Comments on linear feature extraction
Linear transformation for random-data vector z reduction to smaller dimension vector
Henderson, T. L.↗
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Development of iterative techniques for the solution of unsteady compressible viscous flows
During the past two decades, there has been significant progress in the field of numerical simulation of unsteady compressible viscous flows. At present, a variety of solution techniques exist such as the transonic small disturbance analyses (TSD), transonic full potential equation-based methods, unsteady Euler solvers, and unsteady Navier-Stokes solvers. These advances have been made possible by developments in three areas: (1) improved numerical algorithms; (2) automation of body-fitted grid generation schemes; and (3) advanced computer architectures with vector processing and massively parallel processing features. In this work, the GMRES scheme has been considered as a candidate for acceleration of a Newton iteration time marching scheme for unsteady 2-D and 3-D compressible viscous flow calculation; from preliminary calculations, this will provide up to a 65 percent reduction in the computer time requirements over the existing class of explicit and implicit time marching schemes. The proposed method has ben tested on structured grids, but is flexible enough for extension to unstructured grids. The described scheme has been tested only on the current generation of vector processor architecture of the Cray Y/MP class, but should be suitable for adaptation to massively parallel machines.
Hixon, Duane↗
Projection-based multifidelity linear regression for data-scarce applications
Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear regression targeting data-limited applications with high-dimensional outputs. Multifidelity methods integrate many inexpensive low-fidelity model evaluations with limited, costly high-fidelity evaluations. We introduce two projection-based multifidelity linear regression approaches with linear and nonlinear features that leverage principal component basis vectors for dimensionality reduction and combine multifidelity data through: (i) a direct data augmentation using low-fidelity data, and (ii) a data augmentation incorporating explicit linear corrections between low-fidelity and high-fidelity data. The data augmentation approaches combine high-fidelity and low-fidelity data into a unified training set and train the linear regression model through weighted least squares with fidelity-specific weights. We introduce a proximity-based weighting scheme with automatic weight selection strategy through cross-validation. Here, the proposed multifidelity linear regression methods are demonstrated on approximating the surface pressure field of a hypersonic vehicle in flight and the temperature field on an aircraft disc braking system. In an ultra low-data regime of no more than twelve high-fidelity samples, multifidelity linear regression achieves approximately 2% – 12% improvement in median accuracy and a higher R 2 score relative to single-fidelity methods at comparable computational cost.
data augmentation↗
Low-energy electronic structure in the unconventional charge-ordered state of ScV6Sn6
Abstract Kagome vanadates A V 3 Sb 5 display unusual low-temperature electronic properties including charge density waves (CDW), whose microscopic origin remains unsettled. Recently, CDW order has been discovered in a new material ScV 6 Sn 6 , providing an opportunity to explore whether the onset of CDW leads to unusual electronic properties. Here, we study this question using angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). The ARPES measurements show minimal changes to the electronic structure after the onset of CDW. However, STM quasiparticle interference (QPI) measurements show strong dispersing features related to the CDW ordering vectors. A plausible explanation is the presence of a strong momentum-dependent scattering potential peaked at the CDW wavevector, associated with the existence of competing CDW instabilities. Our STM results further indicate that the bands most affected by the CDW are near vHS, analogous to the case of A V 3 Sb 5 despite very different CDW wavevectors.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Radar studies of Venus.
Radar studies of Venus, noting values for rotation vector, latitudes and longitudes of several features and Earth influence on Venus rotation
PLANETARY MOTION↗
Radar studies of Venus.
