大跨屋盖结构风效应不确定性及抗风设计方法研究
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摘要
基于可靠度的抗风设计是结构风工程理论发展的重要方向,而从概率的角度处理结构抗风设计中的各种不确定因素,对结构风荷载和风振响应进行不确定性分析则是构建结构抗风可靠度理论的前提和基础。大跨屋盖结构的抗风问题具有多荷载形态、多响应振型和多等效目标的特点,这种复杂性导致了各种不确定因素对于大跨屋盖结构抗风问题的影响更为显著。因此,以大跨屋盖结构作为研究对象,从理论、实验等多方面开展深入细致的风效应不确定性研究,进而提出基于概率的抗风设计方法,不仅对丰富和发展现有抗风设计理论具有重要价值,对于进一步推动我国大跨屋盖结构的应用与发展亦具有重要的现实意义。本文主要进行了如下几方面的工作
1、构建结构风效应不确定性研究的理论框架
以Davenport"风荷载链”概念为基础,构建了结构风效应不确定性研究的理论框架：确定以概率相关系数检验法和极大似然估计法对结构风效应各阶统计量的概率分布拟合优度进行定量评价,建立最优概率分布模型；以参数灵敏度分析方法定量评估各种不确定因素对结构风振响应不确定性的贡献率,获得不确定性在风荷载与风振响应间的传递规律；采用基于极值理论的估计方法计算具有确定保证率的极值风荷载和风振响应。
2、大跨屋盖风荷载的不确定性分析
对具有典型形式的大跨屋盖刚性模型进行了超过1000次的独立采样风洞试验,获得大量脉动风压样本。通过对风荷载各阶统计量(均值、标准差、偏度、峰度)进行不确定性分析,建立了相应的概率描述模型,研究发现正态分布和对数正态分布是脉动风压前3阶统计量的最优分布,广义极值分布是峰度系数的最优分布。基于极值理论建立了极值风压的概率模型,探讨了极值风压概率分布与特征湍流的关系；对传统峰值因子法的荷载保证率进行了评估,发现峰值因子法无法给出具有一致保证率的极值风压分布,且较大程度的低估了最不利负压,误差率在20%-30%之间。
3、空间结构风振响应的不确定性分析
以多次独立采样风洞试验获得的大量脉动风荷载样本为激励,应用全局灵敏度分析方法-Sobol'方差分解法对空间结构极值风振响应进行了参数灵敏度分析,定量评估了各种不确定因素对结构风振响应不确定性的贡献率,研究发现：①结构风振响应的不确定性主要受风荷载不确定性控制；②结构风振响应的参数灵敏度与共振响应在总响应中的比重有关,共振响应越大,结构对风荷载越敏感。建立了结构动力极值响应的概率分布模型,探讨了极值风响应的概率分布特征,并与峰值因子法进行了对比,发现峰值因子法无法给出具有一致保证率的极值风振响应。
4、提出具有确定保证率的围护结构设计风荷载分析方法
为获得具有确定保证率的围护结构设计风荷载,提出了针对较小容量样本的高效概率分析方法-改进“独立风暴法”,其基本思路是设定某一荷载阂值,将连续超出该阂值的时段记为一个独立脉冲,将每个独立脉冲的最大值作为一个极值样本进行概率分析。由于样本抽取时保证了各脉冲极值的独立性,且各独立脉冲的形成机制具有较好的一致性,因此应用这一方法可对较小容量样本获得较为精确的概率模型。
5、提出具有确定保证率的主体结构设计风荷载分析方法
针对大跨屋盖结构多振型参振、等效目标众多的特点,提出了具有确定保证率的主体结构设计风荷载确定方法-一致等效静风荷载分析方法,其基本思想是：分别建立多目标等效方程组和约束方程组,前者的目的是获得与各等效目标吻合程度最好的解,后者的目的是限制某些奇异荷载作用模式的出现,从而解决了大跨屋盖结构等效静风荷载研究中突出存在的多目标等效问题,使主体结构设计风荷载在整体上具有一致的保证率
Reliability based wind-resistant design is an important development directionin the research of wind engineering field. The probabilistic assessment of windloads and load effects on structures, which considers various uncertainties, isessential for a reliability-based risk-consistent structural design to strong winds.Wind-resistant design of large-span structures is characterized as: complex time andspatial distribution of fluctuating wind; multi-mode vibration of wind-inducedresponse; multiple equivalent objectives to calculate equivalent static wind load(ESWL), which makes the effect of uncertainties more significant. Therefore, it hasimportant theoretical value in wind-resistant design and practical significance in thedevelopment of large-span space structures to carry out thorough research onuncertainty of wind response of large-span space structures by both theoretical andexperimental methods. The main contents in this paper are shown as following:
1. The research framework of wind effect uncertainty analysis
Based on the concept of wind load chains proposed by Davenport, the researchframework of wind effect uncertainty analysis is established. Probability plotcorrelation coefficient (PPCC) method and maximum likelihood estimation methodare adopted to identify the appropriate marginal probability distribution of thestatistics of wind effect. Then global sensitivity analysis is performed in order todiscuss the mechanism of uncertainty propagation. The extreme wind load andresponse under a certain guaranteed ratio are calculated by estimation method basedon extreme value theory.
