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NASA NTRS1988

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

Freund, Roland↗

NASA NTRS2022

Learning-Based State-Dependent Coefficient Form Task Space Tracking Control of Soft Robot

n this paper, a data-driven modeling and control framework is developed for task space control of a soft robot gripper which consists of four individual soft fingers. Each of the four fingers is modeled as a manipulator with high degrees of freedom. The corresponding task space dynamics of the manipulator are derived using a rigid-link approximation of the continuum manipulator. A neural network approach is used to learn the derived dynamics in State Dependent Coefficient (SDC) form. Using the learned SDC matrices, an asymptotically stable optimal closed-loop tracking controller which is based on solving the State Dependent Riccati Equation (SDRE) is derived. The model learning and trajectory tracking controller is implemented on an open source Soft Motion (SoMo) platform simulating the soft gripper motion and corresponding tracking results are presented.

Rounak Bhattacharya↗

NASA NTRS1987

On computing eigensolution sensitivity data using free vibration solutions

A simplified method of computing eigensolution sensitivity derivatives in structural dynamics is developed. It is shown that if the elements of stiffness and mass matrices associated with a design variable are homogeneous functions of that design variable, then eigenvalue derivatives can be computed from element strain and kinetic energies. Furthermore, if cross-mode energies are known, eigensolution derivatives of modified systems can be computed approximately using assume mode reanalysis formulation. A ten bar truss example is used to illustrate the present formulations.

Wang, B. P.↗

DOE OSTI2024

Generalized Quasi-Static Mooring System Modeling with Analytic Jacobians

This paper presents a generalized and efficient method for quasi-static analysis of mooring systems, including complex scenarios such as when shared mooring lines interconnect multiple floating wind or wave energy devices. While quasi-static mooring models are well established, most published formulations are focused on specific applications, and no publicly available implementations provide efficient handling of large mooring system networks. The present formulation addresses these gaps by: (1) formulating solutions for edge cases not typically supported by quasi-static models; (2) creating a fully generalized model structure such that any combination of mooring lines, point masses, and floating bodies can be assembled; and (3) deriving analytic expressions for the system Jacobians (stiffness matrices) so that systems with many degrees of freedom can be solved efficiently. These techniques form the theory basis of MoorPy, an open-source mooring analysis library. The model is demonstrated on nine scenarios of increasing complexity with features of interest for offshore renewable energy applications. When compared with steady-state results from a lumped-mass dynamic model, the results show that the quasi-static formulation accurately calculates profiles and tensions and that its analytic approach provides more efficient and reliable computation of system stiffness matrices than finite-differencing methods. These results verify the accuracy of the MoorPy model.

16 TIDAL AND WAVE POWER↗

NASA NTRS1971

Multiple scattering of polarized light in planetary atmospheres. II - Sunlight reflected by terrestrial water clouds.

The intensity and polarization of sunlight reflected by terrestrial water clouds are computed with the doubling method. The calculations illustrate that this method can be effectively used in problems involving strongly anisotropic phase matrices. The method can, therefore, be used to derive information about planetary clouds, including those of the earth, from polarimetric observations. The results of the computations indicate that the polarization is more sensitive than the intensity to cloud microstructure, such as particle size and shape.

Hansen, J. E.↗

NASA NTRS1979

A program to compute three-dimensional subsonic unsteady aerodynamic characteristics using the doublet lattice method, L216 (DUBFLEX). Volume 2: Supplemental system design and maintenance document

The information necessary for execution of the digital computer program L216 on the CDC 6600 is described. L216 characteristics are based on the doublet lattice method. Arbitrary aerodynamic configurations may be represented with combinations of nonplanar lifting surfaces composed of finite constant pressure panel elements, and axially summetric slender bodies composed of constant pressure line elements. Program input consists of configuration geometry, aerodynamic parameters, and modal data; output includes element geometry, pressure difference distributions, integrated aerodynamic coefficients, stability derivatives, generalized aerodynamic forces, and aerodynamic influence coefficient matrices. Optionally, modal data may be input on magnetic field (tape or disk), and certain geometric and aerodynamic output may be saved for subsequent use.

