混凝土结构抗震性能的不确定性分析与研究
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摘要
不确定性分析是土木工程领域的一个重要而广泛的研究方向。不确定性分析的理论及方法既是真实反映实际工程不确定性问题的数学语言,也是有效处理实际工程不确定性问题的计算逻辑。包括贝叶斯理论、区间分析等在内的不确定性基本理论,使结构不确定性分析方法具有更为广泛的理论基础,拓展了以往经典概率为基础的分析方法所涉及的工程应用领域。围绕结构抗震分析,本文主要的研究内容总结如下：
(1)构造了基于贝叶斯网的专家系统通用原型机用于结构工程的诊断评估。在该系统中,领域知识采用离散贝叶斯网表达,系统的推理采用合树算法。系统的构造采用了模块化设计思路。系统依据功能可划分为用户界面模块、贝叶斯网编辑模块以及推理模块。用户界面模块接受用户的输入,包括贝叶斯网的编辑、证据的输入以及最终结果的输出；推理模块负责将贝叶斯网编译为合树、根据证据进行不确定性推理以及边缘化最终的联合概率；编辑模块实现用户界面动作到贝叶斯网构造的转变。本文以钢筋混凝土耐久性诊断为例,说明了贝叶斯网合树算法的推理过程；结合钢筋混凝土结构的抗震性能评估,演示了该系统如何在信息不完备这类土木工程中常见的不确定性环境下的具体应用。
(2)根据所搜集到的1918条地震记录,对具有不同屈服水平系数及周期的单自由度体系作了弹塑性时程分析,通过拟合得到了简化的延性需求计算公式；根据回归分析构造了一个新的参数用于描述地震频谱特性对延性需求的影响。在此基础上,建立了一个10节点的连续型贝叶斯网用于地震延性概率需求分析。该模型可以根据观测数据不断修正概率分布从而得到更准确的后验分布。贝叶斯网的后验分布是一个非常复杂的高维积分问题。本文引进马尔科夫链蒙特卡罗模拟方法,即基于Metropolis-Hastings采样及收敛性检验算法,计算给定地震强度观察值条件下延性需求的后验分布。算例分析了各地震强度参量及观测值对延性需求预测结果的影响。
(3)通过收集12次近场地震的71条地震纪录,分析了三种典型框架结构在近场地震作用下的响应,提出了两个基于模糊代表值的新地震强度指标。第一个地震强度指标是根据结构模糊周期,通过扩张原理获得相应的谱速度平方值模糊集,再由模糊集取重心而确定的代表值。对于中长周期的两种典型框架结构,新指标相较于已有的9种指标表现出较好的充分性和有效性。另一个强度指标则以推覆分析中模糊化的加载力向量为基础,通过扩张原理及推覆分析得到结构位移延性模糊集再取代表值求得。分析表明该指标对中短周期结构具有较好的充分性和有效性。总体说来,模糊代表值化的新地震强度指标考虑了结构在环境作用下所具有的模糊性,因此具有较高的充分性和有效性。
(4)“强剪弱弯”是保证结构延性的一个重要设计概念。本文采用区间变量表达认知不确定性,对钢筋混凝土框架柱的强剪弱弯性能进行了非经典概率可靠性分析。根据失效事件对基本事件的包含关系建立了“强剪弱弯”可靠性概率区间模型。对于含有区间值参数的结构承载力计算,引进泰勒模型以减少由于区间扩张而导致的过大误差。引进考虑“不可行度”的模拟退火遗传算法确定“强剪弱弯”的大致设计区间,根据该设计区间进行重要性采样模拟从而得到了失效概率区间。误差分析表明该方法具有较好的精度。最后通过算例分析了各设计因素对“强剪弱弯”可靠性的影响,并提出了相应的设计建议。
Uncertainty analysis is an important and comprehensive aspect in civil engineering. Uncertainty analysis theorems and methods are not only the mathematic languages for describing the uncertain realistic engineering problems, but also the computational logic to handle the uncertain realistic engineering problems. Uncertainty theorems, including Bayesian theory, interval analysis theory etc, have made the uncertainty structural analysis based on more broader theory foundations and extent the application domains of uncertainty analysis used to be based on classic probabilistic theorem. Around structural seismic analysis, primary research works of this dissertation conclude as following:
(1) Generic prototype of expert system based on Bayesian network is built for structure assessment and diagnosis. In this system, domain knowledge is expressed as discrete Bayesian network, the inference system is based on junction tree algorithm. Modular design is adopted in construction of the expert system. The whole system can be divided into user interface module, Bayesian network edit module and inference module according to the function. The user interface module accepts the user input, including edit of the Bayesian network, evidence input, and outputs results; inference module compiles the Bayesian network to junction tree, inference uncertainties with given evidences and marginalizes the result joint distribution, Bayesian network edit module converts the activity of user interface to the construction of Bayesian network. Take the example of durability diagnosis of reinforced concrete to illuminate the inference process of junction tree algorithm for discrete Bayesian network; combined with seismic performance evaluation of reinforced concret frame structures, demonstrates how the reasoning can be performed in the situation where the input information is uncertain and incomplete that frequently encountered in civil engineering.
