多次随机载荷作用下结构动态可靠性预测的概率密度演化方法

A probability density evolution method for prediction of the dynamic reliability of the structures under several times stochastic loadings

对多次随机载荷作用下结构动态可靠性预测的概率密度演化方法进行了研究。首先由一次作用载荷的概率分布函数，求得多次作用载荷的概率密度函数。在考虑结构承受多次随机载荷作用下结构强度退化和不退化的情况下，根据应力．强度干涉理论和概率密度演化方法，建立了结构的动态可靠度预测模型。应用向前差分方法求解该模型中的概率密度演化微分方程，获得任意时刻结构强度裕度的概率密度函数，进而再利用积分方法获得结构动态可靠度的预测结果。通过两个算例表明，该方法实用易行，且具有较高的计算精度。

The research on predicting the dynamic reliability of a structure under probability density evolution method was performed. Firstly, the probability chastic loadings was obtained according to that of one time stochastic loading. repeated random loadings based on a density function of several times sto- Then, the models for structural relia- bility prediction from the time response under several times stochastic loadings with strength degeneration and with- out degeneration over time were constructed by using the stress-strength interference theory and the probability den- sity evolution method. The differential equation for probability density evolution in the models was solved by using the forward differential method, thus the probability density functions of the structural strength redundancy in any time were obtained, and then, the structure＇ s dynamic reliability prediction was obtained by using an integral method. Two examples were presented to illustrate the method, and they showed it was practicable, feasible, and more accurate in prediction.