基于贝叶斯融合理论和CART-DT的梁结构损伤识别

兰州理工大学学报 ›› 2026, Vol. 52 ›› Issue (2): 119-128.

基于贝叶斯融合理论和CART-DT的梁结构损伤识别

项长生^*1, 刘海龙¹, 周宇², 刘辰雨¹

1.兰州理工大学土木与水利工程学院, 甘肃兰州 730050;
2.安徽建筑大学土木工程学院, 安徽合肥 230601

收稿日期:2022-09-24 出版日期:2026-04-28 发布日期:2026-04-28
通讯作者: 项长生(1976-),男,安徽安庆人,博士,副教授. Email:xiangcs@lut.edu.cn
基金资助:
国家自然科学基金(51868045),甘肃省科技创新人才计划项目(25RCKA014)

Damage identification of beam structures based on bayesian fusion theory and CART-DT

XIANG Chang-sheng¹, LIU Hai-long¹, ZHOU Yu², LIU Chen-yu¹

1. School of Civil and Hydraulic Engineering, Lanzhou University of Technology, Lanzhou 730050, China;
2. School of Civil Engineering, Anhui Jianzhu University, Hefei 230601, China

Received:2022-09-24 Online:2026-04-28 Published:2026-04-28

摘要/Abstract

摘要： 为提高梁结构损伤识别的可靠性,融合贝叶斯理论与分类回归决策树(CART-DT)算法,提出一种损伤识别方法.在传统模态应变能及模态应变能曲率差(MSECD)指标基础上,构建改进模态应变能(IMSE)与改进模态应变能曲率差(IMSECD)指标,并进行相关误差分析.通过ANSYS软件建立简支梁模型,分别采用MSECD、IMSECD、贝叶斯融合方法及CART-DT算法开展损伤识别分析,并完成模型试验验证.结果表明:IMSECD指标具有更高的损伤定位精度与抗噪性能;基于贝叶斯数据融合的方法可综合多阶模态指标识别结果,有效降低非损伤位置的干扰,提升定位准确性;基于CART-DT算法的方法在10%噪声以内损伤程度识别准确率保持在80%以上;在试验与噪声影响下,所提方法仍表现出良好的鲁棒性,能够有效识别简支梁结构的损伤位置.

关键词: 梁结构, 损伤识别, 改进模态应变能, 贝叶斯数据融合理论, CART-DT算法

Abstract: To improve the reliability of beam structure damage identification, a damage identification method integrating Bayesian theory and the classification and regression tree (CART-DT) algorithm is proposed. Based on traditional modal strain energy and modal strain energy curvature difference (MSECD) indicators, improved modal strain energy (IMSE) and improved modal strain energy curvature difference (IMSECD) indicators are developed, accompanied by an error analysis. A simply supported beam model is established using ANSYS software, and damage identification analyses are conducted using MSECD, IMSECD, Bayesian fusion, and the CART-DT algorithm, followed by experimental validation. The results show that the IMSECD indicator achieves higher damage localization accuracy and better noise resistance. The Bayesian data fusion-based method integrates multi-order modal identification results, effectively reducing interference from non-damage locations and improving localization accuracy. The CART-DT-based method identifies damage severity with an accuracy of over 80% under a noise level of up to 10%. Under testing conditions and measurement noise, the proposed method exhibits strong robustness and effectively identifies damage locations in simply supported beam structures.

Key words: beam structure, damage identification, improved modal strain energy, bayesian data fusion theory, CART-DT algorithm

中图分类号:

TU311

项长生, 刘海龙, 周宇, 刘辰雨. 基于贝叶斯融合理论和CART-DT的梁结构损伤识别[J]. 兰州理工大学学报, 2026, 52(2): 119-128.

XIANG Chang-sheng, LIU Hai-long, ZHOU Yu, LIU Chen-yu. Damage identification of beam structures based on bayesian fusion theory and CART-DT[J]. Journal of Lanzhou University of Technology, 2026, 52(2): 119-128.

