تحلیل حساسیت و ارزیابی پارامترهای بهینه میراگر جرمی مایع تنظیم‌شونده با رویکرد یادگیری ماشین

The increasing vulnerability of modern structures to seismic excitations has motivated the development of efficient passive control systems capable of reducing structural responses while maintaining design simplicity, reliability, and robustness. Among these systems, tuned liquid mass dampers (TLMDs) have gained increasing attention due to their ability to combine the advantages of traditional tuned mass dampers (TMDs) and tuned liquid dampers (TLDs). This hybrid mechanism is particularly attractive for buildings equipped with deep liquid tanks, such as rooftop water reservoirs, where existing architectural features can be effectively utilized for vibration control without imposing significant additional construction costs. Despite their practical advantages, the optimal design of TLMD parameters remains computationally demanding because of the complex interaction between structural dynamics, fluid motion, and the geometric characteristics of the liquid container. The coupled behavior of the structure–fluid system, together with the nonlinear influence of liquid height and tank dimensions, makes conventional trial-and-error or optimization-based design approaches time-consuming, especially when multiple seismic records and structural configurations are considered. To address these challenges, this study proposes a hybrid numerical–data-driven framework for predicting the optimal parameters of TLMDs and analyzing their sensitivity in both one-story and five-story shear structures subjected to seismic loading. The TLMD is mounted on elastomeric pads to enhance tuning flexibility and to allow independent adjustment of stiffness and damping properties. The dynamic behavior of the fluid–structure interaction is modeled using the well-established Housner lumped mass model, which decomposes the liquid motion into impulsive and convective components, thereby providing an efficient yet accurate representation of sloshing effects. Six real earthquake ground motion records with diverse frequency contents and intensity characteristics are employed to ensure the robustness and general applicability of the results under different seismic conditions. For each structural configuration, the optimal frequency ratio and damping ratio of the elastomeric pads are determined using the pattern search optimization algorithm over a wide range of liquid heights and depth ratios. This extensive parametric investigation captures the nonlinear and coupled influence of geometric variables on the optimal TLMD performance. Based on the numerical optimization results, a comprehensive dataset consisting of 1,800 samples is generated. In this dataset, liquid height and depth ratio are considered as input variables, while the corresponding optimal TLMD parameters are treated as output targets. After data standardization, six machine learning algorithms—linear regression, decision tree, random forest, gradient boosting, k-nearest neighbors, and support vector regression—are trained and evaluated using five-fold cross-validation to ensure reliable performance assessment and to mitigate overfitting. Model performance is evaluated using multiple statistical metrics, including mean squared error, root mean squared error, mean absolute error, and the coefficient of determination. The results demonstrate that the prediction accuracy of machine learning models depends on both the structural configuration and the specific TLMD parameter being predicted. For the one-story structure, the random forest model provides the most accurate predictions for the optimal frequency ratio, whereas linear regression achieves the highest accuracy for estimating the optimal damping ratio. In contrast, for the five-story structure, linear regression performs best in predicting the frequency ratio, while random forest yields superior accuracy for damping ratio estimation. Residual analyses confirm unbiased predictions and good generalization capability of the selected models. Sensitivity analysis further reveals that liquid height and depth ratio have a coupled and nonlinear influence on the optimal TLMD parameters. Shorter structures exhibit higher sensitivity to geometric variations of the tank, whereas taller structures show smoother response surfaces and reduced sensitivity. Overall, the proposed framework significantly reduces computational cost and time while providing reliable and accurate predictions, making it a practical and efficient tool for the optimal design of TLMDs under various structural and seismic conditions.