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Recent tests of signals observed through the ionosphere, the solar wind, and a laboratory plasma have revealed a surprising consistency in parameters describing the first order statistics of a signal caused to scintillate by a randomly structured plasma. This paper describes a means for exploiting these new findings in a transionospheric communication channel model.
Four design problems are considered: two on the optimal minimum order observer-based compensator design and two on the optimal limited state variable feedback controller. The problem of designing an optimal discrete time linear time-invariant observer-based compensator for the regulation of an n dimensional linear discrete time time-invariant plant with m independent outputs is considered. This is a stochastic design problem to the extent that the initial plant state is assumed to be a random vector with known first and second order statistics. The compensator parameters are obtained by minimizing the expectation, with respect to the initial conditions, of the standard cost, quadratic in the state and control vectors with the inclusion of cross terms.
Many optical ranging systems currently use laser pulses of approximately Gaussian shape with widths of a few nanoseconds or less. The present paper shows that a substantial improvement in accuracy can be obtained for a given pulse length by means of laser ranging systems using conventional length (long) pulses with a sharp leading edge pulse distribution. The accuracy in such a case will improve roughly linearly with the signal strength. Order statistics is used to estimate the round-trip level travel time from the arrival time of the earliest photoelectron.
This paper presents results from a comprehensive investigation of large-eddy simulations of homogeneous isotropic turbulence. Calculations have been made using grid meshes, a number of flowfield filters, and two simple subgrid scale turbulence models. Particular attention has been paid to the degree of isotropy and the ability of the approach to predict higher-order statistical quantities (skewness and flatness). Directions for needed improvement in the simulation approach are indicated, and a plea is made to experimenters to process their data in a way which will facilitate comparison with large eddy simulations.
Report describes application of order statistics to analysis of failure modes in redundant systems. Report provides detailed mathematical discussion of approach, accompanied by graphs and equations. Techniques are relevant to process that demand high reliability, such as manufacture of dangerous chemicals. It also includes discussion of quad-redundant system.
Population model coefficients were chosen to simulate a saturated 2 to the fourth power fixed effects experiment having an unfavorable distribution of relative values. Using random number studies, deletion strategies were compared that were based on the F distribution, on an order statistics distribution of Cochran's, and on a combination of the two. Results of the comparisons and a recommended strategy are given.
Population model coefficients were chosen to simulate a saturated 2 to the 4th fixed-effects experiment having an unfavorable distribution of relative values. Using random number studies, deletion strategies were compared that were based on the F-distribution, on an order statistics distribution of Cochran's, and on a combination of the two. The strategies were compared under the criterion of minimizing the maximum prediction error, wherever it occurred, among the two-level factorial points. The strategies were evaluated for each of the conditions of 0, 1, 2, 3, 4, 5, or 6 center points. Three classes of strategies were identified as being appropriate, depending on the extent of the experimenter's prior knowledge. In almost every case the best strategy was found to be unique according to the number of center points. Among the three classes of strategies, a security regret class of strategy was demonstrated as being widely useful in that over a range of coefficients of variation from 4 to 65%, the maximum predictive error was never increased by more than 12% over what it would have been if the best strategy had been used for the particular coefficient of variation. The relative efficiency of the experiment, when using the security regret strategy, was examined as a function of the number of center points, and was found to be best when the design used one center point.
The structure of the attached turbulent flow in the vicinity of a NACA 4412 airfoil equipped with a single-slotted flap was studied. The airfoil/flap configuration was tested at a Mach number of 0.06 and a Reynolds number of 1.3 x 10 to the 6th in a 7- by 10-Foot Wind Tunnel. Surface-pressure measurements were made on the main airfoil and on the flap. Detailed measurements, obtained using a high-spatial-resolution laser Doppler anemometer, were made of the mean velocity flow field and of the second-order statistical quantities (Reynolds stresses) in the boundary layers, wakes, and merging shear layers. The experimental observations are compared with theoretical predictions of pressure, mean velocity, and Reynolds stress.
