Asessment of roughness characterization methods for data-driven predictions

Abstract

A comparative analysis is undertaken to explore the impact of various roughness characterization methods as input variables on the performance of data-driven predictive models for estimating the roughness equivalent sand-grain size $k_s$.%All models developed in this work are realized in the form of fully connected multi-layer perceptron (MLP).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, $\text{NN}_\text{PA}$, utilizes a finite set of 17 roughness statistical parameters as input variables.Furthermore, a simplified parameter-based model, denoted as $\text{NN}_\text{PAM}$, is considered, which features only 6 input roughness parameters.%A training database consisting of 85 artificially generated roughness samples along with their direct numerical simulation results is employed. The models are trained based on identical databases and evaluated using roughness samples similar to the training databases as well as an external testing database based on literature.%those provided in the literature. While the predictions based on p.d.f. and PS achieves a stable error level of around 10\% among all considered testing samples, a notable deterioration in performance is observed for the parameter-based models for the external testing database, %on the external surfaces, indicating a lower extrapolating capability to diverse roughness types.Finally, the sensitivity analysis on different types of roughness confirms an effective identification of distinct roughness effects by $\text{NN}_\text{PAM}$, which is not observed for $\text{NN}_\text{PA}$.We hypothesize that the successful training of $\text{NN}_\text{PAM}$ is attributed to the enhanced training efficiency linked to the lower input dimensionality.