有限元模型修正中的贝叶斯深度神经网络构架优化设计

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (6) : 184-190.

土木工程

有限元模型修正中的贝叶斯深度神经网络构架优化设计

何宇轩，尹涛*，王曦

作者信息 +

Architecture design of the Bayesian deep neural network in structural model updating

HE Yuxuan,YIN Tao*,WANG Xi

Author information +

文章历史 +

摘要

贝叶斯神经网络（BNN）相较于传统人工神经网络具有更强的噪声鲁棒性，在结构系统识别与健康监测领域逐渐受到关注，目前该领域的相关文献主要集中于单隐含层BNN的应用及其构架设计。具有一定深度的多隐含层构架相比于单隐含层在复杂高维数据拟合上通常具有更强的泛化能力，但针对多隐含层BNN构架优化设计问题的研究目前尚未见报道。本文旨在针对多隐含层BNN并结合有限元模型修正问题开展构架优化设计研究，发展基于证据对数的多隐含层BNN网络性能定量量度，并提出一种实现多隐含层BNN各隐含层神经元数量同步优化的高效算法，获得针对具体模型修正问题的多隐含层BNN构架优化设计方案。通过基于现场实测模态参数的某大跨度钢结构人行桥模型修正验证了所提出方法的正确性和有效性。

Abstract

Bayesian Neural Network (BNN) generally has stronger noise robustness than ordinary neural networks, and has gradually attracted attention in the fields of structural system identification and health monitoring. Currently, relevant literature in this field mainly focuses on the application and architecture design of single-hidden-layer BNN. Multi-hidden-layer architectures with a certain depth usually have stronger generalization capabilities in fitting complex high-dimensional data than single-hidden-layer ones, but research on the optimal design of multi-hidden-layer BNN architectures has not yet been reported in the current literature. This paper aims to carry out optimal architecture design on multi-hidden-layer BNN combined with finite element (FE) model updating problems. A quantitative measure of multi-hidden-layer BNN performance based on evidence logarithm is developed, and an efficient algorithm is also proposed to simultaneously configure the number of neurons in each hidden layer to achieve an optimal architecture design solution of multi-hidden-layer BNN for model updating problems. The correctness and effectiveness of the proposed method are verified by refining the initial FE model of a large-span steel pedestrian bridge utilizing field measured data.

导出引用

何宇轩, 尹涛, 王曦. 有限元模型修正中的贝叶斯深度神经网络构架优化设计[J]. 振动与冲击, 2025, 44(6): 184-190

HE Yuxuan, YIN Tao, WANG Xi. Architecture design of the Bayesian deep neural network in structural model updating[J]. Journal of Vibration and Shock, 2025, 44(6): 184-190

参考文献

[1] IMREGUN M. A review of model updating techniques [J]. Shock and Vibration digest, 1991, 23(1): 9-20.
[2] 翁顺, 朱宏平. 基于有限元模型修正的土木结构损伤识别方法 [J]. 工程力学, 2021, 38(3): 1-16.
WENG S, ZHU H P. Damage identification of civil structures based on finite element model updating [J]. Engineering Mechanics, 2021, 38(3): 1-16.
[3] YIN T, ZHU H P. An efficient algorithm for architecture design of Bayesian neural network in structural model updating [J]. Computer‐Aided Civil and Infrastructure Engineering, 2020, 35(4): 354-72.
[4] 赵敏龙,彭珍瑞,张亚峰.基于Kriging模型和无迹卡尔曼滤波的转向架构架模型修正[J].振动与冲击,2022,41(04):270-277.
ZHAO Minlong,PENG Zhenrui,ZHANG Yafeng.Model updating of a bogie frame based on the Kriging model and the unscented Kalman filter[J].Journal of Vibration and Shock,2022,41(04):270-277.
[5] 李波, 屈文忠, 曾又林. 基于有限元模型修正技术的结构损伤检测[J]. 武汉大学学报（工学版）,2008,41(5):102-105. 2008.
LI B, QU W Z, ZENG Y L. Research on structural damage detection based on finite element modal updating[J].Engineering Journal of Wuhan University,2008,41(5):102-105.
[6] LAM H, KO J, WONG C. Localization of damaged structural connections based on experimental modal and sensitivity analysis [J]. Journal of sound and vibration, 1998, 210(1): 91-115.
[7] ZHENG Z, LU Z, CHEN W, et al. Structural damage identification based on power spectral density sensitivity analysis of dynamic responses [J]. Computers & Structures, 2015, 146: 176-84.
[8] ZHU T, TIAN W, WENG S, et al. Sensitivity-based finite element model updating using dynamic condensation approach [J]. International Journal of Structural Stability and Dynamics, 2018, 18(08): 1840004.
[9] YUEN K V, BECK J L, KATAFYGIOTIS L S. Efficient model updating and health monitoring methodology using incomplete modal data without mode matching [J]. Structural Control and Health Monitoring: The Official Journal of the International Association for Structural Control and Monitoring and of the European Association for the Control of Structures, 2006, 13(1): 91-107.
[10] 王修勇, 陈政清. 基于柔度矩阵和神经网络的结构损伤识别法 [J]. 机械强度, 2002, 24(2): 164-7.
WANG X Y, CHEN Z Q. Approach of structural damage detection based on flexibility and neural network technique [J]. Journal of Mechanical Strength, 2002, 24(2): 164-7.
[11] 李永梅, 周锡元, 高向宇. 基于柔度差曲率矩阵的结构损伤识别方法 [J]. 工程力学, 2009, (2): 188-95.
LI Y M, ZHOU X Y, GAO X Y. Detection indictor of structural nondestructive damage based on curvature-flexibility-difference matrix [J]. Engineering Mechanics, 2009, (2): 188-95.
[12] 邱飞力, 张立民, 张卫华. 基于模态柔度矩阵的结构损伤识别 [J]. 噪声与振动控制, 2015, 35(4): 101-6.
QIU F L, ZHANG L M, ZHANG W H. Structure damage detection based on modal flexibility matrix [J]. Noise and Vibration Control, 2015, 35(4): 101-6.
[13] YE X, JIN T, YUN C. A review on deep learning-based structural health monitoring of civil infrastructures [J]. Smart Struct Syst, 2019, 24(5): 567-85.
[14] 马亚飞,李诚,何羽,等.基于小波散射卷积神经网络的结构损伤识别[J].振动与冲击,2023,42(14):138-146.DOI:10.13465/j.cnki.jvs.2023.14.016.
MA Yafei,LI Cheng,HE Yu, et al.Structural damage identification based on the wavelet scattering convolution neural network[J].Journal of Vibration and Shock,2023,42(14):138-146.
[15] BISHOP C M, NASRABADI N M. Pattern recognition and machine learning [M]. Springer, 2006.
[16] LAM H F, NG C T. The selection of pattern features for structural damage detection using an extended Bayesian ANN algorithm [J]. Engineering Structures, 2008, 30(10): 2762-70.
[17] LAM H F, YUEN K V, BECK JL. Structural health monitoring via measured Ritz vectors utilizing artificial neural networks [J]. Computer‐Aided Civil and Infrastructure Engineering, 2006, 21(4): 232-41.
[18] YIN T, ZHU H P. Probabilistic damage detection of a steel truss bridge model by optimally designed Bayesian neural network [J]. Sensors, 2018, 18(10): 3371.