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NASA NTRS1987

Projection filters for modal parameter estimate for flexible structures

Single-mode projection filters are developed for eigensystem parameter estimates from both analytical results and test data. Explicit formulations of these projection filters are derived using the pseudoinverse matrices of the controllability and observability matrices in general use. A global minimum optimization algorithm is developed to update the filter parameters by using interval analysis method. Modal parameters can be attracted and updated in the global sense within a specific region by passing the experimental data through the projection filters. For illustration of this method, a numerical example is shown by using a one-dimensional global optimization algorithm to estimate model frequencies and dampings.

Huang, Jen-Kuang↗

NASA NTRS1987

Single-mode projection filters for identification and state estimation of flexible structures

Single-mode projection filters are developed for eigensystem parameter identification and state estimation from both analytical results and test data. Explicit formulations of these projection filters are derived using the pseudoinverse matrices of the controllabilty and observability matrices in the general sense. A global minimum optimization algorithm is developed to update the filter parameters by using the interval analysis method. Modal parameters can be identified and updated in the global sense within a specified region of parameters by passing the experimental data through the projection filters. For illustration of this new approach, a numerical example is shown by using a one-dimensional global optimization algorithm to estimate modal frequencies and damping.

Huang, Jen-Kuang↗

NASA NTRS1988

Single-Mode Projection Filters for Modal Parameter Identification for Flexible Structures

Single-mode projection filters are developed for eigensystem parameter identification from both analytical results and test data. Explicit formulations of these projection filters are derived using the orthogonal matrices of the controllability and observability matrices in the general sense. A global minimum optimization algorithm is applied to update the filter parameters by using the interval analysis method. The updated modal parameters represent the characteristics of the test data. For illustration of this new approach, a numerical simulation for the MAST beam structure is shown by using a one-dimensional global optimization algorithm to identify modal frequencies and damping. Another numerical simulation of a ten-mode structure is also presented by using a two-dimensional global optimization algorithm to illustrate the feasibility of the new method. The projection filters are practical for parallel processing implementation.

Huang, Jen-Kuang↗

NASA NTRS1989

Single-mode projection filters for modal parameter identification for flexible structures

Single-mode projection filters are developed for eigensystem parameter identification from both analytical results and test data. Explicit formulations of these projection filters are derived using the orthogonal matrices of the controllability and observability matrices in the general sense. A global minimum optimization algorithm is applied to update the filter parameters by using the interval analysis method. The updated modal parameters represent the characteristics of the test data. For illustration of this new approach, a numerical simulation for the MAST beam structure is shown by using a one-dimensional global optimization algorithm to identify modal frequencies and damping. The projection filters are practical for parallel processing implementation.

Huang, Jen-Kuang↗

NASA NTRS1991

Probabilistic Structures Analysis Methods (PSAM) for select space propulsion system components

The basic formulation for probabilistic finite element analysis is described and demonstrated on a few sample problems. This formulation is based on iterative perturbation that uses the factorized stiffness on the unperturbed system as the iteration preconditioner for obtaining the solution to the perturbed problem. This approach eliminates the need to compute, store and manipulate explicit partial derivatives of the element matrices and force vector, which not only reduces memory usage considerably, but also greatly simplifies the coding and validation tasks. All aspects for the proposed formulation were combined in a demonstration problem using a simplified model of a curved turbine blade discretized with 48 shell elements, and having random pressure and temperature fields with partial correlation, random uniform thickness, and random stiffness at the root.

Source record↗

NASA NTRS1992

Identifiability of linear systems in physical coordinates

Identifiability of linear, time-invariant systems in physical coordinates is discussed. It is shown that identification of the system matrix in physical coordinates can be accomplished by determining a transformation matrix that relates the physical locations of actuators and sensors to the test-data-derived input and output matrices. For systems with symmetric matrices, the solution of a constrained optimization problem is used to characterize all the possible solutions of the transformation matrix. Conditions for the existence of a unique transformation matrix are established easily from the explicit form of the solutions. For systems with limited inputs and outputs, the question about which part of the system can be uniquely identified is also answered. A simple mass-spring system is used to verify the conclusions of this study.

