A general method of improving the accuracy of approximate solutions of circular cylindrical shells.
Improved Donnell equations for concentrated load of circular cylindrical shell
CYLINDRICAL SHELL↗
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Compressible laminar boundary layers with large acceleration and cooling
The paper extends an approximate prediction method involving the integral form of the momentum equation to deduce the flow quantities of interest when compressibility effects become important and heat transfer may occur. The approximate method is applicable to a two-dimensional laminar boundary layer on an impermeable surface of negligible curvature for a specified integral momentum equation. The proposed approximate method involves the use of similar solutions in conjunction with the integral momentum equation for isentropic freestream flow of a perfect gas by assuming that viscosity is proportional to stagnation condition and Prandtl number is unity. The study pertains to larger values of acceleration (acceleration parameter to 20 rather than 2) than previously considered to account for rapidly accelerating flows such as in supersonic nozzles. A discussion of some applications confirms the advantages of the method in establishing better confidence in the predictions.
Back, L. H.↗
Less-Complex Method of Classifying MPSK
An alternative to an optimal method of automated classification of signals modulated with M-ary phase-shift-keying (M-ary PSK or MPSK) has been derived. The alternative method is approximate, but it offers nearly optimal performance and entails much less complexity, which translates to much less computation time. Modulation classification is becoming increasingly important in radio-communication systems that utilize multiple data modulation schemes and include software-defined or software-controlled receivers. Such a receiver may "know" little a priori about an incoming signal but may be required to correctly classify its data rate, modulation type, and forward error-correction code before properly configuring itself to acquire and track the symbol timing, carrier frequency, and phase, and ultimately produce decoded bits. Modulation classification has long been an important component of military interception of initially unknown radio signals transmitted by adversaries. Modulation classification may also be useful for enabling cellular telephones to automatically recognize different signal types and configure themselves accordingly. The concept of modulation classification as outlined in the preceding paragraph is quite general. However, at the present early stage of development, and for the purpose of describing the present alternative method, the term "modulation classification" or simply "classification" signifies, more specifically, a distinction between M-ary and M'-ary PSK, where M and M' represent two different integer multiples of 2. Both the prior optimal method and the present alternative method require the acquisition of magnitude and phase values of a number (N) of consecutive baseband samples of the incoming signal + noise. The prior optimal method is based on a maximum- likelihood (ML) classification rule that requires a calculation of likelihood functions for the M and M' hypotheses: Each likelihood function is an integral, over a full cycle of carrier phase, of a complicated sum of functions of the baseband sample values, the carrier phase, the carrier-signal and noise magnitudes, and M or M'. Then the likelihood ratio, defined as the ratio between the likelihood functions, is computed, leading to the choice of whichever hypothesis - M or M'- is more likely. In the alternative method, the integral in each likelihood function is approximated by a sum over values of the integrand sampled at a number, 1, of equally spaced values of carrier phase. Used in this way, 1 is a parameter that can be adjusted to trade computational complexity against the probability of misclassification. In the limit as 1 approaches infinity, one obtains the integral form of the likelihood function and thus recovers the ML classification. The present approximate method has been tested in comparison with the ML method by means of computational simulations. The results of the simulations have shown that the performance (as quantified by probability of misclassification) of the approximate method is nearly indistinguishable from that of the ML method (see figure).
Hamkins, Jon↗
Approximate two layer (inviscid/viscous) methods to model aerothermodynamic environments
Aeroassisted orbital transfer vehicles (AOTVs) and HSTs fly hypersonically at altitudes higher than those of Apollo and Space Shuttle type, whose flowfield could be considered a continuum with insignificant chemical nonequilibrium effects; AOTVs and HSTs will by contrast fly in the transitional regime between continuum and free molecule flow, where chemical nonequilibrium within the shock layer can be significant. Attention is presently given to the numerical and approximate methods of hypersonic flowfield calculation, emphasizing the role of aerodynamic heating. The development status of boundary layer methods, fully viscous methods, and gas models is evaluated.
