非高斯风压极值估计:基于矩的转换过程法的抽样误差对比研究

吴凤波1,黄国庆2,刘敏2,彭留留2

振动与冲击 ›› 2020, Vol. 39 ›› Issue (18) : 20-26.

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (18) : 20-26.
论文

非高斯风压极值估计:基于矩的转换过程法的抽样误差对比研究

  • 吴凤波1,黄国庆2,刘敏2,彭留留2
作者信息 +

Extremes estimation of non-Gaussian wind pressures: a comparative study on sampling errors based on a moment-based translation process model

  • WU Fengbo1,HUANG Guoqing2,LIU Min2,PENG Liuliu2
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摘要

非高斯风压极值的准确估计对于建筑结构抗风设计非常重要。由于使用方便,转换过程法被广泛用于非高斯风压极值估计。转换过程法中典型的转换函数模型有Hermite多项式模型(Hermite polynomial model,HPM)、Johnson转换模型(Johnson transformation model, JTM)及平移广义对数正态分布 (Shifted generalized lognormal distribution, SGLD)模型。通常,这三个转换函数模型的参数估计仅需数据的前四阶矩,因而这些模型被称为基于矩的转换函数模型。实际工程设计中用于计算风压极值的数据通常是有限长度的,而基于有限长度数据计算的前四阶矩具有抽样误差,致使基于矩的转换函数模型估计的风压极值亦具有抽样误差。现阶段对于以上三种模型估计非高斯风压极值所引起的极值抽样误差的区别尚不清楚。为了对三种模型估计极值时的抽样误差进行对比研究,本文首先介绍了HPM、JTM和SGLD三个模型;其次,给出了三个模型估计非高斯极值的抽样误差的理论方法;随后基于理论方法的计算结果对比了三个模型估计的极值的抽样误差;最后,基于超长风压风洞试验数据对三种模型极值估计时的抽样误差进行了系统的评估和验证。结果表明:HPM对非高斯风压极值抽样误差的估计效果通常比SGLD模型和JTM估计的效果更好。本文研究结果可为合理选择非高斯风压极值估计模型提供一定的指导。

Abstract

Accurate estimation of extreme values of non-Gaussian wind pressures is important for building structural wind resistance design. Due to its ease of use, translation process method is widely used to estimate the non-Gaussian extremes. Hermite polynomial model (HPM), Johnson transformation model (JTM) and Shifted generalized lognormal distribution (SGLD) model are representatives of the translation function used in the translation process method. The model coefficients in three models are usually estimated based on the first four statistical moments from data, thus the three models are described as moment-based translation function models. In practical design, the length of wind pressure data used for analysis is often limited, resulting in sampling errors in the first four moments. These sampling errors will subsequently cause some sampling errors of the estimated extreme values. However, the differences among the sampling errors in moments and uncertainties in estimation of extremes by these three models are unclear. To compare the sampling errors in estimation of extremes by three models, HPM、JTM and SGLD are firstly introduced in this study; Next, the method of estimating the sampling error of peak factors based on moment-based translation function models are given; Then, the sampling errors of moments and peak factors by three models are given and compared based on the theoretical analysis. Finally, the performance of sampling errors in HPM, JTM and SGLD are compared with each other using a very long wind pressure data. Results showed the performance of estimating sampling errors of non-Gaussian extremes by HPM is generally more satisfactory compared to that by JTM and SGLD. The results can provide the guidance for reasonable selection of models.

关键词

非高斯风压 / 极值 / 转换过程法 / Hermite多项式模型 / Johnson转换模型 / 平移广义对数正态分布 / 抽样误差

Key words

 Non-Gaussian wind pressures / Extremes / Translate process method / Hermite polynomial model / Johnson

引用本文

导出引用
吴凤波1,黄国庆2,刘敏2,彭留留2. 非高斯风压极值估计:基于矩的转换过程法的抽样误差对比研究[J]. 振动与冲击, 2020, 39(18): 20-26
WU Fengbo1,HUANG Guoqing2,LIU Min2,PENG Liuliu2. Extremes estimation of non-Gaussian wind pressures: a comparative study on sampling errors based on a moment-based translation process model[J]. Journal of Vibration and Shock, 2020, 39(18): 20-26

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