Examining random forests for predicting elastic floor response spectra involving dynamic primary-secondary structure interaction

The evaluation of Floor Response Spectrum (FRS) holds paramount significance in assessing the seismic behaviour of secondary structures. Precise FRS prediction empowers engineers to make informed decisions concerning structural design, retrofitting, and safety precautions. This study aims to scrutinize the impact of dynamic interaction between primary and secondary structures on FRS. Both the elastic primary structure (PS) and elastic secondary structure (SS) employ a single-degree-of-freedom (SDOF) system. Governing motion equations for both coupled (with dynamic interaction) and uncoupled (without dynamic interaction) systems are formulated and solved numerically. The study investigates how variations in the vibration period of PS ( \({T}_{p}\) ), tuning ratio ( \({T}_{r}\) ), mass ratio ( \(\mu\) ), and damping ratio ( \({\xi }_{s}\) ) of SS influence FRS. The FRS impact remains minimal at \(\mu\) = 0.001 (0.1%); however, with increasing mass ratio, PS-SS dynamic interaction significantly affects SS’s spectral acceleration response. Coupled analysis is crucial only for secondary structures tuned to primary structure’s vibration period ( \(0.8\le {T}_{r}\le 1.2\) .). This study utilizes Random Forest (RF) for FRS prediction. The assessment of our proposed predictive model involved the utilization of three widely recognized statistical parameters: coefficient of determination ( \({R}^{2}\) ), mean absolute percentage error ( \(MAPE\) ), and root mean square error ( \(RMSE\) ). The Shapley Additive Explanation (SHAP) method was used to elucidate the significance of input parameters on the target variable.