随机桥梁地震可靠度分析的改进最大熵方法

Improved maximum entropy method for seismic reliability analysis of bridges under uncertainty

摘要:

为了对复杂非线性桥梁结构进行随机地震作用下的动力可靠度分析,基于最大熵原理,构建了一种高效的桥梁非线性地震可靠度分析方法。首先阐述了桥梁结构地震可靠度分析与极值分布估计的关系,将桥梁结构的地震可靠度分析转化为对应的极值分布估计；然后建立了复杂桥梁结构非线性地震响应极值分布估计的最大熵方法,针对现有的最大熵分布求解过程受初值影响较大、不容易收敛等问题,提出一种基于似然函数的最大熵分布求解方法,从而实现了桥梁结构地震响应极值分布和地震可靠度的高效求解；最后以一座典型的高墩大跨连续刚构桥为例,通过蒙特卡洛模拟验证所提方法的精度和效率,并将结果与核密度估计和对数正态分布拟合的计算结果进行对比分析。结果表明:基于似然函数的最大熵分布求解方法不仅能够获得全局最优解,而且求解过程不受初值的影响、具有较好的数值稳定性,所提方法能够对随机地震作用下桥梁结构地震响应的极值分布和动力可靠度进行精确估计；核密度估计和对数正态分布无法对小失效概率水平下结构地震响应的极值分布进行估计,建议采用最大熵方法对桥梁结构进行地震可靠度分析。

Abstract:

For the dynamic reliability analysis of complex nonlinear bridge structures under stochastic ground motions, an efficient seismic reliability analysis method was developed based on the principle of maximum entropy. First, the relationship between the seismic reliability and extreme value distribution (EVD) of bridges was clarified. The seismic reliability of bridge structures was transformed into the corresponding EVD estimation. Then, the maximum entropy method (MEM) for estimating the EVD of nonlinear seismic responses of complex bridge structures was established. In view of the fact that the iterative solution of the existing MEM is greatly affected by the initial value and is not easy to converge, a method based on likelihood function was proposed to solve the EVD and seismic reliability of bridge structures more efficiently. Finally, a typical high-pier and long-span continuous rigid frame bridge was taken as an example. The accuracy and efficiency of the proposed method were verified via Monte Carlo simulation, and the results were compared with the results of kernel density estimation (KDE) and lognormal distribution fitting. Results show that the proposed MEM based on likelihood function could obtain the global optimal solution of EVD, and the solution process was not affected by the initial value and had good numerical stability. The method could accurately estimate the EVD and dynamic reliability of complex bridge structures under stochastic earthquakes. Both KDE and lognormal distribution failed to estimate the EVD of the structural seismic responses at small failure probability levels. It is thereby recommended that MEM is adopted for the seismic reliability analysis of bridge structures.