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NASA NTRS1993

Trajectory optimization based on differential inclusion

A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a I-D rocket ascent problem ('Goddard Problem') in presence of a dynamic pressure constraint.

Seywald, Hans↗

NASA NTRS1993

On eigensystem assignment with dissipativity constraints

Stability of the closed-loop system is of vital importance when controller synthesis is being performed using a reduced order model of the open-loop plant. For passive systems such as flexible space structures, closed-loop stability is often ensured by low-authority dissipative controllers using collocated and compatible sensors and actuators. This paper considers the problem of eigensystem assignment for flexible structures using constant-gain output feedback, under the dissipativity constraints requiring that the gain matrices be nonnegative definite. A novel method is developed in which a sequential procedure is used to assign one complex-conjugate pair of closed-loop eigenvalues in each step. At each step, an iterative technique is employed for generating a nonnegative definite gain matrix that assigns a new pair while keeping the previously assigned pairs unchanged. This method can assign up to m closed-loop system eigenvalues, where m is the number of control inputs. A numerical example of damping enhancement for a large flexible structure is presented to demonstrate the approach.

Maghami, Peiman G.↗

NASA NTRS1993

Normalization and calibration of geostationary satellite radiances for the International Satellite Cloud Climatology Project

Procedures are described for normalizing the radiometric calibration of image radiances obtained from geostationary weather satellites that contributed data to the International Satellite Cloud Climatology Project. The key step is comparison of coincident and collocated measurements made by each satellite and the concurrent AVHRR on the 'afternoon' NOAA polar-orbiting weather satellite at the same viewing geometry. The results of this comparison allow transfer of the AVHRR absolute calibration, which has been established over the whole series, to the radiometers on the geostationary satellites. Results are given for Meteosat-2, 3, and 4, for GOES-5, 6, and 7, for GMS-2, 3, and 4 and for Insat-1B. The relative stability of the calibrations of these radiance data is estimated to be within +/- 3 percent; the uncertainty of the absolute calibrations is estimated to be less than 10 percent. The remaining uncertainties are at least two times smaller than for the original radiance data.

Desormeaux, Yves↗

NASA NTRS1993

A multidomain spectral method for viscous compressible flows

We present a new multidomain spectral method for the solution of the compressible Navier-Stokes equations. In the subdomain interiors, Chebyshev spectral collocation is used. At interfaces, the advective terms are upwinded and the viscous terms are treated by a penalty method. The method is applied to the solution of a viscous hypersonic flow over a blunt body.

Kopriva, David A.↗

NASA NTRS1993

Thermocapillary migration of a small chain of bubbles

The quasistatic thermocapillary migration of a chain of two or three spherical bubbles in an unbounded fluid possessing a uniform temperature gradient is investigated in the limit of vanishing Reynolds and Peclet numbers. The line of bubble centers is permitted to be either parallel or perpendicular to the direction of the undisturbed temperature gradient. The governing equations are solved by a truncated-series, boundary-collocation technique. Results are presented which demonstrate the impact of the presence of other bubbles on a test bubble. In the three-bubble case, a simple pairwise-additive approximation is constructed from the reflections solution, and found to perform well except when the bubbles are close to each other. Also, features of the flow topology in the fluid are explored. Separated reverse flow wakes are found in the axisymmetric problem, and other interesting structures are noted for the case in which the line of centers is perpendicular to the applied temperature gradient. The observed flow structure is shown to be the result of superposition of simpler basic flows.

Wei, Huailiang↗

NASA NTRS1992

On the application of multifrequency polarimetric radar observations for sea-ice classification

The use of multifrequency polarimetric radar imagery to enhance the ability to separate different sea-ice types using single-frequency, single-polarization synthetic aperture radar (SAR) data is investigated. Backscatter characteristics of six radiometrically and polarimetrically distinct sea-ice types are selected in an unsupervised range-dependent analysis of multifrequency polarimetric SAR data using the maximum a posteriori (MAP) polarimetric classifier. Maximum ice discrimination is achieved with combined C- and L-band full polarimetry, and collocated passive microwave imagery suggests greater than 90 percent classification accuracy. C-band VV-pol alone achieves only 68 percent relative accuracy because it confuses multiyear and rough compressed first year ice. L-band, relative classification accuracy is 75 percent, 83 percent, and 85 percent, using HH-pol, HH- and VV-combined, or the full polarimetry, respectively. P-band is less accurate. Combinations of two frequencies at a single polarization show the greatest improvement over a single channel.

Rignot, Eric↗

NASA NTRS1993

Effect of curvature on stationary crossflow instability of a three-dimensional boundary layer

An incompressible three-dimensional laminar boundary-layer flow over a swept wing is used as a model to study both the wall-curvature and streamline-curvature effects on the stationary crossflow instability. The basic state is obtained by solving the full Navier-Stokes (N-S) equations numerically. The linear disturbance equations are cast on a fixed, body-intrinsic, curvilinear coordinate system. Those nonparallel terms which contribute mainly to the streamline-curvature effect are retained in the formulation of the disturbance equations and approximated by their local finite difference values. The resulting eigenvalue problem is solved by a Chebyshev collocation method. The present results indicate that the convex wall curvature has a stabilizing effect, whereas the streamline curvature has a destabilizing effect. A validation of these effects with an N-S solution for the linear disturbance flow is provided.

