Search NASA⌕ Search

SEARCH · Search NASA

Results for “Newton-Raphson”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Fast algorithm for calculating chemical kinetics in turbulent reacting flow

This paper addresses the need for a fast batch chemistry solver to perform the kinetics part of a split operator formulation of turbulent reacting flows, with special attention focused on the solution of the ordinary differential equations governing a homogeneous gas-phase chemical reaction. For this purpose, a two-part predictor-corrector algorithm which incorporates an exponentially fitted trapezoidal method was developed. The algorithm performs filtering of ill-posed initial conditions, automatic step-size selection, and automatic selection of Jacobi-Newton or Newton-Raphson iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm, termed CREK1D (combustion reaction kinetics, one-dimensional), compared favorably with the code LSODE when tested on two representative problems drawn from combustion kinetics, and is faster than LSODE.

Radhakrishnan, K.↗
NASA NTRS1987

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Rodriguez, G.↗
NASA NTRS1987

Distributed parameter modeling of the structural dynamics of the Solar Array Flight Experiment

A distributed-parameter model of the structural dynamics of the space-shuttle-deployed Solar Array Flight Experiment is developed and used to produce estimates of the modal frequencies and mode shapes. A lumped parameter version of the distributed model is used to estimate model characteristics by analyzing the measured responses of 32 targets. To make the modeling more tenable, a distributed parameter system is used to reduce the number of unknown parameters, a modified Newton-Raphson technique is used for rapid convergence, and a parallel processing supercomputer is used for more efficient computation. The performances of computers with a high-speed serial processor and with a high-speed parallel processor are compared. The best results are obtained with the modeling approach in which maximum likelihood estimation is applied to distributed parameter models.

Taylor, L. W., Jr.↗
NASA NTRS1988

Calculation of symmetric and asymmetric vortex seperation on cones and tangent ogives based on discrete vortex models

An inviscid discrete vortex model, with newly derived expressions for the tangential velocity imposed at the separation points, is used to investigate the symmetric and asymmetric vortex separation on cones and tangent ogives. The circumferential locations of separation are taken from experimental data. Based on a slender body theory, the resulting simultaneous nonlinear algebraic equations in a cross-flow plane are solved with Broyden's modified Newton-Raphson method. Total force coefficients are obtained through momentum principle with new expressions for nonconical flow. It is shown through the method of function deflation that multiple solutions exist at large enough angles of attack, even with symmetric separation points. These additional solutions are asymmetric in vortex separation and produce side force coefficients which agree well with data for cones and tangent ogives.

Chin, S.↗
NASA NTRS1988

MHOST: An efficient finite element program for inelastic analysis of solids and structures

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Nakazawa, S.↗
NASA NTRS1988

Aircraft interior noise reduction by alternate resonance tuning

Model problem development and analysis continues with the Alternate Resonance Tuning (ART) concept. The various topics described are presently at different stages of completion: investigation of the effectiveness of the ART concept under an external propagating pressure field associated with propeller passage by the fuselage; analysis of ART performance with a double panel wall mounted in a flexible frame model; development of a data fitting scheme using a branch analysis with a Newton-Raphson scheme in multiple dimensions to determine values of critical parameters in the actual experimental apparatus; and investigation of the ART effect with real panels as opposed to the spring-mass-damper systems currently used in much of the theory.

Bliss, Donald B.↗
NASA NTRS1987

Fast simulation techniques for switching converters

Techniques for simulating a switching converter are examined. The state equations for the equivalent circuits, which represent the switching converter, are presented and explained. The uses of the Newton-Raphson iteration, low ripple approximation, half-cycle symmetry, and discrete time equations to compute the interval durations are described. An example is presented in which these methods are illustrated by applying them to a parallel-loaded resonant inverter with three equivalent circuits for its continuous mode of operation.

King, Roger J.↗
NASA NTRS1988

A multiple-vortex-ring model of the DFW microburst

A multiple-vortex-ring model of the winds associated with a microburst is verified by matching the model-generated winds to those encountered at the Dallas-Ft. Worth (DFW) microburst. The basis of the model consists of time-invariant vortex ring filaments embedded in irrotational flow. Each ring's viscous core is modeled by distributing the vorticity over a small distance (relative to the ring diameter) radially from the filaments. Parameters such as the size and strength of the vortex rings are identified using a modified Newton-Raphson technique. The parameters identified from the analysis of the DFW microburst encounter indicate a large ring with a radius of 8500 ft and a smaller ring with a radius of 1700 ft.

Schultz, Thomas A.↗
NASA NTRS1988

Forced periodic vibration of unsymmetric piecewise-linear systems

The forced steady response of a single degree of freedom system involving a large nonlinearity, represented by unsymmetric piecewise-linear stiffness, is determined by a harmonic balance Newton-Raphson method with the application of the fast Fourier transformation (FFT) algorithm. All possible subharmonic, harmonic, and superharmonic responses are sought. The responses of two systems involving subharmonic and superharmonic dominant motions are calculated by the newly developed method and compared with previously published findings. The results obtained by using this method reveal the details of the response of the systems more efficiently than previous methods.

