An extended criterion for statistical linearization
Random-input describing function as linear approximation to instantaneous nonlinearity in terms of minimum mean-squared error
Curry, R. E.↗
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Efficient computation of the complex error function
Complex error function computation using approximation method with single algorithm
Gautschi, W.↗
Coarse roll-rate gain-control circuit
Circuit is used in spin-rate computing unit of control system for solar pointing rocket during its acquisition mode. Direction cosines from magnetometers and coarse sun sensors derive function that is approximately roll-rate times sum of absolute value of direction cosines.
Cooke, W. A.↗
Experimental study of visual accommodation
A summary report of a research effort related to the human visual accommodation system is presented. A theoretical study of the accommodation system was made. Subsequent effort was aimed at the development of specialized instrumentation for experiments designed to lead to understanding the nature of the control system in human accommodation. The necessary instrumentation consisted primarily of: (1) an automatic optometer to measure the state of eye focus, (2) a focus stimulator device to control the apparent optical distance to any target, and (3) a two-dimensional eye tracker. The concepts and designs of the first two instruments have been published in the open literature, but this report contains the first detailed treatment of the Purkinje eye tracker developed under this program. The report also discusses an accommodation lag model to explain the ability of the eye to apparently know the polarity of focus error even though the blur on the retina is to a first-approximation an even function. The interaction of the accommodation and eye movement systems is also discussed, as is the ability to train the visual accommodation system to a surprisingly responsive condition in only a few hours of training.
Cornsweet, T. N.↗
Aeroelastic stability of periodic systems with application to rotor blade flutter
The dynamics of a helicopter blade in forward flight are described by a system of linear differential equations with periodic coefficients. The stability of this periodic aeroelastic system is determined, using multivariable Floquet-Liapunov theory. The transition matrix at the end of the period is evaluated by: (1) direct numerical integration, and (2) a new, approximate method, which consists in approximating a periodic function by a series of step functions. The numerical accuracy and efficiency of the methods is compared, and the second method is shown to be superior by far. Results illustrating the effect of the periodic coefficients and various blade parameters are presented.
Friedmann, P.↗
An empirical analysis of the quantitative effect of data when fitting quadratic and cubic polynomials
A study is made of the extent to which the size of the sample affects the accuracy of a quadratic or a cubic polynomial approximation of an experimentally observed quantity, and the trend with regard to improvement in the accuracy of the approximation as a function of sample size is established. The task is made possible through a simulated analysis carried out by the Monte Carlo method in which data are simulated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to either quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sizes and diminishes drastically for moderate and large amounts of experimental data.
Canavos, G. C.↗
Calculation of autoionization of He and H/-/ using the projection-operator formalism
Improved calculations are reported for the first several autoionization states of the lower symmetries of He and H(-). Unshifted energies are calculated by diagonalizing QHQ using a Hylleraes basis with more terms than previously used; shifts, widths, and photoabsorption shape parameters are obtained with the additional use of exchange-approximate nonresonant continuum functions. Previous calculations of H(-) resonances are reviewed and slightly augmented by applying various nonresonant continua and correcting small errors. A comparison is made between the calculations and experimental results and is found to be very satisfactory except for the lowest 1P autoionization state of He, which is shown to need a more accurate experimental determination.
Bhatia, A. K.↗
Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations
A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.
Cooke, C. H.↗
Rock failure analysis by combined thermal weakening and water jet impact
The influence of preheating on the initiation of fracture in rocks subjected to the impingement of a continuous water jet is studied. Preheating the rock is assumed to degrade its mechanical properties and strength in accordance with existing experimental data. The water jet is assumed to place a quasi-static loading on the surface of the rock. The loading is approximated by elementary functions which permit analytic computation of the induced stresses in a rock half-space. The resulting stresses are subsequently coupled with the Griffith criteria for tensile failure to estimate the change, due to heating, in the critical stagnation pressure and velocity of the water jet required to cause failure in the rock.
Nayfeh, A. H.↗
Core noise source diagnostics on a turbofan engine using correlation and coherence techniques
Fluctuating pressure measurements at several locations within the core of a turbofan engine were made simultaneously with far field acoustic measurements. Correlation and coherence techniques were used to determine the relative amplitude and phase relationships between core pressures at these various locations and between the core pressures and far field acoustic pressure. The combustor is a low frequency source region for acoustic propagation through the core nozzle and out to the far field. The relation between source pressure and the resulting sound pressure involves a 180 degree phase shift and an amplitude transfer function which varies approximately as frequency squared. This is consistent with a simplified model using fluctuating entropy as a source term.