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链接本文: https://journal.lut.edu.cn/CN/

https://journal.lut.edu.cn/CN/Y2026/V52/I2/119

参考文献

[1] 张青霞,ĿUKASZ J.基于移动质量-频率曲线的结构损伤识别方法 [J].中国测试,2019,45(3):1-6.
[2] 项长生,李凌云,周宇,等.基于模态曲率效用信息熵的梁结构损伤识别 [J].振动与冲击,2020,39(17):234-244.
[3] 唐盛华,罗承芳,方志,等.基于柔度矩阵曲率范数差的结构损伤识别方法 [J].应用力学学报,2020,37(3):982-989.
[4] 梁振彬,董聪.考虑质量变化的刚架结构损伤识别方法研究 [J].计算力学学报,2018,35(3):321-325.
[5] 梁振彬,董聪,张华昕.基于修正模态应变能指标的板结构损伤定位 [J].力学与实践,2017,39(6):585-590.
[6] 彭伟强.环境激励下基于应变模态的结构损伤识别方法研究 [D].大连:大连理工大学,2019.
[7] 项长生,原子,周宇.基于广义局部曲率模态信息熵和BF神经网络的结构损伤识别方法 [J].兰州理工大学学报,2021,47(1):129-135.
[8] 史治宇,罗绍湘,张令弥.结构破损定位的单元模态应变能变化率法 [J].振动工程学报,1998,11(3):356-360.
[9] 周计祥,吴邵庆,董萼良,等.基于应变模态的模态应变能损伤识别方法 [J].振动·测试与诊断,2019,39(1):25-31.
[10] 伍晓顺,夏巨伟,胡岳芳.基于跨模型模态应变能指标的网架结构损伤定位 [J].浙江大学学报(工学版),2020,54(2):248-256.
[11] 卫军,杜永潇,吴志强,等.基于模态应变能和Bayes理论的梁结构损伤识别 [J].铁道科学与工程学报,2019,16(8):2052-2061.
[12] 孙爽,梁力,李明,等.基于动力指纹和Bayes数据融合的桥梁损伤识别 [J].东北大学学报(自然科学版),2017,38(2):290-294.
[13] 李有堂,汤雷武,黄华,等.基于优化最小二乘支持向量机的数控机床热误差建模分析 [J].兰州理工大学学报,2022,48(3):35-41.
[14] LI X,MA Y,ZHU J J.An online dual filters RUL prediction method of lithium-ion battery based on unscented particle filter and least squares support vector machine [J].Measurement,2021,184:109935.
[15] 曾滨,周臻,张庆方,等.基于数据融合的张弦桁架损伤识别方法与试验研究 [J].土木工程学报,2020,53(8):28-37.
[16] 任娟娟,杜威,LIU J,等.基于指标融合的浮置板道床钢弹簧损伤识别 [J].华中科技大学学报(自然科学版),2021,49(11):95-100.
[17] 刘涛,李爱群,缪长青,等.基于数据融合的结构损伤识别方法研究 [J].工程力学,2008,25(1):16-21.
[18] HIDAYAT A A,PARDAMEAN B.A bayesian-based approach for extracting the pion charge radius from electron-electron scattering data [J].Chinese Physics C,2021,45(8):083101.
[19] 李红蕾,陈石,庄建仓,等.多源布格重力异常数据贝叶斯融合算法及其在川滇地区的应用 [J].地球物理学报,2021,64(9):3232-3245.
[20] 李雪艳,刘力菖.利用振动响应协方差参数和数据融合的损伤识别方法 [J].振动工程学报,2021,34(1):141-149.
[21] 朱文会,王夏晖,杨欣桐,等.基于决策树的区域地块风险管控模式预测 [J].中国环境科学,2021,41(12):5771-5778.
[22] 李鹏,雷雨秋,刘宗杰,等.基于决策树算法的断路器弹簧操动机构振动诊断技术 [J].高压电器,2021,57(9):1-8.
[23] 董红召,许慧鹏,卢滨,等.城市交通道路氮氧化物浓度的 CART 回归树预测研究 [J].环境科学学报,2019,39(4):1086-1094.
[24] 丁愫,陈报章,王瑾,等.基于决策树的统计预报模型在臭氧浓度时空分布预测中的应用 [J].环境科学学报,2018,38(8):3229-3242.
[25] 张秀英,孙棋,王珂,等.基于决策树的土壤Zn含量预测 [J].环境科学,2008,29(12):3508-3512.
[26] 庞梦洋,索中英,郑万泽,等.基于RS-CART决策树的航空发动机小样本故障诊断 [J].航空动力学报,2020,35(7):1559-1568.
[27] 马立元,郭俊龙,李永军,等.基于模态应变能曲率差的结构损伤识别方法 [J].海军工程大学学报,2015,27(6):83-86.