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
引用本文: 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 Jian-xin. A FINITE ELEMENT MODEL UPDATING METHOD BASED ON IMPROVED MCMC METHOD[J]. Engineering Mechanics, 2016, 33(6): 138-145. DOI: 10.6052/j.issn.1000-4750.2014.10.0887
Citation: LIU Gang, LUO Jun, QIN Yang, ZHANG Jian-xin. A FINITE ELEMENT MODEL UPDATING METHOD BASED ON IMPROVED MCMC METHOD[J]. Engineering Mechanics, 2016, 33(6): 138-145. DOI: 10.6052/j.issn.1000-4750.2014.10.0887

基于改进MCMC方法的有限元模型修正研究

A FINITE ELEMENT MODEL UPDATING METHOD BASED ON IMPROVED MCMC METHOD

  • 摘要: 针对马尔可夫链蒙特卡罗(MCMC)模型修正方法在待修正参数维数较高时不易收敛和计算效率低下的问题,建立了融合自适应算法和相关向量机的快速模型修正方法。基于广义无偏见先验分布,推导了待修正参数的后验分布;在标准MCMC方法的基础上,引入延缓拒绝算法以提高新样本接受概率;引入自适应算法以自主调整建议分布的带宽。通过相关向量机建立待修正参数与有限元模型理论计算值之间的回归模型,以提高模型修正的计算效率。数值模拟和试验结构的模型修正结果表明,该方法的收敛速度较快,计算效率优于传统的一阶优化模型修正方法,为解决不确定性模型修正中的计算效率提供了一种新手段。

     

    Abstract: To copy with the shortage of the convergence and computational efficiency in high dimension parameters, a fast finite element model updating method is proposed based on an adaptive fusion algorithm and its relevance vector machine. The posterior distribution for correction parameters is deduced based on the generalized without prejudice prior distribution. An adaptive algorithm is introduced to adjust the bandwidth of the proposal distribution based on Markov Chain Monte Carlo (MCMC) simulation method. Refusal by a delaying algorithm is introduced to improve the new sample acceptance probability. In order to improve the computational efficiency, the regression model between the correction parameters and the theoretical calculation values of the finite element model is established. Simulation and experimental results show that the method owns fast convergence speed and computation efficiency. It is superior to the traditional first-order optimization model modification method, providing a new way to improve the calculation efficiency of uncertainty model updating.

     

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