Karchmer, A. M.↗
A dual-loop model of the human controller in single-axis tracking tasks
A dual loop model of the human controller in single axis compensatory tracking tasks is introduced. This model possesses an inner-loop closure which involves feeding back that portion of the controlled element output rate which is due to control activity. The sensory inputs to the human controller are assumed to be system error and control force. The former is assumed to be sensed via visual, aural, or tactile displays while the latter is assumed to be sensed in kinesthetic fashion. A nonlinear form of the model is briefly discussed. This model is then linearized and parameterized. A set of general adaptive characteristics for the parameterized model is hypothesized. These characteristics describe the manner in which the parameters in the linearized model will vary with such things as display quality. It is demonstrated that the parameterized model can produce controller describing functions which closely approximate those measured in laboratory tracking tasks for a wide variety of controlled elements.
Hess, R. A.↗
Simplified unsteady aerodynamic concepts, with application to parameter estimation
A simplified aerodynamic force model based on the physical principle of Prandtl's lifting line theory and trailing vortex concept has been developed to account for unsteadiness in the aircraft dynamics. The wake is assumed to be compressed to a single shed vortex element of appropriate strength moving downstream at a speed sufficient to approximate the Wagner function. Results are presented illustrating the ability of the simplified theory to duplicate exact solutions in unsteady aerodynamics. Further, consideration is given to the utility of the model in a parameter identification application.
Wells, W. R.↗
Core noise source diagnostics on a turbofan engine using correlation and coherence techniques
Fluctuating pressure measurements at several locations within the core of a turbofan engine were made simultaneously with far-field acoustic measurements. Correlation and coherence techniques were used to determine the relative amplitude and phase relationships between core pressures at these various locations and between the core pressures and far-field acoustic pressure. The results indicate that the combustor is a low-frequency source region for acoustic propagation through the core nozzle and out to the far-field. Specifically, it was found that the relation between source pressure and the resulting sound pressure involves a 180 deg phase shift and an amplitude transfer function which varies approximately as frequency squared. This is shown to be consistent with a simplified model using fluctuating entropy as a source term.
Karchmer, A.↗
Dual-loop model of the human controller
A dual-loop model of the human controller in single-axis compensatory tracking tasks is introduced. This model possesses an inner-loop closure that involves feeding back that portion of controlled element output rate that is due to control activity. A novel feature of the model is the explicit appearance of the human's internal representation of the manipulator-controlled element dynamics in the inner loop. The sensor inputs to the human controller are assumed to be system error and control force. The former can be sensed via visual, aural, or tactile displays, whereas the latter is assumed to be sensed in kinesthetic fashion. A set of general adaptive characteristics for the model is hypothesized, including a method for selecting simplified internal models of the manipulator-controlled element dynamics. It is demonstrated that the model can produce controller describing functions that closely approximate those measured in four laboratory tracking tasks in which the controlled element dynamics vary considerably in terms of ease of control. An empirically derived expression for the normalized injected error remnant spectrum is introduced.
Hess, R. A.↗
Multivariate approximation methods and applications to geophysics and geodesy
The first report in a series is presented which is intended to be written by the author with the purpose of treating a class of approximation methods of functions in one and several variables and ways of applying them to geophysics and geodesy. The first report is divided in three parts and is devoted to the presentation of the mathematical theory and formulas. Various optimal ways of representing functions in one and several variables and the associated error when information is had about the function such as satellite data of different kinds are discussed. The framework chosen is Hilbert spaces. Experiments were performed on satellite altimeter data and on satellite to satellite tracking data.
Munteanu, M. J.↗
On the optimality of the MAP estimation loop for carrier phase tracking BPSK and QPSK signals
Starting with MAP estimation theory as a basis for optimally estimating carrier phase of BPSK and QPSK modulations, it is shown in this paper that the closed loop phase trackers, which are motivated by this approach, are indeed closed loop optimum in the minimum mean-square phase tracking jitter sense. The corresponding squaring loss performance of these so-called MAP estimation loops is compared with that of more practical implementations wherein the hyperbolic tangent nonlinearity is approximated by simpler functions.
Simon, M. K.↗
Discrete Tchebycheff orthonormal polynomials and applications
Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.
Lear, W. M.↗
Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams
Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.
Noor, A. K.↗