Su, Tzu-Jeng↗

NASA NTRS1987

Polarization analysis of a balloon-borne solar magnetograph

The main text of the report contains the particular results of our research which relate to the Experimental Vector Magnetograph (EXVM) and the Balloon-borne Vector Magnetograph (BVM). A brief overview of which elements in the EXVM and BVM that are relevant to this polarization analysis are presented. The possible meaning of the 10(exp -5) polarization specification for the BVM is discussed qualitatively. A recommendation of which polarization specification is most relevant for the BVM is provided. A diattenuation budget for the various surfaces in the BVM which will allow the polarization specification to be met is discussed. An explanation of the various coating specifications which are recommended is presented. Optical design of the EXVM and coating specification sheets for the BVM are presented. The appendices of this report contain the more general results of our research on the general topic of polarization aberrations. A general discussion of polarization aberration theory, in terms of the SAMEX solar magnetograph, and rigorous derivations for the Mueller matrices of optical systems are also presented in the appendices.

Reiley, Daniel J.↗

NASA NTRS1992

Automating FEA programming

In this paper we briefly describe a combined symbolic and numeric approach for solving mathematical models on parallel computers. An experimental software system, PIER, is being developed in Common Lisp to synthesize computationally intensive and domain formulation dependent phases of finite element analysis (FEA) solution methods. Quantities for domain formulation like shape functions, element stiffness matrices, etc., are automatically derived using symbolic mathematical computations. The problem specific information and derived formulae are then used to generate (parallel) numerical code for FEA solution steps. A constructive approach to specify a numerical program design is taken. The code generator compiles application oriented input specifications into (parallel) FORTRAN77 routines with the help of built-in knowledge of the particular problem, numerical solution methods and the target computer.

Sharma, Naveen↗

NASA NTRS1994

Advance finite element modeling of rotor blade aeroelasticity

An advanced beam finite element has been developed for modeling rotor blade dynamics and aeroelasticity. This element is part of the Element Library of the Second Generation Comprehensive Helicopter Analysis System (2GCHAS). The element allows modeling of arbitrary rotor systems, including bearingless rotors. It accounts for moderately large elastic deflections, anisotropic properties, large frame motion for maneuver simulation, and allows for variable order shape functions. The effects of gravity, mechanically applied and aerodynamic loads are included. All kinematic quantities required to compute airloads are provided. In this paper, the fundamental assumptions and derivation of the element matrices are presented. Numerical results are shown to verify the formulation and illustrate several features of the element.

Straub, F. K.↗

NASA NTRS1954

Matrix methods for determining the longitudinal-stability derivatives of an airplane from transient flight data

Three matrice methods are developed and presented for determining the longitudinal-stability derivatives from transient flight data. In these methods the expressions for some of the stability derivatives are in the form generally used in stability calculations. The first method requires the combination of four measurements in time-history form, two of which must be incremental elevator deflection and incremental tail load and the other two measurements can be chosen from a possible three, namely incremental load factor, pitching velocity, and angle of attack. The method demonstrates the use of the tail load to separate the pitching-moment derivatives and to determine the downwash derivative. (author)

Donegan, James J↗

NASA NTRS2026

Biobased Polybenzoxazine Derived from Furfurylamine and Piceol with Low Cure Temperature and Advanced Properties for Composite Matrices

A novel benzoxazine made from furfurylamine, paraformaldehyde, and piceol, Bz-FA-HA, is assessed for applications in fiber reinforced (FR) composites. Piceol is a biobased phenolic compound derived from the roots of Norwegian spruce trees and contains a methyl ketone group at the para position. Bz-FA-HA is a liquid at room temperature, has a viscosity of < 1 Pa.s at temperatures above 90 °C, and a Tonset of cure at 132 °C. The carbonyl is found to react with the furan ring, yielding a crosslinking reaction, when cured above 180 °C as indicated by differential scanning calorimetry and thermogravimetric analysis coupled with Fourier transform infrared spectroscopy. Poly(Bz-FA-HA) has a Tg > 350 °C, attributed to the crosslinking reaction. Furthermore, the storage modulus is > 3 GPa, regardless of cure temperature. Poly(Bz-FA-HA) has a char yield at 800 °C of 65.0 % (62.3 % at 1000 °C), and a Tonset of decomposition of 357 °C in nitrogen. The resulting carbon formed during pyrolysis shrinks during the carbonization reaction and scanning electron microscopy imaging shows a cross-section with micro cracks. The high processability, advanced mechanical properties, and exceptional char yield make it a promising candidate as the matrix for FR composites.

