基于改进SCAM算法的结构物理参数识别贝叶斯方法

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摘要

针对贝叶斯估计中逐分量自适应Metropolis（single component adaptive Metropolis ，SCAM）算法易生成重复性样本，导致抽样效率低、结果误差大等问题，重新定义了提议分布方差的表达式，提出了改进的SCAM算法，使得抽样样本序列构成的马尔可夫链相对稳定。进而将贝叶斯理论与改进的SCAM算法相结合，求解结构物理参数的后验边缘概率分布、最优估计值以识别和估计结构损伤，通过理论分析和结构数值模拟算例验证了改进的SCAM算法的有效性。结果表明，改进的SCAM算法既提高了抽样效率，又提高了计算结果准确性，可应用于物理参数识别及损伤识别与评估等工作。
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	赵一男
	公茂盛
	左占宣
	高艳滨

关键词 ：结构物理参数识别')" href="#">

结构物理参数识别, 贝叶斯估计, 马尔可夫蒙特卡罗（MCMC）抽样, 提议分布, 逐分量自适应Metropolis（SCAM）算法

Abstract：

The traditional SCAM (single component adaptive Metropolis) algorithm was improved to solve the problems such as repetitive samples, low sampling efficiency and large error.A new expression for the variance of the proposal distribution was defined and proposed to make the Markov chain, composed of sample sequences, relatively stable.Then, the Bayesian theory and the improved SCAM algorithm were combined to obtain the posterior marginal probability distribution and optimal estimation value of structural physical parameters to identify structural damages.The effectiveness of the improved SCAM algorithm was verified by the theoretical analysis and numerical simulation.The results show that the improved SCAM algorithm raises not only the accuracy of calculation results, but also the sampling efficiency.The method can be applied to physical parameter identification, damage identification and damage evaluation.

Key words： structural physical parameter identification Bayesian estimation Markow Chain Monte Carlo(MCMC) sampling proposal distribution single component adaptive Metropolis(SCAM) algorithm

收稿日期: 2019-10-24 出版日期: 2021-03-28

引用本文:

赵一男，公茂盛，左占宣，高艳滨. 基于改进SCAM算法的结构物理参数识别贝叶斯方法[J]. 振动与冲击, 2021, 40(6): 121-126.
ZHAO Yinan，GONG Maosheng，ZUO Zhanxuan，GAO Yanbin. Bayesian method for structural physical parameter identification based on an improved SCAM algorithm. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(6): 121-126.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2021/V40/I6/121

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