Lin, Ray-Sing↗

NASA NTRS1991

Control for two cooperating disparate manipulators

This research seeks to provide an advanced force control strategy for a flexible manipulator. Two main issues with force control of flexible arms are discussed: non-collocation and robustness.

Lew, Jae Young↗

NASA NTRS1988

An adaptive identification and control scheme for large space structures

A unified identification and control scheme capable of achieving space at form performance objectives under nominal or failure conditions is described. Preliminary results are also presented, showing that the methodology offers much promise for effective robust control of large space structures. The control method is a multivariable, adaptive, output predictive controller called Model Predictive Control (MPC). MPC uses a state space model and input reference trajectories of set or tracking points to adaptively generate optimum commands. For a fixed model, MPC processes commands with great efficiency, and is also highly robust. A key feature of MPC is its ability to control either nonminimum phase or open loop unstable systems. As an output controller, MPC does not explicitly require full state feedback, as do most multivariable (e.g., Linear Quadratic) methods. Its features are very useful in LSS operations, as they allow non-collocated actuators and sensors. The identification scheme is based on canonical variate analysis (CVA) of input and output data. The CVA technique is particularly suited for the measurement and identification of structural dynamic processes - that is, unsteady transient or dynamically interacting processes such as between aerodynamics and structural deformation - from short, noisy data. CVA is structured so that the identification can be done in real or near real time, using computationally stable algorithms. Modeling LSS dynamics in 1-g laboratories has always been a major impediment not only to understanding their behavior in orbit, but also to controlling it. In cases where the theoretical model is not confirmed, current methods provide few clues concerning additional dynamical relationships that are not included in the theoretical models. CVA needs no a priori model data, or structure; all statistically significant dynamical states are determined using natural, entropy-based methods. Heretofore, a major limitation in applying adaptive controllers to LSS problems has been the requirement for accurate models. We feel that MPC coupled with the CVA identification scheme will resolve this limitation. The results are based on research performed under an SBIR grant, administered by the Air Force Office of Scientific Research.

Carroll, J. V.↗

NASA NTRS1992

Flow transitions in a 2D directional solidification model

Flow transitions in a Two Dimensional (2D) model of crystal growth were examined using the Bridgman-Stockbarger me thod. Using a pseudo-spectral Chebyshev collocation method, the governing equations yield solutions which exhibit a symmetry breaking flow tansition and oscillatory behavior indicative of a Hopf bifurcation at higher values of Ra. The results are discussed from fluid dynamic viewpoint, and broader implications for process models are also addressed.

Larroude, Philippe↗

NASA NTRS1993

Investigation of passive atmospheric sounding using millimeter and submillimeter wavelength channels

Progress by investigators at the Georgia Institute of Technology in the development of techniques for passive microwave retrieval of water vapor, cloud, and precipitation parameters using millimeter- and sub-millimeter wavelength channels is reviewed. Channels of particular interest are in the tropospheric transmission windows at 90, 166, 220, 340, and 410 GHz and centered around the water vapor lines at 183 and 325 GHz. Collectively, these channels have potential application in high-resolution mapping (e.g., from geosynchronous orbit), remote sensing of cloud and precipitation parameters, and retrieval of water vapor profiles. During the period from 1 Jan. 1993 through 30 Jun. 1993 the Millimeter-wave Imaging Radiometer (MIR) completed data flights during a two-month long deployment in conjunction with TOGA/COARE. Coincident data was collected from several other ground-based, airborne, and satellite sensors, including the NASA/MSFC AMPR, MIT MTS, DMSP SSM/T-2 satellite, collocated radiosondes, ground- and aircraft-based radiometers and cloud lidars, airborne infrared imagers, solar flux probes, and airborne cloud particle sampling probes.

Gasiewski, A. J.↗

NASA NTRS1993

A preliminary C-band scatterometer model function for the ERS-1 AMI instrument

Backscatter cross section (sigma(sub 0)) measurements from the ERS-1 scatterometer are collocated with surface wind velocity data from operational Numerical Weather Prediction (NWP) analyses to yield a fully empirical C band model function. The empirical model does not obey a power law at speeds less than 5 m/s, and upwind/crosswind ratios are small for all incidence angles at low wind speeds and for small incidence angles at all wind speeds. Downwind sigma(sub 0) exceeds upwind values for incidence angles below approximately 28 degrees. The full ERS-1 scatterometer data set has been reprocessed using the NWP model function.

