Fault diagnosis is crucial for repairing aircraft and ensuring their proper functioning. However, with the higher complexity of aircraft, some traditional diagnosis methods that rely on experience are becoming less effective. Therefore, this paper explores the construction and application of an aircraft fault knowledge graph to improve the efficiency of fault diagnosis for maintenance engineers. Firstly, this paper analyzes the knowledge elements required for aircraft fault diagnosis, and defines a schema layer of a fault knowledge graph. Secondly, with deep learning as the main method and heuristic rules as the auxiliary method, fault knowledge is extracted from structured and unstructured fault data, and a fault knowledge graph for a certain type of craft is constructed. Finally, a fault question-answering system based on a fault knowledge graph was developed, which can accurately answer questions from maintenance engineers. The practical implementation of our proposed methodology highlights how knowledge graphs provide an effective means of managing aircraft fault knowledge, ultimately assisting engineers in identifying fault roots accurately and quickly.

To enhance aircraft fault diagnosis efficiency, this paper proposes HybridRAG, an intelligent-guided troubleshooting framework that integrates knowledge graphs and large language models (LLMs). Unlike conventional retrieval-augmented generation (RAG) methods that rely on single-modal retrieval, HybridRAG adopts a multi-dimensional retrieval strategy, combining graph-based reasoning with both vector-based and BM25-based text retrieval techniques. This hybrid approach ensures comprehensive extraction of relevant information from both unstructured text and structured fault graphs, enhancing diagnostic precision, relevance, and robustness. Experimental results demonstrate that HybridRAG achieves an F1 score improvement of at least 4% and reduces hallucination rates by over 7% compared to mainstream RAG baselines. These advancements, combined with its unique integration of multi-modal retrieval, position HybridRAG as a novel framework for addressing complex aircraft maintenance challenges. Additionally, the paper presents an agent-based intelligent troubleshooting assistant that supports more interactive, adaptive, and flexible diagnostic Q&A, providing maintenance personnel with a significant advanced intelligent, context-aware diagnostic tool.

When an aircraft malfunctions, quickly and accurately identifying the faulty unit is essential for ensuring normal operation. Unfortunately, maintenance engineers often struggle to acquire the necessary fault-related knowledge due to poor management and utilization of aircraft fault documents. To address this issue, we introduce knowledge graph technology into the field of aircraft fault diagnosis, exploring its construction and application for effective knowledge management. Our work starts by analyzing the critical knowledge elements required for aircraft fault diagnosis and designing a schema layer for fault knowledge graphs. We then we then combine deep learning and heuristic rules to extract fault knowledge from both structured and unstructured data, enabling the construction of aircraft fault knowledge graphs. Finally, we develop a fault question-answering system based on fault knowledge graphs that can accurately give solutions to questions posed by maintenance engineers. Our practice demonstrates that knowledge graphs provide an effective means of managing aircraft fault knowledge, assisting engineers in locating fault reasons accurately and quickly.

This paper develops a third-order fully decoupled numerical scheme for the hydrodynamically-coupled binary phase-field crystal (BPFC) model based on the relaxed exponential scalar auxiliary variable (E-SAV) approach. The governing equations are derived from the $ L^2 $-gradient flow and coupled with the incompressible Navier-Stokes equations. To preserve total mass conservation, two nonlocal Lagrange multipliers are introduced into the chemical potentials. For temporal discretization, a third-order backward differentiation formula (BDF3) combined with explicit extrapolation techniques is adopted, leading to a linear and fully decoupled time-marching scheme. In addition, a relaxation strategy is incorporated into the E-SAV framework to improve the consistency between the modified energy and the original energy functional. Compared with existing second-order relaxed E-SAV schemes, the proposed method achieves higher temporal accuracy while retaining the advantages of linearity, decoupling, and energy stability. The proposed scheme only requires solving several linear elliptic equations with constant coefficients at each time step, making the algorithm computationally efficient and easy to implement. The unique solvability and discrete energy dissipation property of the numerical scheme are theoretically established. Furthermore, a consistency analysis is provided to show that the relaxation step preserves the third-order temporal accuracy of the primary variables and does not affect the overall convergence order of the scheme. Numerical experiments verify the expected third-order convergence rate, demonstrate the unconditional energy stability of the proposed scheme, and illustrate its effectiveness for long-time simulations of hydrodynamically-coupled crystal growth problems.

The symmetric regularized long waves (SRLW) equation is a fundamental model for describing small-amplitude long-wavelength waves in dispersive media, yet existing studies have predominantly focused on solitary waves, leaving periodic solutions underexplored. This study addresses this research gap by investigating the periodic properties and critical dynamic behavior of the SRLW equation. First, the SRLW equation is transformed into an ODE via traveling wave transformation, then simplified using physical constraints (finite amplitude and non-unbounded linear variation). He’s frequency formulation is subsequently applied to derive the explicit form of periodic solutions. Moreover, the "pull-down motion", a phenomenon where periodic waves lose oscillatory characteristics and disappear, is clarified, and its critical criterion is derived through extremum analysis of wave amplitude. Two numerical examples with different parameter sets validate the theoretical findings: stable periodic solutions exist when system parameters are below a critical threshold, with constant upper amplitude and asymmetrically decreasing lower amplitude and pull-down motion is triggered when the pull-down criterion is satisfied, and parameters exceeding the critical value lead to direct pull-down without stable periodicity. This work enriches the solution theory of the SRLW equation, corrects the misconception of "symmetric waves" associated with the equation, and provides valuable insights for simulating non-linear wave phenomena in fluid mechanics, plasma physics, and related fields.