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At least 109 records · Page 6

Smoothing properties of neutral equations

A neutral functional differential equation is defined as d/dt(Dx sub t) = f(x sub t), with D linear, continuous, atomic at zero. The solution generally is no smoother than the initial data after any finite number of steps. A more restrictive class of D-operators for which some smoothing takes place after an infinite number of steps is defined. This result indicates that a solution can be in an omega-limit set only if it corresponds to initial data which are smooth. A space which can be considered as a Banach space with the topology of uniform convergence is also defined.

Hale, J. K.↗

A low-cost inertial smoothing system for landing approach guidance

Accurate position and velocity information with low noise content for instrument approaches and landings is required for both control and display applications. In a current VTOL automatic instrument approach and landing research program, radar-derived landing guidance position reference signals, which are noisy, have been mixed with acceleration information derived from low-cost onboard sensors to provide high-quality position and velocity information. An in-flight comparison of signal quality and accuracy has shown good agreement between the low-cost inertial smoothing system and an aided inertial navigation system. Furthermore, the low-cost inertial smoothing system has been proven to be satisfactory in control and display system applications for both automatic and pilot-in-the-loop instrument approaches and landings.

Niessen, F. R.↗

Power spectral density estimation by spline smoothing in the frequency domain

An approach, based on a global averaging procedure, is presented for estimating the power spectrum of a second order stationary zero-mean ergodic stochastic process from a finite length record. This estimate is derived by smoothing, with a cubic smoothing spline, the naive estimate of the spectrum obtained by applying FFT techniques to the raw data. By means of digital computer simulated results, a comparison is made between the features of the present approach and those of more classical techniques of spectral estimation.

Defigueiredo, R. J. P.↗

Power spectral density estimation by spline smoothing in the frequency domain.

An approach, based on a global averaging procedure, is presented for estimating the power spectrum of a second order stationary zero-mean ergodic stochastic process from a finite length record. This estimate is derived by smoothing, with a cubic smoothing spline, the naive estimate of the spectrum obtained by applying Fast Fourier Transform techniques to the raw data. By means of digital computer simulated results, a comparison is made between the features of the present approach and those of more classical techniques of spectral estimation.-

De Figueiredo, R. J. P.↗

A smoothing algorithm using cubic spline functions

Two algorithms are presented for smoothing arbitrary sets of data. They are the explicit variable algorithm and the parametric variable algorithm. The former would be used where large gradients are not encountered because of the smaller amount of calculation required. The latter would be used if the data being smoothed were double valued or experienced large gradients. Both algorithms use a least-squares technique to obtain a cubic spline fit to the data. The advantage of the spline fit is that the first and second derivatives are continuous. This method is best used in an interactive graphics environment so that the junction values for the spline curve can be manipulated to improve the fit.

Smith, R. E., Jr.↗

Smooth plains and continuous deposits of craters and basins

Apollo 16 photographic data are analyzed which suggest that smooth plains are related in origin to large primary cratering events, and that the plains material is mainly the ejecta of local and regional primary impact craters with only minor contributions from distant craters and basins. This material, then, has been emplaced in its present location by secondaries of distant craters and directly by primary craters near the site. Calculations indicate that the material excavated from large primary craters typically excavates much larger amounts of material from local terrain when it impacts in the secondary crater field. There is a correlation between the extent of development of smooth plains inside large high-land craters and the erosional state of the crater rims and walls. It is incorrect to consider the continuous deposits to be solely basin ejecta.

Oberbeck, V. R.↗

Active controls for ride smoothing

Active controls technology offers great promise for significantly smoothing the ride, and thus improving public and air carrier acceptance, of certain types of transport aircraft. Recent findings which support this promise are presented in the following three pertinent areas: (1) Ride quality versus degree of traveler satisfaction; (2) significant findings from a feasibility study of a ride smoothing system; and (3) potential ride problems identified for several advanced transport concepts.

Conner, D. W.↗

Smoothing the output from a DAC

Circuit smooths stepped waveform from analog-to-digital converter without appreciable phase shift between stepped input signal and smoothed output signal and without any effect from stepping rate. Waveform produced is suitable for driving controls used in manufacturing processes, aerospace systems, and automobiles.

Wagner, C.↗

An analytical procedure for computing smooth transitions between two specified cross sections with applications to blended wing body configuration

An analytical procedure is described for designing smooth transition surfaces for blended wing-body configurations. Starting from two specified cross section shapes, the procedure generates a gradual transition from one cross section shape to the other as an analytic blend of the two shapes. The method utilizes a conformal mapping, with subsequent translation and scaling, to transform the specified and shapes to curves that can be combined more smoothly. A sample calculation is applied to a blended wing-body missile type configuration with a top mounted inlet.

Barger, R. L.↗

Radar scattering from a diffuse vegetation layer over a smooth surface

A simple model is presented for the oblique backscatter and bistatic scatter from a smooth surface overlain by a diffuse layer. Only single scattering in the diffuse layer is taken into account. The model analysis shows that the combination of volume scattering and oblique reflection at the surface may increase appreciably the waves scattering. The scattering strongly depends on the properties of the smooth surface. These results support some of the observations made with the Seasat spaceborne imaging radar over flooded regions with heavy vegetation cover.