Harrison, B. A.↗

NASA NTRS1979

A program to compute three-dimensional subsonic unsteady aerodynamic characteristics using the doublet lattic method, L216 (DUBFLX). Volume 1: Engineering and usage

The program input presented consists of configuration geometry, aerodynamic parameters, and modal data; output includes element geometry, pressure difference distributions, integrated aerodynamic coefficients, stability derivatives, generalized aerodynamic forces, and aerodynamic influence coefficient matrices. Optionally, modal data may be input on magnetic file (tape or disk), and certain geometric and aerodynamic output may be saved for subsequent use.

Richard, M.↗

NASA NTRS1987

Component mode synthesis and large deflection vibration of complex structures. Volume 2: Single-mode large deflection vibrations of beams and plates using finite element method

A finite element method is presented for the large amplitude vibrations of complex structures that can be modelled with beam and rectangular plate elements subjected to harmonic excitation. Both inplane deformation and inertia are considered in the formulation. Derivation of the harmonic force and nonlinear stiffness matrices for a beam and a rectangular plate element are presented. Solution procedures and convergence characteristics of the finite element method are described. Nonlinear response to uniform and concentrated harmonic loadings and improved nonlinear free vibration results are presented for beams and rectangular plates of various boundary conditions.

Mei, Chuh↗

NASA NTRS1989

Integrated aerodynamic-structural design of a transport wing

The integrated aerodynamic-structural design of a subsonic transport wing for minimum weight subject to required range is formulated and solved. The problem requires large computational resources, and two methods are used to alleviate the computational burden. First, a modular sensitivity method that permits the usage of black-box disciplinary software packages, is used to reduce the cost of sensitivity derivatives. In particular, it is shown that derivatives of the aeroelastic response and divergence speed can be calculated without the costly computation of derivatives of aerodynamic influence coefficient and structural stiffness matrices. A sequential approximate optimization is used to further reduce computational cost. The optimization procedure is shown to require a relatively small number of analysis and sensitivity calculations.

Grossman, B.↗

NASA NTRS1989

Discrete-time adaptive control of robot manipulators

A discrete-time model reference adaptive control scheme is developed for trajectory tracking of robot manipulators. Hyperstability theory is utilized to derive the adaptation laws for the controller gain matrices. It is shown that asymptotic trajectory tracking is achieved despite gross robot parameter variation and uncertainties. The method offers considerable design flexibility and enables the designer to improve the performance of the control system by adjusting free design parameters. The discrete-time adaptation algorithm is extremely simple and is therefore suitable for real-time implementation.

Tarokh, M.↗

NASA NTRS1990

A discrete-time adaptive control scheme for robot manipulators

A discrete-time model reference adaptive control scheme is developed for trajectory tracking of robot manipulators. The scheme utilizes feedback, feedforward, and auxiliary signals, obtained from joint angle measurement through simple expressions. Hyperstability theory is utilized to derive the adaptation laws for the controller gain matrices. It is shown that trajectory tracking is achieved despite gross robot parameter variation and uncertainties. The method offers considerable design flexibility and enables the designer to improve the performance of the control system by adjusting free design parameters. The discrete-time adaptation algorithm is extremely simple and is therefore suitable for real-time implementation. Simulations and experimental results are given to demonstrate the performance of the scheme.

Tarokh, M.↗

NASA NTRS1990

A probabilistic model for the evaluation of fault-tolerant multiprocessor systems using concurrent error detection

A probabilistic model to evaluate fault-tolerant multiprocessor systems has been developed. The matrix-based model and the analysis algorihtms based on it are described. Various probabilities associated with an algorithm-based fault tolerance system are discussed and the fault coverage of a given check is derived analytically and illustrated with examples. The probability matrices that are formed by introducing the spatial probabilities into the matrix model are considered. Based on these matrices, a technique is developed to determine the combined coverage of multiple numbers of checks. Examples of the analysis of systems using the model are given.

