基于最大熵原理与最优化方法的隧道衬砌结构可靠度分析

针对隧道衬砌结构参数的随机性、分布的多样性与极限状态功能函数高度非线性的特征,运用最大熵原理对隧道衬砌结构参数进行估计,得到符合实际的参数估计值；然后,根据隧道衬砌结构稳定的极限状态方程,从结构可靠度指标的几何涵义出发,建立其可靠度指标计算的优化数学模型,并运用Microsoft Excel工作表中的规划求解功能得到其可靠度指标.结合工程实际,给出具体算例,且指出提高隧道衬砌结构可靠度的途径.研究结果表明:该方法用于计算工程结构可靠度指标无需将状态函数线性化,不受基本变量维数限制,收敛速度快,计算效率高,且与蒙特卡罗100万次直接抽样法计算结果相比,具有很高的精度,能广泛适用于隧道及地下工程领域的可靠度计算和分析.

Structural reliability analysis of tunnel lining based on maximal entropy principle and optimization method

Considering the facts that the parameters of tunnel lining structures are random,the distributions are various,and the limit state functions are highly nonlinear,the practical parameters of tunnel lining structures were estimated and presented.The calculations were formulated in maximal entropy principle,so that the actual parameters were obtained.According to the limit state equation of stability of tunnel lining and the geometry meaning of structural reliability index,a reliability?index?calculating model was established based on optimum algorithm.The structural reliability index was calculated by using the function of programming solver in Microsoft Excel.Detailed calculation procedures,an example and the methods to improve the reliability of tunnel lining structure were given.The results show that this method with a fast convergence and a high calculation efficiency does not linearizate the limit state function and the limit of dimensions of essential variables,and it has high calculating precision compared with that calculated by the one-million-time Monte-Carlo direct sampling method.