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NASA NTRS1988

Optimal post-experiment estimation of poorly modeled dynamic systems

Recently, a novel strategy for post-experiment state estimation of discretely-measured dynamic systems has been developed. The method accounts for errors in the system dynamic model equations in a more general and rigorous manner than do filter-smoother algorithms. The dynamic model error terms do not require the usual process noise assumptions of zero-mean, symmetrically distributed random disturbances. Instead, the model error terms require no prior assumptions other than piecewise continuity. The resulting state estimates are more accurate than filters for applications in which the dynamic model error clearly violates the typical process noise assumptions, and the available measurements are sparse and/or noisy. Estimates of the dynamic model error, in addition to the states, are obtained as part of the solution of a two-point boundary value problem, and may be exploited for numerous reasons. In this paper, the basic technique is explained, and several example applications are given. Included among the examples are both state estimation and exploitation of the model error estimates.

Mook, D. Joseph↗

NASA NTRS1988

Development of sputter coatings for the gravity probe B gyroscope housings

Cu/Ti coatings have been applied by sputter deposition to fused quartz housings to serve as the electrodes and lands of electrostatically supported gyroscopes. Niobium-coated fused quartz gyro rotors have been successfully suspended and spun up in those housings. The Cu/Ti bilayer coating and alternative multilayer coatings (Cu/Mo, Mo/Cu/Ti and Mo/Cu/Mo) with 2-micron thickness produced by sputter deposition on flat, fused quartz substrates have been examined with scanning electron microscopy, X-ray diffraction, X-ray photoelectron spectroscopy, and four-point resistivity measurement techniques. The multilayer coatings with a molybdenum bonding layer appear to produce smoother surfaces than those with a titanium bonding layer. All multilayer coatings survived thermal cycling to 77 K without adhesion failure.

Zhou, P.↗

NASA NTRS1989

The inverse gravimetric problem in gravity modelling

One of the main purposes of geodesy is to determine the gravity field of the Earth in the space outside its physical surface. This purpose can be pursued without any particular knowledge of the internal density even if the exact shape of the physical surface of the Earth is not known, though this seems to entangle the two domains, as it was in the old Stoke's theory before the appearance of Molodensky's approach. Nevertheless, even when large, dense and homogeneous data sets are available, it was always recognized that subtracting from the gravity field the effect of the outer layer of the masses (topographic effect) yields a much smoother field. This is obviously more important when a sparse data set is bad so that any smoothing of the gravity field helps in interpolating between the data without raising the modeling error, this approach is generally followed because it has become very cheap in terms of computing time since the appearance of spectral techniques. The mathematical description of the Inverse Gravimetric Problem (IGP) is dominated mainly by two principles, which in loose terms can be formulated as follows: the knowledge of the external gravity field determines mainly the lateral variations of the density; and the deeper the density anomaly giving rise to a gravity anomaly, the more improperly posed is the problem of recovering the former from the latter. The statistical relation between rho and n (and its inverse) is also investigated in its general form, proving that degree cross-covariances have to be introduced to describe the behavior of rho. The problem of the simultaneous estimate of a spherical anomalous potential and of the external, topographic masses is addressed criticizing the choice of the mixed collection approach.

Sanso, F.↗

NASA NTRS1990

Mode-medium instability and its correction with a Gaussian reflectivity mirror

A high power CO2 laser beam is known to deteriorate after a few microseconds due to a mode-medium instability (MMI) which results from an intensity dependent heating rate related to the vibrational-to-translational decay of the upper and lower CO2 lasing levels. An iterative numerical technique is developed to model the time evolution of the beam as it is affected by the MMI. The technique is used to study the MMI in an unstable CO2 resonator with a hard-edge output mirror for different parameters like the Fresnel number and the gas density. The results show that the mode of the hard edge unstable resonator deteriorates because of the diffraction ripples in the mode. A Gaussian-reflectivity mirror was used to correct the MMI. This mirror produces a smoother intensity profile which significantly reduces the effects of the MMI. Quantitative results on peak density variation and beam quality are presented.

