基于随机函数-谱表示的高阶矩结构动力可靠度分析方法  

Structural dynamic reliability analysis method of high-order moment based on random function-spectral representation

作　　者：张龙文 卢朝辉 ZHANG Long-wen;LU Zhao-hui(College of Water Resources and Civil Engineering,Hunan Agricultural University,Changsha 410128,China;Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]湖南农业大学水利与土木工程学院,湖南长沙410128 [2]北京工业大学城市与工程安全减灾教育部重点实验室,北京100124

出　　处：《振动工程学报》2020年第2期265-275,共11页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51820105014);湖南农业大学青年基金资助项目(18QN23)。

摘　　要：基于随机函数-谱表示模型,提出了结构响应极值前四阶矩的计算方法 ,发展了非高斯随机激励下的结构动力可靠度分析的高阶矩方法:(1)修正了随机函数单个基本随机变量的离散点集表达式;(2)根据修正的离散点集生成少量的非高斯加速度时程样本并进行结构时程分析,从而估计得到结构响应极值的前四阶矩(均值、标准差、偏度、峰度);(3)提出了四阶矩可靠指标的完整表达,并应用于计算在非高斯随机激励下的结构动力可靠度。最后,以双自由度系统及八层框架结构的动力可靠度分析为算例,验证了本文方法的精确性与高效性:在样本数量明显减少的情形下,本文方法计算的前四阶矩与Monte Carlo模拟结果相比最大相对误差为5.54%,且动力可靠度分析结果几乎一致。A method for calculating the first four moments of structural extremum responses is proposed based on the random function-spectral representation model.A high-order moment method for structural dynamic reliability analysis under nonGaussian random excitation is developed.The discrete point set expression of a single basic random variable of a random function is modified.A small amount of non-Gaussian acceleration processes is generated according to the modified discrete point set,and the time history analysis of the structure is performed,then the first four moments(i.e.,mean,standard deviation,skewness and kurtosis)of non-Gaussian structural extreme responses are estimated.The complete expression of the fourth-order moment reliability index is proposed and applied to calculate the structural dynamic reliability under non-Gaussian random excitation.Finally,the accuracy and efficiency of the proposed method are demonstrated by the dynamic reliability analysis of a two-degree-of-freedom system and an eight-story frame structure.Although the number of samples is significantly reduced,the maximum relative error of the first four moments calculated by the proposed method is 5.54%compared with the Monte Carlo simulation results.The results of dynamic reliability analysis by the proposed method are almost the same with those of Monte Carlo simulation.

关 键 词：随机函数-谱表示 动力可靠度 非高斯随机激励 前四阶矩 四阶矩法 

分 类 号：O324[理学—一般力学与力学基础] TU311.3[理学—力学]