| 张雪萍,彭珍瑞,张亚峰.基于Kriging模型和改进MCMC算法的随机有限元模型修正[J].计算力学学报,2021,38(6):712~721 |
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| 基于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：10.7511/jslx20201019001 |
| 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（51768035）；甘肃省高校协同创新团队项目（NO.2018C-12）资助项目. |
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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MCMC （Markov Chain Monte Carlo）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，以待修正参数作为输入，以应变模态作为输出，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，将花朵授粉算法融入MH （Metropolis-Hasting）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，所提方法修正后较高维参数的马尔可夫链能够快速收敛且样本接受率也有所提高，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 the Kriging model is established by using the parameters to be updated as the inputs and the strain mode as the output.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-Hastings (MH) sampling algorithm to improve the local and global search ability.Finally,numerical examples of a three-DOF spring-mass system and a three-dimensional truss are used to verify the proposed model updating method,and relative error of the updated parameters are found to be less than 0.86%.The results show that the updated Markov chains with higher dimensional parameters can converge rapidly and the sample acceptance rate is high,and the proposed method is also robust to random noise. |
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