Radar studies of Venus noting values for rotation vector, latitudes and longitudes of several features and Earth influence on Venus rotation
VENUS↗
On differentiating the probability of error in multipopular feature selection
A method of linear feature selection for n dimensional observation vectors which belong to one of m populations is presented. Each population has a known apriori probability and is described by a known multivariate normal density function. Specifically we consider the problem of finding a k x n matrix B of rank k (k n) for which the transformed probability of misclassification is minimized. Providing that the transformed a posterior probabilities are distinct theoretical results are obtained which, for the case k = l, give rise to a numerically tractable formula for the derivative of the probability of misclassification. It is shown that for the two population problem this condition is also necessary. The dependence of the minimum probability of error on the a priori probabilities is investigated. The minimum probability of error satisfies a uniform Lipschitz condition with respect to the a priori probabilities.
Peters, B. C.↗
Integrated control system concept for high-speed aircraft
The synthesis and evaluation of flight control system architectures for future aircraft are discussed in terms of design features and the requirements for fighter aircraft. Advanced fighter configurations may feature canards, flaperons, two-dimensional vectoring nozzles, a mixing compression inlet, and an advanced turbojet engine. Survey and evaluation technology will also progress to include distributed microprocessors, VLSI and VHSIC microcircuitry, optical circuits, analytic redundancy, etc. Bottom-p and top-down architectures have been investigated to fulfill the reliability, maintainability, cost, and performance goals. A centralized architecture has been devised with line-removable units to facilitate maintainability and reduce weight. Descriptions are provided of the performance parameters and applications of optical elements, photoelastic pressure sensors, rare earth sensors, computing elements, and information transfer system.
Carlin, C. M.↗
Piecewise linear approximation for hereditary control problems
Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.
Propst, Georg↗
Reconnection of vorticity lines and magnetic lines
Magnetic field and fluid vorticity share many features. First, as divergence-free vector fields they are conveniently visualized in terms of their field lines, curves that are everywhere tangent to the field. The lines indicate direction and their density indicates field strength. The question arises of the extent to which the evolution of the fields can be treated in terms of the evolution of their field lines. Newcomb (1958) derived the general conditions on the evolution of vector fields that permit the identification of field lines from one instant to the next. The equations of evolution of the vorticity field and the magnetic field fall within Newcomb's analysis. The dynamics of the flows differ between these two systems, so that geometrically similar phenomena happen in different ways in the two systems. In this paper the geometrical similarities are emphasized. Reconnection will be defined here as evolution in which it is not possible to preserve the global identification of some field lines. There is a close relation between reconnection and the topology of the vector field lines. Nontrivial topology occurs where the field has null points or there are field lines that are closed loops.
Greene, John M.↗
Visualizing Vector Fields Using Line Integral Convolution and Dye Advection
We present local and global techniques to visualize three-dimensional vector field data. Using the Line Integral Convolution (LIC) method to image the global vector field, our new algorithm allows the user to introduce colored 'dye' into the vector field to highlight local flow features. A fast algorithm is proposed that quickly recomputes the dyed LIC images. In addition, we introduce volume rendering methods that can map the LIC texture on any contour surface and/or translucent region defined by additional scalar quantities, and can follow the advection of colored dye throughout the volume.
Shen, Han-Wei↗
Estimating the Crustal Power Spectrum From Vector Magsat Data: Crustal Power Spectrum
The Earth's magnetic field can be subdivided into core and crustal components and we seek to characterize the crustal part through its spatial power spectrum (R(sub l)). We process vector Magsat data to isolate the crustal field and then invert power spectral densities of flight-local components along-track for R(sub l) following O'Brien et al. [1999]. Our model (LPPC) is accurate up to approximately degree 45 (lambda=900 km) - this is the resolution limit of our data and suggests that global crustal anomaly maps constructed from vector Magsat data should not contain features with wavelengths less than 900 km. We find continental power spectra to be greater than oceanic ones and attribute this to the relative thicknesses of continental and oceanic crust.
