基于贝叶斯理论的非线性结构模型修正及其动力可靠度分析

丁雅杰; 王佐才; 辛宇; 戈壁; 袁子青

doi:10.6052/j.issn.1000-4750.2021.07.0556

基于贝叶斯理论的非线性结构模型修正及其动力可靠度分析

doi: 10.6052/j.issn.1000-4750.2021.07.0556

丁雅杰^1,,
王佐才^{1, 2, 3, ,},
辛宇^{1, 3,},
戈壁^1,,
袁子青^1,

1.
合肥工业大学土木与水利工程学院，安徽，合肥 230009
2.
土木工程防灾减灾安徽省工程技术研究中心，安徽，合肥 230009
3.
安徽省基础设施安全检测与监测工程实验室，安徽，合肥 230009

基金项目: 国家自然科学基金优秀青年科学基金项目(51922036)；安徽省重点研发计划项目(1804a0802204)；中央高校基本科研业务费专项资金项目(JZ2020HGPB0117)

详细信息

作者简介:
丁雅杰(1991−)，男，安徽滁州人，博士生，从事非线性结构模型修正及其参数不确定性分析研究(E-mail: dingyajie@mail.hfut.edu.cn)

辛　宇(1991−)，男，安徽蚌埠人，博士，主要从事桥梁健康监测方面研究(E-mail: 2020800133@hfut.edu.cn)

戈　壁(1990−)，男，安徽六安人，博士生，主要从事桥梁健康监测方面研究(E-mail: gebi@mail.hfut.edu.cn)

袁子青(1997−)，女，甘肃兰州人，博士生，主要从事桥梁健康监测方面研究(E-mail: 2019110605@mail.hfut.edu.cn)

通讯作者:
王佐才(1982−)，男，湖南双峰人，教授，博士，博导，主要从事桥梁健康监测方面研究(E-mail: wangzuocai@hfut.edu.cn)

中图分类号: TU311
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- 被引次数: 0
出版历程
- 收稿日期: 2021-07-20
- 修回日期: 2021-09-19
- 网络出版日期: 2021-09-30
- 刊出日期: 2022-12-01

BAYESIAN-BASED NONLINEAR MODEL UPDATING AND DYNAMIC RELIABILITY ANALYSIS

DING Ya-jie^1
,,
WANG Zuo-cai^{1, 2, 3
, ,},
XIN Yu^{1, 3
,},
GE Bi^1
,,
YUAN Zi-qing^1
,

1.
Department of Civil Engineering, Hefei University of Technology, Hefei, Anhui 230009, China
2.
Anhui Engineering Technology Research Center for Civil Engineering Disaster Prevention and Mitigation, Hefei, Anhui 230009, China
3.
Anhui Engineering Laboratory of Infrastructural Safety Inspection and Monitoring, Hefei University of Technology, Hefei, Anhui 230009, China

摘要

摘要: 提出一种基于贝叶斯推理的非线性结构模型修正方法，同时考虑激励的随机性，建立了复合随机振动系统的动力可靠度分析方法。利用实测结构动力响应主分量的瞬时特征参数作为非线性指标构建似然函数，结合拒绝延缓自适应(Delayed Rejection and Adaptive Metropolis, DRAM)算法和高斯过程替代模型实现了非线性结构模型修正及其参数的不确定性量化。根据首次超越破坏准则，利用广义概率密度演化方法，分别对仅考虑激励随机性的确定性模型和同时考虑结构参数与激励不确定性的复合随机振动模型进行动力可靠度分析，并利用蒙特卡洛随机抽样方法验证了计算结果的准确性。研究结果表明：基于振动响应瞬时特征参数的贝叶斯推理方法能够快速、准确地实现结构的非线性模型修正及其参数的不确定性量化。与具有初始设计参数名义值的确定性模型相比，考虑参数不确定性的复合随机模型的动力可靠度总体偏低，因此，在结构安全评估中应考虑非线性模型参数不确定性的影响，使评估结果更加安全、可靠。
- 贝叶斯理论 /
- 非线性模型修正 /
- 瞬时特征参数 /
- 动力可靠度 /
- 复合随机振动
Abstract: A Bayesian-based method for nonlinear model updating is proposed. Considering the randomness of excitation, a dynamic reliability analysis method of compound random vibration systems is established. The instantaneous characteristic parameters of the principal components decomposed from the measured structural dynamic response are considered as the nonlinear index that is applied to construct the likelihood function. The DRAM-Gaussian process model combined method is further performed for the uncertainty quantification of the calibrated model parameters. According to the first transcendental failure criterion, the generalized probability density evolution method is used to calculate the structural dynamic reliability. Both the deterministic nominal model and the compound random vibration system are considered. The accuracy of the calculated reliability is subsequently verified by Monte Carlo simulation. The results show that the Bayesian-based measured instantaneous characteristics can be used to quantify the uncertainty of the nonlinear model parameters with the advantages of high accuracy and efficiency. In addition, the dynamic reliability of the compound random model that considers the uncertainty of structural parameters is generally lower than that of the deterministic nominal model. Thus, it will make the evaluation results safer and more reliable by considering the effects of model parameters uncertainties in structural safety state assessment.
- Bayesian theory /
- nonlinear model updating /
- instantaneous characteristic parameter /
- dynamic reliability /
- compound random vibration