Choi, Y. S.↗
NASA NTRS1987

Development and experimental evaluation of the techniques for automated measurement of birefringence

The general design and principle of operation of the spectral contents analysis (SCA) system, a newly developed system for the automated measurement of birefringence, are described. Several approaches that have been tested for the evaluation of birefringence using the SCA are then discussed; these include the error-summation approach, the Newton-Raphson approach, and the data base approach. Of these, the error-summation technique is found to be the most effective and accurate for extracting the value of retardation from the acquired spectral contents.

Voloshin, Arkady S.↗
NASA NTRS1988

The equation of state for stellar envelopes. II - Algorithm and selected results

A free-energy-minimization method for computing the dissociation and ionization equilibrium of a multicomponent gas is discussed. The adopted free energy includes terms representing the translational free energy of atoms, ions, and molecules; the internal free energy of particles with excited states; the free energy of a partially degenerate electron gas; and the configurational free energy from shielded Coulomb interactions among charged particles. Internal partition functions are truncated using an occupation probability formalism that accounts for perturbations of bound states by both neutral and charged perturbers. The entire theory is analytical and differentiable to all orders, so it is possible to write explicit analytical formulas for all derivatives required in a Newton-Raphson iteration; these are presented to facilitate future work. Some representative results for both Saha and free-energy-minimization equilibria are presented for a hydrogen-helium plasma with N(He)/N(H) = 0.10. These illustrate nicely the phenomena of pressure dissociation and ionization, and also demonstrate vividly the importance of choosing a reliable cutoff procedure for internal partition functions.

Mihalas, Dimitri↗
NASA NTRS1987

Hierarchically partitioned nonlinear equation solvers

By partitioning solution space into a number of subspaces, a new multiply constrained partitioned Newton-Raphson nonlinear equation solver is developed. Specifically, for a given iteration, each of the various separate partitions are individually and simultaneously controlled. Due to the generality of the scheme, a hierarchy of partition levels can be employed. For finite-element-type applications, this includes the possibility of degree-of-freedom, nodal, elemental, geometric substructural, material and kinematically nonlinear group controls. It is noted that such partitioning can be continuously updated, depending on solution conditioning. In this context, convergence is ascertained at the individual partition level.

Padovan, Joseph↗
NASA NTRS1988

Input-output-controlled nonlinear equation solvers

To upgrade the efficiency and stability of the successive substitution (SS) and Newton-Raphson (NR) schemes, the concept of input-output-controlled solvers (IOCS) is introduced. By employing the formal properties of the constrained version of the SS and NR schemes, the IOCS algorithm can handle indefiniteness of the system Jacobian, can maintain iterate monotonicity, and provide for separate control of load incrementation and iterate excursions, as well as having other features. To illustrate the algorithmic properties, the results for several benchmark examples are presented. These define the associated numerical efficiency and stability of the IOCS.

Padovan, Joseph↗
NASA NTRS1986

Efficient numerical techniques for complex fluid flows

The central feature in any flow prediction method is the treatment of the coupling between the momentum and continuity equations. In natural-convection flows, the energy equation also becomes strongly coupled with the momentum equations. Because of the nonlinear nature of the coupling, these equations are solved iteratively. Iterative methods are often prone to slow convergence, divergence, and extreme sensitivity to underrelaxation factors. The aim of the present research is to develop more efficient and reliable solution schemes for the coupled flow equations. Such schemes will significantly reduce the expense of computing complex flows encountered in combustion chambers, gas turbines, heat exchangers, and other practical equipment. In the work completed so far, a technique employing norm reduction in conjunction with the successive-substitution and Newton-Raphson techniques was developed. Also, a block-correction procedure for the flow equations is currently being formulated and tested.

Patankar, Suhas V.↗
NASA NTRS1987

Fast and stable recursive algorithms for continuous-time and discrete-time model conversions

Based on the Newton-Raphson method, this paper presents recursive algorithms that are rapidly convergent and more stable for modeling the equivalent continuous-time (discrete-time) model from the available discrete-time (continuous-time) model for a fixed sampling period. The newly developed recursive algorithms relax the constraints imposed upon the existing model conversion algorithms, and, thus, enhance the applications of microprocessors and associated microelectronics to digital control systems. A practical example is presented to demonstrate the effectiveness of the proposed procedures.

Shieh, L. S.↗
NASA NTRS1988

The determination of the propagation constant for the traveling wave in an infinite ground plane

The propagation constant for the traveling wave in a trough in an infinite ground plane is examined. The null-field integral is used to determine the EM field in the trough structure, and pulse basis functions give the distribution of the aperture fields. From this, the propagation constant is solved for, using the Newton-Raphson iterative scheme. Various sizes of geometries are examined. The far-field patterns are calculated and compared with other solutions, thereby validating the integral formulation which subsequently provided the propagation constant. Measurements of two trough geometries are performed to validate the theoretical results.

Shamansky, Harry T.↗
NASA NTRS1988

Optical matrix-vector processing for computational fluid dynamics

An optical processor to solve partial differential equations for computational fluid dynamics applications is considered. This application is new and original for optical processors. The algorithms that are used are optical realizations of the Newton-Raphson method for nonlinear equations and a new optical LU direct decomposition and Gauss-Seidel iterative solution to the resultant linear algebraic equations. These algorithms are used to solve Burger's equation (a specific form of the momentum equation in fluid dynamics). The nonlinear equations provide 1-D velocity data at each time step. Simulation results of optical processing with these algorithms on computational fluid dynamics data is included.

Perlee, Caroline J.↗
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↗