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用Kriging模型和改进MCMC算法的随机有限元 模型修正
Stochastic finite element model updating based on Kriging model and improved MCMC algorithm
投稿时间:2020-10-19  修订日期:2020-12-26
DOI:
中文关键词:  模型修正  贝叶斯估计  MCMC算法  花朵授粉算法  Kriging模型
英文关键词:model updating  Bayesian estimates  Markov Chain Monte Carlo (MCMC) algorithm  Flower pollination algorithm (FPA)  Kriging model
基金项目:国家自然科学基金资助项目(51768035); 甘肃省高校协同创新团队项目(NO.2018C-12); 兰州市人才创新创业项目(2017-RC-66).
作者单位邮编
张雪萍 兰州交通大学 730070
彭珍瑞 兰州交通大学 730070
张亚峰 兰州交通大学 
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中文摘要:
      针对待修正参数维数较高时标准马尔可夫链蒙特卡罗(Markov Chain Monte Carlo,MCMC)算法不易收敛、拒绝率高的问题,提出了基于Kriging模型和在MCMC中融合花朵授粉算法的修正方法。首先,以应变模态作为响应,建立Kriging模型,通过蝙蝠算法确定Kriging模型的相关系数;然后,采用最大熵的贝叶斯方法估计参数的后验概率密度函数,花朵授粉算法融入Metropolis-Hasting(MH)抽样算法,提高局部寻优和全局寻优能力;最后,通过三自由度弹簧-质量系统和三维桁架结构的数值算例验证所提模型修正方法,修正后参数相对误差均低于0.86%。结果表明,所提方法修正后参数的马尔可夫链能够快速收敛、样本接受率高,该方法也对随机噪声具有一定的鲁棒性。
英文摘要:
      Aiming at the problems of poor convergence and high rejection rate of standard Markov Chain Monte Carlo (MCMC) algorithm when the dimension of parameters to be updated is high, an efficient updating method combining flower pollination algorithm and Kriging model is proposed. Firstly, taking the strain mode as the response, the Kriging model is established. The correlation coefficients of the Kriging model are optimized by bat algorithm. Then, the maximum entropy Bayesian method is adopted to estimate the posterior probability density function of parameters. The flower pollination algorithm is incorporated to Metropolis-Hasting (MH) sampling algorithm to improve the local and global search ability. Finally, numerical examples of three-DOF spring-mass system and three dimensional truss system are used to verify the proposed model updating method, and relative error of the updated parameters are less than 0.86%. The results show that the updated Markov chains can converge rapidly and high sample acceptance rate, and the proposed method is also robust to random noise.
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