HTML全文

图 1 DRAM算法流程图

Figure 1. Flow chart of DRAM algorithm

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图 2 五层非线性剪切模型 /m

Figure 2. Five-layer nonlinear shear model

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图 3 Bouc-Wen模型

Figure 3. Bouc-Wen model

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图 4 结构顶层的加速度响应

Figure 4. Acceleration response of top floor

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图 5 结构主分量瞬时特征参数

Figure 5. Instantaneous characteristics of principal component response

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图 6 残差正态分位图

Figure 6. Normal quantile-quantile plot

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图 7 参数γ的马尔科夫链

Figure 7. Markov chain of γ

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图 8 模拟的30次瞬时加速度幅值

Figure 8. 30 sets of simulated instantaneous acceleration amplitudes

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图 9 参数γ的后验样本

Figure 9. Posterior samples of γ

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图 10 不同时刻概率分布

Figure 10. Probability distribution of different time

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图 11 不同时刻概率密度演化

Figure 11. Probability density evolution of different time

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图 12 结构顶层位移时程均值和标准差对比

Figure 12. Comparison of time history mean and standard deviation of top floor displacement

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图 13 不同位移界限条件下结构动力可靠度

Figure 13. Dynamic reliability under different displacement boundary conditions

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图 14 不同速度界限条件下结构动力可靠度

Figure 14. Dynamic reliability under different velocity boundary conditions

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表 1 非线性Bouc-Wen模型参数的名义值

Table 1. Nominal value of nonlinear Bouc-Wen model parameters

参数	α	A	μ	β/m^−μ	γ/m^−μ
名义值	0.4	1.0	3.0	0.5	0.5

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表 2 非线性Bouc-Wen模型参数修正结果

Table 2. Updated results of nonlinear Bouc-Wen model parameters

参数	名义值	DRAM			MH
参数	名义值	后验均值	变异系数	样本接受率	后验均值	变异系数	样本接受率
$ \alpha $	0.4	0.39	0.031	0.47	0.38	0.074	0.28
A	1.0	1.02	0.012	0.39	1.05	0.038	0.11
$ \mu $	3.0	2.98	0.040	0.51	2.96	0.084	0.14
$ \beta $/m^−μ	0.5	0.51	0.024	0.46	0.51	0.032	0.29
$ \gamma $/m^−μ	0.5	0.48	0.025	0.49	0.47	0.059	0.22

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表 3 非线性结构模型修正结果

Table 3. Updated results of nonlinear model

参数	名义值	后验均值	变异系数	样本接受率
$ \mit\alpha $	0.4	0.39	0.023	0.53
A	1.0	1.08	0.017	0.48
$ \mit\mu $	3.0	2.97	0.026	0.65
$ \mit\beta $/m^−μ	0.5	0.52	0.037	0.44
$ \mit\gamma $/m^−μ	0.5	0.49	0.031	0.57

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表 4 非线性模型随机参数与激励随机参数

Table 4. Random parameters of nonlinear model and excitation

随机参数	分布概型	均值	变异系数
$ \mit\alpha $	正态分布	0.39	0.031
A	正态分布	1.02	0.012
$\mit\mu $	正态分布	2.98	0.040
$ \mit\beta $/m^−μ	正态分布	0.51	0.024
$ \mit\gamma $/m^−μ	正态分布	0.48	0.025
PGA/g	正态分布	0.20	0.100

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表 5 不同位移界限条件下结构动力可靠度对比

Table 5. Dynamic reliability for different displacement boundary conditions

界限值$ {x_{\lim }} $/m	动力可靠度R(t)
界限值$ {x_{\lim }} $/m	名义模型	复合随机模型	蒙特卡洛模拟
0.060	0.3766	0.2909	0.2946
0.070	0.8851	0.8163	0.8224
0.080	1.0000	0.9808	0.9852
0.085	1.0000	0.9994	0.9997
0.090	1.0000	1.0000	1.0000

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表 6 不同速度界限条件下结构动力可靠度对比

Table 6. Comparison of dynamic reliability for different velocity boundary conditions

界限值$ {\dot x_{\lim }} $/(cm/s)	动力可靠度R(t)
界限值$ {\dot x_{\lim }} $/(cm/s)	名义模型	复合随机模型	蒙特卡洛模拟
20	0.4179	0.3453	0.3394
22	0.7818	0.5841	0.5803
24	0.9475	0.8512	0.8702
26	1.0000	0.9475	0.9413
28	1.0000	0.9997	0.9992
30	1.0000	1.0000	1.0000

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