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提出了基于通用生成函数的可靠性分析方法。首先把连续随机变量离散化,并用离散变量的概率质量函数予以表示;其次根据通用生成函数运算法则计算极限状态函数的概率质量函数,再对极限状态函数的概率质量函数求各阶导数,得到极限状态函数的各阶矩;最后利用极大熵原理建立设计优化问题的数学模型,求解极限状态函数的概率密度函数和累积分布函数。文中所提出的方法避免了对极限状态函数进行灵敏度分析,也不需要求解设计验算点(MostProbable Point,MPP),适于求解混合离散变量和高度非线性问题。实例分析和与蒙特卡洛仿真对比结果验证了所提方法的有效性。
A reliability analysis method based on common generation function is proposed. Firstly, the continuous random variables are discretized and expressed by the probability mass function of the discrete variables. Secondly, the probability mass function of the limit state function is calculated according to the common generation function algorithm, and then the derivatives of the derivatives of the limit state function are obtained. Order moments of the state function. Finally, the mathematical model of the design optimization problem is established by using the principle of maximum entropy to solve the probability density function and the cumulative distribution function of the limit state function. The proposed method avoids the sensitivity analysis of the limit state function and does not require solving the MostProbable Point (MPP). It is suitable for solving the mixed discrete variables and highly nonlinear problems. The results of example analysis and Monte Carlo simulation verify the effectiveness of the proposed method.