## 1 Introduction
### Background and Literature Review  
A portion of the study involved a pantograph reliability analysis [1]. The reliability indexes and reliability of the structural strength of pantographs were analyzed using simulated sample data extracted from Latin hypercube sampling with a single-arm pantograph as the object of study [2]. Combining the rain flow counting method, the life prediction method and the reliability prediction method, the reliability analysis of the V500 pantograph was carried out, and the fatigue life results under different working intensities were predicted, which provided data support for the structure, material, design and operation management of the device [3]. A dynamic model was developed for the pantograph of the TSG19 type, and the contact stresses were analyzed to obtain the fatigue life and reliability of the component, and its structural model was analyzed based on the stress data. Currently, there are fewer studies on pantograph reliability alone, and most of them are based on structural reliability rather than actual operation data. Therefore, this paper will draw on the data-driven [4] reliability research method to study the dynamic reliability of pantographs. Fault tree analysis (FTA) is a powerful tool for assessing the reliability of complex systems [5]. When using the traditional fault tree analysis method to analyze the reliability of pantograph systems, in addition to the common problem of few component failure data and difficulty in calculating the failure rate, there is also the problem that the failure states are only based on two-state assumptions and cannot accommodate the multiple failure states that exist in the practical system. Therefore, the T-S fuzzy fault tree analysis method is generated [6] by introducing the fuzzy theory and uses fuzzy numbers to describe the failure rate and failure probability; the polymorphic representation of fault states is realized by T-S gates in the T-S fault tree. When using the T-S fuzzy fault tree for reliability assessment, a large number of calculations are generated when finding the top event state (forward inference), and reverse inference is not possible. In addition, the fault tree analysis method is not suitable for dynamic reliability analysis of the system, which leads to its limitation in practical engineering applications. Many studies have applied optimized fault trees to reliability analysis. [PERSON] et al. [7] Introduced the concept of Dynamic fault tree (DFT) by defining additional gates (called dynamic gates) on the traditional fault tree, which overcame the shortcomings of the traditional static fault tree in not being able to adequately simulate the dynamic failures of a complex system and effectively assessed the reliability of real complex systems. In [8], an extended approach for collaborative data-driven fault tree analysis (DDFTA) of a system is presented, which extracts repairable fault trees from time series data streaming from multiple systems/machines sharing similar functionalities. This method is not limited to binary (two states) components nor to exponential distributions. [PERSON] et al. [9] proposed fault tree analysis based on fuzzy set theory and applied it to wind energy systems; this technique combines the effects of operational failures of wind energy system configurations and errors in fuzzy environments using fuzzy risk indices combining probabilistic inaccuracy and engineering inaccuracy for greater flexibility and adaptability. [PERSON] et al. [10] established a polymorphic fuzzy fault tree for the high-voltage power battery system of a pure electric commercial vehicle based on the combination of polymorphic theory, fuzzy mathematical theory, group decision-making theory, and fault tree and carried out qualitative and quantitative analyses to determine the system's weak links.