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At least 1,135 records · Page 63
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NASA NTRS1974

Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations

This paper discusses numerical aspects of computing maximum likelihood estimates for linear dynamical systems in state-vector form. Different gradient-based nonlinear programming methods are discussed in a unified framework and their applicability to maximum likelihood estimation is examined. The problems due to singular Hessian or singular information matrix that are common in practice are discussed in detail and methods for their solution are proposed. New results on the calculation of state sensitivity functions via reduced order models are given. Several methods for speeding convergence and reducing computation time are also discussed.

Gupta, N. K.↗
NASA NTRS1975

Convergence acceleration and shock fitting for transonic aerodynamics computations

Two problems in computational fluid dynamics are studied in the context of transonic small-disturbance theory - namely, (1) how to speed up the convergence for currently available iterative procedures, and (2) how a shock-fitting method may be adapted to existing relaxation procedures with minimal alterations in computer programming and storage requirements. The paper contributes to a clarification of error analyses for sequence transformations based on the power method (including also the nonlinear transforms of Aitken, Shanks, and Wilkinson), and to developing a cyclic iterative procedure applying the transformations. Examples testing the procedure for a model Dirichlet problem and for a transonic airfoil problem show that savings in computer time by a factor of three to five are generally possible, depending on accuracy requirements and the particular iterative procedure used.-

Hafez, M. M.↗
NASA NTRS1974

Spark chamber track finding program

A spark-chamber track-finding program has been written. The accuracy of the location of the track is good, and if the chamber contains many spurious sparks the computation time is much less than the time used by a least-squares fit routine. Multiple tracks can be found and interaction vertices can thereby be determined.

Arens, J. F.↗
NASA NTRS1974

Results from the direct combination of satellite and gravimetric data

Results have been obtained for the solution of 184 15-deg equal-area blocks directly from the analysis of satellite orbits, and from a combination of the satellite results with terrestrial gravity material. This test computation, made to verify the method, used 17,632 optical observations from ten satellites in 29 arcs averaging in length seven days. Analysis of the satellite results were made by comparing the solved for anomalies with the terrestrial anomaly set, and by developing the solved for anomalies into potential coefficients which were compared to the GEM 3 set of potential coefficients to degree 12. These comparisons indicated improvement in each solution as more arcs were added. The programs used in this solution can easily be used to solve for smaller size blocks and handle additional data types. The only limitation will be computer core availability and computer time.

Rapp, R. H.↗
NASA NTRS1975

Computational procedure for three-dimensional boundary layers on aircraft and aerospace vehicles

An implicit numerical procedure is developed to solve the full three-dimensional laminar, boundary layer equations over realistic aircraft and spacecraft configurations. This procedure utilizes splined functions in the direction normal to the surface and finite differences in the cross flow direction. Calculation of off-pitch plane attachment and detachment lines can be calculated. The solution procedure permits the incorporation of a wide variety of turbulent models and boundary conditions including; entropy layer procedures, specified surface temperatures or heat flux distributions, surface catalysis, mass addition, and the coupling to both three-dimensional inviscid codes and surface ablation codes. In addition, reasonable computing times are obtained.

Kendall, R. M.↗
NASA NTRS1975

A fast semidirect method for computing transonic aerodynamic flows

A fast, semidirect, iterative computational method, previously introduced for finite-difference solution of subsonic and slightly supercritical flow over airfoils, is extended both to apply to strongly supercritical conditions and to include full second-order accuracy in computing inviscid flows over airfoils. The nonlinear small-disturbance equations are solved iteratively by a direct, linear, elliptic solver. General, fully conservative, type-dependent difference equations are formulated, including parabolic- and shock-point transition operators that provide consistency with the integral conservation laws. These equations specialize to either first-order or to fully second-order-accurate equations. Various free parameters are evaluated for rapid convergence of the first-order scheme. Resulting pressure distributions and computing times are compared with the improved Murman-Cole line-relaxation method.

