Wake-induced vibration of a downstream cylinder in tandem configurations: an activation-modulation framework

Wake-induced vibration (WIV) of a downstream cylinder in tandem configurations is governed by coupled wake development and structural dynamics, yet robust quantitative interpretation across diverse experimental conditions remains challenging. In this study, a comprehensive multi-source database of downstream-cylinder WIV cases is established and analyzed using an interpretable machine-learning framework integrating Random Forest (RF) regression and accumulated local effects (ALE). The RF model achieves strong predictive performance on an independent test set ( R 2 ≈ 0.98, RMSE ≈ 0.06), and additional stratified sampling checks confirm the consistency of key parameter distributions between training and test subsets. ALE-based interpretations reveal that the reduced velocity U r and the spacing ratio L/D dominate the response and exhibit intrinsically coupled, non-separable effects that control excitation onset. Structural parameters (mass ratio, damping, and diameter ratio) primarily modulate vibration amplitude after activation, while no universal amplitude envelope can be identified across the assembled dataset even under normalization by the activation measure. Guided by these findings, an explicit activation function g ( U r , L/D ) is proposed to represent conditional excitation, enabling an “activation-modulation” framework that disentangles wake-driven activation from post-activation structural modulation. The study provides a physically grounded and reproducible pathway for organizing tandem-cylinder WIV responses beyond conventional empirical amplitude correlations.