基于逆有限元的板壳结构贝叶斯损伤监测方法

陈冰雨; 黄天翔; 袁慎芳

doi:10.7527/S1000-6893.2026.33716

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DOI: https://doi.org/10.7527/S1000-6893.2026.33716

基于逆有限元的板壳结构贝叶斯损伤监测方法

陈冰雨 ,
黄天翔 ,
袁慎芳

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南京航空航天大学

收稿日期: 2026-04-13

修回日期: 2026-08-15

网络出版日期: 2026-08-21

基金资助

国家自然科学基金;江苏省前沿技术研发计划;航空航天结构力学及控制全国重点实验室自主研究课题（南京航空航天大学）;南京航空航天大学前瞻布局科研专项资金;中央高校基本科研业务费

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A Bayesian Approach for Damage Monitoring in Plate Structures Based on the Inverse Finite Element Method

CHEN Bing-Yu ,
HUANG Tian-Xiang ,
YUAN Shen-Fang

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1. Nanjing University of Aeronautics and Astronautics
2.

Received date: 2026-04-13

Revised date: 2026-08-15

Online published: 2026-08-21

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摘要

针对传统基于逆有限元法（inverse Finite Element Method，iFEM）的损伤监测方法难以实现损伤的定量化评估的问题，本文提出一种融合iFEM与贝叶斯统计框架的板壳结构概率化损伤监测方法。方法利用iFEM的应变外推能力，在不同损伤假设下重构损伤邻域的外推应变场，通过构建外推应变与实测应变的似然函数，实现对损伤参数的后验概率评估，从而实现无需依赖健康基准的贝叶斯损伤监测。研究对矩形板和梯形加筋板分别进行仿真建模分析，验证了采用iFEM在位移与应变重构时的平均误差均低于1.0%，并且得出贝叶斯损伤监测方法在识别损伤时的误差小于7.8%。进一步基于不同尺寸损伤的邻域应变变化趋势，研究了网格划分对该方法准确度的影响，仿真结果表明损伤半径和刚度折减系数均会影响损伤监测准确度。研究搭建梯形加筋板的实验平台，验证了该方法在实际工况下的损伤定量化有效性，监测误差小于6.5%，实现了损伤区域的识别、定位与概率化评估。本文所提方法为板壳结构健康监测提供了一种兼具高效性、准确性与工程适用性的损伤评估新途径。

关键词： 结构健康监测; 逆有限元法; 贝叶斯框架; 损伤识别; 板壳结构

本文引用格式

陈冰雨 , 黄天翔 , 袁慎芳 . 基于逆有限元的板壳结构贝叶斯损伤监测方法[J]. 航空学报, 0 : 1 -0 . DOI: 10.7527/S1000-6893.2026.33716

Abstract

To address the challenge that traditional damage monitoring methods based on the inverse Finite Element Method (iFEM) are difficult to achieving quantitative assessment, this paper proposes a probabilistic damage monitoring method for plate structures that combines iFEM with a Bayesian framework. This method uses the strain extrapolation capability of iFEM to reconstruct the extrapolated strain field near the damage under different damage hypotheses. By constructing a likelihood function between the extrapolated and measured strains, it achieves a posterior probability of the damage parameters, thereby achieving Bayesian damage monitoring without a healthy baseline. Simulation analyses were performed on rectangular plates and trapezoidal stiffened plates. The results show that the average errors of displacement and strain reconstruction using iFEM are below 1.0%, and the damage monitoring error is below 7.8%. The simulation results indicate that both the damage radius and the stiffness reduction factor influence the accuracy of damage monitoring.Furthermore, based on the variation of the strain field near damages of different sizes, the influence of mesh discretization on the accuracy of the method was investigated. A test platform for a trapezoidal stiffened plate was built to verify the effectiveness of the method under practical working. The damage monitoring error below 6.5%, achieving identification, localization, and probabilistic assessment of the damage.