(2) Nonlinear time history analysis of SDOF with various yield strength coefficient and period are performed based on1918earthquake ground motion records; simplified formula of ductility demand is acquired by curve fitting. A new parameter that quantifies the earthquake spectrum character effect on the ductility demand is constructed by regression analysis. Based on above, a ten-node continuous Bayesian network is established for seismic ductility demand probability analysis. The Bayesian network can acquire the posterior distribution which is more accurate updated by observed data. The posterior probability distribution involved in Bayesian network updating is a complicated multi-dimensional integral, Markov Chain Monte Carlo method, more specifically, Metropolis-Hastings sampling algorithm and convergence diagnosis algorithm, is introduced to update the ductility demand posterior probability distribution with earthquake intensity observations. Case study is carried out to analyze how the earthquake intensity parameters and given observations effect on the calculation results.
(3) Based on71time history acceleration records of12near-fault earthquakes occurred in recent years, responses of three typical frame structures are analyzed and two new intensity measures are proposed. First intensity measure, based on the fuzzy structure vibration period, acquiring the corresponding squared spectrum velocity fuzzy set according to extension principle, is determined as representative value by taking the center of gravity of fuzzy set. For the frame structures with medium and long period, the new measure exhibits more efficiency and sufficiency than other9present available intensity measures. Another intensity measure, based on fuzzy valued force shape vector used in pushover analysis, obtaining the fuzzy set of displacement ductility by extension principle and pushover analysis, is also determined as representative value. This new measure is efficiency and sufficiency for the frame structures with medium and short period. In general, new fuzzy representative valued IMs are more efficiency and sufficiency than other available IMs for consideration of vague uncertainty of structure under complicated realistic circumstance.
(4) In the seismic design of reinforced concrete structures,"strong shear weak bending" is an important design conception to guarantee the ductibility of the structure. Interval variable is introduced to express the epistemic uncertainty and failure probability interval of strong shear weak bending of reinforced concrete column is analyzed. The interval-valued probabilistic reliability model for "strong shear weak bending" is formulated according to the inclusion relationship of the element events and the failure event. For the calculation of the resistance capability involving interval-valued parameters, Taylor model is introduced in computation to reduce the error induced by interval inflation. The simulated annealing genetic algorithm considering "infeasible degree" is applied to determine the approximate design interval of the "strong shear weak bending". A specific sampling function constructed by such design interval is adopted to obtain the interval-valued probabilistic reliability index; error analysis indicates that the precision of the method is acceptable. Case study is carried out to analyze the different design parameters affecting the reliability and corresponding design suggestions are proposed.
(1)构造了基于贝叶斯网的专家系统通用原型机用于结构工程的诊断评估。在该系统中,领域知识采用离散贝叶斯网表达,系统的推理采用合树算法。系统的构造采用了模块化设计思路。系统依据功能可划分为用户界面模块、贝叶斯网编辑模块以及推理模块。用户界面模块接受用户的输入,包括贝叶斯网的编辑、证据的输入以及最终结果的输出；推理模块负责将贝叶斯网编译为合树、根据证据进行不确定性推理以及边缘化最终的联合概率；编辑模块实现用户界面动作到贝叶斯网构造的转变。本文以钢筋混凝土耐久性诊断为例,说明了贝叶斯网合树算法的推理过程；结合钢筋混凝土结构的抗震性能评估,演示了该系统如何在信息不完备这类土木工程中常见的不确定性环境下的具体应用。
(2)根据所搜集到的1918条地震记录,对具有不同屈服水平系数及周期的单自由度体系作了弹塑性时程分析,通过拟合得到了简化的延性需求计算公式；根据回归分析构造了一个新的参数用于描述地震频谱特性对延性需求的影响。在此基础上,建立了一个10节点的连续型贝叶斯网用于地震延性概率需求分析。该模型可以根据观测数据不断修正概率分布从而得到更准确的后验分布。贝叶斯网的后验分布是一个非常复杂的高维积分问题。本文引进马尔科夫链蒙特卡罗模拟方法,即基于Metropolis-Hastings采样及收敛性检验算法,计算给定地震强度观察值条件下延性需求的后验分布。算例分析了各地震强度参量及观测值对延性需求预测结果的影响。
(3)通过收集12次近场地震的71条地震纪录,分析了三种典型框架结构在近场地震作用下的响应,提出了两个基于模糊代表值的新地震强度指标。第一个地震强度指标是根据结构模糊周期,通过扩张原理获得相应的谱速度平方值模糊集,再由模糊集取重心而确定的代表值。对于中长周期的两种典型框架结构,新指标相较于已有的9种指标表现出较好的充分性和有效性。另一个强度指标则以推覆分析中模糊化的加载力向量为基础,通过扩张原理及推覆分析得到结构位移延性模糊集再取代表值求得。分析表明该指标对中短周期结构具有较好的充分性和有效性。总体说来,模糊代表值化的新地震强度指标考虑了结构在环境作用下所具有的模糊性,因此具有较高的充分性和有效性。
(4)“强剪弱弯”是保证结构延性的一个重要设计概念。本文采用区间变量表达认知不确定性,对钢筋混凝土框架柱的强剪弱弯性能进行了非经典概率可靠性分析。根据失效事件对基本事件的包含关系建立了“强剪弱弯”可靠性概率区间模型。对于含有区间值参数的结构承载力计算,引进泰勒模型以减少由于区间扩张而导致的过大误差。引进考虑“不可行度”的模拟退火遗传算法确定“强剪弱弯”的大致设计区间,根据该设计区间进行重要性采样模拟从而得到了失效概率区间。误差分析表明该方法具有较好的精度。最后通过算例分析了各设计因素对“强剪弱弯”可靠性的影响,并提出了相应的设计建议。
Uncertainty analysis is an important and comprehensive aspect in civil engineering. Uncertainty analysis theorems and methods are not only the mathematic languages for describing the uncertain realistic engineering problems, but also the computational logic to handle the uncertain realistic engineering problems. Uncertainty theorems, including Bayesian theory, interval analysis theory etc, have made the uncertainty structural analysis based on more broader theory foundations and extent the application domains of uncertainty analysis used to be based on classic probabilistic theorem. Around structural seismic analysis, primary research works of this dissertation conclude as following:
(1) Generic prototype of expert system based on Bayesian network is built for structure assessment and diagnosis. In this system, domain knowledge is expressed as discrete Bayesian network, the inference system is based on junction tree algorithm. Modular design is adopted in construction of the expert system. The whole system can be divided into user interface module, Bayesian network edit module and inference module according to the function. The user interface module accepts the user input, including edit of the Bayesian network, evidence input, and outputs results; inference module compiles the Bayesian network to junction tree, inference uncertainties with given evidences and marginalizes the result joint distribution, Bayesian network edit module converts the activity of user interface to the construction of Bayesian network. Take the example of durability diagnosis of reinforced concrete to illuminate the inference process of junction tree algorithm for discrete Bayesian network; combined with seismic performance evaluation of reinforced concret frame structures, demonstrates how the reasoning can be performed in the situation where the input information is uncertain and incomplete that frequently encountered in civil engineering.
(2) Nonlinear time history analysis of SDOF with various yield strength coefficient and period are performed based on1918earthquake ground motion records; simplified formula of ductility demand is acquired by curve fitting. A new parameter that quantifies the earthquake spectrum character effect on the ductility demand is constructed by regression analysis. Based on above, a ten-node continuous Bayesian network is established for seismic ductility demand probability analysis. The Bayesian network can acquire the posterior distribution which is more accurate updated by observed data. The posterior probability distribution involved in Bayesian network updating is a complicated multi-dimensional integral, Markov Chain Monte Carlo method, more specifically, Metropolis-Hastings sampling algorithm and convergence diagnosis algorithm, is introduced to update the ductility demand posterior probability distribution with earthquake intensity observations. Case study is carried out to analyze how the earthquake intensity parameters and given observations effect on the calculation results.
(3) Based on71time history acceleration records of12near-fault earthquakes occurred in recent years, responses of three typical frame structures are analyzed and two new intensity measures are proposed. First intensity measure, based on the fuzzy structure vibration period, acquiring the corresponding squared spectrum velocity fuzzy set according to extension principle, is determined as representative value by taking the center of gravity of fuzzy set. For the frame structures with medium and long period, the new measure exhibits more efficiency and sufficiency than other9present available intensity measures. Another intensity measure, based on fuzzy valued force shape vector used in pushover analysis, obtaining the fuzzy set of displacement ductility by extension principle and pushover analysis, is also determined as representative value. This new measure is efficiency and sufficiency for the frame structures with medium and short period. In general, new fuzzy representative valued IMs are more efficiency and sufficiency than other available IMs for consideration of vague uncertainty of structure under complicated realistic circumstance.
(4) In the seismic design of reinforced concrete structures,"strong shear weak bending" is an important design conception to guarantee the ductibility of the structure. Interval variable is introduced to express the epistemic uncertainty and failure probability interval of strong shear weak bending of reinforced concrete column is analyzed. The interval-valued probabilistic reliability model for "strong shear weak bending" is formulated according to the inclusion relationship of the element events and the failure event. For the calculation of the resistance capability involving interval-valued parameters, Taylor model is introduced in computation to reduce the error induced by interval inflation. The simulated annealing genetic algorithm considering "infeasible degree" is applied to determine the approximate design interval of the "strong shear weak bending". A specific sampling function constructed by such design interval is adopted to obtain the interval-valued probabilistic reliability index; error analysis indicates that the precision of the method is acceptable. Case study is carried out to analyze the different design parameters affecting the reliability and corresponding design suggestions are proposed.
引文
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