Webster, K. L.↗

NASA NTRS1989

Einstein SSS and MPC observations of Aql X-1 and 4U1820-30

The results of timing and spectral analyses of the X-ray sources Aql X-1 (X1908+005) and 4U1820-30 (NGC6624) are reported using data obtained with the Einstein SSS (Solid State Spectrometer) and MPC (Monitor Proportional Counter) instruments. A classic type I burst was observed from Aql X-1 in both detectors and a coherent modulation with a period of 131.66 + or - 0.02 ms and a pulsed fraction of 10 percent was detected in the SSS data. There is no evidence for a loss of coherance during the approximately 80 sec when the burst is observable. The 2 sigma upper limit on the rate of change of the pulse period is 0.00005s/s. It is argued that an asymmetrical burst occurring on a neutron star rotating at 7.6 Hz offers a plausible explanation for the oscillation. The data from 4U1820-30 show that the amplitude of the 685 sec modulation, identified as the orbital period, is independent of energy down to 0.6 keV. The SSS data show that the light curve in the 0.6 to 4.5 keV band is smoother than at higher energies.

Kelley, R. L.↗

NASA NTRS1990

Multigrid for hypersonic inviscid flows

The use of multigrid methods to solve the Euler equations for hypersonic flow is discussed. The steady state equations are considered with a Runge-Kutta smoother based on the time accurate equations together with local time stepping and residual smoothing. The effect of the Runge-Kutta coefficients on the convergence rate was examined considering both damping characteristics and convection properties. The importance of boundary conditions on the convergence rate for hypersonic flow is discussed. Also of importance are the switch between the second and fourth difference viscosity. Solutions are given for flow around the bump in a channel and flow around a biconic section.

Decker, Naomi H.↗

NASA NTRS1990

Fully elliptic incompressible flow calculations on regular grid by a new pressure substitution method

A new method is presented for the solution of incompressible flow in generalized coordinates. This method is based on the substitution of the pressure weighted form of the momentum equations into the continuity equation. The algorithm is rigorously derived and a Fourier analysis is used to assess its suitability to act as an error smoother. Linear stability analysis results indicate that the performance of the new pressure substitution method (PSM) and the pressure correction method (PCM) is about the same at low Reynolds numbers, with no significant pressure gradient. At high Reynolds numbers the PSM shows much faster convergence. Likewise prediction of various flows indicate that the PSM has better accuracy for high Reynolds number flows with significant pressure gradients. Since most practical aerodynamic flows have significant pressure gradients, the PSM seems to be attractive for such flows. Solutions for both laminar and turbulent flow are compared with the experimental data. A two-equation low Reynolds number turbulence model is used to resolve the turbulent flowfield.

Hobson, G. V.↗

NASA NTRS1990

Galaxy evolution and large-scale structure in the far-infrared. II - The IRAS faint source survey

The new IRAS Faint Source Survey data base is used to confirm the conclusion of Hacking et al. (1987) that the 60 micron source counts fainter than about 0.5 Jy lie in excess of predictions based on nonevolving model populations. The existence of an anisotropy between the northern and southern Galactic caps discovered by Rowan-Robinson et al. (1986) and Needham and Rowan-Robinson (1988) is confirmed, and it is found to extend below their sensitivity limit to about 0.3 Jy in 60 micron flux density. The count anisotropy at f(60) greater than 0.3 can be interpreted reasonably as due to the Local Supercluster; however, no one structure accounting for the fainter anisotropy can be easily identified in either optical or far-IR two-dimensional sky distributions. The far-IR galaxy sky distributions are considerably smoother than distributions from the published optical galaxy catalogs. It is likely that structure of the large size discussed here have been discriminated against in earlier studies due to insufficient volume sampling.

Lonsdale, Carol J.↗

NASA NTRS1991

Reed Valve Regulates Welding Back-Purge Pressure

Simple modification yields welds of better quality. Reed valve halves fluctuations in pressure in back-purge chamber attached to workpiece undergoing keyhole plasma arc welding. Identical to one used in fuel system of two-cycle gasoline engine. Backbead smoother, and weld penetrates more uniformly.

