Nonparametric regression analysis

textNonparametric regression uses nonparametric and flexible methods in analyzing complex data with unknown regression relationships by imposing minimum assumptions on the regression function. The theory and applications of nonparametric regression methods with an emphasis on kernel regression, smoothing spines and Gaussian process regression are reviewed in this report. Two datasets are analyzed to demonstrate and compare the three nonparametric regression models in R.Statistic

Aircraft geometry verification with enhanced computer generated displays

A method for visual verification of aerodynamic geometries using computer generated, color shaded images is described. The mathematical models representing aircraft geometries are created for use in theoretical aerodynamic analyses and in computer aided manufacturing. The aerodynamic shapes are defined using parametric bi-cubic splined patches. This mathematical representation is then used as input to an algorithm that generates a color shaded image of the geometry. A discussion of the techniques used in the mathematical representation of the geometry and in the rendering of the color shaded display is presented. The results include examples of color shaded displays, which are contrasted with wire frame type displays. The examples also show the use of mapped surface pressures in terms of color shaded images of V/STOL fighter/attack aircraft and advanced turboprop aircraft

A Spline LR Test for Goodness-of-Fit

Goodness-of-Fit tests, nuisance parameters, cubic spline, Neyman smooth test, Lagrange Multiplier test, stable distributions, student t distributions

Approximation by planar elastic curves

We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient-driven optimization is then used to find the approximating elastic curve.Comment: 18 pages, 10 figures. Version2: new section 5 added (conclusions and discussions

Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy

Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations.Peer ReviewedPostprint (author’s final draft

Extrapolation-CAM Theory for Critical Exponents

By intentionally underestimating the rate of convergence of exact-diagonalization values for the mass or energy gaps of finite systems, we form families of sequences of gap estimates. The gap estimates cross zero with generically nonzero linear terms in their Taylor expansions, so that $\nu = 1$ for each member of these sequences of estimates. Thus, the Coherent Anomaly Method can be used to determine $\nu$. Our freedom in deciding exactly how to underestimate the convergence allows us to choose the sequence that displays the clearest coherent anomaly. We demonstrate this approach on the two-dimensional ferromagnetic Ising model, for which $\nu = 1$. We also use it on the three-dimensional ferromagnetic Ising model, finding $\nu \approx 0.629$, in good agreement with other estimates.Comment: 21 pages, Submitted to Journal of Physics A; new section added discussing rate of convergence and relation to Finite-Size Scalin

Simulation of seismic attributes for earth models with different continuity properties

The combination of kinematic and dynamic ray tracing has been used since the 1970s for simulation (modelling) of seismic energy in the subsurface. Kinematic/dynamic ray tracing is used to simulate the travel time, amplitude and wavefront curvature of a seismic wave— these results are typically presented in the form of curves, maps or synthetic seismograms. Kinematic/dynamic ray tracing is known as a flexible and fast method with the advantage of allowing the user to choose which parts of the wavefield to be simulated. For calculation of amplitudes using dynamic ray tracing, the second-order derivatives of the velocity field must be known. As a consequence, the function representing the velocity field must be, as a minimum, C2 continuous, and this is why cubic splines traditionally has been used. In this study, I test the use of the quintic (fifth degree) B-spline representation. The main objective is to examine whether a quintic B-spline can make kinematic and dynamic ray tracing more robust with respect to local variations in the velocity field. I have done tests of direct ray tracing and two-point ray tracing in the Marmousi model and in a salt model. Both models were exposed to different degrees of smoothing. I compare the results obtained using the cubic and the quintic B-spline representations. For each representation I calculated a number of ray paths, travel times, amplitudes and seismograms, and I monitored the computation times. The results show that for a model with a relatively strong local velocity variation, a quintic representation provides a considerably higher degree of robustness for two-point ray tracing. For models with a higher degree of smoothness, I observe only small differences in the modelling results for the cubic and quintic representations. The quintic B-spline gives increased computation time, but on the other hand a general improvement in robustness.Masteroppgave i geovitenskapGEOV399MAMN-GEO