A technique is described for providing a means of evaluating the influence of spatial sampling on the determination of global mean total columnar ozone. A finite number of coefficients in the expansion are determined, and the truncated part of the expansion is shown to contribute an error to the estimate, which depends strongly on the spatial sampling and is relatively insensitive to data noise. First and second order statistics are derived for each term in a spherical harmonic expansion which represents the ozone field, and the statistics are used to estimate systematic and random errors in the estimates of total ozone.
A solid on solid (SOS) Monte Carlo computer simulation employing a potential energy scaling technique was used to model the initial stages of thin film growth. The model monitors variations in the vertical interaction potential that occur due to the arrival or departure of selected adatoms or impurities at all sites in the 400 sq. ft. array. Boltzmann ordered statistics are used to simulate fluctuations in vibrational energy at each site in the array, and the resulting site energy is compared with threshold levels of possible atomic events. In addition to adsorption, desorption, and surface migration, adatom incorporation and diffusion of a substrate atom to the surface are also included. The lateral interaction of nearest, second nearest, and third nearest neighbors is also considered. A series of computer experiments are conducted to illustrate the behavior of the model.
A previous report described a backward deletion procedure of model selection that was optimized for minimum prediction error and which used a multiparameter combination of the F - distribution and an order statistics distribution of Cochran's. A computer program is described that applies the previously optimized procedure to real data. The use of the program is illustrated by examples.
An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.
A general theory of image texture models is proposed and its applicability to the problem of scene segmentation using texture classification is discussed. An algorithm, based on half-plane autoregressive filtering, which optimally utilizes second order statistics to discriminate between texture classes represented by arbitrary wide sense stationary random fields is described. Empirical results of applying this algorithm to natural and sysnthesized scenes are presented and future research is outlined.
Experiments were conducted to determine the mean turbulence characteristics of the noise-producing region of a 3 in. cold excited round jet. The jet was excited by plane acoustic waves with a high amplitude of excitation (2 percent of the jet dynamic head), and at a Strouhal number of 0.5. The flow Reynolds number was 280,000. The exit boundary layer was made turbulent by artificially tripping it with sandpaper strips. The data were obtained with single and X-hot-wires and processed in digital form. Mean and higher order statistics were also deduced. The results showed an increase in all three velocity components and stresses. However, most of the increase was noticed from the longitudinal component, while the changes in the radial velocity and the azimuthal component were much smaller. Substantial widening of the jet occurred, accompanied by a shortening of the potential core. Increased rates of production of energy close to the lip-line were a characteristic feature of the mixing region behavior.
An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal esimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed. While this paper focuses on theoretical developments, applications arising in the area of large structure static shape determination are contained in a closely related paper (Rodriguez and Scheid, 1982).
A discrete and, as approximation to it, a continuous model for the software reliability growth process are examined. The discrete model is based on independent multinomial trials and concerns itself with the joint distribution of the first occurrence time of its underlying events (bugs). The continuous model is based on the order statistics of N independent nonidentically distributed exponential random variables. It is shown that the spacings between bugs are not necessarily independent or exponentially (geometrically) distributed. However, there is a statistical rationale for viewing them so conditionally. Some identifiability problems are pointed out and resolved. In particular, it appears that the number of bugs in a program is not identifiable. Estimated upper bounds and confidence bounds for the residual program eror content are given based on the spacings of the first k bugs removed.
Single and dual hot-wire probes have been used to accomplish a first look at the large-eddy structure of a supersonic turbulent boundary layer. The investigation was performed in an axisymmetric turbulent boundary layer in the Ames High Reynolds Number wind tunnel. Freestream Mach number was 2.97, the boundary layer was approximately 1.2 cm thick, and Reynolds number = 15,000. Quantities measured were streamwise turbulence intensity and higher order statistics of mass-flow fluctuations, and space-time correlations of instantaneous streamwise velocity at two locations. Conditional sampling of the hot-wire signals was performed to detect the passage and describe the character of the large turbulent eddies. Results indicate that the large scale structure in compressible turbulence is similar to that at low subsonic flow speeds except at the boundary layer edge, where the intermittency region is narrowed in compressible flow.
This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.