时间：5月16日 16:45 -17:10
报告题目：非高斯风压极值估计——基于矩的Hermite多项式模型新进展/Estimation of Non-Gaussian Extreme: New Strategy for the Moment-Based Hermite Model
摘要：研究表明，部分危险性较高的风荷载效应呈现明显的非高斯特性，如何求得非高斯过程极值的概率分布及峰值因子是风工程界一直以来非常关注的一个理论问题。高斯过程极值的概率分布及峰值因子已有理论解。由于基于矩的Hermite多项式模型具有需要较短的时程信息的优点，因此采用基于矩的Hermite多项式模型建立起非高斯过程和高斯过程之间的联系，从而获得非高斯过程极值的概率分布及峰值因子是目前常用的一种方法。本研究以非高斯风压为例，通过1590个不同的非高斯风压时程对基于矩的Hermite多项式模型的有效性进行了系统验证。研究表明，现有基于矩的Hermite多项式模型对于某些非高斯过程具有一定的局限性，其原因在于该模型目前采用的偏斜和峰态同时受该非高斯过程概率分布左尾和右尾的影响，因此有可能并不能较好的同时代表该概率分布单一尾部的特征。本研究提出采用非高斯过程的时程中大于和小于中位数的数据重新计算两套新的前四阶矩分别更好的表达右尾和左尾的特征，基于右尾和左尾的新四阶矩分别计算极大值和极小值的概率分布及峰值因子。结果表明，该方法可以有效的提高Hermite多项式模型的适用性。此外，针对基于矩的Hermite多项式模型采用短时距存在抽样误差的问题，本研究提出了估算非高斯相关过程偏斜和峰态抽样误差的解析表达式，在此基础上基于一次二阶矩方法提出了估计Hermite模型抽样误差的解析表达式。
Title: Revisiting the Estimation of Extreme Value Distribution and Peak factor of non-Gaussian Process by Moment-based Hermite Model
Abstract: The extreme value distribution and peak factor of a non-Gaussian process are often estimated through those of the underlying Gaussian process by moment-based Hermite polynomial function model. The performance of this model is comprehensively investigated as applied to various non-Gaussian wind pressures on a large span saddle type roof, by comparing the estimated peak factors with those directly derived from the long-term wind tunnel data. The results showed that the moment-based model approach can be less accurate for a large number of non-Gaussian pressure data. One of the reasons is that the skewness and kurtosis are statistical moments affected by both positive and negative probability distribution tails, thus are less specific in defining only one of the distribution tails which determines the statistics of maximum or minimum. To improve the accuracy of the moment-based model approach, new statistical moments are defined using the distribution greater or lower than the median for the estimation of distribution of maximum or minimum, respectively. The distributions of maximum and minimum are addressed separately using newly defined two sets of statistical moments with zero skewness. The effectiveness of the newly proposed approach is examined for various non-Gaussian wind pressures.
The moment-based Hermite model coefficients are determined by the skewness and kurtosis of the non-Gaussian process. This study further examines the sampling errors in the estimations of skewness and kurtosis and peak factor of non-Gaussian process when limited length of data is used for the estimations. Formulations are provided to determine the sampling errors of the skewness and kurtosis based on the estimated four statistical moments. The mean and variance of peak factor are then calculated based on the first order second moment (FOSM) method. The proposed approach is applied to various non-Gaussian wind pressures on a large span saddle type roof. Its accuracy and effectiveness are examined by comparing the estimated standard error of peak factor with those directly derived from the long-term wind tunnel data.
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