Benzoxazine↗

NASA NTRS1992

Measurement and calibration of differential Mueller matrix of distributed targets

A rigorous method for calibrating polarimetric backscatter measurements of distributed targets is presented. By characterizing the radar distortions over the entire mainlobe of the antenna, the differential Mueller matrix is derived from the measured scattering matrices with a high degree of accuracy. It is shown that the radar distortions can be determined by measuring the polarimetric response of a metallic sphere over the main lobe of the antenna. Comparison of results obtained with the new algorithm with the results derived from the old calibration method show that the discrepancy between the two methods is less than 1 dB for the backscattering coefficients. The discrepancy is more drastic for the phase-difference statistics, indicating that removal of the radar distortions from the cross products of the scattering matrix elements cannot be accomplished with the traditional calibration methods.

Sarabandi, Kamal↗

NASA NTRS1975

A new approach to radiative transfer theory using Jones's vectors. I Fundamentals

Radiative transfer of partially polarized radiation in an anisotropically scattering, inhomogeneous atmosphere containing an arbitrary polydispersion of particles is described using Jones's (1941) amplitude vectors and matrices. This approach exploits the close analogy between the quantum-mechanical states of spin 1/2 systems and the polarization states of electromagnetic radiation described by Jones's vector. The complete equivalence between the transport equation for Jones's vectors and the classical radiative-transfer equation for Stokes's intensity vectors is demonstrated in two independent ways after deriving the transport equations for the polarization coherency matrices and for the quaternions corresponding to the Jones's vectors. A compact-operator formulation of the theory is provided and used to derive the necessary equations for both a local and a global description of the transport of Jones's vectors. The integro-differential equations for the amplitude reflection and transmission matrices are derived and related to the usual corresponding equations.

Fymat, A. L.↗

NASA NTRS2019

Observations on the Computation of Eigenvalue and Eigenvector Jacobians

Many scientific and engineering problems benefit from analytic expressions for eigenvalue and eigenvector derivatives with respect to the elements of the parent matrix. While there exists extensive literature on the calculation of these derivatives, which take the form of Jacobian matrices, there are a variety of deficiencies that have yet to be addressed — including the need for both left and right eigenvectors, limitations on the matrix structure, and issues with complex eigenvalues and eigenvectors. This work addresses these deficiencies by proposing a new analytic solution for the eigenvalue and eigenvector derivatives. The resulting analytic Jacobian matrices are numerically efficient to compute and are valid for the general complex case. It is further shown that this new general result collapses to previously known relations for the special cases of real symmetric matrices and real diagonal matrices. Finally, the new Jacobian expressions are validated using forward finite differencing and performance is compared with another technique.

Jacobian↗

NASA NTRS1975

Computation of transform domain covariance matrices

It is often of interest in applications to compute the covariance matrix of a random process transformed by a fast unitary transform. Here, the recursive definition of fast unitary transforms is used to derive recursive relations for the covariance matrices of the transformed process. These relations lead to fast methods of computation of covariance matrices and to substantial reductions of the number of arithmetic operations required.

Fino, B. J.↗

NASA NTRS1993

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.

Fijany, Amir↗

NASA NTRS1984

Design of helicopter rotor blades for optimum dynamic characteristics

The optimal design of helicopter rotor blades is addressed. The forced response of an initial (i.e., non-optimized) blade to those of a final (optimized) blade are compared. Response of starting design and optimal designs for varying forcing frequencies, blade response to harmonics of rotor speed, and derivation of mass and stiffness matrices or functions of natural frequencies are discussed.

Peters, D. A.↗

NASA NTRS1986

Implicit hybrid schemes for the flux-difference split, three-dimensional Navier-Stokes equations

Implicit hybrid algorithms employing symmetric planar Gauss-Seidel (SPGS) relaxation and either block-tridiagonally structured coefficient matrices (AF-SPGS) or block-triangular coefficient matrices (LU-SPGS) are derived to solve the flux-difference-split Navier-Stokes equations for three-dimensional incompressible flow in an upwind scheme. The physical basis of the approach is discussed, and results for problems involving vortex flow around a thin delta wing at Reynolds numbers 900,000 and 10,000 are presented graphically. It is found that AF-SPGS converges faster on vector computers which depend on long vector lengths to achieve optimum performance, whereas LU-SPGS is preferable on sequentially operating machines and vector computers using shorter vector lengths.

Hartwich, P.-M.↗