不同结构复杂度下结合集成学习的模型修正方法

林光伟; 张熠

doi:10.6052/j.issn.1000-4750.2021.05.S030

不同结构复杂度下结合集成学习的模型修正方法

doi: 10.6052/j.issn.1000-4750.2021.05.S030

林光伟,
张熠^,

清华大学土木工程系，北京 100084

基金项目: 国家自然科学基金项目(51908324，52111540161)

详细信息

作者简介:
林光伟(1999−)，男，宁夏人，博士生，主要从事防灾减灾研究(E-mail: lin-gw19@mails.tsinghua.edu.cn)

通讯作者:
张　熠(1987−)，男，湖北人，副教授，博士，博导，主要从事防灾减灾研究(E-mail: zhang-yi@tsinghua.edu.cn)

中图分类号: TP181；TU31
计量
- 文章访问数: 76
- HTML全文浏览量: 36
- PDF下载量: 27
- 被引次数: 0
出版历程
- 收稿日期: 2021-05-30
- 修回日期: 2022-02-22
- 网络出版日期: 2022-03-11
- 刊出日期: 2022-06-06

EFFICIENT MODEL UPDATING APPROACHES INTEGRATING ENSEMBLE LEARNING METHODS FOR DIFFERENT STRUCTURAL COMPLEXITY

LIN Guang-wei,
ZHANG Yi^,

Department of Civil Engineering, Tsinghua University, Beijing 100084, China

摘要

摘要: 模型不确定性不可避免地影响到数值模型分析精度和可靠性，需要找到一种合适的方法，根据实测数据对模型参数值进行修正。该研究采用结合了过渡马尔科夫链蒙特卡罗(TMCMC)方法的贝叶斯模型修正理论对结构模型参数进行修正。采用Kriging法和多项式混沌展开法(PCE)构造代理模型。将该修正方法应用于两个不同结构复杂度的实例，这两个模型分别代表高维线性模型和非线性模型。在两个实例下验证了代理模型的有效性和准确性，讨论了基于代理模型的修正方法在不同结构复杂度下的优缺点。针对代理模型存在的不足，提出了一种代理集成学习框架进行改进。
- 模型修正 /
- 贝叶斯推断 /
- 结构复杂度 /
- 马尔科夫蒙特卡洛采样 /
- Kriging代理模型 /
- 多项式混沌展开 /
- 集成学习
Abstract: Model uncertainty inevitably affects the accuracy and reliability of numerical model-based analysis. It is necessary to obtain an appropriate updating method which could determine the reasonable values of model parameter from measurements. A Bayesian model updating method is proposed combined with the transitional Markov chain Monte Carlo (TMCMC). Kriging predictor and polynomial chaos expansion (PCE) are utilized to construct surrogate models to reduce the computational burden. The proposed model updating methods are applied to two structural examples with different complexity, which stand for the high-dimensional linear model and the high-dimensional nonlinear model, respectively. The validity and accuracy of two surrogate models are investigated in the numerical examples. The advantages and limitations of the surrogate models-based updating approaches are also discussesed for different structural complexity. For the deficiency of surrogate models, it proposes an ensemble learning method to improve the model updating.
- model updating /
- Bayesian inference /
- structural complexity /
- Markov chain Monte Carlo /
- Kriging /
- polynomial chaos expansion /
- ensemble learning

HTML全文

图 1 不同方法下结构特征的对比

Figure 1. Comparison of features in different methods

下载: 全尺寸图片幻灯片

图 2 国家体育场有限元模型

Figure 2. Finite element model of the National Stadium

下载: 全尺寸图片幻灯片

表 1 十层框架中待修正参数的描述

Table 1. Description of updated parameters in ten-storey frame

参数	真实值	变异系数	先验分布	区间
θ₁	1.5	0.01	均匀分布	[0,3]
θ₂~θ₉	1.0	0.01	均匀分布	[0,3]