Key words： structural health monitoring; inverse finite element method; Bayesian framework; damage monitoring; plate and shell structures

参考文献

[1] 王超凡,周焕林,王选.基于RBF增强直接概率积分法的板壳结构随机屈曲分析[J].航空学报,2026,47(03):206-215.
[2] 王博,郝鹏,田阔,等.航空航天结构轻量化设计与实验方法研究进展[J].宇航学报,2023,44(04):596-606.
[3] 卢文书,马元春,梁伟,等.机身复合材料加筋板壳的稳定性及强度分析系统[J].航空学报,2009,30(05):895-900.
[4] Belur M Y, Kefal A, Abdollahzadeh M A, et al. Damage diagnosis of plates and shells through modal parameters reconstruction using inverse finite-element method[J]. Structural Health Monitoring, 2024:14759217241249678. DOI: 10.1177/14759217241249678.
[5] Kefal A, Diyaroglu C, Yildiz M, et al. Coupling of peridynamics and inverse finite element method for shape sensing and crack propagation monitoring of plate structures[J]. Computer methods in applied mechanics and engineering, 2022, 391:114520. DOI: 10.1016/j.cma.2021.114520.
[6] 孙侠生,肖迎春.飞机结构健康监测技术的机遇与挑战[J].航空学报,2014,35(12):3199-3212.
[7] 田童,李建乐,邓德双,等.飞行器结构健康监测技术研究进展[J].航空制造技术,2024,67(13):41-67+98.DOI:10.16080/j.issn1671-833x.2024.13.041.
[8] SAE. Guidelines for implementation of structural healthmonitoring on fixed wing aircraft：SAE ARP6461A［R］.W arrendale：SAE International，2021.
[9] 袁慎芳,徐秋慧,陈健.可靠性评价：从无损检测到结构健康监测[J].航空学报,2025,46(05):342-362.
[10] 袁慎芳.结构健康监控.北京:国防工业出版社,2007.
[11] Giurgiutiu V, Cuc A, Goodman P. Review of vibration-based helicopters health and usage monitoring methods[J]. 2001.
[12] 耿荣生,景鹏,雷洪,等.飞机主梁疲劳裂纹萌生声发射信号的识别方法[J].航空学报,1996,(03):368-372.
[13] Yang S, Yuan F G. Transient wave propagation of isotropic plates using a higher-order plate theory[J]. International Journal of Solids and Structures, 2005, 42(14): 4115-4153.
[14] 黄尚廉,陈伟民,饶云江,等.光纤应变传感器及其在结构健康监测中的应用[J].测控技术,2004,(05):1-4+8.DOI:10.19708/j.ckjs.2004.05.001.
[15] 王彬文,聂小华,万春华,等.全机静强度虚拟试验技术研究及应用[J].航空学报,2022,43(06):171-183.
[16] 姚卫星,孙文,薛济坤.基于物理原型的结构疲劳寿命评估方法[J].南京航空航天大学学报,2014,46(03):335-340.DOI:10.16356/j.1005-2615.2014.03.003.
[17] 芦吉云,梁大开,潘晓文.基于准分布式光纤光栅传感器的机翼盒段载荷监测[J].南京航空航天大学学报,2009,41(02):217-221.DOI:10.16356/j.1005-2615.2009.02.026.
[18] Tessler A,Spangler J L. A least-squares variational method for full-field reconstruction of elastic deformations in shear-deformable plates and shells[J]. Com-puter Methods in Applied Mechanics and Engineering，2005，194(2/3/4/5):327-339. DOI:10.1016/jcma.2004.03.015.
[19] Kefal, A.; Emami, I.; Yildiz, M.; Tessler, A. A Smoothed IFEM Approach for Efficient Shape-Sensing Applications: Numerical and Experimental Validation on Composite Structures. Mech. Syst. Signal Process. 2021, 152, 107486.
[20] Kefal A ,Oterkus E ,Tessler A , et al.A quadrilateral inverse-shell element with drilling degrees of freedom for shape sensing and structural health monitoring[J].Engineering Science and Technology, an International Journal,2016,19(3):1299-1313.DOI:10.1016/j.jestch.2016.03.006.
