Existing research predominantly focuses on developing design methods for the structural configuration of inerter systems. However, the authors find that these optimization methods often overlook the non-stationary characteristics associated with seismic response. Additionally, traditional approximation algorithms yield significant errors in non-stationary processes, resulting in inaccurate predictions of the structural responses with inerter systems, which compromises the effectiveness of the optimization designs. This paper proposes a novel approach that combines the parameters of the inerter system with a modified Vanmarcke approximation to obtain unified calculation formulas for inerter parameters. The accuracy and computational efficiency in solving spectral moments are crucial for the feasibility of this method. The study presents an efficient calculation method to accurately determine non-stationary response spectral moments of structures with inerter systems. Using the complex modal method (CMM) and pseudo-excitation method (PEM), a unified solution for structural responses under seismic actions is obtained. The quadratic decomposition of the power spectral density function (QD-PSDF) is employed to derive analytical solutions for response spectral moments and non-geometric spectral characteristics (NGSC). Substituting the obtained moment values into the parameter calculation formulas allows effective determination of the inerter system parameters. Finally, Finite Element Method (FEM) modeling verifies the validity and general applicability of this approach. The results demonstrate that the proposed method accounts for non-stationary characteristics of structures with inerter systems under seismic excitations, enhancing seismic design reliability and structural safety. Moreover, the obtained inerter system parameters at each floor effectively achieve the target performance while providing a broader range of design options for enhanced flexibility in system configuration.
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