Functional regression in tribology : an application of methods of functional regression for a comprehensive evaluation of tribometrical data

Abstract

In this thesis we employ methods from functinal data analysis (FDA) tocarry out a comprehensive analysis of tribometrical data (coefficient of frictioncurves, and chemical composition of fluids with lubricating properties). Wepresent the tools of FDA that are used in this thesis including data representation by basis expansions, functional principal component analysis (FPCA)and function-on-scalar regression. In the data, we find many cases wheredifferent coefficient of friction (cof) curves result from the same gasoline, andovercame this problem by selecting one curve to represent the duplicates. Theregression methods employed (OLS, GLS, PCR, Group Lasso) give moderateresults with regards to the accuracy of prediction (measured with RMSEP)which does not allow to draw conclusions about the effect of the compositionof the fluids with lubricating properties on the shape of the cof curves. Thereason for this could be twofold. Firstly, many of the independent variablesare extremely biased and, secondly, the regression methods used are sensitiveto outliers. We suggest balancing the independent variables and use robustregression methods as an approach to improvement.