Freilich, M. H.↗

NASA NTRS1993

Experience and results of the 1991 MTLRS-1 USSR campaign

The year 1991 was a special year for the mobile laser ranging systems. Due to the scheduled upgrades of the Modular Transportable Laser Ranging Systems, MTLRS#1 and MTLRS#2, neither a WEGENER MEDLAS nor a Crustal Dynamics Project campaign was carried out in 1991. After the successful upgrade of MTLRS#1 in the first half of 1991 the system departed from Wettzell in August to make measurements at two sites in the USSR. In Riga/Latvia, we operated close to the fixed SLR system. In Simeiz/Ucrainea, the place for MTLRS#1 pad was choosen to collocate the two fixed SLR stations in Simeiz (300 m distance to MTLRS#1) and Kazivelli (about 3 km distance).

Sperber, Peter↗

NASA NTRS1993

On the design of structural components using materials with time-dependent properties

The application of the elastic-viscoelastic correspondence principle is presented as a design tool for structural design engineers for composite material applications. The classical problem of cantilever beams is used as the illustration problem. Both closed-form and approximate numerical solutions are presented for several different problems. The application of the collocation method is presented as a viable and simple design tool to determine the time-dependent behavior and response of viscoelastic composite beams under load.

Rodriguez, Pedro I.↗

NASA NTRS1993

ERS-1 and Seasat scatterometer measurements of ocean winds: Model functions and the directional distribution of short waves

Calculation of accurate vector winds from scatterometers requires knowledge of the relationship between backscatter cross-section and the geophysical variable of interest. As the detailed dynamics of wind generation of centimetric waves and radar-sea surface scattering at moderate incidence angles are not well known, empirical scatterometer model functions relating backscatter to winds must be developed. Less well appreciated is the fact that, given an accurate model function and some knowledge of the dominant scattering mechanisms, significant information on the amplitudes and directional distributions of centimetric roughness elements on the sea surface can be inferred. accurate scatterometer model functions can thus be used to investigate wind generation of short waves under realistic conditions. The present investigation involves developing an empirical model function for the C-band (5.3 GHz) ERS-1 scatterometer and comparing Ku-band model functions with the C-band model to infer information on the two-dimensional spectrum of centimetric roughness elements in the ocean. The C-band model function development is based on collocations of global backscatter measurements with operational surface analyses produced by meteorological agencies. Strengths and limitations of the method are discussed, and the resulting model function is validated in part through comparison with the actual distributions of backscatter cross-section triplets. Details of the directional modulation as well as the wind speed sensitivity at C-band are investigated. Analysis of persistent outliers in the data is used to infer the magnitudes of non-wind effects (such as atmospheric stratification, swell, etc.). The ERS-1 C-band instrument and the Seasat Ku-band (14.6 GHz) scatterometer both imaged waves of approximately 3.4 cm wavelength assuming that Bragg scattering is the dominant mechanism. Comparisons of the C-band and Ku-band model functions are used both to test the validity of the postulated Bragg mechanism and to investigate the directional distribution of the imaged waves under a variety of conditions where Bragg scatter is dominant.

Freilich, Michael H.↗

NASA NTRS1993

An improved gravity model for Mars: Goddard Mars Model-1 (GMM-1)

Doppler tracking data of three orbiting spacecraft have been reanalyzed to develop a new gravitational field model for the planet Mars, GMM-1 (Goddard Mars Model-1). This model employs nearly all available data, consisting of approximately 1100 days of S-bank tracking data collected by NASA's Deep Space Network from the Mariner 9, and Viking 1 and Viking 2 spacecraft, in seven different orbits, between 1971 and 1979. GMM-1 is complete to spherical harmonic degree and order 50, which corresponds to a half-wavelength spatial resolution of 200-300 km where the data permit. GMM-1 represents satellite orbits with considerably better accuracy than previous Mars gravity models and shows greater resolution of identifiable geological structures. The notable improvement in GMM-1 over previous models is a consequence of several factors: improved computational capabilities, the use of optimum weighting and least-squares collocation solution techniques which stabilized the behavior of the solution at high degree and order, and the use of longer satellite arcs than employed in previous solutions that were made possible by improved force and measurement models. The inclusion of X-band tracking data from the 379-km altitude, near-polar orbiting Mars Observer spacecraft should provide a significant improvement over GMM-1, particularly at high latitudes where current data poorly resolves the gravitational signature of the planet.

Smith, D. E.↗

NASA NTRS1993

A dual reciprocal boundary element formulation for viscous flows

The advantages inherent in the boundary element method (BEM) for potential flows are exploited to solve viscous flow problems. The trick is the introduction of a so-called dual reciprocal technique in which the convective terms are represented by a global function whose unknown coefficients are determined by collocation. The approach, which is necessarily iterative, converts the governing partial differential equations into integral equations via the distribution of fictitious sources or dipoles of unknown strength on the boundary. These integral equations consist of two parts. The first is a boundary integral term, whose kernel is the unknown strength of the fictitious sources and the fundamental solution of a convection-free flow problem. The second part is a domain integral term whose kernel is the convective portion of the governing PDEs. The domain integration can be transformed to the boundary by using the dual reciprocal (DR) concept. The resulting formulation is a pure boundary integral computational process.

Lafe, Olu↗

NASA NTRS1994

A spectral boundary integral equation method for the 2-D Helmholtz equation

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

Hu, Fang Q.↗