## 1 Introduction  
China's railway construction is progressing steadily in the western plateau regions and challenging mountainous terrains. The tunnels on these routes are primarily defined by high altitudes, steep gradients, and extended lengths, collectively known as 'extreme tunnels' [1, 2]. As an electric multiple unit (EMU) train enters a tunnel, the train-tunnel coupling generates compression and expansion waves that propagate through the tunnel at the local speed of sound. After multiple reflections and overlaps, these waves induce pressure fluctuations within the tunnel [3]. Pressure fluctuations within these tunnels are conveyed into the carriage, causing variations in internal pressure, which may lead to passenger discomfort such as dizziness, nausea, tinnitus, and ear pain, severely threatening operational safety and passenger comfort [4, 5, 6, 7]. Under extreme tunnel conditions, tunnel pressure waves combine with baseline pressure variations, resulting in rapidly changing and higher-amplitude extreme tunnel pressure waves. These extreme tunnel pressure waves interact with various factors such as air ducts, airtight gaps, carbody deformation, oxygen supply systems, and temperature, causing the internal pressure transmission system to exhibit strong nonlinear characteristics. Traditional models of internal pressure fluctuations in tunnels, developed for plains regions, are inadequate to fully explain the mechanisms of internal pressure comfort for passengers under current extreme tunnel conditions. The transmission mechanisms and models of internal pressure fluctuations in extreme tunnels remain unclear, posing greater challenges for addressing the resulting internal pressure comfort issues. Furthermore, the unique climate conditions of high altitude, cold temperatures, and low oxygen levels along the railway have introduced new demands for thermal comfort and oxygen supply within train carriages. A single comfort evaluation method is insufficient to fully and effectively assess the impact of the internal environment on passenger comfort. The coupling relationships between various comfort-related physical variables inside the train remain unclear, posing greater challenges for maintaining and regulating comprehensive environmental comfort under extreme tunnel conditions. Therefore, this study investigates and models the mechanisms of internal pressure fluctuations under extreme tunnel conditions, considering the coupling of multiple factors. It aims to predict and summarize the patterns of internal pressure changes in EMU trains during dynamic operation in such tunnels, ensuring operational safety and addressing the pressure comfort needs of drivers and passengers. The research process is illustrated in Figure 1. To support future research on developing a comprehensive multivariable comfort evaluation system and coordinated regulation under extreme tunnel conditions, this study explores the interaction and coupling relationships among various internal variables, along with analyzing the impact of temperature and oxygen supply on internal pressure fluctuations. Since the 1960s, scholars have conducted extensive research on the impact of tunnel pressure waves on internal pressure fluctuations within trains. In terms of on-train experiments, countries such as China [4], South Korea [5], Germany [6], and Japan [7] have conducted real-world railway tests and analyzed influencing factors related to tunnel pressure waves and their effects on internal pressure fluctuations, intending to improve train design and mitigate adverse pressure effects inside the carriages. In terms of model experiments, scholars have utilized water tunnel and wind tunnel models to appropriately adjust empirical parameters, such as train speed and head shape, to optimize the reduction of internal pressure fluctuations [8; 9; 10].