Abstract: Excessive displacement of isolation layer in a base isolation structure (BIS) under near-fault pulse-like ground motions can lead to the damage of the isolation layer.The BIS-TMDI system formed by installing tuned mass damper inert (TMDI) can effectively reduce the displacement of the isolator.However, few studies have investigated the stochastic dynamic response and parameter optimization of BIS-TMDI system under near-fault impulsive seismic excitations from the perspective of stochastic vibration.For this purpose, this paper simulates near-fault pulse-like ground motions by combining the deterministic narrowband harmonics and broadband random excitations.Additionally, a novel approach is used based on statistical linearization to determine the stochastic dynamic response of a controlled structure subjected to combined excitations.The core of the approach lies in equivalently decomposing the nonlinear dynamic equation into two sets of coupled nonlinear differential equations, in which the deterministic response and the broadband random response are taken as the unknown processes.The stochastic differential equation is handled by resorting to the statistical linearization method, and the deterministic differential equation is simultaneously combined to obtain the total response.The study demonstrates that the deterministic and stochastic response components of the structure are coupled, and pulse excitations result in significant fluctuations in the standard deviation of the stochastic response;TMDI can effectively reduce the displacement of BIS isolation layer;Both deterministic and stochastic response components need to be considered to better optimize the TMDI control parameters in a probabilistic sense.