基于多链差分进化的贝叶斯有限元模型修正方法
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摘要
针对传统贝叶斯算法在高维参数下采样效率低且收敛难的问题,建立了基于多链差分进化算法的贝叶斯有限元模型修正方法。在标准马尔可夫链蒙特卡罗(MCMC)方法的基础上,引入差分进化算法,通过多条马氏链间的随机差分运算来自适应选择条件分布的大小和方向以快速逼近目标分布;引入子空间采样算法,通过自适应选择优良的参数维度进行采样以提高采样效率;引入异常链检测算法,通过在采样的非平稳期对马氏链进行异常检测与剔除以提高在平稳期的采样效率。简支梁理论模型和实验室4层框架结构的模型修正结果表明:该方法修正精度较高,且具有良好的抗噪性,在高阶频率以及振型下的修正效果均优于DRAM算法,为解决不确定性模型修正中的计算精度提供了一种新手段。
To cope with the shortages of low sampling efficiency and difficult convergence of traditional Bayesian method under high-dimension parameters, a Bayesian based finite element model is proposed by the base of a multi-chain differential evolution algorithm. Based on the standard Markov chain Monte Carlo(MCMC)method, a differential evolution algorithm is introduced, and a random difference operation among multiple Markov chains is derived from the size and direction of an adaptive selection condition distribution to quickly approximate the target distribution. A subspace sampling algorithm which uses adaptive selection to select good parameter dimensions for sampling is introduced to improve sampling efficiency. Also, an anomaly Markov chain detection algorithm which detects and eliminates abnormities in Markov chains in the non-stationary period is introduced to improve the sampling efficiency in the stationary phase. The correction results of a simply-supported-beam model and a four-floor-frame-structure model show that the proposed method has a higher correction accuracy, better noise resistance, and better correction effects than that of DRAM algorithm under high order frequency and mode shapes, which provides a new way to improve the computational accuracy in uncertainty model correction.
To cope with the shortages of low sampling efficiency and difficult convergence of traditional Bayesian method under high-dimension parameters, a Bayesian based finite element model is proposed by the base of a multi-chain differential evolution algorithm. Based on the standard Markov chain Monte Carlo(MCMC)method, a differential evolution algorithm is introduced, and a random difference operation among multiple Markov chains is derived from the size and direction of an adaptive selection condition distribution to quickly approximate the target distribution. A subspace sampling algorithm which uses adaptive selection to select good parameter dimensions for sampling is introduced to improve sampling efficiency. Also, an anomaly Markov chain detection algorithm which detects and eliminates abnormities in Markov chains in the non-stationary period is introduced to improve the sampling efficiency in the stationary phase. The correction results of a simply-supported-beam model and a four-floor-frame-structure model show that the proposed method has a higher correction accuracy, better noise resistance, and better correction effects than that of DRAM algorithm under high order frequency and mode shapes, which provides a new way to improve the computational accuracy in uncertainty model correction.
引文
[1]Mosavi A A,Sedarat H,O’Connor S M,et al.Calibrating a high-fidelity finite element model of a highway bridge using a multi-variable sensitivity-based optimization approach[J].Structure and Infrastructure Engineering,2014,10(5):627―642.
[2]Collins J D,Hart G C,Hasselman T K,et al.Statistical identification of structures[J].AIAA Journal,1974,12(2):185―190.
[3]Jiang C,Han X,Liu G R.Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval[J].Computer Methods in Applied Mechanics and Engineering,2007,196(49):4791―4800.
[4]Hanss M.Applied fuzzy arithmetic[M].Berlin Heidelberg:Springer-Verlag,2005:128.
[5]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.
[6]Katafygiotis L S,Beck J L.Updating models and their uncertainties II:Model identify ability[J].Journal of Engineering Mechanics,1998,124(4):463―467.
[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-ASCE,2002,128(4):380―391.
[8]易伟建,周云,李浩,等.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 Weijian,Zhou Yun,Li Hao,et al.Damage assessment research on frame structure based on Bayesian statistical inference[J].Engineering Mechanics,2009,26(5):121―129.(in Chinese)
[9]房长宇,张耀庭.基于参数不确定性的预应力混凝土梁模型修正[J].华中科技大学学报(自然科学版),2011,39(11):87―91.Fang Changyu,Zhang Yaoting.Model updating of prestressed concrete beams using parameters uncertainty[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2011,39(11):87―91.(in Chinese)
[10]韩芳,钟冬望,汪君.基于贝叶斯法的复杂有限元模型修正研究[J].振动与冲击,2012,31(1):39―43.Han Fang,Zhong Dongwang,Wang Jun.Complicated finite element model updating based on Bayesian method[J].Journal of Vibration and Shock,2012,31(1):39―43.(in Chinese)
[11]Ching J Y,Chen Y C.Transitional Markov chain Monte Carlo method for Bayesian model updating,model class selection,and model averaging[J].Journal of Engineering Mechanics,2007,133(7):816―832.
[12]Cheung S H,Beck J L.Bayesian model updating using hybrid Monte Carlo simulation with application to structural dynamic models with many uncertain parameters[J].Journal of Engineering Mechanics,2009,135(4):243―255.
[13]刘纲,罗钧,秦阳,等.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.Liu Gang,Luo Jun,Qin Yang,et al.A finite element model updating method based on improved MCMCmethod[J].Engineering Mechanics,2016,33(6):138―145.(in Chinese)
[14]Wang F S,Li X C,Lu M Y.Adaptive Hamiltonian MCMC sampling for robust visual tracking[J].Multimedia Tools and Applications,2017,76(11):13087―13106.
