Non-Parametric Approximations for Anisotropy Estimation in Two-dimensional Differentiable Gaussian Random Fields

Spatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a reference axis and the aspect ratio of the principal correlation lengths. Since these parameters are unknown a priori, sample estimates are needed to define suitable spatial models for the interpolation of incomplete data. The distribution of the anisotropy statistics is determined by a non-Gaussian sampling joint probability density. By means of analytical calculations, we derive an explicit expression for the joint probability density function of the anisotropy statistics for Gaussian, stationary and differentiable random fields. Based on this expression, we obtain an approximate joint density which we use to formulate a statistical test for isotropy. The approximate joint density is independent of the autocovariance function and provides conservative probability and confidence regions for the anisotropy parameters. We validate the theoretical analysis by means of simulations using synthetic data, and we illustrate the detection of anisotropy changes with a case study involving background radiation exposure data. The approximate joint density provides (i) a stand-alone approximate estimate of the anisotropy statistics distribution (ii) informed initial values for maximum likelihood estimation, and (iii) a useful prior for Bayesian anisotropy inference.Comment: 39 pages; 8 figure

On a Model for the Prediction of the Friction Coefficient in Mixed Lubrication Based on a Load-Sharing Concept with Measured Surface Roughness

A new model was developed for the simulation of the friction coefficient in lubricated sliding line contacts. A half-space-based contact algorithm was linked with a numerical elasto-hydrodynamic lubrication solver using the load-sharing concept. The model was compared with an existing asperity-based friction model for a set of theoretical simulations. Depending on the load and surface roughness, the difference in friction varied up to 32 %. The numerical lubrication model makes it possible to also calculate lightly loaded contacts and can easily be extended to solve transient problems. Experimental validation was performed by measuring the friction coefficient as a function of sliding velocity for the stationary case