Lowe, David A. J.↗
Magnetic TRAnsition Region Probe (MTRAP)
MTRAP (Magnetic Transition Region Probe) will reveal the fine-scale physical processes in the Sun's magnetic transition region, the complex layer from the upper photosphere to the upper chromosphere/lower transition region. In the magnetic transition region plasma forces and magnetic forces are of comparable strength, which results in complex interplay of the two, which interplay governs the coupling of the convectively-driven deeper layers to the magnetically-driven upper transition region and inner corona. The fine-scale magnetic structure, processes, and events in the magnetic transition region are key to the genesis of the Sun's entire hot, dynamic outer atmosphere and to the initiation of large eruptive events. MTRAP will be a single spacecraft in Sun-synchronous Earth orbit. Because MTRAP will probe and measure the 3-D structure and dynamics of the magnetic field and plasma in the chromosphere and transition region with unprecedented resolution, the required telescope size and telemetry rates dictate that MTRAP be in Earth orbit, not in deep space. The observations will feature visible and infrared maps of vector magnetic and velocity fields in the magnetic transition region and photosphere. These will have large field of view (greater than 100,000 km), high resolution (greater than 100 km), and high sensitivity (greater than 30 G in transverse field). These observations of the lower atmosphere will be complemented by UV maps of the structure, velocity, and magnetic field (including the full vector field if technically feasible) higher up, in the upper chromosphere and lower transition region. MTRAP will also have an EUV imaging spectrograph observing coronal structure and dynamics in the same field of view with comparable resolution. Specific phenomena to be analyzed include spicules, bright points, jets, the base of plumes, and the triggering of eruptive flares and coronal mass ejections. Additional information is included in the original extended abstract.
Moore, R. L.↗
Onboard Classifiers for Science Event Detection on a Remote Sensing Spacecraft
Typically, data collected by a spacecraft is downlinked to Earth and pre-processed before any analysis is performed. We have developed classifiers that can be used onboard a spacecraft to identify high priority data for downlink to Earth, providing a method for maximizing the use of a potentially bandwidth limited downlink channel. Onboard analysis can also enable rapid reaction to dynamic events, such as flooding, volcanic eruptions or sea ice break-up. Four classifiers were developed to identify cryosphere events using hyperspectral images. These classifiers include a manually constructed classifier, a Support Vector Machine (SVM), a Decision Tree and a classifier derived by searching over combinations of thresholded band ratios. Each of the classifiers was designed to run in the computationally constrained operating environment of the spacecraft. A set of scenes was hand-labeled to provide training and testing data. Performance results on the test data indicate that the SVM and manual classifiers outperformed the Decision Tree and band-ratio classifiers with the SVM yielding slightly better classifications than the manual classifier.
classification↗
Hybrid NN/SVM Computational System for Optimizing Designs
A computational method and system based on a hybrid of an artificial neural network (NN) and a support vector machine (SVM) (see figure) has been conceived as a means of maximizing or minimizing an objective function, optionally subject to one or more constraints. Such maximization or minimization could be performed, for example, to optimize solve a data-regression or data-classification problem or to optimize a design associated with a response function. A response function can be considered as a subset of a response surface, which is a surface in a vector space of design and performance parameters. A typical example of a design problem that the method and system can be used to solve is that of an airfoil, for which a response function could be the spatial distribution of pressure over the airfoil. In this example, the response surface would describe the pressure distribution as a function of the operating conditions and the geometric parameters of the airfoil. The use of NNs to analyze physical objects in order to optimize their responses under specified physical conditions is well known. NN analysis is suitable for multidimensional interpolation of data that lack structure and enables the representation and optimization of a succession of numerical solutions of increasing complexity or increasing fidelity to the real world. NN analysis is especially useful in helping to satisfy multiple design objectives. Feedforward NNs can be used to make estimates based on nonlinear mathematical models. One difficulty associated with use of a feedforward NN arises from the need for nonlinear optimization to determine connection weights among input, intermediate, and output variables. It can be very expensive to train an NN in cases in which it is necessary to model large amounts of information. Less widely known (in comparison with NNs) are support vector machines (SVMs), which were originally applied in statistical learning theory. In terms that are necessarily oversimplified to fit the scope of this article, an SVM can be characterized as an algorithm that (1) effects a nonlinear mapping of input vectors into a higher-dimensional feature space and (2) involves a dual formulation of governing equations and constraints. One advantageous feature of the SVM approach is that an objective function (which one seeks to minimize to obtain coefficients that define an SVM mathematical model) is convex, so that unlike in the cases of many NN models, any local minimum of an SVM model is also a global minimum.
