A first-passage reliability assessment method for MDOF systems under non-stationary excitation using an energy-conservative S-transform

Engineering structures routinely experience non-stationary dynamic loads such as earthquakes, making accurate assessment of first-passage dynamic reliability for multi-degree-of-freedom (MDOF) systems essential to seismic design and performance evaluation. Conventional Monte Carlo simulation (MCS) incurs prohibitive computational cost, limiting its applicability to practical engineering problems. This paper develops an analytical framework for non-stationary random vibration assessment founded on the S-transform. A constant scaling factor and a frequency-dependent inverse-square-root weighting mechanism are introduced to derive a rigorous energy-conservation-corrected S-transform, establishing a time-frequency power spectral density (TFPSD) model that resolves both energy distortion and the need for intricate time-frequency convolution inherent in existing approaches. The modal superposition method is then integrated with the S-transform convolution theorem to obtain an explicit analytical expression for the non-stationary response that fully accounts for multi-modal cross-coupling effects. Building on non-stationary spectral moment theory, an efficient structural first-passage dynamic reliability assessment framework is constructed. Validation against a five-story shear-type frame model demonstrates that the proposed method preserves computational accuracy while circumventing high-dimensional convolution operations, thereby markedly improving assessment efficiency. The framework is directly applicable to dynamic response analysis and first-passage reliability assessment of MDOF systems under non-stationary excitation, offering both theoretical significance and practical engineering utility.