A Novel Nonlinear Nonparametric Correlation Measurement With A Case Study on Surface Roughness in Finish Turning

TL;DR

This paper introduces g-correlation, a universal nonlinear nonparametric correlation measure that effectively captures all types of correlations, demonstrated through applications in surface roughness prediction during finish turning.

Contribution

The paper proposes the g-correlation coefficient, a novel correlation measure that does not assume data patterns and outperforms existing methods in capturing both linear and nonlinear correlations.

Findings

G-correlation is robust on linear datasets.

G-correlation outperforms existing methods on nonlinear datasets.

Application to surface roughness shows g-correlation's central role.

Abstract

Estimating the correlation coefficient has been a daunting work with the increasing complexity of dataset's pattern. One of the problems in manufacturing applications consists of the estimation of a critical process variable during a machining operation from directly measurable process variables. For example, the prediction of surface roughness of a workpiece during finish turning processes. In this paper, we did exhaustive study on the existing popular correlation coefficients: Pearson correlation coefficient, Spearman's rank correlation coefficient, Kendall's Tau correlation coefficient, Fechner correlation coefficient, and Nonlinear correlation coefficient. However, no one of them can capture all the nonlinear and linear correlations. So, we represent a universal non-linear non-parametric correlation measurement, g-correlation coefficient. Unlike other correlation measurements, g-correlation doesn't require assumptions and pick the dominating patterns of the dataset after examining all the major patterns no matter it is linear or nonlinear. Results of testing on both linearly correlated and non-linearly correlated dataset and comparison with the introduced correlation coefficients in literature show that g-correlation is robust on all the linearly correlated dataset and outperforms for some non-linearly correlated dataset. Results of the application of different correlation concepts to surface roughness assessment show that g-correlation has a central role among all standard concepts of correlation.