Nair, V. S. S.↗

NASA NTRS1992

Computation of antenna vibration mode elastic-rigid and effective-weight coefficients

A significant amount of both qualitative and quantitative information about structures can be derived from the elastic-rigid structural coupling matrices, and from the effective modal inertias and masses. Typical finite-element analysis programs do not provide this information as part of the regular output. This report presents an easy way to develop the necessary information from ordinary program output, and shows how to deal with alternative origins for the reference coordinate system.

Levy, R.↗

NASA NTRS1994

Applying transfer matrix method to the estimation of the modal characteristics of the NASA Mini-Mass Truss

It is beneficial to use a distributed parameter model for large space structures because the approach minimizes the number of model parameters. Holzer's transfer matrix method provides a useful means to simplify and standardize the procedure for solving the system of partial differential equations. Any large space structures can be broken down into sub-structures with simple elastic and dynamical properties. For each single element, such as beam, tether, or rigid body, we can derive the corresponding transfer matrix. Combining these elements' matrices enables the solution of the global system equations. The characteristics equation can then be formed by satisfying the appropriate boundary conditions. Then natural frequencies and mode shapes can be determined by searching the roots of the characteristic equation at frequencies within the range of interest. This paper applies this methodology, and the maximum likelihood estimation method, to refine the modal characteristics of the NASA Mini-Mast Truss by successively matching the theoretical response to the test data of the truss. The method is being applied to more complex configurations.

Shen, Ji-Yao↗

NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. IV: Coherent Backscattering

The problem of backscattering of light by a discrete random medium illuminated by an obliquely incident plane electromagnetic wave is considered.The analysis is performed in a linear-polarization basis and includes a complete derivation of the cross reflection matrix for a layer with densely and sparsely distributed particles, the design of an approximate method for computing the ladder and cross reflection matrices in the case of a semi-infinite medium with a sparse distribution of particles, the derivation of the relations between the elements of the ladder and cross reflection matrices in the exact backscattering direction for dense and sparse media, and the development of practical algorithms for solving the underlying integral equations by the method of Picard iterations and the discrete ordinate method. Simulation results for particles with large size parameters are also presented.

Adrian Doicu↗

NASA NTRS1979

A program for calculating load coefficient matrices utilizing the force summation method, L218 (LOADS). Volume 2: Supplemental system design and maintenance document

The LOADS computer program L218 which calculates dynamic load coefficient matrices utilizing the force summation method is described. The load equations are derived for a flight vehicle in straight and level flight and excited by gusts and/or control motions. In addition, sensor equations are calculated for use with an active control system. The load coefficient matrices are calculated for the following types of loads: (1) translational and rotational accelerations, velocities, and displacements; (2) panel aerodynamic forces; (3) net panel forces; and (4) shears, bending moments, and torsions.

Anderson, L. R.↗

NASA NTRS1979

A program for calculating load coefficient matrices utilizing the force summation method, L218 (LOADS). Volume 1: Engineering and usage

The LOADS program L218, a digital computer program that calculates dynamic load coefficient matrices utilizing the force summation method, is described. The load equations are derived for a flight vehicle in straight and level flight and excited by gusts and/or control motions. In addition, sensor equations are calculated for use with an active control system. The load coefficient matrices are calculated for the following types of loads: translational and rotational accelerations, velocities, and displacements; panel aerodynamic forces; net panel forces; shears and moments. Program usage and a brief description of the analysis used are presented. A description of the design and structure of the program to aid those who will maintain and/or modify the program in the future is included.

Miller, R. D.↗

NASA NTRS1972

Power series evaluation of transition and covariance matrices.

Reexamination power series solutions to the matrix covariance differential equation and the transition differential equation. Truncation error bounds are derived which are computationally attractive and which extend previous results. Polynomial approximations are obtained by exploiting the functional equations satisfied by the transition and covariance matrices. The series-functional equation propagation technique represents a fast and accurate alternative to the numerical integration of the time-invariant transition and covariance equations.

Bierman, G. J.↗