Rai, Man Mohan↗
Magnetization of the Lunar Crust
Magnetic fields measured by the satellite Lunar Prospector show large scale features resulting from remanently magnetized crust. Vector data synthesized at satellite altitude from a spherical harmonic model of the lunar crustal field, and the radial component of the magnetometer data, have been used to produce spatially continuous global magnetization models for the lunar crust. The magnetization is expressed in terms of localized basis functions, with a magnetization solution selected having the smallest root-mean square magnetization for a given fit to the data, controlled by a damping parameter. Suites of magnetization models for layers with thicknesses between 10 and 50 km are able to reproduce much of the input data, with global misfits of less than 0.5 nT (within the uncertainties of the data), and some surface field estimates. The magnetization distributions show robust magnitudes for a range of model thicknesses and damping parameters, however the magnetization direction is unconstrained. These global models suggest that magnetized sources of the lunar crust can be represented by a 30 km thick magnetized layer. Average magnetization values in magnetized regions are 30-40 mA/m, similar to the measured magnetizations of the Apollo samples and significantly weaker than crustal magnetizations for Mars and the Earth. These are the first global magnetization models for the Moon, providing lower bounds on the magnitude of lunar crustal magnetization in the absence of multiple sample returns, and can be used to predict the crustal contribution to the lunar magnetic field at a particular location.
Lunar↗
Wind direction alias removal studies of Seasat scatterometer-derived wind fields
Seasat SASS fields for the North Atlantic were employed to test if meteorological features were discernible within the Seasat-produced wind fields, and if the features aided in determining a unique wind vector solution. Two groups were formed to work in isolation from each other until a true wind vector field was obtained for each SASS observation. The SASS data covered 1500 km swaths, and the angle of the Seasat antennas relative to the earth was known. Visible and IR data, along with surface weather stations, ship and ship buoy data were also available to the interpreters. Two-vector solutions by the two teams showed almost perfect agreement, and the alias problem was noted to reduce to a selection of two vectors 180 deg apart. Comparisons with the surface measurements in regards to wind directions resulted in agreement to within a standard deviation of 20% for direction. The SASS data is concluded to be useful for producing streamlines, isotachs, and mesoscale as well as cyclone-scale features.
Wurtele, M. G.↗
Three-dimensional unsteady flow calculations in an advanced gas generator turbine
This paper deals with the application of a three-dimensional, unsteady Navier-Stokes code for predicting the unsteady flow in a single stage of an advanced gas generator turbine. The numerical method solves the three-dimensional thin-layer Navier-Stokes equations, using a system of overlaid grids, which allow for relative motion between the rotor and stator airfoils. Results in the form of time averaged pressures and pressure amplitudes on the airfoil surfaces will be shown. In addition, instantaneous contours of pressure, Mach number, etc. will be presented in order to provide a greater understanding of the inviscid as well as the viscous aspects of the flowfield. Also, relevant secondary flow features such as cross-plane velocity vectors and total pressure contours will be presented. Prior work in two-dimensions has indicated that for the advanced designs, the unsteady interactions can play a significant role in turbine performance. These interactions affect not only the stage efficiency but can substantially alter the time-averaged features of the flow. This work is a natural extension of the work done in two-dimensions and hopes to address some of the issues raised by the two-dimensional calculations. These calculations are being performed as an integral part of an actual design process and demonstrate the value of unsteady rotor-stator interaction calculations in the design of turbomachines.
Rangwalla, Akil A.↗