Engheta, N.↗

Smoothing splines: Regression, derivatives and deconvolution

The statistical properties of a cubic smoothing spline and its derivative are analyzed. It is shown that unless unnatural boundary conditions hold, the integrated squared bias is dominated by local effects near the boundary. Similar effects are shown to occur in the regularized solution of a translation-kernel intergral equation. These results are derived by developing a Fourier representation for a smoothing spline.

Rice, J.↗

The computation of Laplacian smoothing splines with examples

Laplacian smoothing splines (LSS) are presented as generalizations of graduation, cubic and thin plate splines. The method of generalized cross validation (GCV) to choose the smoothing parameter is described. The GCV is used in the algorithm for the computation of LSS's. An outline of a computer program which implements this algorithm is presented along with a description of the use of the program. Examples in one, two and three dimensions demonstrate how to obtain estimates of function values with confidence intervals and estimates of first and second derivatives. Probability plots are used as a diagnostic tool to check for model inadequacy.

Wendelberger, J. G.↗

A function space approach to smoothing with applications to model error estimation for flexible spacecraft control

A function space approach to smoothing is used to obtain a set of model error estimates inherent in a reduced-order model. By establishing knowledge of inevitable deficiencies in the truncated model, the error estimates provide a foundation for updating the model and thereby improving system performance. The function space smoothing solution leads to a specification of a method for computation of the model error estimates and development of model error analysis techniques for comparison between actual and estimated errors. The paper summarizes the model error estimation approach as well as an application arising in the area of modeling for spacecraft attitude control.

Rodriguez, G.↗

Radar data smoothing filter study

The accuracy of the current Wallops Flight Facility (WFF) data smoothing techniques for a variety of radars and payloads is examined. Alternative data reduction techniques are given and recommendations are made for improving radar data processing at WFF. A data adaptive algorithm, based on Kalman filtering and smoothing techniques, is also developed for estimating payload trajectories above the atmosphere from noisy time varying radar data. This algorithm is tested and verified using radar tracking data from WFF.

White, J. V.↗

Investigations of the Mars Cratered Terrain: Smooth Plains Boundary in the Eastern Equatorial Region

As part of an ongoing study to place geologic constraints on, and to interpret the origin of the ancient cratered terrain - smooth plains boundary on Mars, structural features in the eastern hemisphere were mapped, looking at wide-scale variations in aereal percentage of crater vocer and distinctive landforms. Maps and a digitized data set for graben, scarps, ridges and elongate plateaus in the eastern hemisphere were completed for 30 deg N to 30 deg. In the equatorial region, results indicate a marked change from the N oriented ridges north of the boundary to the NW orientations of those in the inter and intracrater plains south of the boundary. The WNW orientation of the boundary itself is matched by similar orientations of graben and scraps in the southern terrain. In order to determine whether outlying plateaus and isolated knobby hills found north of the boundary are formed from material of the ancient cratered terrain, the Viking 2 approach color data were used to discriminate surface materials in the eastern hemisphere. In the southern half of the Amenthes quadrange (MC-14), several correlations exist among surficial spectral reflectance and observed geologic units. Old terrain on the eastern rim of the Isidis basin is much redder than the smooth volcanic plains on either side of the rim, even though the plains unit east of the rim is located several kilometers higher than the plains on the floor of Isidis. Based on statistics derived from the color data, the plains within Isidis were found to differ from those north of the boundary zone.

Maxwell, T. A.↗

The Mars ancient cratered terrain, smooth plains boundary: Implications of Viking color data for evolution of the Amenthes Region

The global color set compiled by the Mars Consortium was investigated. The problem of application of the martian surface color data to geologic interpretation are atmospheric contributions which increase with latitude, and the high correlation among the three color bands. In southern Amenthes the classified units show areas of possible mixing between cratered tarrain and smooth plains. It is suggested that some geologically meaningful correlation exists between surface units and the transformed color data in the Amenthes region. The knobby terrain protruding through the plains units appears to be remnants of ancient cratered terrain extending northward beneath the more youthful smooth plains.

Maxwell, T. A.↗

Thermal smoothing of rough surfaces in vacuo

The derivation of equations governing the smoothing of rough surfaces, based on Mullins' (1957, 1960, and 1963) theories of thermal grooving and of capillarity-governed solid surface morphology is presented. As an example, the smoothing of a one-dimensional sine-shaped surface is discussed.

Wahl, G.↗

Rotordynamic coefficients and leakage flow of parallel grooved seals and smooth seals

Based on Childs finite length solution for annular plain seals an extension of the bulk flow theory is derived to calculate the rotordynamic coefficients and the leakage flow of seals with parallel grooves in the stator. Hirs turbulent lubricant equations are modified to account for the different friction factors in circumferential and axial direction. Furthermore an average groove depth is introduced to consider the additional circumferential flow in the grooves. Theoretical and experimental results are compared for the smooth constant clearance seal and the corresponding seal with parallel grooves. Compared to the smooth seal the direct and cross-coupled stiffness coefficients as well as the direct damping coefficients are lower in the grooved seal configuration. Leakage is reduced by the grooving pattern.

Nordmann, R.↗