Relationship Between Kendall's tau Correlation and Mutual Information

Mutual information (MI) can be viewed as a measure of multivariate association in a random vector. However, the estimation of MI is difficult since the estimation of the joint probability density function (PDF) of non Gaussian distributed data is a hard problem. Copula function is an appropriate tool for estimating MI since the joint probability density function ofrandom variables can be expressed as the product of the associated copula density function and marginal PDF’s. With a little search, we find that the proposed copulas-based mutual information is much more accurate than conventional methods such as the joint histogram and Parzen window-based MI. In this paper, by using the copulas-based method, we compute MI forsome family of bivariate distribution functions and study the relationship between Kendall’s tau correlation and MI of bivariate distributions. Finally, using a real dataset, we illustrate the efficiency of this approach.

Computational Probabilistic Analysis and Transformation Method in the Earth Remote Research

The article deals with the issues of numerical modeling of problems with random input data. Finding the joint probability density function of the vector of output parameters is considered. It is proposed to use computational probabilistic analysis and the transformation method. A numerical example of the joint probability density function of the vector of a solution of a system of nonlinear equations with random input data is given.

Effects of Correlation Between Waves and Currents on Pipeline Free Span VIV Fatigue: A Case Study

In shallow waters, subsea pipelines can suffer fatigue damage from Vortex Induced Vibrations (VIV) by the combined effects of waves and currents. A full characterization of the joint probability distribution of waves and currents involves at least 5 variables, 2 for currents (magnitude and direction), and 3 for waves (significant wave height, mean wave direction, and wave period at the peak of the spectrum). In lieu of sufficient data to adequately characterize the associated joint probability density function, DNV GL in their “Recommended Practice” propose an approximation: Assume that the direction of current and wave effects is always the same, but for a given direction, waves and currents are assumed statistically independent. In this paper 28 years of hindcast data are used to test the accuracy of this colinearity approximation in the Sea of Okhotsk. Rather than attempting to estimate a joint probability density function in 5 variables, the span fatigue assessment is simply performed for the entire 28 years of the hindcast database to obtain an average rate of fatigue damage. It is found that this history-based approach can lead to fatigue damage rates that are much higher than those derived from the colinearity assumption. This non-conservatism of the colinearity assumption, arises for pipeline orientations for which both waves and currents can contribute strongly to the VIV response without being exactly colinear. It is concluded that caution is needed in using the colinearity assumption, but an update of the span assessment procedure should also address issues for which current assessment procedures are conservative, such as seabed proximity and trench effects, nonlinearity in the pipe-soil interaction, and the change in axial forces due to transverse displacements of the pipe, which are expected under extreme combined current and wave conditions, as envisioned on on-bottom stability design criteria.