An Aero-engine Quality Assessment Method Based on Particle Swarm Optimized Fermatean Fuzzy Structural Equation Model

XÜ Sining; WANG Yuhui; CHENG Xiangjun; YANG Qianjun; SHAN Zhifeng; TANG Xilang

doi:10.12382/bgxb.2025.0905

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An Aero-engine Quality Assessment Method Based on Particle Swarm Optimized Fermatean Fuzzy Structural Equation Model

更新时间：2026-07-06

- An Aero-engine Quality Assessment Method Based on Particle Swarm Optimized Fermatean Fuzzy Structural Equation Model
- Acta Armamentarii Vol. 47, Issue 6, Pages: 250905(2026)
- 作者机构：
  
  空军工程大学装备管理与无人机工程学院，陕西西安 710051
  无人飞行器技术全国重点实验室，陕西西安 710051
  95866部队，河北保定 071000
- 作者简介：
- 基金信息：
- DOI：10.12382/bgxb.2025.0905
  CLC： E926
- Received：13 October 2025，
  
  Online First：27 January 2026，
  
  Published：2026-06
- 稿件说明：
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XÜ Sining, WANG Yuhui, CHENG Xiangjun, et al. An Aero-engine Quality Assessment Method Based on Particle Swarm Optimized Fermatean Fuzzy Structural Equation Model[J]. Acta Armamentarii, 2026, 47(6): 250905.
DOI：

XÜ Sining, WANG Yuhui, CHENG Xiangjun, et al. An Aero-engine Quality Assessment Method Based on Particle Swarm Optimized Fermatean Fuzzy Structural Equation Model[J]. Acta Armamentarii, 2026, 47(6): 250905. DOI： 10.12382/bgxb.2025.0905.

摘要

针对航空发动机质量评估中不确定性信息处理不足与模型易陷局部最优的问题，提出一种融合Fermatean模糊结构方程模型（Structural Equation Modeling，SEM）与粒子群优化（Particle Swarm Optimization，PSO）的评估方法。基于输入-过程-输出-环境（Input-Process-Output-Environment，IPO

E）模型构建含16项指标的评估体系，其中含3项模糊指标；采用Fermatean模糊集理论处理模糊指标，结合专家打分完成去模糊化转换，并在此基础上构建Fermatean模糊SEM；引入PSO算法优化模型参数，提升模型的拟合度与解释力。以56台涡扇发动机数据为样本，与传统结构方程模型、层次分析法-逼近理想解排序（Analytic Hierarchy Process-Technique for Order Preference by Similarity to an Ideal Solution，AHP-TOPSIS）法、BP神经网络三类典型方法进行对比验证。研究结果表明：所提方法近似误差均方根（Root Mean Square Error of Approximation，RMSEA）为0.032、比较拟合指数（Comparative Fit Index，CFI）为0.99、评估准确度

=0.89，维修优先级识别准确率90.9%，留一交叉验证变异系数0.074，均优于对比方法；该方法能够有效处理航空发动机质量评估中的模糊性与复杂性，为装备质量管控与维修决策提供科学依据。

Abstract

To address the issues of insufficient uncertainty information processing and local optimum entrapment in aero-engine quality assessment

an evaluation method integrating the Fermatean fuzzy structural equation model with the particle swarm optimization (PSO) algorithm is proposed. Firstly

an assessment system with 16 indicators

including 3 fuzzy indicators

is established based on the inputprocess-output-environment (IPO&E) model. Secondly

the Fermatean fuzzy set theory is employed to process the fuzzy indicators

and the defuzzification is completed through expert scoring

and on this basis

a Fermatean fuzzy structural equation model is constructed. Finally

the PSO algorithm is introduced for global optimization of model parameters to enhance the fitness and explanatory power of model. Using data from 56 turbofan engines as samples

a comparative validation is conducted against the traditional structural equation model

the analytic hierarchy process-technique for order preference by similarity to an ideal solution (AHP-TOPSIS) and the BP neural network. The results indicate that the proposed method achieves a root mean square error of approximation (RMSEA) of 0.032

a comparative fit index (CFI) of 0.99

the assessment accuracy of 0.89

the maintenance priority identification accuracy of 90.9%

and the leave-one-out cross-validation coefficient of variation of 0.074

all outperforming the comparative methods. The proposed method effectively handles the fuzziness and complexity in aero-engine quality assessment

providing a scientific basis for equipment quality control and maintenance decision-making.

关键词

Keywords

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