## 1 Introduction
In terms of numerical simulations, [PERSON] [11] employed a three-dimensional numerical simulation approach to study the internal pressure variations as trains pass through tunnels of varying lengths, while [PERSON] [12] used numerical simulation, based on experimental results, to investigate how variable cross-section tunnels  
Figure 1: The study process diagram of the internal pressure fluctuation modeling. alleviate internal pressure fluctuations. [PERSON] [13] proposed a method for calculating pressure fluctuations within the carriage based on one-dimensional numerical simulation and the first law of thermodynamics, and [PERSON] [14] numerically simulated tunnel pressure waves, deriving a linear relationship between internal and external pressures by incorporating the train's airtightness index. Meanwhile, scholars have undertaken theoretical analyses to elucidate the mechanisms of internal pressure fluctuations within trains. [PERSON] [15] developed a train airtightness model based on an equivalent leakage model and time constant, using this model along with measured external pressure data to calculate the internal pressure. [PERSON] [16; 17; 18; 19] developed a pressure transmission model for CRH2 and CRH3 trains subjected to the effects of tunnel pressure waves, considering the effects of carbody deformation, gaps, and ventilation ducts. These studies were conducted under standard tunnel conditions in plain regions. However, in high-altitude areas, where oxygen is scarce and the climate is cold, train carriages must be equipped with oxygen supply systems and air conditioning heating systems, making internal pressure changes more complex under extreme tunnel conditions. [PERSON] [20] developed an internal pressure fluctuation model based on the isentropic adiabatic assumption and oxygen supply constraints, but this model does not account for temperature variations or the coupling effects between the oxygen supply system and internal pressure. In the western plateau regions, where annual average temperatures range from 6.3 \({}^{\circ}\)C to 12.5 \({}^{\circ}\)C and can drop to as low as \(-27.4\) \({}^{\circ}\)C [21], significant temperature differences inside and outside the train lead to frequent heat exchanges through conduction, convection, and radiation. Ignoring the interactions between temperature changes, the oxygen supply system, and internal pressure, as well as relying on the isentropic adiabatic assumption, presents limitations for studying internal pressure fluctuations under such extreme tunnel conditions. Existing research has not fully elucidated the strong nonlinear characteristics of internal pressure transmission systems under the disturbance of extreme tunnel pressure waves, which are influenced by multiple factors. Moreover, effectively maintaining and regulating comprehensive comfort in extreme tunnel conditions remains a significant challenge, and the coupling relationships between internal pressure, oxygen supply, and temperature have yet to be thoroughly explored. To address these gaps and clarify the mechanisms of internal pressure fluctuations under the impact of multiple factors, this study first investigates how external pressures through five pathways--air ducts, airtight gaps, carbody deformation, oxygen supply systems, and temperature changes--affect internal pressure fluctuations, as illustrated in Figure 2. Subsequently, the coupling mechanisms of internal pressure fluctuations under multiple factors are analyzed by modeling the air changes within the carriage as a polytropic process, enabling a detailed analysis of air compression states over differential time elements. Based on the law of mass conservation, a transient pressure transmission model under extreme tunnel conditions was developed. The model's fan loss parameters were refined using actual railway line data, and its validity and accuracy were verified through simulation.