Multi-Agent Reinforcement Symbolic Regression for the Fatigue Life Prediction of Aircraft Landing Gear

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.