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中南大学学报(自然科学版)

Journal of Central South University

第44卷    第9期    总第229期    2013年9月

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文章编号:1672-7207(2013)09-3843-06
概率方法在恢复力模型参数识别中的应用分析
刘佩,袁泉,魏庆朝

(北京交通大学 土木建筑工程学院,北京,100044)

摘 要: 考虑模型和模型参数的不确定性,应用贝叶斯概率方法通过实测数据对恢复力模型参数进行识别。首先,推导得到模型参数的负对数似然函数表达式,建立基于贝叶斯理论的恢复力模型参数识别计算框架;其次,根据密肋复合墙体在低周反复荷载作用下所得滞回曲线,建立针对该类型墙体的用于识别的恢复力模型;最后,以2种加载方式下的2块比例为1/2的密肋复合墙体试件的实测滞回数据为例,基于贝叶斯理论识别得到恢复力模型参数的最有可能值和协方差矩阵,分析模型选取的依据和模型误差对反应预测的影响。研究结果表明:由模型参数最有可能值得到的滞回曲线与实测值较吻合,验证了识别结果的合理性;采用贝叶斯概率方法可以定量的确定模型参数的不确定性,为后续计算分析提供依据。

 

关键字: 参数识别;贝叶斯理论;密肋复合墙体;恢复力模型

Application of a probabilistic approach to restoring force model parameter identification
LIU Pei, YUAN Quan, WEI Qingchao

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China

Abstract:Taking into account the uncertainty of model and model parameters, a Bayesian probabilistic approach was applied for parameter identification of restoring force model using tested data. Negative log-likelihood function of model parameters was derived. Bayesian computational frame for parameter identification of restoring force model was proposed. According to the tested hysteresis curves of multi-grid composite walls under low cyclic loadings, a restoring force model for multi-grid composite walls was proposed for identification. The most probable values and covariance matrixes of restoring force model parameters of two multi-grid composite wall specimens of 1/2 scale whose cyclic loading histories were different were identified based on the tested data. The rules for model selection and effect of model error on response prediction were analyzed. The results show that the hysteresis curves obtained through the most probable values without considering the model prediction errors agree well with those tested ones, which validates the identification results. Through Bayesian probabilistic approach, quantitative uncertainty of model parameters is obtained, which can be used for further analysis.

 

Key words: parameter identification; Bayesian theorem; multi-grid composite walls; restoring force model

中南大学学报(自然科学版)
  ISSN 1672-7207
CN 43-1426/N
ZDXZAC
中南大学学报(英文版)
  ISSN 2095-2899
CN 43-1516/TB
JCSTFT
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