- ISSN 0258-2724
- CN 51-1277/U
- EI Compendex
- Scopus
- Indexed by Core Journals of China, Chinese S&T Journal Citation Reports
- Chinese S&T Journal Citation Reports
- Chinese Science Citation Database
| Citation: | LIU Lang, ZHAO Yifei, SONG Yumin. Improvement in Numerical Solution of Probability Density Evolution Equation and Slope Stability Analysis[J]. Journal of Southwest Jiaotong University. doi: 10.3969/j.issn.0258-2724.20250470
|
To improve the computational accuracy and efficiency of the probability density evolution method in analyzing high-dimensional stochastic responses of complex structures, a total variation diminishing (TVD) scheme using Van Leer’s flux limiter and a hypersphere-based uniform point selection method are proposed. First, for the TVD scheme in difference solving, the limitations of the Roe-Sweby flux limiter are analyzed. Van Leer’s flux limiter is selected to optimize numerical solution accuracy, and its effectiveness is verified through numerical examples. Second, based on existing mathematical findings, the probability calculation formulas for the n-dimensional standard normal distribution within hyperspheres and hypercubes are derived, by which the hypersphere-based high-dimensional point selection method is quantitatively validated. Furthermore, a hypersphere-based good lattice point method is developed to generate uniform point sets and perform probability calculations within hyperspheres. Finally, taking a high slope project under construction as a case study, a probability density evolution equation for slope stability is established, and the proposed improved method is applied to calculate the slope stability coefficient. The results show that under normal service conditions and rainfall conditions, compared with 10 000 Monte Carlo simulations, the minimum errors of the probability integral for the slope stability coefficient are 0.4% and 0.2%, and the maximum errors are 2.9% and 4.2%, respectively. When addressing high-dimensional stochastic structural problems, the proposed numerical solution method demonstrates satisfactory computational accuracy and efficiency.
| [1] |
李杰, 陈建兵. 随机结构动力反应分析的概率密度演化方法[J]. 力学学报, 2003, 35(4): 437-442. doi: 10.3321/j.issn:0459-1879.2003.04.008
Li Jie, Chen Jianbing. Probability density evolution method for analysis of stochastic structural dynamic response[J]. Chinese Journal of Theoretical and Applied Mechanics, 2003, 35(4): 437-442. doi: 10.3321/j.issn:0459-1879.2003.04.008
|
| [2] |
陈建兵, 李杰. 概率密度演化理论的基本原理与若干进展[J]. 力学与实践, 2026, 48(2): 203-216. doi: 10.6052/1000-0879-25-313
Chen Jianbing, Li Jie. The fundamental principle and recent a{\mathrm{d}}Vances of the probability density evolution theory[J]. Mechanics in Engineering, 2026, 48(2): 203-216. doi: 10.6052/1000-0879-25-313
|
| [3] |
Zhou H, Fan X P, Liu Y F. Dynamic reliability analysis of the existing bridges based on probability density evolution method[J]. Structures, 2023, 57105245.
|
| [4] |
Xu L, Zhai W M, Gao J M. A probabilistic model for track random irregularities in vehicle/track coupled dynamics[J]. Applied Mathematical Modelling, 2017, 51145-158.
|
| [5] |
余志武, 张鹏, 丁叁叁. 轨道梁参数随机的磁悬浮列车-轨道梁系统概率密度演化分析[J]. 铁道学报, 2023, 45(12): 138-147. doi: 10.3969/j.issn.1001-8360.2023.12.015
Yu Zhiwu, Zhang Peng, Ding Sansan. Probability density evolution analysis of maglev train-guideway system with random guideway parameters[J]. Journal of the China Railway Society, 2023, 45(12): 138-147. doi: 10.3969/j.issn.1001-8360.2023.12.015
|
| [6] |
Zai D Z, Pang R, Xu B, et al. Slope system stability reliability analysis with multi-parameters using generalized probability density evolution method[J]. Bulletin of Engineering Geology and the Environment, 2021, 80(11): 8419-8431. doi: 10.1007/s10064-021-02399-9
|
| [7] |
Li J, Chen J B, Fan W L. The equivalent extreme-value event and evaluation of the structural system reliability[J]. Structural Safety, 2007, 29(2): 112-131. doi: 10.1016/j.strusafe.2006.03.002
|
| [8] |
Chen J B, Li J. Strategy for selecting representative points via tangent spheres in the probability density evolution method[J]. International Journal for Numerical Methods in Engineering, 2008, 74(13): 1988-2014. doi: 10.1002/nme.2246
|
| [9] |
朱志辉, 刘禹兵, 高雪萌, 等. 概率密度演化方程差分格式的计算精度及初值条件改进[J]. 工程力学, 2022, 39(11): 13-21. doi: 10.6052/j.issn.1000-4750.2021.06.0477
