## 4 Conclusions  
This study explored the optimal design and seismic performance of base-isolated structures equipped with TIDs, subjected to both far-fault and near-fault ground motions, respectively. The impact of design factors on the optimal parameters of the TID was examined. The control effectiveness of the TID for base-isolated structures with varying heights was evaluated. The following summarizes the main conclusions:  
1. Considering the impact of ground motion characteristics, the optimal parameters for the base-isolated structure equipped with the TID have been determined. As the natural period and damping ratio of the base-isolated structure increase, both the optimal frequency ratio and damping ratio tend to rise. Due to the impracticality of deriving or fitting simple and accurate closed-form solutions, a parameter optimization analysis based on design conditions has been proposed.
2. The TID is more effective and stable for seismic control of base-isolated structures under far-fault ground motions than under near-fault ground motions. Additionally, the TID is more suitable for low-rise base-isolated structures. The control effectiveness of the TID improves with the mass ratio, however, when the mass ratio exceeds 0.2, the additional benefits of increasing the mass ratio diminish.
3. The TID provides excellent control over the mean square displacement response of the base-isolated structure, but its control effect on the peak displacement response is less significant due to the control hysteresis of the TID. Additionally, the TID demonstrates  
Figure 15: Percentage reduction rate of the peak absolute acceleration response for the base storey of the three base-isolated structures with different mass ratio TIDs.  
effective control over the absolute acceleration response of low-rise base-isolated structures.  
As indicated by the findings of this study, the characteristics of the dynamic loads, such as earthquake and wind load, significantly influence the optimal parameters of vibration reduction systems. The proper selection of these parameters is critical in determining whether the device can effectively demonstrate vibration reduction performance. Designers should also assess the likelihood of the building experiencing near-fault ground motions based on the fault distance. When considering the influence of near-fault effects, it is recommended to use the optimal parameters proposed in this paper that correspond to near-fault non-pulse type ground motion. In the case of near-fault pulse type ground motion, the damping effect of TID is limited and should be combined with other vibration control devices. For high-rise base-isolated structures, equipping TID devices in the isolation storey does not provide significant vibration reduction. It may be more effective to consider placing inerter-based vibration control devices between storeys of the high-rise structure or between adjacent structures to achieve improved vibration control. Additionally, further research on structural nonlinearity, robustness analysis, and sensitivity effects should be prioritized in future studies.  
Formal analysis, Z.Z. ([PERSON]) and X.Z.; Investigation, Z.Z. ([PERSON]); Writing--original draft, Y.K.; Writing--review & editing, Y.K. and Z.Z. ([PERSON]); Supervision, Q.L.; Project administration, Q.L.; Funding acquisition, Q.L. All authors have read and agreed to the published version of the manuscript.  
The authors are grateful for financial support from the National Natural Science Foundation of China (Grant No. 52208493), the Hebei Natural Science Foundation (Grant No. E2022210078), Science and Technology Project of Hebei Education Department (Grant No. BJK2023038).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.