下载: 导出CSV

表 2 十层框架的待修正参数(括号内为误差百分比)

Table 2. Updated parameters in ten-storey frame (% errors in parenthesis)

参数	聚类前			聚类后
参数	解析法	Kriging法	PCE法	解析法	Kriging法	PCE法
θ₁	1.92 (28.0)	1.68 (12.8)	1.97 (38.1)	1.60 (6.5)	1.48 (2.5)	1.55 (3.4)
θ₂	1.15 (15.0)	0.96 (−3.7)	1.09 (8.6)	0.94 (−5.5)	0.93 (6.6)	1.07 (6.8)
θ₃	1.02 (1.9)	1.00 (0.1)	0.97 (−2.6)	1.12 (11.7)	0.98 (2.1)	0.91 (−8.8)
θ₄	0.90 (−10.1)	1.01 (0.7)	1.06 (−5.9)	0.93 (−6.7)	1.05 (4.3)	0.97 (−3.2)
θ₅	1.04 (3.6)	1.05 (4.7)	1.06 (6.4)	1.01 (1.0)	1.04 (4.4)	0.97 (−2.7)
θ₆	1.00 (0.2)	1.06 (6.1)	1.15 (15.4)	0.99 (−0.8)	1.01 (1.1)	0.89 (−9.6)
θ₇	0.98 (−2.4)	1.02 (2.7)	1.11 (10.5)	0.99 (−0.8)	1.03 (2.6)	0.93 (−6.8)
θ₈	1.03 (3.2)	1.06 (5.9)	1.22 (22.5)	0.94 (−6.4)	1.04 (3.8)	0.90 (−9.7)
θ₉	1.00 (−0.3)	1.06 (6.2)	1.03 (3.0)	0.91 (−9.2)	1.08 (7.6)	1.06 (5.7)
θ₁₀	0.96 (−3.8)	1.24 (23.5)	1.25 (24.5)	0.96 (−3.5)	1.07 (6.6)	1.11 (10.7)

下载: 导出CSV

表 3 十层框架中的特征修正结果

Table 3. Updated features in ten-storey frame

参数	实测值	解析模型		Kriging模型		PCE模型
参数	实测值	修正值	误差/(%)	修正值	误差/(%)	修正值	误差/(%)
f₁	1.58	1.57	−0.2	1.60	0.4	1.59	0.2
f₂	4.70	4.69	−0.1	4.85	3.3	4.73	0.7
f₃	7.71	7.78	1.1	7.72	0.2	7.84	1.9
f₄	10.51	10.57	0.6	10.67	1.5	10.76	2.3
f₅	13.08	13.40	2.5	13.35	2.2	13.36	2.2
f₆	15.31	15.72	2.7	16.07	5.0	15.75	3.0
f₇	17.16	17.23	0.3	17.70	3.1	17.71	3.2
f₈	18.62	18.92	1.6	19.25	3.5	19.14	2.8
f₉	19.65	19.76	0.6	20.44	4.0	20.30	3.3
f₁₀	20.24	20.11	−0.7	20.69	2.1	20.40	1.3

下载: 导出CSV

表 4 十层框架中集成前后的修正参数(括号内为误差百分比)

Table 4. Updated parameters before and after ensemble in ten-storey frame (% errors in parenthesis)

待修正参数	Kriging模型	PCE模型	集成模型
θ₁	1.68 (12.8)	1.97 (38.1)	1.55 (3.4)
θ₂	0.96 (−3.7)	1.09 (8.6)	1.07 (6.8)
θ₃	1.00 (0.1)	0.97 (−2.6)	0.91 (−8.8)
θ₄	1.01 (0.7)	1.06 (−5.9)	0.97 (−3.2)
θ₅	1.05 (4.7)	1.06 (6.4)	0.97 (−2.7)
θ₆	1.06 (6.1)	1.15 (15.4)	0.89 (−9.6)
θ₇	1.02 (2.7)	1.11 (10.5)	0.93 (−6.8)
θ₈	1.06 (5.9)	1.22 (22.5)	0.90 (−9.7)
θ₉	1.06 (6.2)	1.03 (3.0)	1.06 (5.7)
θ₁₀	1.24 (23.5)	1.25 (24.5)	1.07 (6.8)

