actual airline CAT encounters. The model consists of an array of vortices with solid-body cores embedded in a potential flow field. Parameters such as the size and strength of the vortices and their locations are identified using a modified Newton-Raphson algorithm. A manual identification start-up scheme is used to minimize errors in the initial parameter estimates, and the identification algorithm is found to be robust in regard to the remaining errors. The analysis of a CAT encounter involving a commercial airliner demonstrates the success of the model and estimation procedure. The analysis finds vortices with core diameters of 1000 ft and tangential velocities of 87 ft/sec in this encounter.

Mehta, R. S.↗
NASA NTRS1985

Optimization of Controlled Structures

A formulation is presented for the coupled optimal design of a structural system and its control by defining a composite objective function as a linear combination of two components: a structural objective and a control objective. For the case when the structural objective is a function of the structural design variables only, and when the control objective is represented by the quadratic functional of the response and control energy, one can analytically express the optimal control in terms of any set of admissible structural design variables. The expression for the optimal control is used recursively in an iterative Newton-Raphson search scheme, the goal of which is to determine a corresponding optimal set of structural design variables that minimize the composite objective function. A numerical example is given to illustrate the computational procedure.

Salama, M.↗
NASA NTRS1985

A Residuals Approach to Filtering, Smoothing and Identification for Static Distributed Systems

An approach for state estimation and identification of spatially distributed parameters embedded in static distributed (elliptic) system models is advanced. The method of maximum likelihood is used to find parameter values that maximize a likelihood functional for the system model, or equivalently, that minimize the negative logarithm of this functional. To find the minimum, a Newton-Raphson search is conducted that from an initial estimate generates a convergent sequence of parameter estimates. For simplicity, a Gauss-Markov approach is used to approximate the Hessian in terms of products of first derivatives. The gradient and approximate Hessian are computed by first arranging the negative log likelihood functional into a form based on the square root factorization of the predicted covariance of the measurement process. The resulting data processing approach, referred to here by the new term of predicted data covariance square root filtering, makes the gradient and approximate Hessian calculations very simple. A closely related set of state estimates is also produced by the maximum likelihood method: smoothed estimates that are optimal in a conditional mean sense and filtered estimates that emerge from the predicted data covariance square root filter.

Rodriguez, G.↗
NASA NTRS1985

Elastohydrodynamic lubrication calculations used as a tool to study scuffing

A new Reynolds equation was developed that takes into account the nonlinear viscous behavior of the fluid. The new Reynolds equation considers the nonlinear viscous fluid model of Eyring, the equilibrium equation, the constant mass flow, and the kinematic boundary condition. The new Reynolds equation and the elasticity equation are solved simultaneously by using a system approach and a Newton-Raphson technique. Comparisons are made with results obtained from the classical Reynolds equation. The effects of sliding speed and introducing a bump or a groove within the conjunction are studied. Results are shown for both moderate and heavy loads.

Houpert, L. G.↗
NASA NTRS1984

Aircraft automatic digital flight control system with inversion of the model in the feed-forward path

A full-flight-envelope automatic trajectory control system concept is being investigated at Ames Research Center. This concept was developed for advanced aircraft configurations with severe nonlinear characteristics. A feature of the system is an inverse of the complete nonlinear aircraft model as part of the feed-forward control path. Simulation and flight tests have been reported at previous Digital Avionics Systems conferences. A new method for the continuous real-time inversion of the aircraft model using a Newton-Raphson trim algorithm instead of the original inverse table look-up procedure has been developed. The results of a simulation study of a vertical attitude takeoff and landing aircraft using the new inversion technique are presented. Maneuvers were successfully carried out in all directions in the vertical-attitude hover mode. Transition runs from conventional flight through the region of lift-curve-slope reversal at an angle of attack of about 32 deg and to hover at zero speed in the vertical attitude showed satisfactory transient response. Simulations were also conducted in conventional flight at high subsonic speed in steep climb and with turns up to 4 g. Successful flight tests of the system with the new model-inversion technique in a UH-1H helicopter have recently been carried out.

Smith, G. A.↗
NASA NTRS1985

A homotopy continuation method for general preliminary orbit determination and special application to the Tracking and Data Relay Satellite System

A recent mathematical technique for solving systems of equations is applied in a very general way to the orbit determination problem. The use of this technique, the homotopy continuation method, was motivated by the possible need to perform preliminary orbit determination in the Tracking and Data Relay Satellite System (TDRSS), using range and Doppler tracking alone. In the formulation studied here, a set of six tracking observations is continuously transformed from a set with known solutions to the given set with unknown solutions, and the corresponding orbit state vector is followed from the a priori orbit state to the solution orbit states. A modular numerical algorithm is developed to follow the state vector. The technique is formulated and then tested, using both real and simulated tracking, with positive results. Direct comparisons show that the basic method has a much larger radius of convergence than standard or simply modified Newton-Raphson methods. An extension of the basic method is formulated that is expected to produce a global method.

