概率密度演化理论的拟对称点法

The Use of Quasi-symmetric Point Method in Probability Density Evolution Theory

概率密度演化方法是进行随机结构动力分析、随机振动及复合随机振动分析卓有成效的新方法,其分析精度与计算效率在很大程度上取决于随机变量空间离散代表点的选取规则。在高维情况下,目前仍无可以兼顾精度与效率的选点规则。基于高维数值积分的拟对称点法,建议了高维随机变量空间选点的拟对称点法,并给出相应赋得概率的计算方法。实际算例表明,拟对称点法在高维情况下有着非常良好的效果。

The probability density evolution method（PDEM） is proved to be an effective way for dynamic analysis of stochastic structures,random vibration analysis and composite random vibration analysis.However,the accuracy and computational efficiency of PDEM is directly dependent on the strategy of selecting discrete representative points in random variables space.Up to now,there is not a strategy which can give consideration to both accuracy and efficiency in very high dimension.Enlightened by the quasi-symmetric point method successfully employed in high-dimensional numerical integration,the strategy of selecting points in high-dimensional random variables space via quasi-symmetric point method is proposed in the present paper.The method for calculating the assigned probability is also given.The actual example indicates that the proposed method has a very good effect for PDEM in high dimension.