广义概率密度演化方程差分解法的计算精度比较与改进  

Comparison and improvement of the calculation accuracy of the difference decomposition method of the generalized probability density evolution equation

作　　者：赵一飞 刘浪[1] ZHAO Yifei;LIU Lang(School of Civil Engineering,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学土木工程学院,重庆400074

出　　处：《南昌大学学报(工科版)》2025年第1期38-43,48,共7页Journal of Nanchang University(Engineering & Technology)

基　　金：国家自然科学基金资助项目(51708069);重庆市基础研究与前沿探索项目(cstc2018jcyjA2535);重庆交通大学研究生创新科研项目(2023S0030)。

摘　　要：为求解结构响应的概率密度函数,常对给定的随机样本点集求解广义概率密度演化方程(GDEE)。在工程应用中,由于GDEE一般没有解析解,采取不同的差分解法通常会带来数值误差。为探究不同差分方法的求解精度,分别对比了相同差分精度下的单边差分、Lax-Wendroff(L-W)双边差分以及Roe-Sweby、Van Leer2种符合总变差不增(TVD)格式差分的求解精度,通过数值算例和工程实例验证了求解结果的正确性以及在GDEE中的适用性。结果表明:在求解GDEE时,采用Van Leer的TVD格式对概率密度函数进行求解的方法准确性要高于Roe-Sweby的TVD格式,可有效降低差分格式所带来的求解误差。The generalized probability density evolution equation(PDEE)is often used to solve the probability density function of the structural response,for a given set of random sample points.In engineering applications,as GDEE generally has no analytical solutions,adopting different difference solution methods usually brings numerical errors.To explore the solution accuracy of different difference methods,this paper compared the solution accuracy of unilateral difference,Lax-Wendroff(L-W)bilateral difference,and Roe-Sweby and Van Leer in the same level of accuracy.Moreover,numerical examples and engineering examples were used to verify the correctness of the solution results and their applicability in GDEE.The results showed that the accuracy of the probability density function by using Van Leer TVD was better than that of Roe-Sweby's TVD format when solving GDEE.The proposed method can effectively reduce the solution error caused by the differential format.

关 键 词：概率密度演化理论 有限差分法 计算精度 边坡稳定性 TVD格式 

分 类 号：O302[理学—力学]