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Friction pendulum systems (FPSs) are increasingly being used for bridge seismic isolation, and the isolated response is generally achieved at the expense of inducing large bearing displacements. Setting up a tuned inerter damper (TID) is an approach for improving seismic performance. Nevertheless, the optimization and performance enhancement of multiple TIDs to mitigate the seismic responses of bridges isolated with the FPSs are limited. In this study, the stochastic optimization of multiple TIDs for controlling stochastically excited bridges with FPS bearings was pursued. By describing the hysteretic characteristics of the FPS using the Bouc–Wen model, augmented systems of the bridge model, FPS bearings, and TIDs were formulated and combined with the modeling of stochastic excitation as filtered Gaussian white noise. A stochastic optimization procedure of multiple TIDs for controlling the bridge response considering the nonlinearity of the FPS bearings is proposed and illustrated using examples of continuous bridges. The effects of FPS friction on the optimization and robustness of the TID parameters were identified. A parametric study was performed to determine the mechanism of TID performance enhancement depending on the number of TIDs, multiple modes of tuning, and inertance distribution. Numerical results indicate that the TIDs designed via stationary-stochastic-global (SSG) optimization significantly reduced the responses of the isolated bridge, and the performance was improved by increasing the TID number. Considering the multi-mode contributions to the transversal responses, the performance of spatially distributed TIDs can be substantially enhanced by adding the TID inertance as a design parameter.

Bridge influence lines (BILs) and bridge influence surfaces (BISs) are inherent static parameters of bridges which can be extracted from moving vehicle-induced bridge responses. Compared with dynamic parameters, these parameters are directly related to the stiffness and internal forces in each cross-section of a bridge therefore can be considered as an effective bridge metamodel. To accelerate the engineering practice of BIL- and BIS-based bridge evaluation, this paper first briefly reviews the current BIL and BIS field test and identification methods. Then, the bridge evaluation guidelines of China and the United States are introduced as the basis of the evaluation methods. Engineering application scenarios for bridge evaluation, including permit load verification, performance degradation checking, and load carrying capacity evaluation, are summarized, and a multiple-scenario bridge evaluation method is established. At the end of this paper, an evaluation example of a four-span continuous bridge is presented to illustrate the application procedure and verify the effectiveness of the proposed method. The outcomes of this paper provide a promising application method of field test BILs and BISs, which may help bridge engineers more effectively use these parameters in engineering practice.