Zhu Zhihui, Liu Yubing, Gao Xuemeng, et al. The calculation precision of probability density evolution equation difference scheme and the improvement of initial condition[J]. Engineering Mechanics, 2022, 39(11): 13-21. doi: 10.6052/j.issn.1000-4750.2021.06.0477
|
| [10] |
石晟, 杜东升, 王曙光, 等. 概率密度演化方程TVD格式的自适应时间步长技术及其初值条件改进[J]. 力学学报, 2019, 51(4): 1223-1234. doi: 10.6052/0459-1879-18-446
Shi Sheng, Du Dongsheng, Wang Shuguang, et al. Non-uniform time step tvd scheme for probability density evolution function with improvement of initial condition[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1223-1234. doi: 10.6052/0459-1879-18-446
|
| [11] |
Papadopoulos V, Kalogeris I. A Galerkin-based formulation of the probability density evolution method for general stochastic finite element systems[J]. Computational Mechanics, 2016, 57(5): 701-716. doi: 10.1007/s00466-015-1256-9
|
| [12] |
陈建兵, 李杰. 基于概率空间剖分的结构非线性随机反应分析[J]. 华中科技大学学报(城市科学版), 2008(4): 1-5. doi: 10.3969/j.issn.2095-0985.2008.04.001
Chen Jianbing, Li Jie. Stochastic nonlinear response analysis of structures based on partition of probability-assigned space[J]. Journal of Huazhong University of Science and Technology, 2008(4): 1-5. doi: 10.3969/j.issn.2095-0985.2008.04.001
|
| [13] |
陈建兵, 李杰. 随机结构反应概率密度演化分析的切球选点法[J]. 振动工程学报, 2006, 19(1): 1-8. doi: 10.3969/j.issn.1004-4523.2006.01.001
Chen Jianbing, Li Jie. Strategy of selecting points via sphere of contact in probability density evolution method for response analysis of stochastic structures[J]. Journal of Vibration Engineering, 2006, 19(1): 1-8. doi: 10.3969/j.issn.1004-4523.2006.01.001
|
| [14] |
陈建兵, 李杰. 结构随机响应概率密度演化分析的数论选点法[J]. 力学学报, 2006, 38(1): 134-140. doi: 10.3321/j.issn:0459-1879.2006.01.019
Chen Jianbing, Li Jie. Strategy of selecting points via number theoretical method in probability density evolution analysis of stochastic response of structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(1): 134-140. doi: 10.3321/j.issn:0459-1879.2006.01.019
|
| [15] |
Li J, Chen J B. The number theoretical method in response analysis of nonlinear stochastic structures[J]. Computational Mechanics, 2007, 39(6): 693-708. doi: 10.1007/s00466-006-0054-9
|
| [16] |
陈建兵, 张圣涵. 非均布随机参数结构非线性响应的概率密度演化[J]. 力学学报, 2014, 46(1): 136-144.
Chen Jianbing, Zhang Shenghan. Probability density evolution analysis of nonlinear response of structures with non-uniform random parameters[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(1): 136-144.
|
| [17] |
Gao K, Liu G, Tang W. High-dimensional reliability analysis based on the improved number-theoretical method[J]. Applied Mathematical Modelling, 2022, 107: 151-164. doi: 10.1016/j.apm.2022.02.030
|
| [18] |
唐树江. 几类高精度高分辨率格式的构造与应用[D]. 湘潭: 湘潭大学, 2019.
|
| [19] |
Li J, Chen J B. Stochastic Dynamics of Structures[M]. New York: John Wiley & Sons, 2009.
|
| [20] |
赵一飞, 刘浪. 广义概率密度演化方程差分解法的计算精度比较与改进[J]. 南昌大学学报(工科版), 2025, 47(1): 38-43, 48. doi: 10.3969/j.issn.1006-0456.2025.01.005
Zhao Yifei, Liu Lang. Comparison and improvement of the calculation accuracy of the difference decomposition method of the generalized probability density evolution equation[J]. Journal of Nanchang University (Engineering & Technology), 2025, 47(1): 38-43,48. doi: 10.3969/j.issn.1006-0456.2025.01.005
|
| [21] |
高凯. 基于概率密度演化方法的斜拉索多幅级非线性疲劳可靠度评估[D]. 重庆: 重庆大学, 2021.
|
| [22] |
Barthe F, Guedon O, Mendelson S, et al. A Probabilistic approach to the geometry of the $ l_{p}^{n} $-Ball[J]. Ann. Probability, 2005, 33: 480-513.
|
| [23] |
杨兵, 杨斐, 盘友峰, 等. 考虑土层倾角影响的层状堆积体基覆型边坡动力失稳研究[J/OL]. 西南交通大学学报, 2025-11-06. | https://kns.cnki.net/kcms/detail/detail.aspx?dbcode=CJFD&dbname=CJFD&filename=XNJT20251105001.
|
| [24] |
GB 50330—2013 建筑边坡工程技术规范[S].
|
| [25] |
张继周, 缪林昌. 岩土参数概率分布类型及其选择标准[J]. 岩石力学与工程学报, 2009, 28(增刊2): 3526-3532. doi: 10.3321/j.issn:1000-6915.2009.z2.034
Zhang Jizhou, Miao Linchang. Types and selection criteria of probability distribution of rock and soil parameters[J]. Chinese Journal of Rock Mechanics and Engineering, 2009, 28(S2): 3526-3532. doi: 10.3321/j.issn:1000-6915.2009.z2.034
|
| [26] |
朱淳, 龚逸非, 宋盛渊, 等. 滑坡多源监测技术及预警模型研究进展与展望[J]. 西南交通大学学报, 2025, 60(6): 1373-1389. doi: 10.3969/j.issn.0258-2724.20230547
Zhu Chun, Gong Yifei, Song Shengyuan, et al. Progress and prospects of landslide multi-source monitoring technology and early warning model[J]. Journal of Southwest Jiaotong University, 2025, 60(6): 1373-1389. doi: 10.3969/j.issn.0258-2724.20230547
|
Figures(7) / Tables(3)
DownLoad:
