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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。
Multivariate distribution models that describe the correlation of variables have a wide range of engineering applications. Using multivariate linear autoregressive model and sorting algorithm, the generation algorithm of multidimensional random variables with specified edge distribution and specified correlation structure is studied. Based on MATLAB language programming to achieve the algorithm. The algorithm is applied to the Monte Carlo simulation of direct sampling of structural reliability and slope reliability, which solves the difficult problem that traditional Monte Carlo simulation can not consider the cross-correlation of variables. Numerical experiments show that the method is accurate and can relax the idealized requirements of the theoretical model, which can reflect the actual situation of the problem more realistically. Comparing the result of this method with that of the second-order moment method, it is found that the first-order second moment method often overestimates the reliability. In addition, the probability of failure is more sensitive to the type of variable distribution, and the same safety factor may correspond to different failure probabilities. The proposed method can be applied to the reliability calculation of complex structural systems and can be applied to the simulation of dependent variables in other fields.