2. Uncertainty analysis of wind load of large-span roof
More than one thousand independent runs of wind tunnel experiments arecarried out in order to obtain a large amount of independent samples. Uncertaintyanalysis is performed with regard to statistics of wind load such as mean value, rootmean square, skewness and kurtosis. Based on these work, corresponding probabilitymodel is established. Then the probability model of extreme wind pressure isproposed based on extreme value theory and the relationship between probabilitydistribution of extreme wind pressure and signature turbulence is discussed. Then theresults from traditional peak factor method are examined. It is found that it isinfeasible for peak factor method to provide distribution of extreme load pressure with consistent guaranteed ratio and the most unfavourable negative pressure isunderestimated, with an error rate of20%~30%.
3. Uncertainty analysis of wind-induced response of space structures
Based on the repeated wind tunnel tests, global parametric sensitivity analysis isperformed in order to quantify the strength and relevance of the inputs in determiningthe variation in wind-induced response. The propagation law of uncertainty betweenwind load and wind-induced response is discussed. It is found that1) the uncertaintyof wind-induced response is mainly controlled by wind load uncertainty;2) theparameter sensitivity of wind-induced response is related to the ratio of resonantresponse to the total response. The sensitivity value is larger with the increase of theratio. Further, the parameters of generalized extreme value distribution of the largestdynamic response on typical wind-sensitive structures are established. The proposedprobability model is compared with peak factor method. It is found that peak factormethod could not provide distribution of extreme wind-induced response withconsistent guaranteed ratio.
4. Determination of design wind load for cladding under a certainguaranteed ratio
In order to determine design wind load for cladding under a certain guaranteedratio, a procedure for statistical estimation of extreme wind pressures and wind-induced response is proposed by improving Cook's "method of independent storms".Autocorrelation analysis is carried out to eliminating any shorter period maximawhich are due to other mechanisms. The new approach usually estimates the extremepressure/response more accurately than the peak factor method. Furthermore, ananalytical solution to the quantiles of pressure/response could be obtained.
5. Determination of design wind load for main structure under a certainguaranteed ratio
In order to determine design wind load for main structure under a certainguaranteed ratio, a new approach to determine the universal ESWL that reproduce thelargest load effects of large-span roof structures simultaneously is proposed. First, amulti-target equivalent equation is constructed to make the ESWL reproduce thelargest load effects of structure at the same time. Then a constraint equation relatedto the direction of wind load is constructed in order to reduce the dimension ofESWL vector and to exclude some unrealistic and curious distributions.
1、构建结构风效应不确定性研究的理论框架
以Davenport"风荷载链”概念为基础,构建了结构风效应不确定性研究的理论框架：确定以概率相关系数检验法和极大似然估计法对结构风效应各阶统计量的概率分布拟合优度进行定量评价,建立最优概率分布模型；以参数灵敏度分析方法定量评估各种不确定因素对结构风振响应不确定性的贡献率,获得不确定性在风荷载与风振响应间的传递规律；采用基于极值理论的估计方法计算具有确定保证率的极值风荷载和风振响应。
2、大跨屋盖风荷载的不确定性分析
对具有典型形式的大跨屋盖刚性模型进行了超过1000次的独立采样风洞试验,获得大量脉动风压样本。通过对风荷载各阶统计量(均值、标准差、偏度、峰度)进行不确定性分析,建立了相应的概率描述模型,研究发现正态分布和对数正态分布是脉动风压前3阶统计量的最优分布,广义极值分布是峰度系数的最优分布。基于极值理论建立了极值风压的概率模型,探讨了极值风压概率分布与特征湍流的关系；对传统峰值因子法的荷载保证率进行了评估,发现峰值因子法无法给出具有一致保证率的极值风压分布,且较大程度的低估了最不利负压,误差率在20%-30%之间。
3、空间结构风振响应的不确定性分析
以多次独立采样风洞试验获得的大量脉动风荷载样本为激励,应用全局灵敏度分析方法-Sobol'方差分解法对空间结构极值风振响应进行了参数灵敏度分析,定量评估了各种不确定因素对结构风振响应不确定性的贡献率,研究发现：①结构风振响应的不确定性主要受风荷载不确定性控制；②结构风振响应的参数灵敏度与共振响应在总响应中的比重有关,共振响应越大,结构对风荷载越敏感。建立了结构动力极值响应的概率分布模型,探讨了极值风响应的概率分布特征,并与峰值因子法进行了对比,发现峰值因子法无法给出具有一致保证率的极值风振响应。
4、提出具有确定保证率的围护结构设计风荷载分析方法
为获得具有确定保证率的围护结构设计风荷载,提出了针对较小容量样本的高效概率分析方法-改进“独立风暴法”,其基本思路是设定某一荷载阂值,将连续超出该阂值的时段记为一个独立脉冲,将每个独立脉冲的最大值作为一个极值样本进行概率分析。由于样本抽取时保证了各脉冲极值的独立性,且各独立脉冲的形成机制具有较好的一致性,因此应用这一方法可对较小容量样本获得较为精确的概率模型。
5、提出具有确定保证率的主体结构设计风荷载分析方法
针对大跨屋盖结构多振型参振、等效目标众多的特点,提出了具有确定保证率的主体结构设计风荷载确定方法-一致等效静风荷载分析方法,其基本思想是：分别建立多目标等效方程组和约束方程组,前者的目的是获得与各等效目标吻合程度最好的解,后者的目的是限制某些奇异荷载作用模式的出现,从而解决了大跨屋盖结构等效静风荷载研究中突出存在的多目标等效问题,使主体结构设计风荷载在整体上具有一致的保证率
