混凝土徐变的Gamma模型参数估计研究  

Research on Parameter Estimation of Concrete Creep Based on Gamma Model

作　　者：陈梦成[1,2] 杨超 方苇[1,2] 温清清 许开成[1,2] 黄宏 CHEN Mengcheng;YANG Chao;FANG Wei;WEN Qingqing;XU Kaicheng;HUANG Hong(School of Civil Engineering and Architecture,East China Jiaotong University,Nanchang 330013,China;State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructures,Nanchang 330013,China)

机构地区：[1]华东交通大学土木建筑学院,江西南昌330013 [2]省部共建轨道交通基础设施性能监测与保障国家重点实验室,江西南昌330013

出　　处：《铁道学报》2021年第5期204-212,共9页Journal of the China Railway Society

基　　金：国家自然科学基金(51878275)。

摘　　要：针对长期荷载作用下的混凝土结构,将混凝土徐变量作为表征混凝土结构服役性能的退化指标,采用Gamma随机过程模拟混凝土徐变发展过程的不确定性。当参数c和尺度参数β为随机变量且其先验分布已知时,可利用Bayesian定理,得到c和β的后验分布和估计。作为特例,给出c为定值、β先验分布服从Gamma分布的后验分布和β后验估计值的解析表达式。最后在给定参数b和c的情况下,使用经典矩估计、极大似然估计与Bayesian估计、后验矩估计、后验极大似然估计等5种算法,融合2组混凝土徐变试验数据,对Gamma过程参数进行估计,实现混凝土徐变过程模拟,并以误差平方和最小为准则,将徐变模拟结果进行比较,结果发现Bayesian估计和后验估计法优于经典估计法,尤以Bayesian估计法为最佳。Concrete creep is usually used as a deterioration index to characterize the service performance of concrete structures under long-term loading.The primary aim of this investigation is to use Gamma stochastic process to simulate the uncertainty of concrete creep process.When the parameter c and scale parameterβwere random variables and their prior distributions were known,the posterior distribution and estimation of parameter c and scale parameterβcould be obtained by the Bayesian theorem.As a special case,the analytical expression,where the parameter c was a given value,the prior distribution of paramaterβfollowed the posterior distribution of the Gamma distribution,and posterior estimation,was established.Finally,given parameters b and c,the model parameters of Gamma process was estimated by the classical moment estimation,maximum likelihood estimation,the Bayesian inference,posterior moment estimation and posterior maximum likelihood estimation in conjunction with two sets of concrete creep data.Then the stochastic process of concrete creep was simulated.Based on the minimum sum of square errors as a criterion,the results of above five methods were compared.The comparison results show that the Bayesian estimation,which is deemed the best method,and the posterior parameter estimation,are superior to the classical parameter estimation.

关 键 词：混凝土徐变 Gamma过程 矩估计 极大似然估计 贝叶斯估计 

分 类 号：TU13[建筑科学—建筑理论] O211.62[理学—概率论与数理统计]