基于贝叶斯理论的多模型结构识别的试验研究
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摘要
基于贝叶斯理论的抽样方法,对结构的多模型结构识别问题进行试验研究.采用基于贝叶斯理论的多模型结构识别的概念与基本框架,以及马尔科夫链-蒙特卡洛模拟(MCMC),建立了有限元模型库.针对MCMC在参数维度较高时不易收敛和计算效率低下等问题,提出了一种改进的MCMC抽样方法来进行多模型结构识别.利用Matlab-Strand7的交互访问技术(API)能够进行大型结构有限元模型的参数自动修正,在获得校验后的有限元模型库后,能基于有限元模型的后验概率分布进行预测.为了验证该理论的可行性和有效性,针对一根简支梁的数值算例和一座实际大跨钢管混凝土桁架系杆拱桥进行了基于贝叶斯理论的结构识别研究与响应评估,并使用传统的单模型结构识别方法——遗传算法(GA)进行对比分析,结果表明本文提出的基于贝叶斯理论的多模型结构识别方法能够更好地进行结构响应预测.
The issue related to multi-model structural identification(MM St-Id)was experimentally researched based on sampling method of Bayesian theory.The concept and basic framework of MM St-Id method based on Bayesian theory were introduced,and then,the Markov chain-Monte Carlo simulation(MCMC)was utilized to build finite element(FE)model libraries.Since MCMC is not easy to converge and it has low calculation efficiency when the parameters have high dimensions,an improved MCMC sampling method for MM St-Id was introduced.The Matlab-Strand7 Application Programming Interface(API)strategy can be used to update the parameters of large structural FE model automatically.After the calibrated FE model libraries were established,they can be used to predict the responses based on the posterior probability distribution of the FE models.In order to verify the feasibility and effectiveness of the proposed theory,a numerical example of a simply-supported beam and an on-site large concrete-steel tubular truss arch bridge St-Id were investigated based on Bayesian theory and response prediction.A simple model St-Id method-genetic algorithm(GA)was used for comparison.The results showed that the proposed MM St-Id method based on Bayesian theory was much better in structural response prediction.
The issue related to multi-model structural identification(MM St-Id)was experimentally researched based on sampling method of Bayesian theory.The concept and basic framework of MM St-Id method based on Bayesian theory were introduced,and then,the Markov chain-Monte Carlo simulation(MCMC)was utilized to build finite element(FE)model libraries.Since MCMC is not easy to converge and it has low calculation efficiency when the parameters have high dimensions,an improved MCMC sampling method for MM St-Id was introduced.The Matlab-Strand7 Application Programming Interface(API)strategy can be used to update the parameters of large structural FE model automatically.After the calibrated FE model libraries were established,they can be used to predict the responses based on the posterior probability distribution of the FE models.In order to verify the feasibility and effectiveness of the proposed theory,a numerical example of a simply-supported beam and an on-site large concrete-steel tubular truss arch bridge St-Id were investigated based on Bayesian theory and response prediction.A simple model St-Id method-genetic algorithm(GA)was used for comparison.The results showed that the proposed MM St-Id method based on Bayesian theory was much better in structural response prediction.
引文
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[2]RAPHAEL B,SMITH I F C.Finding the right model for bridge diagnosis[M]//Artificial Intelligence in Structural Engineering in Computer Science.Heidelberg:Springer,1998:308-319.
[3]ROBERT-NICOUD Y,RAPHAEL B,SMITH I F C.System identification through model composition and stochastic search[J].Journal of Computing in Civil Engineering,2005,19(3):239-247.
[4]GOULET J A,KRIPAKARAN P,SMITH I F C.Multimodel structural performance monitoring[J].Journal of Structural Engineering,2010,136(10):1309-1318.
[5]PASQUIER R,SMITH I F C.Iterative structural identification framework for evaluation of existing structures[J].Engineering Structures,2016,106:179-194.
[6]BECK J L,KATAFYGIOTIS L S.Updating models and their uncertainties I:Bayesian statistical framework[J].Journal of Engineering Mechanics,1998,124(4):455-461.
[7]BECK J L,AU S K.Bayesian updating of structural models and reliability using Markov Chain Monte Carlo simulation[J].Journal of Engineering Mechanics,2002,128(4):380-391.
[8]易伟建,周云,李浩.基于贝叶斯统计推断的框架结构损伤诊断研究[J].工程力学,2009,26(5):121-129.YI W J,ZHOU Y,LI H.Damage assessment research on frame structure based on Bayesian statistical inference[J].Engineering Mechanics,2009,26(5):121-129.(In Chinese)
[9]SUN H,MORDRET A,PRIETO G A,et al.Bayesian characterization of buildings using seismic interferometry on ambient vibrations[J].Mechanical Systems and Signal Processing,2017,85:468-486.
[10]ZHANG J,WAN C F,TADANOBU S.Advanced Markov chain Monte Carlo approach for finite element calibration under uncertainty[J].Computer-Aided Civil and Infrastructure Engineering,2013,28:522-530.
[11]DUBBS N C,MOON F.Comparison and implementation of multi-model structural identification methods[J].Journal of Structural Engineering,2015,141(11):1-13.
[12]FALKENHAINER B,FORBUS K D.Compositional modeling:finding the right model for the job[J].Artificial Intelligence,1991,51(1/3):95-143.
[13]GOULET J A,KRIPAKARAN P,SMITH I F C.Multi-model structural performance monitoring[J].Journal of Structural Engineering,2010,136(10):1309-1318.
[14]GILKS W R,BEST N G,TAN K K C.Adaptive rejection metropolis sampling within Gibbs sampling[J].Journal of the Royal Statistical Society:Series C,1995,44(4):455-472.
[15]HAARIO H,LAINE M,MIRIA A,et al.DRAM:efficient adaptive MCMC[J].Statistics and Computing,2006,16(4):339-354.
[16]周云,蒋运忠,易伟建,等.基于模态柔度理论的结构损伤诊断试验研究[J].湖南大学学报(自然科学版),2015,42(5):36-45.ZHOU Y,JIANG Y Z,YI W J,et al.Experiment research on structural damage detection based on modal flexibility theory[J].Journal of Hunan University(Natural Sciences),2015,42(5):36-45.(In Chinese)
[17]周云,张军凯,陈松柏,等.大跨度拱桥静动力试验与结构识别的实践[J].湖南大学学报(自然科学版),2017,44(5):10-19.ZHOU Y,ZHANG J K,CHEN S B,et al.Structural identification and condition assessment of a long-span arch bridge based on static and dynamic experiments[J].Journal of Hunan University(Natural Sciences),2017,44(5):10-19.(In Chinese)
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