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Control-theory design package, called Optimal Regulator Algorithms for Control of Linear Systems (ORACLS), aids in design of controllers and optimal filters for systems modeled by linear, time invariant differential and difference equations. ORACLS is particularly attractive rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete forms.
The purpose of this presentation is to show that it is possible to use nonsmooth optimization algorithms to design both closed-loop finite dimensional compensators and open-loop optimal controls for flexible structures modeled by partial differential equations. An important feature of our approach is that it does not require modal decomposition and hence is immune to instabilities caused by spillover effects. Furthermore, it can be used to design control systems for structures that are modeled by mixed systems of coupled ordinary and partial differential equations.
In this paper, maximum likelihood estimation for distributed parameter models of large flexible structures has been formulated. Distributed parameter models involve far fewer unknown parameters than independent modal characteristics of finite element models. The closed-form solutions for the partial differential equations with general forced inputs have been derived. The closed-form expressions of the sensitivity functions lead to highly efficient algorithms for analyzing ground or on-orbit test results. Numerical simulations with impulse and step inputs to the NASA Mini-MAST trust have been demonstrated. The estimations of modal properties involve its longitudinal elongation modes, lateral bending modes and torsional modes. The results show that distributed parameter models are promising in the parameter estimation of large flexible structures.
Work done in the period Jan. - June 1994 is summarized. Two threads of research have been followed. First, the thermodynamics approach was used to model the chemical and mechanical responses of composites exposed to high temperatures. The thermodynamics approach lends itself easily to the usage of variational principles. This thermodynamic-variational approach has been applied to the transpiration cooling problem. The second thread is the development of a better algorithm to solve the governing equations resulting from the modeling. Explicit finite difference method is explored for solving the governing nonlinear, partial differential equations. The method allows detailed material models to be included and solution on massively parallel supercomputers. To demonstrate the feasibility of the explicit scheme in solving nonlinear partial differential equations, a transpiration cooling problem was solved. Some interesting transient behaviors were captured such as stress waves and small spatial oscillations of transient pressure distribution.
Multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements are considered. The construction of several coarse-to-fine intergrid transfer operators for nonconforming multigrid algorithms is discussed. The equivalence between the nonconforming and mixed finite element methods with and without projection of the coefficient of the differential problems into finite element spaces is described.
We describe the theory and computer implementation of a newly-derived mathematical model for analyzing the shape of blood pressure waveforms. Input to the program consists of an ECG signal, plus a single continuous channel of peripheral blood pressure, which is often obtained invasively from an indwelling catheter during intensive-care monitoring or non-invasively from a tonometer. Output from the program includes a set of parameter estimates, made for every heart beat. Parameters of the model can be interpreted in terms of the capacitance of large arteries, the capacitance of peripheral arteries, the inertance of blood flow, the peripheral resistance, and arterial pressure due to basal vascular tone. Aortic flow due to contraction of the left ventricle is represented by a forcing function in the form of a descending ramp, the area under which represents the stroke volume. Differential equations describing the model are solved by the method of Laplace transforms, permitting rapid parameter estimation by the Levenberg-Marquardt algorithm. Parameter estimates and their confidence intervals are given in six examples, which are chosen to represent a variety of pressure waveforms that are observed during intensive-care monitoring. The examples demonstrate that some of the parameters may fluctuate markedly from beat to beat. Our program will find application in projects that are intended to correlate the details of the blood pressure waveform with other physiological variables, pathological conditions, and the effects of interventions.
The Space Interferometry Mission (SIM), scheduled for launch in early 2010, is an optical interferometer that will perform narrow angle and global wide angle astrometry with unprecedented accuracy, providing differential position accuracies of 1uas, and 4uas global accuracies in position, proper motion and parallax. SIM astrometric measurements are synthesized from pathlength delay measurements provided by three Michelson-type, white light interferometers. Two of the interferometers are used for making precise measurements of variations in the spacecraft attitude, while the third interferometer performs the science measurement. The ultimate performance of SIM relies on a combination of precise fringe measurements of the interfered starlight with picometer class relative distance measurements made between a set of fiducials that define the interferometer baseline vectors. The focus of the present paper is on the development and analysis of algorithms for accurate white light fringe estimation, and on the preliminary validation of these algorithms on the Micro-Arcsecond Testbed (MAM).
