As one of the critical components in helicopter transmission systems, the flange is prone to fatigue damage and failure under complex operational conditions, which seriously influence operational safety and service life. To improve the structural integrity of flanges, an exponential distribution optimizer (EDO)-based integrated surrogate model (ISM) method is proposed for the fatigue life prediction and reliability evaluation of the flange structure. In this method, the Bayesian model averaging method is adopted to build a high-efficient surrogate model and the EDO is used to find the optimal parameters of the model. The high cycle fatigue (HCF) life prediction and reliability evaluation of the helicopter flange structure are performed by the proposed EDO-ISM method and other methods. Results demonstrated that the EDO-ISM method improves modeling precision by 63.17% and computational efficiency by 8.743%, relative to other methods. The reliability analysis shows a high reliability degree of 0.9981 for the flange structure, while sensitivity analysis reveals that rotational torque (S = 0.386, I = 0.312) and the fatigue ductility index (S = 0.312, I = 0.278) are the most significant parameters affecting the flange HCF life. These results reveal the strengths of the EDO-ISM method in the HCF life prediction and reliability evaluation of the helicopter flange structure. The efforts of this study provide a promising method for the HCF life prediction and reliability evaluation of complex structures besides helicopter flanges under complex working conditions.

Accurate fatigue life prediction of aircraft landing gear is crucial for ensuring flight safety and preventing catastrophic structural failures. However, traditional empirical methods face significant limitations in capturing complex multiaxial loading conditions, while machine learning approaches suffer from lack of interpretability in critical safety applications. To address the dual challenges of prediction accuracy and model interpretability, a multi-agent reinforced symbolic regression (MA-RSR) framework is proposed by integrating multi-agent reinforcement learning with symbolic regression (SR) techniques. Specifically, MA-RSR employs a collaborative mechanism that decomposes complex mathematical expressions into parallel components constructed by independent agents, effectively addressing the search space explosion problem in traditional SR. The system incorporates Transformer-based architecture to enhance symbolic selection capabilities, while an intelligent masking mechanism ensures mathematical rationality through multi-level constraints. To demonstrate effectiveness of the proposed method, validation is conducted using SAE4340 steel multiaxial fatigue data and landing gear finite element simulation. The MA-RSR framework successfully discovers two mathematical expressions achieving R² of 0.96. Compared to traditional empirical formulas, MA-RSR achieves prediction accuracy improvements exceeding 50% while providing complete interpretability that machine learning methods lack. Furthermore, the multi-agent collaborative mechanism significantly enhances search efficiency through parallel expression construction compared to existing symbolic regression approaches.

Reliability analysis of aeroengine structures is a critical task in aerospace engineering, but traditional methods often face challenges of low computational efficiency and insufficient accuracy when dealing with complex, high-dimensional, and nonlinear problems. This paper proposes a novel reliability assessment method (AC-Kriging) based on the Actor–Critic network and Kriging surrogate models to address these issues. The Actor network optimizes the sampling strategy for design variables, making sampling more efficient. The Critic network assesses the reliability of these samples to ensure accurate results, while a Kriging surrogate model replaces expensive finite element simulations and cuts computational cost. Three case studies demonstrate that AC-Kriging significantly outperforms traditional methods in both sampling efficiency and reliability estimation accuracy. This research provides an efficient and reliable solution for reliability analysis of aeroengine structures, with important theoretical and engineering application value. Three case studies demonstrate that AC-Kriging significantly outperforms traditional methods in both sampling efficiency and reliability-estimation accuracy, requiring only 52–147 samples to achieve comparable accuracy while maintaining the relative failure probability error within 0.87–7.27%. This research provides an efficient and reliable solution for the reliability analysis of aeroengine structures.