Augmentation of piezoelectric thin-film flapping velocimetry turbulence strength detection via machine learning

Qualitatively evaluating the fundamental mechanical characteristics of square-fractal-grid (SFG)-generated turbulent flow using piezoelectric thin-film flapping velocimetry (PTFV) is rather time-consuming. More importantly, its sensitivity in detecting high-frequency, fine-scale turbulent fluctuations is constrained by high-speed camera specifications. To reduce dependency on high-speed imaging in future PTFV implementations, regression models are trained with supervised machine learning to determine the correlation between piezoelectric-generated voltage V and the corresponding local equivalent flow velocity fluctuation. Using V and thin-film tip deflection δ data as predictors and responses, respectively, Trilayered Neural Network (TNN) emerges as the best-performing model compared to linear regression, regression trees, support vector machines, Gaussian process regression, and ensembles of trees. TNN models trained on data from the (i) lower quarter, (ii) bottom left corner, and (iii) central opening of the SFG-grid provide accurate predictions of insert-induced centerline streamwise and cross-sectional equivalent lateral turbulence intensity and root mean square-δ, with average errors not exceeding 5%. The output predicted from the V response, which considers small-scale turbulence fluctuations across the entire thin-film surface, better expresses the equivalent lateral integral length scale (38% smaller) and turbulence forcing (270% greater), particularly at the bottom left corner of SFG where small-scale eddies are significant. Furthermore, the TNN model effectively captures the occasional extensive excitation forces from large-scale turbulent eddies, resulting in a more balanced force distribution. In short, this study paves the path for comprehensive and expedited flow dynamics characterization and turbulence forcing detection via PTFV, with potential deployment in high Reynolds number flows generated by various grid configurations.