Martin, E. D.↗
NASA NTRS1975

A hybrid classifier using the parallelepiped and Bayesian techniques

A versatile classification scheme is developed which uses the best features of the parallelepiped algorithm and the Bayesian maximum likelihood algorithm. The parallelepiped technique has the advantage of being very fast, especially when implemented into a table look-up scheme; its disadvantage is its inability to distinguish and classify spectral signatures which are similar in nature. This disadvantage is eliminated by the Bayesian technique which is capable of distinguishing subtle differences very well. The hybrid algorithm developed reduces computer time by as much as 90%. A two- and n-dimensional description of the hybrid classifier is given.

Addington, J. D.↗
NASA NTRS1975

Simulation of multicorrelated random processes using the FFT algorithm

A technique for the digital simulation of multicorrelated Gaussian random processes is described. This technique is based upon generating discrete frequency functions which correspond to the Fourier transform of the desired random processes, and then using the fast Fourier transform (FFT) algorithm to obtain the actual random processes. The main advantage of this method of simulation over other methods is computation time; it appears to be more than an order of magnitude faster than present methods of simulation. One of the main uses of multicorrelated simulated random processes is in solving nonlinear random vibration problems by numerical integration of the governing differential equations. The response of a nonlinear string to a distributed noise input is presented as an example.

Wittig, L. E.↗
NASA NTRS1976

Field distribution in a thin lens

Quasi-optical formulation gives an optical field distribution by computing only two terms. First term represents geometrical optics effect, and second term represents diffraction effect; thus, mathematical expression is simplified, and considerable computer time is saved.

Chi, C. H.↗
NASA NTRS1977

Swept wing aerodynamics

Technique analyzes viscosity-dependent aerodynamic characteristics of multielement infinite swept wings in incompressible flow. Use of source distributions rather than displacement thickness to represent boundary layer effect on potential flow and of iterative technique for matrix inversion reduces computer time for overall analysis.

Dvorak, F. A.↗
NASA NTRS1975

Averaged initial Cartesian coordinates for long lifetime satellite studies

A set of initial Cartesian coordinates, which are free of ambiguities and resonance singularities, is developed to study satellite mission requirements and dispersions over long lifetimes. The method outlined herein possesses two distinct advantages over most other averaging procedures. First, the averaging is carried out numerically using Gaussian quadratures, thus avoiding tedious expansions and the resulting resonances for critical inclinations, etc. Secondly, by using the initial rectangular Cartesian coordinates, conventional, existing acceleration perturbation routines can be absorbed into the program without further modifications, thus making the method easily adaptable to the addition of new perturbation effects. The averaged nonlinear differential equations are integrated by means of a Runge Kutta method. A typical step size of several orbits permits rapid integration of long lifetime orbits in a short computing time.

Pines, S.↗
NASA NTRS1976

Combustion of hydrogen injected into a supersonic airstream (a guide to the HISS computer program)

A computer program based on a finite-difference, implicit numerical integration scheme is described for the prediction of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction. Results of calculations for flow and thermal property distributions were compared with 'cold flow data' taken by NASA/Langley and show excellent correlation. Typical results for equilibrium combustion are presented and exhibit qualitatively plausible behavior. Computer time required for a given case is approximately one minute on a CDC 7600. A discussion of the assumption of parabolic flow in the injection region is given which demonstrates that improvement in calculation in this region could be obtained by a partially-parabolic procedure which has been developed. It is concluded that the technique described provides an efficient and reliable means for analyzing hydrogen injection into supersonic airstreams and the subsequent combustion.

