相关变量生成算法及边坡可靠度Monte Carlo模拟

发布时间：2018-02-25 08:56

本文关键词： 结构可靠度自回归模型随机模拟安全系数　出处：《岩土力学》2017年11期 　论文类型：期刊论文

【摘要】：描述变量相关性的多元分布模型有着广泛的工程应用。利用多元线性自回归模型和排序算法,研究了具有指定边缘分布和指定相关结构的多维随机变量的生成算法。基于MATLAB语言编程实现了该算法。将该算法应用于结构可靠度和边坡可靠度直接抽样Monte Carlo模拟计算问题中,解决了传统Monte Carlo模拟难以考虑变量互相关性的难题。数值实验表明,该方法计算结果精确,可以放松理论模型的理想化要求,能更真实的反映问题实际。将该方法与一次二阶矩方法计算结果对比发现,一次二阶矩方法往往对可靠度有过高的估计。此外失效概率对变量分布类型比较敏感,相同的安全系数可能对应不同的失效概率。提出的方法可以应用于复杂结构系统的可靠度计算问题,并可推广应用于其他领域的相依变量的仿真问题。
[Abstract]:The multivariate distribution model, which describes the correlation of variables, has a wide range of engineering applications, using multivariate linear autoregressive model and sorting algorithm, The algorithm of generating multidimensional random variables with specified edge distribution and specific correlation structure is studied. The algorithm is implemented by programming based on MATLAB language. The algorithm is applied to the direct sampling Monte Carlo simulation of structural reliability and slope reliability. The problem that the traditional Monte Carlo simulation is difficult to consider the interrelation of variables is solved. The numerical experiments show that the method is accurate and can relax the idealized requirements of the theoretical model. Comparing the results of this method with that of the first-order second-moment method, it is found that the first-order second-moment method often has an overestimated reliability. In addition, the failure probability is more sensitive to the type of variable distribution. The same safety factor may correspond to different failure probability. The proposed method can be applied to the reliability calculation of complex structural systems and can be extended to the simulation of dependent variables in other fields.
【作者单位】：三峡大学三峡库区地质灾害教育部重点实验室;三峡大学理学院;中国三峡建设管理有限公司;
【基金】：国家自然科学基金重点项目(No.51439003) 水利部公益性行业科研专项经费项目(No.201401029) 湖北省自然科学基金(2015CFB545)~~
【分类号】：TU43

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