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The limitation of the iterative clustering procedure proposed by Haralick and Dinstein is indicated with the help of two examples and is construed as the effect of the linear structure of the T transformation.
A computer program was developed to account approximately for the effects of finite wing thickness in transonic potential flow over an oscillation wing of finite span. The program is based on the original sonic box computer program for planar wing which was extended to account for the effect of wing thickness. Computational efficiency and accuracy were improved and swept trailing edges were accounted for. Account for the nonuniform flow caused by finite thickness was made by application of the local linearization concept with appropriate coordinate transformation. A brief description of each computer routine and the applications of cubic spline and spline surface data fitting techniques used in the program are given, and the method of input was shown in detail. Sample calculations as well as a complete listing of the computer program listing are presented.
The terminal guidance problem for a fixed-trim re-entry body is formulated with the objective of synthesizing a closed-loop steering law. A transformation of variables and subsequent linearization of the motion, with the sight-line to the target as a reference, reduces the order of the state system for the guidance problem. The reduced order system, although nonlinear and time-varying, is simple enough to lend itself to synthesis of a class of guidance laws. A generalization of the feedforward device of classical control theory is successfully employed for compensation of roll autopilot lags. The proposed steering law exhibits superior miss-distance performance in a computational comparison with existing fixed-trim guidance laws.
The development of the transformation theory is discussed. Results and applications concerning the use of this design technique for automatic flight control of aircraft are presented. The theory examines the transformation of nonlinear systems to linear systems. The tracking of linear models by nonlinear plants is discussed. Results of manned simulation are also presented.
A static analysis is given of the problem of an elastic layer perfectly bonded, except for a frictionless interface crack, to a dissimilar elastic half-plane. The free surface of the layer is loaded by a finite pressure distribution directly over the crack. The problem is formulated using the two dimensional linear elasticity equations. Using Fourier transforms, the governing equations are converted to a pair of coupled singular integral equations. The integral equations are reduced to a set of simultaneous algebraic equations by expanding the unknown functions in a series of Jacobi polynomials and then evaluating the singular Cauchy-type integrals. The resulting equations are found to be ill-conditioned and, consequently, are solved in the least-squares sense. Results from the analysis show that, under a normal pressure distribution on the free surface of the layer and depending on the combination of geometric and material parameters, the ends of the crack can open. The resulting stresses at the crack-tips are singular, implying that crack growth is possible. The extent of the opening and the crack-top stress intensity factors depend on the width of the pressure distribution zone, the layer thickness, and the relative material properties of the layer and half-plane.
The method of parametric differentiation is shown to be an effective means to transform both the time-linearized and the fully nonlinear transonic small disturbance potential flow equations to a linear system of equations. The globally linearized equations are then solved in phase space by finite difference methods and integral equation methods. The predicted birth, growth, and motion of weak shock waves in two-dimensional transonic flows are compared with existing theory and experiment.
Passive microwave brightness temperatures from the Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR) can be used to infer the soil moisture content over agricultural areas such as the southern Great Plains of the United States. A linear regression analysis between three transforms of the five dual polarized SMMR wavelengths of 0.81, 1.36, 1.66, 2.80 and 4.54 cm and an antecedent precipitation index representing the precipitation history showed correlation coefficients greater than 0.90 for pixel aggregates of 25-50 km. The use of surface air temperatures to approximate the temperature of the emitting layer was not required to obtain high correlation coefficients between the transforms and the antecedent precipitation index.
A general dynamic model of a two-link Euler-Bernoulli beam flexible robot arm is presented in the form of partial-differential-integral equations. Observations are made on important properties of the dynamic model. The resulting infinite-dimensional system is then input-output decoupled and partially linearized by a diffeomorphic state transformation and nonlinear state feedback. The local stability issue is addressed for a one-link flexible robot arm.
A modeling approach for linear isentropic flow systems based on the quasi-one-dimensional Euler equations of non-viscous, compressible flow are presented. Such systems are representative of certain high speed propulsion systems. Accurate models useful in control system studies are developed. A supersonic inlet is considered, and the resulting set of partial differential equations with boundary conditions is solved for a linear transfer matrix using Laplace transforms.
A modeling approach for linear isentropic flow systems based on the quasi-one-dimensional Euler equations of non-viscous, compressible flow are presented. Such systems are representative of certain high speed propulsion systems. Accurate models useful in control system studies are developed. A supersonic inlet is considered, and the resulting set of partial differential equations with boundary conditions is solved for a linear transfer matrix using Laplace transforms.
The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.
A system design for aeronautical audio broadcasting, with C-band uplink and L-band downlink, via Inmarsat space segments is presented. Near-transparent-quality compression of 5-kHz bandwidth audio at 20.5 kbit/s is achieved based on a hybrid technique employing linear predictive modeling and transform-domain residual quantization. Concatenated Reed-Solomon/convolutional codes with quadrature phase shift keying are selected for bandwidth and power efficiency. RF bandwidth at 25 kHz per channel, and a decoded bit error rate at 10(exp -6) with E(sub b)/N(sub o) at 3.75 dB are obtained. An interleaver, scrambler, modem synchronization, and frame format were designed, and frequency-division multiple access was selected over code-division multiple access. A link budget computation based on a worst-case scenario indicates sufficient system power margins. Transponder occupancy analysis for 72 audio channels demonstrates ample remaining capacity to accommodate emerging aeronautical services.