De Jarnette, Fred R.↗
Accumulated approximation: A new method for structural optimization by iterative improvement
A new method for the solution of non-linear mathematical programming problems in the field of structural optimization is presented. It is an iterative scheme which for each iteration refines the approximation of objective and constraint functions by accumulating the function values of previously visited design points. The method has proven to be competitive for a number of well-known examples of which one is presented here. Furthermore because of the accumulation strategy, the method produces convergence even when the sensitivity analysis is inaccurate.
Rasmussen, John↗
An approximate viscous shock layer method for calculating the hypersonic flow over blunt-nosed bodies
The approximate axisymmetric method presented for accurately calculating the surface and flowfield properties of fully viscous hypersonic flow over blunt-nosed bodies incorporates the turbulence model of Cebeci-Smith (1970) and the equilibrium air tables of Hansen (1959). The method is faster than the parabolized Navier-Stokes or viscous shock layer solvers that it could replace for preliminary design determinations. Surface heat transfer and pressure predictions for the present method are comparable with the more accurate viscous shock layer method as well as flight test and wind tunnel data. A starting solution is not required.
Grantz, A. C.↗
Optimal Control using Composite Bernstein Approximants
In this work, we present composite Bernstein polynomials as a direct collocation method for approximating optimal control problems. An analysis of the convergence properties of composite Bernstein polynomials is provided, and beneficial properties of composite Bernstein polynomials for the solution of optimal control problems are discussed. The efficacy of the proposed approximation method is demonstrated through a bang-bang example. Lastly, we apply this method to a motion planning problem, offering a practical solution that emphasizes the ability of this method to solve complex optimal control problems.
Gage MacLin↗
Incorporation of varying types of temporal data in a neural network
Most neural network models do not specifically deal with temporal data. Handling of these variables is complicated by the different uses to which temporal data are put, depending on the application. Even within the same application, temporal variables are often used in a number of different ways. In this paper, types of temporal data are discussed, along with their implications for approximate reasoning. Methods for integrating approximate temporal reasoning into existing neural network structures are presented. These methods are illustrated in a medical application for diagnosis of graft-versus-host disease which requires the use of several types of temporal data.
Cohen, M. E.↗
An approximate semi-analytical method for prediction of interlaminar shear stresses in an arbitrarily laminated thick plate
An approximate semianalytical method for determination of interlaminar shear stress distribution through the thickness of an arbitrarily laminated thick plate has been presented. The method is based on the assumptions of transverse inextensibility and layerwise constant shear angle theory (LCST) and utilizes an assumed quadratic displacement potential energy based finite element method (FEM). Centroid of the triangular surface has been proved from a rigorous mathematical point of view (Aubin-Nitsche theory), to be the point of exceptional accuracy for the interlaminar shear stresses. Numerical results indicate close agreement with the available three-dimensional elasticity theory solutions. A comparison between the present theory and that due to an assumed stress hybrid FEM suggest that the (normal) traction-free-edge condition is not satisfied in the latter approach. Furthermore, the present paper is the first to present the results for interlaminar shear stresses in a two-layer thick square plate of balanced unsymmetric angle-ply construction. A comparison with the recently proposed Equilibrium Method (EM) indicates the superiority of the present method, because the latter assures faster convergence as well as simultaneous vanishing of the transverse shear stresses on both of the exposed surfaces of the laminate. Superiority of the present method over the EM, in the case of a symmetric laminate, is limited to faster convergence alone. It has also been demonstrated that the combination of the present method and the reduced (quadratic order) numerical integration scheme yields convergence of the interlaminar shear stresses almost as rapidly as that of the nodal displacements, in the case of a thin plate.
Chaudhuri, Reaz A.↗
Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations, Phase 2
A comparison with NASA conducted simulator studies has shown that the approximate digital method for computing rotor blade flapping responses to random inputs, tentatively suggested in Phase I Report, gives with increasing rotor advance ratio the wrong trend. Consequently, three alternative methods of solution have been considered and are described: (1) an approximate method based on the functional relation between input and output double frequency spectra, (2) a numerical method based on the system responses to deterministic inputs and (3) a perturbation approach. Among these the perturbation method requires the least amount of computation and has been developed in two forms - the first form to obtain the response correlation function and the second for the time averaged spectra of flapping oscillations.
