The purpose of the present work is to examine two possibilities; firstly,
predicting equivalent sand-grain roughness size ks​ based on the roughness
height probability density function and power spectrum leveraging machine
learning as a regression tool, and secondly, extracting information about
relevance of different roughness scales to skin-friction drag by interpreting
the output of the trained data-driven model. The model is an ensemble neural
network consisting of 50 deep neural networks. The data for the training of the
model is obtained from direct numerical simulations (DNSs) of turbulent flow in
plane channels over 85 irregular multi-scale roughness samples at friction
Reynolds number Reτ​=800. The 85 roughness samples are selected from a
repository of 4200 samples, covering a wide parameter space, through an active
learning (AL) framework. The selection is made in several iterations, based on
the informativeness of samples in the repository, quantified by the variance of
ENN predictions. This AL framework aims to maximize the generalizability of the
predictions with a certain amount of data. This is examined using three
different testing data sets with different types of roughness, including 21
surfaces from the literature. The model yields an overall mean error of 5\% to
10\% on different testing data sets. Subsequently, a data interpretation
technique, known as layer-wise relevance propagation, is applied to measure the
contributions of different roughness wave-lengths to the predicted ks​.
High-pass filtering is then applied to the roughness PS to exclude the
wave-numbers identified as drag-irrelevant. The filtered rough surfaces are
investigated using DNS, and it is demonstrated that, despite significant impact
of filtering on the roughness topographical appearance and statistics, the
skin-friction coefficient of the original roughness is successfully preserved.Comment: 24 pages, 11 figures, submitted to JF