下载: 导出CSV

表 5 鸟巢中待修正参数的描述

Table 5. Description of updated parameters in the National Stadium

参数	先验分布	区间	备注	真实值
θ₁	均匀分布	[μ−0.5, μ+0.5]	μ ϵ {1.05, 1.30, 1.50, 1.75, 2.00}	1.75
θ₂	均匀分布	[μ−0.5, μ+0.5]	μ ϵ {1.05, 1.30, 1.50, 1.75, 2.00}	1.75

下载: 导出CSV

表 6 鸟巢中待修正参数(括号内为误差百分比)

Table 6. Updated parameters in the National Stadium (% errors in parenthesis)

先验均值μ	1.05		1.30		1.50		1.75		2.00
参数	θ₁	θ₂	θ₁	θ₂	θ₁	θ₂	θ₁	θ₂	θ₁	θ₂
Kriging模型	1.89 (8.0)	1.80 (2.8)	1.85 (5.6)	1.83 (4.5)	1.85 (5.6)	1.81 (3.4)	1.83 (4.5)	1.82 (4.0)	1.93 (11.2)	1.94 (10.9)
PCE模型	1.87 (6.8)	1.70 (−3.1)	1.82 (4.1)	1.67 (−4.6)	1.85 (5.7)	1.66 (−5.1)	1.72 (−1.5)	1.74 (−0.6)	1.94 (11.3)	1.72 (−1.6)

下载: 导出CSV

表 7 鸟巢中特征修正结果(括号内为误差百分比)

Table 7. Updated features in the National Stadium (% errors in parenthesis)

变量	初始值	Kriging模型	PCE模型	集成模型
f₁/Hz	1.118	1.109 (−0.81)	1.113 (−0.45)	1.114 (−0.37)
f₂/Hz	1.133	1.129 (−0.48)	1.128 (−0.44)	1.129 (−0.35)
f₃/Hz	1.270	1.271 (0.06)	1.265 (−0.37)	1.272 (−0.16)
f₄/Hz	1.838	1.823 (−0.81)	1.830 (−0.44)	1.829 (−0.49)
f₅/Hz	1.964	1.948 (−0.79)	1.956 (−0.43)	1.962 (−0.10)

下载: 导出CSV

表 8 鸟巢中集成前后的修正参数(括号内为误差百分比)

Table 8. Updated parameters before and after ensemble in the National Stadium (% errors in parenthesis)

变量	Kriging模型	PCE模型	集成模型
θ₁	1.83 (4.5)	1.72 (−1.5)	1.75 (0.4)
θ₂	1.82 (4.0)	1.74 (−0.6)	1.74 (−0.6)

下载: 导出CSV

参考文献(15)