Hohenemser, K. H.↗
Skin Friction Extracted from Surface Pressure in Incident Shock-Wave/Boundary-Layer Interaction
High-resolution skin-friction fields are extracted from pressure-sensitive paint (PSP) data obtained in shock-wave/boundary-layer interaction (SWBLI). The method of extracting skin friction from surface pressure is described, including the fundamental relation between skin friction and surface pressure, the variational method, error analysis, and an approximate iterative method. The proposed method is based on a coupling relation between skin friction and surface pressure, where the boundary enstrophy flux is suitably modeled or approximated. This method is applied to unsteady PSP data obtained in incident SWBLIs at Mach 2.5 for different Reynolds numbers, revealing the skin-friction structures of the flows: particularly, the separation bubble induced by the incident shock wave. The extracted results are in good agreement with the data obtained by the surface-stress-sensitive film.
skin friction↗
An approach to sub-optimal feedback control of non-linear systems.
Nonlinear system suboptimal feedback control technique based on method for determining approximate solutions for Hamilton-Jacobi- Bellman equation
OPTIMAL CONTROL↗
Probabilistic Structural Analysis Methods (PSAM) for select space propulsion system structural components
The objective is the development of several modular structural analysis packages capable of predicting the probabilistic response distribution for key structural variables such as maximum stress, natural frequencies, transient response, etc. The structural analysis packages are to include stochastic modeling of loads, material properties, geometry (tolerances), and boundary conditions. The solution is to be in terms of the cumulative probability of exceedance distribution (CDF) and confidence bounds. Two methods of probability modeling are to be included as well as three types of structural models - probabilistic finite-element method (PFEM); probabilistic approximate analysis methods (PAAM); and probabilistic boundary element methods (PBEM). The purpose in doing probabilistic structural analysis is to provide the designer with a more realistic ability to assess the importance of uncertainty in the response of a high performance structure. Probabilistic Structural Analysis Method (PSAM) tools will estimate structural safety and reliability, while providing the engineer with information on the confidence that should be given to the predicted behavior. Perhaps most critically, the PSAM results will directly provide information on the sensitivity of the design response to those variables which are seen to be uncertain.
Cruse, T. A.↗
Probabilistic Structural Analysis Methods for select space propulsion system structural components (PSAM)
The objective is the development of several modular structural analysis packages capable of predicting the probabilistic response distribution for key structural variables such as maximum stress, natural frequencies, transient response, etc. The structural analysis packages are to include stochastic modeling of loads, material properties, geometry (tolerances), and boundary conditions. The solution is to be in terms of the cumulative probability of exceedance distribution (CDF) and confidence bounds. Two methods of probability modeling are to be included as well as three types of structural models - probabilistic finite-element method (PFEM); probabilistic approximate analysis methods (PAAM); and probabilistic boundary element methods (PBEM). The purpose in doing probabilistic structural analysis is to provide the designer with a more realistic ability to assess the importance of uncertainty in the response of a high performance structure. Probabilistic Structural Analysis Method (PSAM) tools will estimate structural safety and reliability, while providing the engineer with information on the confidence that should be given to the predicted behavior. Perhaps most critically, the PSAM results will directly provide information on the sensitivity of the design response to those variables which are seen to be uncertain.
Cruse, T. A.↗
Differential equation based method for accurate approximations in optimization
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Pritchard, Jocelyn I.↗
Difference equation state approximations for nonlinear hereditary control problems
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.
Rosen, I. G.↗
Difference equation state approximations for nonlinear hereditary control problems
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589
Rosen, I. G.↗
Optimum design sensitivity based on approximation concepts and dual methods
An optimum design sensitivity analysis capability is reported which exploits the approximation concepts-dual method formulation of the minimum weight structural sizing problem. An efficient iterative solution technique is used to facilitate determination of sensitivity derivatives for both primal and dual variables. Estimates on the useful range of parameter perturbations, over which the optimum design sensitivity projections can be expected to yield satisfactory revised optimum designs, are also obtained. Numerical results for several example problems will be presented to illustrate the effectiveness of the capability reported.
Schmit, L. A.↗