Dyer, D. F.↗
NASA NTRS1976

The interaction between a solid body and viscous fluid by marker-and-cell method

A computational method for solving nonlinear problems relating to impact and penetration of a rigid body into a fluid type medium is presented. The numerical techniques, based on the Marker-and-Cell method, gives the pressure and velocity of the flow field. An important feature in this method is that the force and displacement of the rigid body interacting with the fluid during the impact and sinking phases are evaluated from the boundary stresses imposed by the fluid on the rigid body. A sample problem of low velocity penetration of a rigid block into still water is solved by this method. The computed time histories of the acceleration, pressure, and displacement of the block show food agreement with experimental measurements. A sample problem of high velocity impact of a rigid block into soft clay is also presented.

Cheng, R. Y. K.↗
NASA NTRS1976

A computer program for anisotropic shallow-shell finite elements using symbolic integration

A FORTRAN computer program for anisotropic shallow-shell finite elements with variable curvature is described. A listing of the program is presented together with printed output for a sample case. Computation times and central memory requirements are given for several different elements. The program is based on a stiffness (displacement) finite-element model in which the fundamental unknowns consist of both the displacement and the rotation components of the reference surface of the shell. Two triangular and four quadrilateral elements are implemented in the program. The triangular elements have 6 or 10 nodes, and the quadrilateral elements have 4 or 8 nodes. Two of the quadrilateral elements have internal degrees of freedom associated with displacement modes which vanish along the edges of the elements (bubble modes). The triangular elements and the remaining two quadrilateral elements do not have bubble modes. The output from the program consists of arrays corresponding to the stiffness, the geometric stiffness, the consistent mass, and the consistent load matrices for individual elements. The integrals required for the generation of these arrays are evaluated by using symbolic (or analytic) integration in conjunction with certain group-theoretic techniques. The analytic expressions for the integrals are exact and were developed using the symbolic and algebraic manipulation language.

Andersen, C. M.↗
NASA NTRS1976

New convergence criteria for the vortex-lattice models of the leading-edge separation

The convergence criterion for the vortex-lattice technique which deals with delta wings exhibiting significant leading-edge separation was studied. It was shown that one can predict pressure distributions without irregularities which agree fairly well with experimental data (which show some irregularities of their own) by replacing the system of discrete vortex lines with a single concentrated core. This core has a circulation equal to the algebraic sum of the circulations around the discrete lines and is located at the centroid of these lines. Moreover, there is a requirement that the position and strength of the core must converge as the number of elements increases. Because the calculation of the position and strength of the core is much less involved than the calculation of the loads, this approach has the additional desirable feature of requiring less computational time.

Kandil, O. A.↗
NASA NTRS1976

Arrangement of vortex lattices

A new method is developed for solving the lifting-surface equation for thin wings. The solution requires the downwash equation to be in the form of Cauchy integrals which can be interpreted as a vortex lattice with the positions of the vortices and control points dictated by the finite sum used to approximate the integrals involved. Lan's continuous loading method is employed for the chordwise integral since it properly accounts for the leading-edge singularity, Cauchy singularity, and Kutta condition. Unlike Lan, the spanwise loading is also continuous and the Cauchy singularity in the spanwise integral is also properly accounted for by using the midpoint trapezoidal rule and the theory of Chebyshev polynomials. This technique yields the exact classical solution to Prandtl's lifting-line equation.The solution to the lifting-surface equation for rectangular wings was found to compare well with other continuous loading methods, but with much smaller computational times, and to converge faster than other vortex lattice methods.

Dejarnette, F. R.↗
NASA NTRS1976

A hybrid computer program for rapidly solving flowing or static chemical kinetic problems involving many chemical species

A hybrid chemical kinetic computer program was assembled which provides a rapid solution to problems involving flowing or static, chemically reacting, gas mixtures. The computer program uses existing subroutines for problem setup, initialization, and preliminary calculations and incorporates a stiff ordinary differential equation solution technique. A number of check cases were recomputed with the hybrid program and the results were almost identical to those previously obtained. The computational time saving was demonstrated with a propane-oxygen-argon shock tube combustion problem involving 31 chemical species and 64 reactions. Information is presented to enable potential users to prepare an input data deck for the calculation of a problem.

Mclain, A. G.↗