Smith, R. L.↗
NASA NTRS1985

Large deflections of circular isotropic membranes subjected to arbitrary axisymmetric loading

Circular membranes with fixed peripheral edges, subjected to arbitrary axisymmetric loading were analyzed. A single governing differential equation in terms of radial stress was used. This nonlinear governing equation was solved using the finite difference method in conjunction with Newton-Raphson method. Three loading cases, namely: (1) uniformly loaded membrane, (2) a membrane with uniform load over an inner portion, and (3) a membrane with ring load, were analyzed. Calculated central displacement and the central and edge radial stresses for uniformly loaded membrane, agreed extremely well with the classical solution.

Kelkar, A.↗
NASA NTRS1986

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.

Murphy, P. C.↗
NASA NTRS1986

Development of computer program NAS3D using Vector processing for geometric nonlinear analysis of structures

An algorithm for vectorized computation of stiffness matrices of an 8 noded isoparametric hexahedron element for geometric nonlinear analysis was developed. This was used in conjunction with the earlier 2-D program GAMNAS to develop the new program NAS3D for geometric nonlinear analysis. A conventional, modified Newton-Raphson process is used for the nonlinear analysis. New schemes for the computation of stiffness and strain energy release rates is presented. The organization the program is explained and some results on four sample problems are given. The study of CPU times showed that savings by a factor of 11 to 13 were achieved when vectorized computation was used for the stiffness instead of the conventional scalar one. Finally, the scheme of inputting data is explained.

Mangalgiri, P. D.↗
NASA NTRS1981

Longitudinal stability and control derivatives obtained from flight data of a PA-30 aircraft

In order to obtain reliable and accurate values of the stability and control derivatives, the Dryden Fligh Research Center (DFRC) developed a technique for extracting the derivatives from flight data. This technique is implemented by a set of FORTRAN computer programs that is based on a modified maximum likelihood estimator that uses the Newton-Raphson algorithm to perform the required minimization of the derivatives. Data was obtained with a PA-30, light twin-engine general aviation aircraft in zero, half, and full flap configuration in level unaccelerated flight with the landing gear retracted. The derivatives were plotted as functions of angle of attack using various graphical arrangements to show variations of wind tunnel and flight determined values at zero flap settings. Also, data was displayed to show the effects of flap deflection and thrust variation on the longitudinal stability derivatives. The angle of attack and angle of sideslip were measured. The dynamic pressure, velocity, and altitude were calculated, using a FORTRAN computer program, from the static and dynamic pressures. The control deflections of the stabilator, ailerons, and rudder also were recorded along with left throttle position, engine rpm, and manifold pressure.

Turley, D. R.↗
NASA NTRS1986

Hierarchial implicit dynamic least-square solution algorithm

This paper develops an implicit type transient solution strategy which possesses hierarchial levels of application. In particular, due to the manner of formulation, stiffness updating, assembly inversion, solution constraint, as well as iteration are all performed at a localized level. The level of iterative calculations depends on the type of hierarchial partitioning employed, namely degree of freedom, nodal, elemental, material/nonlinear group, substructural, and so on. Since the iterative solution process and application of constraints are applied at a local level, the resulting so-called hierarchial implicit solution algorithm possesses very stable and efficient numerical properties and is highly storage efficient. To demonstrate the scheme, the results of several benchmark examples are presented. These enable comparisons with the Newton-Raphson solved implicit transient solution method. Overall the comparisons illustrate the superior stability and efficiency of the hierarchial scheme.

Padovan, J.↗
NASA NTRS1985

Structural parameter identification of distributed systems using finite element approximation

A system identification technique is developed for classes of distributed systems using finite element approximations. Vibrating systems represented by partial differential equations have physical parameters associated with mass, stiffness, and damping distributions which need to be known in order to properly control and design mathematical models of the system. In order to identify these parameters a weighted least-squares algorithm and modified Newton-Raphson method is used for the identification process. The theory and technique is demonstrated by estimating the system parameters of a vibrating cantilever beam made up of several different structural properties.

Lee, K. Y.↗
NASA NTRS1985

On-orbit systems identification of flexible spacecraft

The process of on-orbit systems identification of flexible spacecraft is examined in terms of the difficulties that are expected because of the potentially unmanageable number of unknown model parameters due to the very high order system models involved. A Jordon block canonical form and global model parameters are used to reduce the number of unknown parameters to manageable numbers. A Bayesian approach is discussed which enables the merging of theoretical models with ground or on-orbit test results by using Unconditional Maximum Likelihood Parameter Estimation. A Modified Newton-Raphson technique is proposed for determining the model parameter estimates and an expected fit error criterion is recommended for the determination of the model structure and order reduction.

Taylor, L. W., Jr.↗
NASA NTRS1985

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

Murphy, Patrick Charles↗