Coby, J. Ben, Jr.↗

NASA NTRS1991

One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control

The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

Taasan, Shlomo↗

NASA NTRS1990

A novel potential/viscous flow coupling technique for computing helicopter flow fields

Because of the complexity of helicopter flow field, a zonal method of analysis of computational aerodynamics is required. Here, a new procedure for coupling potential and viscous flow is proposed. An overlapping, velocity coupling technique is to be developed with the unique feature that the potential flow surface singularity strengths are obtained directly from the Navier-Stokes at a smoother inner fluid boundary. The closed-loop iteration method proceeds until the velocity field is converged. This coupling should provide the means of more accurate viscous computations of the near-body and rotor flow fields with resultant improved analysis of such important performance parameters as helicopter fuselage drag and rotor airloads.

Summa, J. Michael↗

NASA NTRS1991

A new flux splitting scheme

A new flux splitting scheme is proposed. The scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of Roe's solver in the Euler and Navier-Stokes solutions performed in this study. The scheme is robust and converges as fast as the Roe splitting. An approximately defined cell-face advection Mach number is proposed using values from the two straddling cells via associated characteristic speeds. This interface Mach number is then used to determine the upwind extrapolation for the convective quantities. Accordingly, the name of the scheme is coined as Advection Upstream Splitting Method (AUSM). A new pressure splitting is introduced which is shown to behave successfully, yielding much smoother results than other existing pressure splittings. Of particular interest is the supersonic blunt body problem in which the Roe scheme gives anomalous solutions. The AUSM produces correct solutions without difficulty for a wide range of flow conditions as well as grids.

Liou, Meng-Sing↗

NASA NTRS1991

E and DE/DT waveshapes for narrow bipolar pulses in intracloud lightning

Wideband electric field and dE/dt waveforms were recorded and digitized at a 100 MS/s rate at KSC during the summer and fall of 1989. These waveforms were combined to produce composite electric fields with an effective bandwidth of 3 to 50 MHz. Bipolar electric field pulses are characterized in terms of their E and dE/dt waveshapes. Half width mean durations were found to be 1.83 and 3.64 microseconds for negative and positive bipolar pulses respectively. Twenty of thirty of these pulses were found to occur independently of any other lightning activity. Analysis of the frequency content of these pulses as a function of time shows that radiation at different frequencies peak at different times. In addition to the initial peak and subsequent overshoot in the composite E waveshape, secondary humps following the initial peak are characterized according to their time of occurrence within the pulse. THe 156 narrow negative bipolar pulses and 10 positive narrow bipolar pulses are analyzed. The dE/dt signatures range from impulsive variations lasting several microseconds both before and after the initial peak of the electric field pulse, to smoother variations closely associated with peak.

Medelius, Pedro J.↗

NASA NTRS1989

Construction of surface pressure field from scatterometer wind field

An account of the construction of surface pressure fields from Seasat-A satellite scatterometer (SASS) winds as carried out by different methods, and the comparison of these pressure fields with those derived from in situ ship observations is presented. On the assumption that the pressure adjusts itself instantaneously to the motion field, it may be computed by various methods. One of these makes use of planetary boundary theory, and of the possible techniques in this category a two-layer iterative scheme admitting of the parametrization of diabatic and baroclinic effects and of secondary flow was chosen. A second method involves the assumption of zero two-dimensional divergence, leading to a Laplace's equation (the balance equation) in pressure, with the wind field serving as a forcing function. This method does not accommodate adiabatic or baroclinic effects, and requires a knowledge of the pressure at all boundary points. Two comparison fields are used for validation: the conventional operational analyses of the US National Meteorological Center (NMC), and the special analyses of the Gulf of Alaska Experiment (GOASEX), which were done by hand. The results of the computations were as follows: (1) The pressure fields, as computed from the SASS winds alone, closely approximated the NMC fields in regions where reasonable in situ coverage was available (typically, one or two mb differences over most of the chart, three to four mb in extreme cases); (2) In some cases the SASS-derived pressure fields displayed high-resolution phenomena not detected by the NMC fields, but evident in the GOASEX data; and, (3) As expected, the pressure fields derived from the balance equation were much smoother and less well resolved than the SASS-derived or NMC fields. The divergence as measured from the SASS winds is smaller than, but of the same order of magnitude as, the vorticity.

