Assessing different roughness description methods in skin friction prediction

A comparative analysis is conducted to investigate the effect of different roughness description methods as input parameters on data-driven predictive models for determining the roughness equivalent sand-grain size $k_s$. All models developed in this work are realized in form of deep neural networks (NN). The first type of model, denoted as $\text{NN}_\text{PS}$, incorporates the roughness height probability density function (p.d.f.) and power spectrum (PS), while the second type of model, $\text{NN}_\text{ST}$, utilizes several roughness statistical parameters as inputs. The architecture of the models are individually determined through Bayesian optimization. Ensemble prediction technique is adopted in the present work. Specifically, 50 individual NNs, either $\text{NN}_\text{PS}$ or $\text{NN}_\text{ST}$, are trained and combined to create ensemble neural networks (ENN) denoted as $\text{ENN}_\text{PS}$ and $\text{ENN}_\text{ST}$, respectively. A database consisting of 85 artificially generated roughness samples, along with direct numerical simulation results for those samples are employed to train both ENN models. Finally, the models are evaluated using roughness samples from both internal and external sources. ... mehrThe $\text{ENN}_\text{PS}$ model achieves an average error of around 10\%, while a notable declined performance is observed for the $\text{ENN}_\text{ST}$ model particularly for external test samples. Therefore, better universality of the roughness description approach using p.d.f. and PS in representing a wide range of roughness features is demonstrated. Furthermore, it is found that using p.d.f. and PS enables a more accurate recovery of surface drag with lower model complexity.