基于Matlab优化工具箱的工程结构可靠度计算

Research for reliability of engineering structures based on Matlab's optimization tool box

将服从任意概率分布的随机变量Xi映射为标准正态随机变量Yi。从正态空间中可靠度指标β的几何意义出发,建立了求解可靠度指标β的优化模型。利用Matlab的强大优化功能求解该模型,得到可靠度指标β及验算点Y ,并讨论了该模型解的存在条件。最后给出了算例及结果比较。

Stochastic variable X_i following any probability distribution function is mapped to stochastic variable Y_i with standard normal distribution function. Optimization model for solving engineering structures reliability index β is founded based on β's geometry significance in the normal space. While solving the model,Matlab's optimization tool box is used fully. β and checking point Y~* have been gained together. At the same time,existing condition of solution of the model is discussed. Some examples are given and the results are compared in the end.