Bayesian-based probabilistic models for the ultimate drift capacity of rectangular reinforced concrete columns failed in flexure mode矩形钢筋混凝土柱弯曲失效模式下极限位移承载力的 Bayes 概率模型
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Ma Y, Wang DS, Sun ZG, Mi JH, Wu ZB, 2024. Bayesian-based probabilistic models for the ultimate drift capacity of rectangular reinforced concrete columns failed in flexure mode. Probabilistic Engineering Mechanics, 76: 103614.DOI: 10.1016/j.probengmech.2024.103614
摘要 | Abstract
为准确预测地震作用下钢筋混凝土 (reinforced concrete, RC) 柱弯曲失效模式的极限位移承载力，提出了一种概率方法来修正确定性模型中的偏差并建立了概率模型。基于 Bayes 更新构建了概率修正模型，该模型可考虑潜在关键影响，并生成与模型参数和预测相关的概率分布。通过 Bayes 更新简化概率模型，以识别重要信息项。然后，讨论了样本物理性质和尺寸对概率模型的影响。结果表明，Bayes 修正方法可提高预测精度并量化不确定性。此外，在 Bayes 更新中增加不同物理特性的样本可扩大概率模型的适用范围，且样本数量应至少为 Bayes 更新中涉及变量数量的两倍。关键词: 弯曲失效钢筋混凝土柱, 极限位移比, 概率修正, Bayes 更新, 样本物理性质, 样本大小To accurately predict the ultimate drift capacity of reinforced concrete (RC) columns failed in flexure mode under seismic loading, a probabilistic methodology is proposed to correct the biases in deterministic models and establish probabilistic models. Probabilistic correction models are constructed based on Bayesian updating, which can consider potential critical influences and also yield probability distribution associated with the model parameters and predictions. The probabilistic models are simplified to identify the significant informative terms by Bayesian updating. Then, the influences of the physical properties and size of the sample on the probabilistic models are discussed. The results show that the Bayesian-based correction method can increase the accuracy of predictions and quantify uncertainties. Additionally, adding new samples with different physical properties in Bayesian updating can expand the scope of application of probabilistic models, and the sample size should be at least two times the number of variables involved in Bayesian updating.Keywords: Flexure failure RC columns; Ultimate drift ratio; Probabilistic correction; Bayesian updating; Sample physical properties; Sample size![]()
图 1: 普通钢筋混凝土柱基于确定性模型与平均概率模型的预测值与实测值对比Fig. 1. Comparison between predicted and measured values based on the deterministic model and mean probabilistic model for normal RC columns
图 2: 高强混凝土与高强箍筋下钢筋混凝土柱基于确定性模型与平均概率模型的预测值与实测值对比Fig. 2. Comparison between predicted and measured values based on the deterministic model and mean probabilistic model for RC columns with HSC and HSS
图 3: 预测标准差、实测标准差、中心均方根误差与相关系数的几何关系Fig. 3. Geometric relationships among SD_p, SD_m, CRMSE and ρ
图 4: 确定性与基于 Bayes 更新概率位移承载力模型的归一化 Taylor 图表现对比Fig. 4. Normalized Taylor diagram comparing performance of the deterministic and Bayesian updating-based probabilistic drift capacity models
图 5: 普通钢筋混凝土柱确定性与概率位移承载力模型的归一化 Taylor 图表现对比Fig. 5. Normalized Taylor diagram comparing performance of the deterministic and probabilistic drift capacity models for normal RC columns
图 6: 高强混凝土与高强箍筋下钢筋混凝土柱确定性与概率位移承载力模型的归一化 Taylor 图表现对比Fig. 6. Normalized Taylor diagram comparing performance of the deterministic and probabilistic drift capacity models for RC columns with HSC and HSS
图 7: 不同样本数下基于七类确定性模型的概率位移承载力模型归一化 Taylor 图表现对比Fig. 7. Normalized Taylor diagram comparing performance of probability drift capacity models based on seven deterministic model with different sample sizes
作者信息 | Authors
浙大宁波理工学院 (NingboTech University) 土木建筑工程学院
王东升 Dong-Sheng Wang, 通讯作者 (Corresp.) 河北工业大学 (Hebei University of Technology) 土木与交通学院Email: pangrui@dlut.edu.cn
防灾科技学院 (Institute of Disaster Prevention) 中国地震局建筑物破坏机理与防御重点实验室
华北水利水电大学 (North China University of Water Resources & Electric Power) 水利学院
华北水利水电大学 (North China University of Water Resources & Electric Power) 水利学院
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