This paper presents an algorithm for estimating the angular rate vector of a satellite which is based on the time derivatives of vector measurements expressed in a reference and body coordinate. The computed derivatives are fed into a spacial Kalman filter which yields an estimate of the spacecraft angular velocity. The filter, named Extended Interlaced Kalman Filter (EIKF), is an extension of the Kalman filter which, although being linear, estimates the state of a nonlinear dynamic system. It consists of two or three parallel Kalman filters whose individual estimates are fed to one another and are considered as known inputs by the other parallel filter(s). The nonlinear dynamics stem from the nonlinear differential equation that describes the rotation of a three dimensional body. Initial results, using simulated data, and real Rossi X ray Timing Explorer (RXTE) data indicate that the algorithm is efficient and robust.
One of the objectives of the WFIRST Coronagraph Instrument is to demonstrate post-processing algorithms for space-based exoplanet imaging data in the regime of very high contrast ratios (< 1E-8). We analyzed two 15-hour time series of laboratory images acquired with prototype coronagraph designs on a vacuum chamber testbed at JPL. These data sets enabled us to test the performance of reference differential imaging (RDI) PSF subtraction as a function of time and Euclidean (L2) speckle pattern distance. Starting from an analytical relationship between speckle pattern stability and classical subtraction gain, we compared the classical subtraction result to those of the KLIP RDI algorithm. In both data sets, KLIP RDI contrast gains are typically 3-4× greater than those of classical subtraction. These results suggest that a diverse reference PSF library will enable a significant gain in sensitivity beyond that suggested by the raw, frame-to-frame speckle pattern stability.
The Space Interferometry Mission (SIM) scheduled for launch in early 2010, is an optical interferometer that will perform narrow angle and global wide angle astrometry with unprecedented accuracy, providing differential position accuracies of 1uas, and 4uas global accuracies in position, proper motion and parallax. The astrometric observations of the SIM instrument are performed via delay measurements provided by three Michelson-type, white light interferometers. Two 'guide' interferometers acquire fringes on bright guide stars in order to make highly precise measurements of variations in spacecraft attitude, while the third interferometer performs the science measurement. SIM derives its performance from a combination of precise fringe measurements of the interfered starlight (a few ten-thousandths of a wave) and very precise (tens of picometers) relative distance measurements made between a set of fiducials. The focus of the present paper is on the development and analysis of algorithms for accurate white light estimation, and on validating some of these algorithms on the MicroArcsecond Testbed.
The performance of densitometers used for photometric data reduction of high dynamic range electrographic plate material is analyzed. Densitometer repeatability is tested by comparing two scans of one plate. Internal densitometer errors are examined by constructing histograms of digitized densities and finding inoperative bits and differential nonlinearity in the analog to digital converter. Such problems appear common to the four densitometers used in this investigation and introduce systematic algorithm dependent errors in the results. Strategies to improve densitometer performance are suggested.
Conditions, based on the multipliers of a linear differential equation with periodic coefficients, for the occurrence of false lock in a phase lock loop (PLL) are presented. Two new and powerful algorithms are presented for computing the frequency difference between the reference and voltage controlled oscillator when the loop is false locked. The first algorithm expresses omega f sup -1 as a power series in the closed loop gain. The second algorithm expresses omega sup -1 as part of a solution to a nonlinear algebraic system of equations which can be solved by numerical methods. The power of both algorithms is illustrated by application and comparison.
An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.
The objective of this paper is to stimulate ideas concerning alternative approaches to discretizing fluid flow problems, i.e., the so-called gridless approach. The gridless approach uses only clouds of points and does not require that the points be connected to form a grid as is necessary in conventional CFD algorithms. The governing equations are solved directly by performing local least-squares curve fits in each cloud of points and then analytically differentiating the resulting curve fits to approximate the derivatives. A discussion of these topics is presented in viewgraph form.