Reliability based wind-resistant design is an important development directionin the research of wind engineering field. The probabilistic assessment of windloads and load effects on structures, which considers various uncertainties, isessential for a reliability-based risk-consistent structural design to strong winds.Wind-resistant design of large-span structures is characterized as: complex time andspatial distribution of fluctuating wind; multi-mode vibration of wind-inducedresponse; multiple equivalent objectives to calculate equivalent static wind load(ESWL), which makes the effect of uncertainties more significant. Therefore, it hasimportant theoretical value in wind-resistant design and practical significance in thedevelopment of large-span space structures to carry out thorough research onuncertainty of wind response of large-span space structures by both theoretical andexperimental methods. The main contents in this paper are shown as following:
1. The research framework of wind effect uncertainty analysis
Based on the concept of wind load chains proposed by Davenport, the researchframework of wind effect uncertainty analysis is established. Probability plotcorrelation coefficient (PPCC) method and maximum likelihood estimation methodare adopted to identify the appropriate marginal probability distribution of thestatistics of wind effect. Then global sensitivity analysis is performed in order todiscuss the mechanism of uncertainty propagation. The extreme wind load andresponse under a certain guaranteed ratio are calculated by estimation method basedon extreme value theory.
2. Uncertainty analysis of wind load of large-span roof
More than one thousand independent runs of wind tunnel experiments arecarried out in order to obtain a large amount of independent samples. Uncertaintyanalysis is performed with regard to statistics of wind load such as mean value, rootmean square, skewness and kurtosis. Based on these work, corresponding probabilitymodel is established. Then the probability model of extreme wind pressure isproposed based on extreme value theory and the relationship between probabilitydistribution of extreme wind pressure and signature turbulence is discussed. Then theresults from traditional peak factor method are examined. It is found that it isinfeasible for peak factor method to provide distribution of extreme load pressure with consistent guaranteed ratio and the most unfavourable negative pressure isunderestimated, with an error rate of20%~30%.
3. Uncertainty analysis of wind-induced response of space structures
Based on the repeated wind tunnel tests, global parametric sensitivity analysis isperformed in order to quantify the strength and relevance of the inputs in determiningthe variation in wind-induced response. The propagation law of uncertainty betweenwind load and wind-induced response is discussed. It is found that1) the uncertaintyof wind-induced response is mainly controlled by wind load uncertainty;2) theparameter sensitivity of wind-induced response is related to the ratio of resonantresponse to the total response. The sensitivity value is larger with the increase of theratio. Further, the parameters of generalized extreme value distribution of the largestdynamic response on typical wind-sensitive structures are established. The proposedprobability model is compared with peak factor method. It is found that peak factormethod could not provide distribution of extreme wind-induced response withconsistent guaranteed ratio.
4. Determination of design wind load for cladding under a certainguaranteed ratio
In order to determine design wind load for cladding under a certain guaranteedratio, a procedure for statistical estimation of extreme wind pressures and wind-induced response is proposed by improving Cook's "method of independent storms".Autocorrelation analysis is carried out to eliminating any shorter period maximawhich are due to other mechanisms. The new approach usually estimates the extremepressure/response more accurately than the peak factor method. Furthermore, ananalytical solution to the quantiles of pressure/response could be obtained.
5. Determination of design wind load for main structure under a certainguaranteed ratio
In order to determine design wind load for main structure under a certainguaranteed ratio, a new approach to determine the universal ESWL that reproduce thelargest load effects of large-span roof structures simultaneously is proposed. First, amulti-target equivalent equation is constructed to make the ESWL reproduce thelargest load effects of structure at the same time. Then a constraint equation relatedto the direction of wind load is constructed in order to reduce the dimension ofESWL vector and to exclude some unrealistic and curious distributions.
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