采用重要抽样法的结构动力可靠度计算

Dynamic reliability calculation based on importance sampling method

首次对比分析了结构动力可靠度计算的三种重要抽样法,并对部分方法进行了补充修正。单元失效域法补充了依据随机数决定抽样区间的产生方法,根据单元失效域的条件概率和权重系数给出重要抽样密度函数。方差放大系数法直接通过激励过程的特性给出重要抽样密度函数的具体表达式。功率谱法的重要抽样密度函数仅为激励幅值的函数,根据结构反应的功率谱密度增大激励幅值的方差,建议幅值样本值的联合概率密度函数可表示为幅值样本值分量的概率密度函数的连乘形式。结果表明:对于线性体系三种方法的计算效率均比Monte-Carlo法有显著提高,而单元失效域法的计算效率又比另两种方法高。

Three importance sampling methods for dynamic reliability calculation are compared for the first time. Some complement and modification are made to the original three methods. The first approach is a new approach named elementary failure regions method. The method of generating random numbers is proposed. Importance sampling density function is proposed according to conditional proba- bility density functions of elementary failure regions and the weights. The second approach presents de- tailed importance sampling density function through amplificatory factor of variance and character of the excitation. The amplification of variance can increase the chance of structural failure. Only the amplitudes of the excitation are generated with importance sampling density function for the third approach. The power spectral density of the structural response is used to augment variances of amplitudes. Joint probability density function of amplitude sample is suggested to equal to the product of probability density functions of amplitude sample elements. Characters of the three approaches are compared through an example. The results show that the calculation efficiency of each of the three approaches is much higher than Monte-Carlo method. Calculation efficiency of the first approach is the best.