Vertical stiffness of the bridge is of paramount importance in guaranteeing optimal driving performance for high-speed railway (HSR) trains. Initially, the Auto Regression and Moving Average model with eXogenous input (ARMAX) model is employed as the surrogate model for the train-bridge (TB) coupling system. Then, the framework for analyzing vertical bridge stiffness is proposed employing the surrogate model, and the relationship between the train response affected by excitation randomness and the vertical stiffness indicators of the bridge is established. Finally, the influence of various factors such as train speed, train type, car body mass, and bridge span on stiffness limit of 400 km/h HSR simple-supported bridge (SSB) is examined. The results indicate that the surrogate model offers a notable advantage in computational efficiency, while maintaining a satisfactory accuracy in predicting the train response. With higher train speeds, lighter car body masses, and longer spans, the demand for stricter bridge stiffness limits becomes more pronounced. Based on the driving performance of the train types analyzed, the recommended stiffness limit is proposed for the prestressed concrete simply supported beam (SSB) bridges used in HSR, with a span length of less than 40 m and operating at a speed of 400 km/h.
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