# Fatigue Crack and Residual Life Prediction Based on an Adaptive Dynamic Bayesian Network
## 1 Introduction  
Modern aerospace vehicles must withstand complex service environments, posing an increasingly strict requirement for structural performance. As the service load condition becomes severer, coupled with inevitable defects and residual stresses from manufacturing processes, the degradation of material and structural performance is an issue that cannot be ignored. The harsh service environment can generate structural damage in terms of cracks, delamination, etc., which poses a serious threat to structural safety and integrity. On the other hand, the reusability of aerospace structures has been a core concern in recent years [1]. Reusability is achieved through a combination of a \"safety factor + regular maintenance\" approach, that is, by increasing the safety margin to enhance structural durability and ensuring reliability through inspections and maintenance [2]. This challenge necessitates a deep understanding of the service environment and load-bearing capacity of structures, as well as effective prediction and management of potential damages. To further enhance the confidence in structural integrity assessments, structural health monitoring technologies for real-time monitoring and evaluation of the service state of structures play a significant role in improving structural performance, ensuring service safety, and reducing maintenance costs [3]. Currently, there are two main methods for structural health monitoring [4]: one is based on artificial intelligence data analysis, and the other is based on physical models (PMs). However, the use of pure data-driven models can be expensive, as it requires costly experiments to obtain data. Meanwhile, simulation-driven PM/FEM models have modeling errors that deviate from actual structures. Practical systems inevitably encounteruncertainties [5], such as sensor noise, material defects, mechanical damage, vibration, and load interference, which can interfere with their diagnostic reasoning and health assessment. Additionally, real-world systems are dynamic and change over time with their health status. Therefore, there is a crucial need to combine physical models with data-driven models to solve health monitoring problems. Recently, the concept of digital twins has gained widespread attention in the field of intelligent manufacturing due to the development of communication technology in intelligent algorithms [6; 7]. Digital twins establish an interactive relationship between the physical and digital worlds. They provide simulation models based on physical mechanisms and health monitoring services for data obtained in the physical world. Complex systems collect sensor data from the physical world and send them to digital twin virtual models through communication technology. The digital twin virtual model processes these data, updates the simulated physical model in real time, and sends control commands to provide optimization and decision support for physical systems. The U.S. Air Force adopted the \"Airframe Digital Twin\" (ADT) for aircraft design, maintenance, and performance prediction. It employs digital twins to replicate the physical and mechanical attributes of aircraft, enabling the prediction of structural fatigue cracks and extension of the aircraft's remaining service life [8; 9; 10]. The ADT encompasses three core modules: online monitoring, condition assessment, and lifespan prediction. It integrates aerodynamic and finite element analyses along with other structural models, which monitor the evolution of fatigue, vibration, and other material states in flight structures. Through dynamic updates incorporating specific geometry, material properties, flight history, and maintenance data, the ADT precisely forecasts aircraft behavior. This allows decision-makers to tailor personalized management strategies for each aircraft, thereby prolonging service life and reducing maintenance expenses.