Wurtele, Morton G.↗

NASA NTRS1989

Inference of geophysical parameters from multifrequency polarimetric radar observations and model inversion

In summer 1988 an intensive field experiment was conducted in the vicinity of the Pisgah lava flow in the Mojave Desert. Physical properties such as microtopography, composition, soil moisture, and dielectric constant were measured at five sites representing surfaces with rms heights varying from less than one centimeter to tens of centimeters. In addition, polarimetric radar images at P-band, L-band, and C-band were acquired at three different incidence angles with the NASA/JPL airborne imaging radar polarimeter. Using trihedral corner reflectors deployed in the area prior to imaging, the L- and C-band images were calibrated to provide sigma0 values for each resolution element in the scene. The results of inferring geophysical parameters such as rms surface height and correlation length of the measured surfaces by fitting the observed signatures with those predicted by the small-perturbation model are presented: for smoother surfaces, the rms height values inferred are in good agreement with in situ measurements.

Van Zyl, J. J.↗

NASA NTRS1991

Cosmic backgrounds from primeval dust

A general formalism is developed for describing the spectrum and the anisotropy of radiation from primeval dust as a nearly isotropic cosmic background with fluctuations. The theory incorporates spatial and temporal variations in the density of both luminosity and dust and is sufficiently robust to treat emission by point sources, as well as smoother emission, in high and low optical depth situations. The fluctuations are calculated using linear perturbation theory for arbitrary dust and luminosity clumping, and are calculated nonperturbatively for compact IR sources using shot-noise models. For many realistic models, a large accompanying NIR background is predicted. It is shown that, while spectal information alone provides only coarse information about the dust abundance and type, the redshift, and the other parameters, it may provide a powerful probe of pregalactic history when used in combination with the anisotropy signal.

Bond, J. R.↗

NASA NTRS1991

Grid convergence for adaptive methods

The ability of adaptive methods to obtain accurate results is examined using two different Euler solvers for a near-sonic flow containing several important flow features. It is shown that the accuracy obtained can be greatly affected by the lack of resolution of smooth portions of the flow caused by adapting only to the more prevalent flow features such as discontinuities. In particular, common methods of adaptation can lead to results in which shocks are well resolved but whose locations are highly inaccurate due to the lack of resolution of the smoother regions. An explanation for this behavior is given and a correction is proposed.

Warren, Gary P.↗

NASA NTRS1991

Microwave simulations of a tropical rainfall system with a three-dimensional cloud model

A three-dinensional cloud model-microwave radiative transfer model combination is used to study the relations among the precipitation and other microphysical characteristics of a tropical oceanic squall line and the upwelling radiance at pertinent microwave frequencies. Complex brightness temperature-rain rate relations are evident at the full horizontal resolution (1.5 km) of the models, with spatial averaging producing smoother, shifter relations in most cases. Nonprecipitating cloud water is shown to be important in understanding the resulting distribution of brightness temperature. At the mature stage, convective portions of the cloud system are shown to produce different brightness temperature relations than the stratiform portion, primarily related to the distribution of cloud water. The evolution of the convective system from a small convective complex through its mature stage and the beginning of its dissipation also is shown to result in a variation of brightness temperature-rain relations, related to the distribution of cloud water and the evolution of ice in the precipitating system. The results of the study point to the need to take into account the evolution of nonprecipitating cloud water and precipitation-sized ice in the retrieval of rain from passive microwave space observations. This effect is evident for both the life cycle of individual convective elements and the life cycle of the convective system as a whole.

Adler, Robert A.↗