[21] Kefal A .An efficient curved inverse-shell element for shape sensing and structural health monitoring of cylindrical marine structures[J].Ocean Engineering,2019,188106262-106262.DOI:10.1016/j.oceaneng.2019.106262.
[22] Khalid I, Qureshi Z A, Ali Y, et al. Structural health monitoring of shell structures with preexisting cracks[J]. Mechanical Systems and Signal Processing, 2025, 231:112663. DOI: 10.1016/j.ymssp.2025.112663.
[23] 张科,袁慎芳,任元强,等.基于逆向有限元法的变形机翼鱼骨的变形重构[J].航空学报,2020,41(08):250-260.
[24] 顾叶青,操卫忠,袁慎芳,等.热载荷下星载天线逆有限元变形重构方法[J].东南大学学报(自然科学版),2024,54(04):997-1004.
[25] 付书山,孙广开,何彦霖,等.基于逆有限元的机翼蒙皮变形监测方法仿真研究[J].航空制造技术,2022,65(06):107-114.DOI:10.16080/j.issn1671-833x.2022.06.107.
[26] Quach C, Vazquez S, Tessler A, et al. Structural Anomaly Detection Using Fiber Optic Sensors and Inverse Finite Element Method[R]:NASA, 2005.
[27] Colombo L, Sbarufatti C, Giglio M. Definition of a load adaptive baseline by inverse finite element method for structural damage identification[J]. Mechanical Systems and Signal Processing, 2019, 120:584–607. https://www.sciencedirect.com/science/article/pii/S0888327018307179. DOI: 10.1016/j.ymssp.2018.10.041.
[28] Li M ,Kefal A ,Cerik C B , et al.Dent damage identification in stiffened cylindrical structures using inverse Finite Element Method[J].Ocean Engineering,2020,198106944-106944.DOI:10.1016/j.oceaneng.2020.106944.
[29] Ghasemzadeh M, Mokhtari M, Bilgin M H, et al. Pitting corrosion identification approach based on inverse finite element method for marine structure applications[J]. Ocean Engineering, 2023, 273:113953. https://www.sciencedirect.com/science/article/pii/S0029801823003372. DOI: 10.1016/j.oceaneng.2023.113953.
[30] Oboe D, Poloni D, Sbarufatti C, et al. Towards Automatic Crack Size Estimation with iFEM for Structural Health Monitoring[J]. Sensors (Basel, Switzerland), 2023, 23(7). DOI: 10.3390/s23073406.
[31] Zhao L, You R, Ren L. Inverse finite element method and support vector regression for automated crack detection with OFDR-Distributed fiber optic sensors[J]. Measurement, 2024, 234:114916.https://www.sciencedirect.com/science/article/pii/S0263224124008017. DOI: 10.1016/j.measurement.2024.114916.
[32] Zhao L, Zhang J, You R, et al. Automatic detection of crack depth and width combining inverse finite-element and PSO-optimized SVR method with OFDR fiber-optic sensors[J]. Structural Health Monitoring, 2025:14759217251327728. DOI: 10.1177/14759217251327728.
[33] Belur M Y, Kefal A, Abdollahzadeh M A, et al. Damage diagnosis of plates and shells through modal parameters reconstruction using inverse finite-element method[J]. Structural Health Monitoring, 2024:14759217241249678. DOI: 10.1177/14759217241249678.
[34] Huang T ,Schr?der K .A Bayesian probabilistic approach for damage identification in plate structures using responses at vibration nodes[J].Mechanical Systems and Signal Processing,2021,146DOI:10.1016/j.ymssp.2020.106998.

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