Reliability-informed design table for optimizing tuned mass-damper-inerter systems to improve structural seismic performance

As a promising device for seismic mitigation of structures, the tuned mass-damper-inerter (TMDI) has attracted considerable attention in recent years. However, existing design methods of TMDI such as the fixed-point theory-based formulas and stochastic optimization methods, often suffer from insufficient control gains or excessive computational demands. To address these issues, this study develops a reliability-informed multi-parameter design table (MPDT) for optimizing TMDI in a fast, accurate, and non-iterative manner. The MPDT is developed through repeated reliability-based design optimization (RBDO), integrating the probability density evolution method (PDEM) with genetic algorithms. It ensures robust TMDI performance under stochastic ground motions and facilitates efficient selection of key parameters, including mass ratio, inertance-to-mass ratio, damping ratio, and frequency ratio, across varying structural periods and seismic conditions. Additionally, it provides guidance for rational selection of TMDI topology, such as TMD, TID, or full TMDI. The MPDT is validated via case studies on a base-isolated structure and a five-story shear frame structure with various TMDI configurations. The results demonstrate that the MPDT-based TMDI designs achieve comparable control performance to full RBDO designs while significantly reducing computational effort. Key influences such as structural modal frequency, inerter connection, and TMDI placement are examined, revealing the robustness of the proposed method even if the design assumptions are partially fulfilled. Furthermore, design trends, such as the relationship between inertance and structural period are uncovered. Overall, the MPDT provides a reliable, efficient, and scalable framework for performance-based seismic design of TMDI systems, supporting practical engineering applications.