[1]	Mottershead J E, Friswell M I. Model Updating In Structural Dynamics: A Survey [J]. Journal of Sound & Vibration, 1993, 167(2): 347 − 375.
[2]	Liang Y, Feng Q, Li H. Damage detection of shear buildings using frequency-change-ratio and model updating algorithm [J]. Smart Structures and Systems, 2019, 23(2): 107 − 122.
[3]	Zhang F L, Yang Y P, Ye X W. Structural modal identification and MCMC-based model updating by a Bayesian approach [J]. Smart Structures and Systems, 2019, 24(5): 631 − 639.
[4]	Ching J, Muto M, Beck J L . Structural model updating and health monitoring with incomplete modal data using Gibbs sampler [J]. Computer‐Aided Civil and Infrastructure Engineering, 2006, 21(4): 242 − 257. doi: 10.1111/j.1467-8667.2006.00432.x
[5]	Yu E, Lan C. Seismic damage detection of a reinforced concrete structure by finite element model updating [J]. Smart Structures & Systems, 2012, 9(3): 253 − 271.
[6]	姜东, 吴邵庆, 史勤丰, 费庆国. 基于薄层单元的螺栓连接结构接触面不确定性参数识别[J]. 工程力学, 2015, 32(4): 220 − 227. doi: 10.6052/j.issn.1000-4750.2013.10.0920 Jiang Dong, Wu Shaoqing, Shi Qinfeng, Fei Qingguo. Contact interface parameter identification of bolted structure with uncertainty using thin layer element method [J]. Engineering Mechanics, 2015, 32(4): 220 − 227. (in Chinese) doi: 10.6052/j.issn.1000-4750.2013.10.0920
[7]	韩建平, 骆勇鹏, 郑沛娟, 刘云帅. 基于响应面的刚构-连续组合梁桥有限元模型修正[J]. 工程力学, 2013, 30(12): 85 − 90. doi: 10.6052/j.issn.1000-4750.2012.04.0276 Han Jianping, Luo Yongpeng, Zheng Peijuan, Liu Yunshuai. Finite element model updating for a rigid frame-continuous girders bridge based on response surface method [J]. Engineering Mechanics, 2013, 30(12): 85 − 90. (in Chinese) doi: 10.6052/j.issn.1000-4750.2012.04.0276
[8]	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. doi: 10.6052/j.issn.1000-4750.2020.06.ST02 Weng Shun, Zhu Hongping. Damage identification of civil structures based on finite element model updating [J]. Engineering Mechanics, 2021, 38(3): 1 − 16. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.06.ST02
[9]	刘纲, 罗钧, 秦阳, 张建新. 基于改进MCMC方法的有限元模型修正研究[J]. 工程力学, 2016, 33(6): 138 − 145. doi: 10.6052/j.issn.1000-4750.2014.10.0887 Liu Gang, Luo Jun, Qin Yang, Zhang Jianxin. A finite element model updating method based on improved mcmc method [J]. Engineering Mechanics, 2016, 33(6): 138 − 145. (in Chinese) doi: 10.6052/j.issn.1000-4750.2014.10.0887
[10]	夏志远, 李爱群, 李建慧, 陈鑫. 基于GMPSO的有限元模型修正方法验证[J]. 工程力学, 2019, 36(10): 66 − 74. doi: 10.6052/j.issn.1000-4750.2018.09.0506 Xia Zhiyuan, Li Aiqun, Li Jianhui, Chen Xin. Validation of finite element model updating methodology based on GMPSO [J]. Engineering Mechanics, 2019, 36(10): 66 − 74. (in Chinese) doi: 10.6052/j.issn.1000-4750.2018.09.0506
[11]	Ewins D J . Modal Testing, Theory, Practice and Application [M]. New York: John Wiley & Sons, 2009.
[12]	Feng Z, Y Lin, Wang W, et al. Probabilistic Updating of Structural Models for Damage Assessment Using Approximate Bayesian Computation [J]. Sensors (Basel, Switzerland), 2020, 20(11): 3197.
[13]	Zhou Y, Lu Z. An enhanced Kriging surrogate modeling technique for high-dimensional problems [J]. Mechanical Systems and Signal Processing, 2020, 140: 106687. doi: 10.1016/j.ymssp.2020.106687
[14]	Jacquelin E, Friswell M I, Adhikari S, et al. Polynomial chaos expansion with random and fuzzy variables [J]. Mechanical Systems and Signal Processing, 2016, 75: 41 − 56. doi: 10.1016/j.ymssp.2015.12.001
[15]	He W, Hao P, Li G. A novel approach for reliability analysis with correlated variables based on the concepts of entropy and polynomial chaos expansion [J]. Mechanical Systems and Signal Processing, 2021, 146: 106980.