基于概率密度演化的锈蚀混凝土梁时变可靠性分析

建立了锈蚀钢筋混凝土梁的极限状态函数，其中引入了锈蚀不均匀系数考虑钢筋锈蚀不均匀性和随机性。根据概率守恒原理引出锈蚀钢筋混凝土梁极限状态函数的广义概率密度演化方程，并介绍了其TVD(total variation diminishing)差分格式的有限差分方法。运用“吸收边界条件”提出了基于概率密度演化理论的锈蚀钢筋混凝土梁时变可靠度计算方法。以三个锈蚀钢筋混凝土梁为例，展示广义概率密度演化方程以及时变可靠度的计算结果。通过100万次Monte Carlo模拟方法以及2范数误差指标考察了概率密度演化及时变可靠度计算结果的精准度。二阶矩信息和可靠度的对比结果显示：概率密度演化法能够以较小的计算代价，较为精确地捕捉锈蚀钢筋混凝土梁在服役期间的概率密度演化信息，较为准确地预测其时变可靠度。

Time-dependent reliability analysis for corroded RC beams based on probability density evolution theory

The limit state function for corroded reinforced concrete beams was established, in which the non-uniformity coefficient of corrosion was introduced to consider the non-uniformity of corrosion and randomness of steel bars. Then, according to the principle of conservation of probability, the generalized probability density evolution equation of the limit state function for corroded reinforced concrete beams was derived. Meanwhile,the finite difference method of TVD (total variation diminishing) difference scheme was recommended. Next, the time-dependent reliability calculation method based on the probability density evolution theory was proposed for corroded reinforced concrete beams through ‘absorption boundary conditions’. Further, the generalized probability density evolution equation and the calculation results of time-varying reliability were shown by taking three corroded reinforced concrete beams as examples. Moreover, the accuracies of the probability density evolution and the time-dependent reliability calculation were investigated through one million-scale of Monte Carlo simulation and the two-norm error index. The comparison results of the second-order moment information and the reliability show that the probability density evolution method can accurately capture the probability density evolution information of corroded reinforced concrete beams during its service period with a relative low calculation cost, and then accurately predict the time-varying reliability.