The thermodynamics of austenite
First order statistical model for temperature dependence of carbon activity in austenite
Dunn, W. W.↗
SEARCH · Engineering Papers
Results for “ordered statistics”
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Some sequential, distribution-free pattern classification procedures with applications
Some sequential, distribution-free pattern classification techniques are presented. The decision problem to which the proposed classification methods are applied is that of discriminating between two kinds of electroencephalogram responses recorded from a human subject: spontaneous EEG and EEG driven by a stroboscopic light stimulus at the alpha frequency. The classification procedures proposed make use of the theory of order statistics. Estimates of the probabilities of misclassification are given. The procedures were tested on Gaussian samples and the EEG responses.
Poage, J. L.↗
Analytical methods for performance evaluation of nonlinear filters.
In the investigation, the filtering problem is considered in the continuous time domain. The postulated simple suboptimal nonlinear filter structure closely parallels the structure of the Kalman-Bucy optimal linear filter algorithm. Two filter performance evaluation methods are developed based on the Kolmogorov equations for the transition density of Markov processes. The expansions in the approximations for the nonlinear system and observation functions are in effect carried out up to second-order terms in both methods. The description of the filter's performance is sought in terms of second-order statistics in both methods.
Bejczy, A. K.↗
Image coding by adaptive block quantization.
A new source encoder called the adaptive block quantizer is proposed for coding data sources that emit a sequence of correlated real numbers with known first- and second-order statistics. Blocks of source output symbols are first classified and then block quantized in a manner that depends on their classification. The system is optimized relative to both the mean square error and the subjective quality of the reconstructed data for a certain class of pictorial data, and the resulting system performance demonstrated. Some interesting relationships between mean square error and subjective picture quality are presented.
Tasto, M.↗
Exact intervals and tests for median when one sample value possibly an outliner
Available are independent observations (continuous data) that are believed to be a random sample. Desired are distribution-free confidence intervals and significance tests for the population median. However, there is the possibility that either the smallest or the largest observation is an outlier. Then, use of a procedure for rejection of an outlying observation might seem appropriate. Such a procedure would consider that two alternative situations are possible and would select one of them. Either (1) the n observations are truly a random sample, or (2) an outlier exists and its removal leaves a random sample of size n-1. For either situation, confidence intervals and tests are desired for the median of the population yielding the random sample. Unfortunately, satisfactory rejection procedures of a distribution-free nature do not seem to be available. Moreover, all rejection procedures impose undesirable conditional effects on the observations, and also, can select the wrong one of the two above situations. It is found that two-sided intervals and tests based on two symmetrically located order statistics (not the largest and smallest) of the n observations have this property.
Keller, G. J.↗
A sequential nonparametric pattern classification algorithm based on the Wald SPRT
A sequential nonparametric pattern classification procedure is presented. The method presented is an estimated version of the Wald sequential probability ratio test (SPRT). This method utilizes density function estimates, and the density estimate used is discussed, including a proof of convergence in probability of the estimate to the true density function. The classification procedure proposed makes use of the theory of order statistics, and estimates of the probabilities of misclassification are given. The procedure was tested on discriminating between two classes of Gaussian samples and on discriminating between two kinds of electroencephalogram (EEG) responses.
Poage, J. L.↗
Ionospheric and tropospheric scintillation as a form of noise
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.
Fremouw, E. J.↗
On the optimal minimum order observer-based compensator and the limited state variable feedback controller
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.
Llorens-Ortiz, B.↗
Laser range measurements using non-Gaussian pulse shapes
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.
Ghigo, F. D.↗
Large eddy simulation of homogeneous isotropic turbulence
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.
Ferziger, J. H.↗
Model for redundant-sensor signal errors
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.
Sowada, D. J.↗
Backward deletion to minimize prediction errors in models from factorial experiments with zero to six center points
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.
Holms, A. G.↗
Backward deletion to minimize prediction errors in models from factorial experiments with zero to six center points
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.
Holms, A. G.↗
On the structure of turbulent wakes and merging shear layers of multielement airfoils
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.
Olson, L. E.↗
A technique for evaluating the influence of spatial sampling on the determination of global mean total columnar ozone
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.
Tolson, R. H.↗
A potential-energy scaling model to simulate the initial stages of thin-film growth
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.
Heinbockel, J. H.↗
Computer program to minimize prediction error in models from experiments with 16 hypercube points and 0 to 6 center points
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.
Holms, A. G.↗
A function space approach to state and model error estimation for elliptic systems
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.
Rodriguez, G.↗