结合近似贝叶斯计算和改进群体蒙特卡洛抽样的结构损伤识别

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摘要为避免陷入低概率区抽样并提高抽样效率，改进了群体蒙特卡洛（PMC）抽样算法，再结合近似贝叶斯计算（ABC）和随机响应面（SRS）提出一种概率损伤识别方法。首先将ABC和改进PMC算法进行嵌套，利用每个迭代步的样本方差来搅动粒子群和求取自适应权重系数，再构造衡量仿真和实测样本间相似度的误差函数，用于替代似然函数；然后使用SRS建立结构随机响应的显式表达式，大幅提高响应统计特征值的计算效率；最后将求得的参数后验概率分布统计特征值作为损伤指标，根据损伤前后指标值的变化来判断损伤位置和程度。对试验钢筋混凝土梁的单、多工况损伤进行了识别，验证了所提出方法在保证参数后验分布估计精度的条件下，可以有效提高贝叶斯推断过程的计算效率。

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	方圣恩1
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	陈杉1

关键词 ：概率损伤识别, 近似贝叶斯计算, 改进PMC抽样, 随机响应面, 参数后验概率分布

Abstract：In order to avoid sampling being immersed in low-probability areas and to raise sampling efficiency, the population Monte Carlo (PMC) sampling algorithm was improved and then combined with the approximate Bayesian calculation (ABC) and stochastic response surface (SRS) to propose a probabilistic damage identification method.Firstly, PMC algorithm was embedded in ABC, and sample variance in each iteration step was used to perturb a particle swarm, and obtain adaptive weight coefficients.An error function was constructed to measure the similarity between simulated and measured samples, and replace the likelihood function.Then the explicit expression for structural stochastic response was established using SRS to greatly improve the calculation efficiency of response statistical features.Finally, obtained statistical values of parametric posterior probability distribution were taken as damage indexes.According to indexes’ changes before and after damage, damage locations and degrees were judged.Damages of a test reinforced concrete beam under a single working condition and multiple working conditions were identified, respectively.It was shown that the proposed method can be used to effectively improve the calculation efficiency of Bayesian inference process under the condition of ensuring parametric posterior distribution’s estimation accuracy.

Key words： probabilistic damage identification approximate Bayesian calculation (ABC) improved population Monte Carlo (PMC) sampling stochastic response surface (SRS) parametric posterior probability distribution

收稿日期: 2018-08-03 出版日期: 2020-02-28

引用本文:

方圣恩1,2，陈杉1. 结合近似贝叶斯计算和改进群体蒙特卡洛抽样的结构损伤识别[J]. 振动与冲击, 2020, 39(5): 143-149.
FANG Sheng’en1,2, CHEN Shan1. Structural damage identification using ABC combined with improved PMC sampling. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(5): 143-149.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I5/143

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