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Marco Negri
A new representation of roughness, which exploits statistical shape analysis and machine learning (ML) techniques, is here presented.
A geometric database is generated to investigate the effect of several topographical features. The surface elevation of these geometries, scaled in viscous units, is written as a linear combination of the eigenfunctions of the Laplace-Beltrami (LB) operator, discretized on a reference smooth wall with the same physical domain sizes and grid resolution of the rough surfaces. Coefficients of these equations are then computed with the Least Absolute Shrinkage and Selection Operator (LASSO) method, which highlights the relevant predictors (LB eigenfunction) in the definition of the different geometries. Lastly, it is assessed the possibility of computing a universal roughness correlation tying the equivalent sand-grain roughness height k s related to a rough surface to its topographical properties, which is the main goal of the state-of-art approach to address the roughness problem.
This works proposes a physically reliable representation of roughness by means of a model which uses a relatively small number of predictors, thus representing an efficient input for many ML applications, as model predictions through neural networks, that might represent the main tool to analyse roughness in future works.