[15]Agostinho N B,Machado K S,Werhli A V.Inference of regulatory networks with a convergence improved MCMC sampler[J].BMC Bioinformatics,2015,306(16):1―10.
[16]Kennedy D A,Dukic V,Dwyer G.Combining principal component analysis with parameter line-searches to improve the efficacy of Metropolis-Hastings MCMC[J].Environmental and Ecological Statistics,2015,22(2):247―274.
[17]Mengersen K L,Robert C P.IID sampling using self-avoiding population Monte Carlo:The pinball sampler[J].Bayesian Statistics,2003,7:277―292.
[18]茆诗松,程依明,濮晓龙,等.概率论与数理统计教程[M].北京:高等教育出版社,2011:107―108.Mao Shisong,Chen Yiming,Pu Xiaolong,et al.Probability and statistics[M].Beijing:Higher Education Press,2011:107―108.(in Chinese)
[19]Gelman A,Rubin D B.Inference from iterative simulation using multiple sequences[J].Statistical Science,1992,7(4):457―472.
[20]Vrugt J A,ter Braak C J F,Diks C G H,et al.Accelerating markov chain monte carlo simulation by differential evolution with self-adaptive randomized subspace sampling[J].International Journal of Nonlinear Sciences and Numerical Simulation,2009,10(3):273―290.
[21]Kim G H,Park Y S.An improved updating parameter selection method and finite element model update using multiobjective optimisation technique[J].Mechanical Systems and Signal Processing,2014,18(1):59―78.
[2]Collins J D,Hart G C,Hasselman T K,et al.Statistical identification of structures[J].AIAA Journal,1974,12(2):185―190.
[3]Jiang C,Han X,Liu G R.Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval[J].Computer Methods in Applied Mechanics and Engineering,2007,196(49):4791―4800.
[4]Hanss M.Applied fuzzy arithmetic[M].Berlin Heidelberg:Springer-Verlag,2005:128.
[5]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.
[6]Katafygiotis L S,Beck J L.Updating models and their uncertainties II:Model identify ability[J].Journal of Engineering Mechanics,1998,124(4):463―467.
[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-ASCE,2002,128(4):380―391.
[8]易伟建,周云,李浩,等.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 Weijian,Zhou Yun,Li Hao,et al.Damage assessment research on frame structure based on Bayesian statistical inference[J].Engineering Mechanics,2009,26(5):121―129.(in Chinese)
[9]房长宇,张耀庭.基于参数不确定性的预应力混凝土梁模型修正[J].华中科技大学学报(自然科学版),2011,39(11):87―91.Fang Changyu,Zhang Yaoting.Model updating of prestressed concrete beams using parameters uncertainty[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2011,39(11):87―91.(in Chinese)
[10]韩芳,钟冬望,汪君.基于贝叶斯法的复杂有限元模型修正研究[J].振动与冲击,2012,31(1):39―43.Han Fang,Zhong Dongwang,Wang Jun.Complicated finite element model updating based on Bayesian method[J].Journal of Vibration and Shock,2012,31(1):39―43.(in Chinese)
[11]Ching J Y,Chen Y C.Transitional Markov chain Monte Carlo method for Bayesian model updating,model class selection,and model averaging[J].Journal of Engineering Mechanics,2007,133(7):816―832.
[12]Cheung S H,Beck J L.Bayesian model updating using hybrid Monte Carlo simulation with application to structural dynamic models with many uncertain parameters[J].Journal of Engineering Mechanics,2009,135(4):243―255.
[13]刘纲,罗钧,秦阳,等.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.Liu Gang,Luo Jun,Qin Yang,et al.A finite element model updating method based on improved MCMCmethod[J].Engineering Mechanics,2016,33(6):138―145.(in Chinese)
[14]Wang F S,Li X C,Lu M Y.Adaptive Hamiltonian MCMC sampling for robust visual tracking[J].Multimedia Tools and Applications,2017,76(11):13087―13106.
[15]Agostinho N B,Machado K S,Werhli A V.Inference of regulatory networks with a convergence improved MCMC sampler[J].BMC Bioinformatics,2015,306(16):1―10.
[16]Kennedy D A,Dukic V,Dwyer G.Combining principal component analysis with parameter line-searches to improve the efficacy of Metropolis-Hastings MCMC[J].Environmental and Ecological Statistics,2015,22(2):247―274.
[17]Mengersen K L,Robert C P.IID sampling using self-avoiding population Monte Carlo:The pinball sampler[J].Bayesian Statistics,2003,7:277―292.
[18]茆诗松,程依明,濮晓龙,等.概率论与数理统计教程[M].北京:高等教育出版社,2011:107―108.Mao Shisong,Chen Yiming,Pu Xiaolong,et al.Probability and statistics[M].Beijing:Higher Education Press,2011:107―108.(in Chinese)
[19]Gelman A,Rubin D B.Inference from iterative simulation using multiple sequences[J].Statistical Science,1992,7(4):457―472.
[20]Vrugt J A,ter Braak C J F,Diks C G H,et al.Accelerating markov chain monte carlo simulation by differential evolution with self-adaptive randomized subspace sampling[J].International Journal of Nonlinear Sciences and Numerical Simulation,2009,10(3):273―290.
[21]Kim G H,Park Y S.An improved updating parameter selection method and finite element model update using multiobjective optimisation technique[J].Mechanical Systems and Signal Processing,2014,18(1):59―78.
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