| 徐阳冰,刘骁骁,彭泽靖,吴子燕,司建辉.基于概率地震需求模型与Beta-二项分布的建筑结构预测地震易损性研究[J].计算力学学报,2025,42(2):292~299 |
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| 基于概率地震需求模型与Beta-二项分布的建筑结构预测地震易损性研究 |
| Bayesian prediction-based seismic fragility research of building structures by combining probabilistic seismic demand model with Beta-binomial distribution |
| 投稿时间：2023-09-08 修订日期：2023-11-21 |
| DOI：10.7511/jslx20230907003 |
| 中文关键词: 预测地震易损性 统计相关性 概率地震需求模型 β-二项分布 贝叶斯更新 |
| 英文关键词:Prediction seismic vulnerability statistical correlation probabilistic seismic demand model beta-binomial distribution Bayesian updating theorem |
| 基金项目:西安理工大学教师启动基金(107-451122005)资助项目. |
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| 摘要点击次数: 11 |
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| 中文摘要: |
| 传统地震易损性模型忽略地震激励和结构物理参数等随机不确定性导致的响应统计相关性影响,从而过高评估了结构的抗震性能。为此,提出了基于概率地震需求模型与β-二项分布的贝叶斯预测地震易损性研究方法。首先,采用线性对数回归概率地震需求模型建立工程需求参数与地震强度指标的函数映射关系。其次,采用β-二项分布得到考虑响应统计相关性的模型参数,再通过β-二项分布累积分布函数计算结构的失效概率,基于贝叶斯更新定理推导出结构的贝叶斯预测地震易损性公式。最后,结合K-out-of-N系统理论,提出基于贝叶斯估计的系统预测地震易损性方法论。以某一钢筋混凝土框架结构为算例,通过非线性动力时程分析,获得结构最大层间位移角,采用马尔科夫链蒙特卡洛模拟(MCMC)方法获得更新的地震模型参数,建立不同损伤状态下的结构和系统易损性曲线。结果表明,当结构遭受完全倒塌状态时,结构响应统计相关性的影响显著,考虑EDP统计相关性的地震易损性较传统地震易损性增大,曲线偏上移动。当结构组成系统时,对于各损伤状态,随着IDR的增加,考虑统计相关性时结构的失效概率增加幅度开始增大,后逐渐减小。因此,相比忽略结构响应统计相关性的情形,考虑统计相关性的地震易损性更趋于保守,增加了结构可靠性的安全设计,为工程抗震设计和减少震后经济损失提供更为准确的理论依据。 |
| 英文摘要: |
| In the traditional seismic vulnerability model,the combined effects of random uncertainties of seismic excitation and structural physical parameters are ignored.Then,the effects of the statistical correlations among structural responses on seismic fragility are ignored,which overestimates the seismic capability of the structural system.Therefore,Bayesian prediction-based seismic fragility research is proposed by combining probabilistic seismic demand model with Beta-Binomial distribution.First of all,the probabilistic seismic demand model is used to establish the relationship between the EDP and the intensity measure.Secondly,the model parameters with the statistical correlation are obtained by Beta-Binomial distribution.Then the structural failure probability can be obtained by cumulative distribution function of Beta-Binomial distribution.The Bayesian prediction-based seismic fragility formulation can be obtained by Bayesian updating theorem.Finally,a system prediction seismic fragility methodology is proposed by combining Bayesian estimation with the K-out-of-N system theory.Taking a reinforced concrete frame structure as an example,the maximum interstory displacement angle of the structure is obtained by nonlinear dynamic time history analysis.The updated model parameters can be obtained by MCMC and then the fragility curves of the structure and system can be established under different damage states.The results show that when the structure suffers a complete collapse,the influence of the structural response statistical correlation is significant.The seismic vulnerability considering the EDP statistical correlation increases compared with the traditional seismic vulnerability,and the curve moves upward.When the structure is composed of the system,for each damage state,with the increase of IDR,the increase of the failure probability of the structure increases at the beginning,and then gradually decreases.Therefore,the seismic vulnerability considering statistical correlations is more conservative than that without the statistical correlation of structural response.The numerical analysis mentioned-above increases the safety design of structural reliability,and provides a more accurate theoretical basis for seismic designs of engineering structures as well as the reduction of post-earthquake economic losses. |
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