The errors incurred in producing a thermal inertia map are of three general types: measurement, analysis, and model simplification. To emphasize the geophysical relevance of these errors, they were expressed in terms of uncertainty in thermal inertia and compared with the thermal inertia values of geologic materials. Thus the applications and practical limitations of the technique were illustrated. All errors were calculated using the parameter values appropriate to a site at the Raft River, Id. Although these error values serve to illustrate the magnitudes that can be expected from the three general types of errors, extrapolation to other sites should be done using parameter values particular to the area. Three surface temperature algorithms were evaluated: linear Fourier series, finite difference, and Laplace transform. In terms of resulting errors in thermal inertia, the Laplace transform method is the most accurate (260 TIU), the forward finite difference method is intermediate (300 TIU), and the linear Fourier series method the least accurate (460 TIU).
The paper provides an engineering analysis approach for assessing reliability of NDE flaw detection using smaller number of demonstration data points. It explores dependence of probability of detection (POD), probability of false positive (POF), on contrast-to-noise ratio, and net decision threshold-to-noise ratio in a simulated data; and draws some generically applicable inferences to devise the approach. ASTM nondestructive evaluation standards provide requirements on signal-to-noise ratio and/or contrast-to-noise ratio in order to provide reliable flaw detection and limit false positive calls. POD analysis of inspection test data results in an estimated flaw size, denoted by 𝑎90/95. This flaw size has 90% POD and minimum 95% confidence. POF is also estimated in the analysis. POD demonstration requires specimens with flaws of known size. In many situations, it is very expensive to produce the large number of flaws required for the POD analysis. In some situations, only real flaws can truly represent the flaws for demonstration. Real flaws of correct size and location in part configuration specimen may be difficult to produce, if not impossible. Here, an engineering analysis approach is devised using simulation to assess reliability of NDE technique when a limited number of flaws are available for demonstration. In this simulation, a technique is considered reliable, if it provides flaw detectability size equal to or better than the theoretical 𝑎90𝑡ℎ used in simulation and also provides a POF less than or equal to a chosen value. The paper uses simulated signal response versus flaw size data to devise the approach. Linear correlation is used between the signal response data and flaw size. POD software mh1823 uses generalized linear model (GLM) in POD analysis after transforming the flaw size and signal response, if needed, using logarithm. Therefore, this approach is in agreement with the linear signal correlation used in mh1823. Using the POD analysis of data, generic conditions on contrast-to-noise ratio and net decision threshold-to-noise ratio are derived for reliable flaw detection. In order to assess technique reliability using the engineering approach, signal response-to-flaw size correlation about the flaw size of concern is needed. In addition, measurement of noise is also needed. If the technique meets the above requirements, assumption of linear signal-to-flaw size correlation and conditions on noise, then the technique can be assessed using this analysis as it fits the underlying POD model used here. The approach is conservative and is designed to provide a larger flaw size compared to the POD approach. Such NDE technique assessment approach, although, not as rigorous as POD, can be cost effective if the larger flaw size can be tolerated. Typically, this is a situation for all quality control NDE inspections. Here, an NDE technique needs to be reliable and 𝑎90/95 is not estimated, but the assessed flaw size is assumed to be larger than the unknown a90 due to conservative factors or margins. Applicability of the approach for assessing reliability of flaw detection in x-ray radiography and 2D imaging in general is also explored.
This paper associates the Riccati group and its group action on linear-quadratic optimal control problems to the action of a Lie transformation group on a set of Hamiltonian matrices. In this Lie theoretic setting results are presented concerning the associated orbit structure and the structure of the group itself. These results are of importance in understanding the solution structure of matrix Riccati differential equations, and thus also of importance in linear-quadratic optimal control.
In quantum physics the direct observables are probabilities of events. We ask how observed probabilities must be combined to achieve what we call maximum predictive power. According to this concept the accuracy of a prediction must only depend on the number of runs whose data serve as input for the prediction. We transform each probability to an associated variable whose uncertainty interval depends only on the amount of data and strictly decreases with it. We find that for a probability which is a function of two other probabilities maximum predictive power is achieved when linearly summing their associated variables and transforming back to a probability. This recovers the quantum mechanical superposition principle.
Considerable interest lies in the ability to characterize the onset of spontaneous instabilities within liquid propellant rocket engine (LPRE) combustion devices. Linear techniques, such as fast Fourier transforms, various correlation parameters, and critical damping parameters, have been used at great length for over fifty years. Recently, nonlinear time series methods have been applied to deduce information pertaining to instability incipiency hidden in seemingly stochastic combustion noise. A technique commonly used in biological sciences known as the Multifractal Detrended Fluctuation Analysis has been extended to the combustion dynamics field, and is introduced here as a data analysis approach complementary to linear ones. Advancing, a modified technique is leveraged to extract artifacts of impending combustion instability that present themselves a priori growth to limit cycle amplitudes. Analysis is demonstrated on data from J-2X gas generator testing during which a distinct spontaneous instability was observed. Comparisons are made to previous work wherein the data were characterized using linear approaches. Verification of the technique is performed by examining idealized signals and comparing two separate, independently developed tools.
This paper addresses the steady, incompressible, two-dimensional flow past a flat plate with suction through porous strips. Closed-form solutions for each flow quantity are developed in the context of linearized triple-deck theory using Fourier transforms. To demonstrate the validity of these closed-form solutions, we compare the wall shear stress and pressure coefficients and the streamwise velocity profiles from the linearized theory with those obtained by the numerical integration of both interacting and nonsimilar boundary-layer equations. The agreement between the linearized triple-deck and interacting boundary-layer equations is good; however, the nonsimilar boundary layers, which fail to account for upstream influence, are shown to be in poor agreement with both interacting boundary layers and the linearized triple deck. The linearized closed-form solutions will therefore be very useful in future stability calculations.