The interaction of climate and topography in mountainous regions is dramatically expressed in the spatial distribution of glaciers and snowcover. Monitoring existing alpine glaciers and snow extent provides insight into the present mountain climate system and how it is changing, while mapping the positions of former glaciers as recorded in landforms such as cirques and moraines provide a record of the large past climate change associated with the last glacial maximum. The Andes are an ideal mountain range in which to study the response of snow and ice to past and present climate change. Their expansive latitudinal extent offers the opportunity to study glaciers in diverse climate settings from the tropical glaciers of Peru and Bolivia to the ice caps and tide-water glaciers of sub-polar Patagonia. SAR has advantages over traditional passive remote sensing instruments for monitoring present snow and ice and differentiating moraine relative ages. The cloud penetrating ability of SAR is indispensable for perennially cloud covered mountains. Snow and ice facies can be distinguished from SAR's response to surface roughness, liquid water content and grain size distribution. The combination of SAR with a coregestered high-resolution DEM (TOPSAR) provides a promising tool for measuring glacier change in three dimensions, thus allowing ice volume change to be measured directly. The change in moraine surface roughness over time enables SAR to differentiate older from younger moraines. Polarimetric SAR data have been used to distinguish snow and ice facies and relatively date moraines. However, both algorithms are still experimental and require ground truth verification. We plan to extend the SAR classification of snow and ice facies and moraine age beyond the ground truth sites to throughout the Cordillera Real to provide a regional view of past and present snow and ice. The high resolution DEM will enhance the SAR moraine dating technique by discriminating relative ages based on moraine slope degradation.
A microsystem architecture for real-time, on-site, robust bioinformatic patterns recognition and analysis has been proposed. This system is compatible with on-chip DNA analysis means such as polymerase chain reaction (PCR)amplification. A corresponding novel artificial neural network (ANN) learning algorithm using new sigmoid-logarithmic transfer function based on error backpropagation (EBP) algorithm is invented. Our results show the trained new ANN can recognize low fluorescence patterns better than the conventional sigmoidal ANN does. A differential logarithmic imaging chip is designed for calculating logarithm of relative intensities of fluorescence signals. The single-rail logarithmic circuit and a prototype ANN chip are designed, fabricated and characterized.
Remote sensing of global ocean color is a valuable tool for understanding the ecology and biogeochemistry of the worlds oceans, and provides critical input to our knowledge of the global carbon cycle and the impacts of climate change. Ocean polarized reflectance contains information about the constituents of the upper ocean euphotic zone, such as colored dissolved organic matter (CDOM), sediments, phytoplankton, and pollutants. In order to retrieve the information on these constituents, remote sensing algorithms typically rely on radiative transfer models to interpret water color or remote-sensing reflectance; however, this can be resource-prohibitive for operational use due to the extensive CPU time involved in radiative transfer solutions. In this work, we report a fast model based on machine learning techniques, called Neural Network Reflectance Prediction Model (NNRPM), which can be used to predict ocean bidirectional polarized reflectance given inherent optical properties of ocean waters. This supervised model is trained using a large volume of data derived from radiative transfer simulations for coupled atmosphere and ocean systems using the successive order of scattering technique (SOS-CAOS). The performance of the model is validated against another large independent test dataset generated from SOS-CAOS. The model is able to predict both polarized and unpolarized reflectances with an absolute error (AE) less than 0.004 for 99% of test cases. We have also shown that the degree of linear polarization (DoLP) for unpolarized incident light can be predicted with an AE less than 0.002 for 99% of test cases. In general, the simulation time of SOS-CAOS depends on optical depth, and required accuracy. When comparing the average speeds of the NNRPM against the SOS-CAOS model for the same parameters, we see that the NNRPM is able to predict the Ocean BRDF 6000 times faster than SOS-CAOS. Both ultraviolet and visible wavelengths are included in the model to help differentiate between dissolved organic material and chlorophyll in the study of the open ocean and the coastal zone. The incorporation of this model into the retrieval algorithm will make the retrieval process more efficient, and thus applicable for operational use with global satellite observations.
A second-order finite-difference procedure is used to evaluate the inviscid supersonic flowfield surrounding an external axial corner composed of swept planar compression surfaces and representing the inlets on existing high-speed aircraft. The governing partial differential equations in conservation-law form are hyperbolic with respect to the axial coordinate and are solved iteratively by means of MacCormack's algorithm. The procedure treats both the peripheral shock wave and vortical singularities as discontinuities. Numerical results are presented for two parametric studies regarding the effects on the flowfield of varying the free-stream Mach number and the leading edge sweep of the horizontal wedge. Results of parametric Mach number study agree with the Mach number independence principle in that as the Mach number increases, such characteristics as shock shape, cross-flow sonic line location, and vortical singularity position approach an asymptote.