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浙江大学学报(工学版)  2020, Vol. 54 Issue (2): 241-247    DOI: 10.3785/j.issn.1008-973X.2020.02.004
土木与交通工程     
基于拟蒙特卡罗方法的供水管网抗震可靠性分析并行化研究
龙立1,2(),郑山锁1,2,*(),周炎1,2,贺金川3,孟宏立1,2,蔡永龙1,2
1. 西安建筑科技大学 土木工程学院,陕西 西安 710055
2. 西安建筑科技大学 结构工程与抗震教育部重点实验室,陕西 西安 710055
3. 西安建筑科技大学 建筑设计研究院,陕西 西安 710055
Parallel study of seismic reliability analysis of water supply pipe network based on quasi-Monte Carlo method
Li LONG1,2(),Shan-suo ZHENG1,2,*(),Yan ZHOU1,2,Jin-chuan HE3,Hong-li MENG1,2,Yong-long CAI1,2
1. School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
2. Key Laboratory of Structural Engineering and Earthquake Resistance, Ministry of Education, Xi’an University of Architecture and Technology, Xi’an 710055, China
3. Institute of Architectural Design and Research, Xi’an University of Architecture and Technology, Xi’an 710055, China
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摘要:

为了提高基于蒙特卡罗(Monte Carlo)方法的供水管网抗震可靠性分析效率,以低偏差Sobol点列替代伪随机数序列对供水管网节点和管段破坏概率进行抽样,结合宽度优先搜索算法,提出基于拟Monte Carlo方法和统一计算设备架构(CUDA)的供水管网抗震可靠性分析并行算法,并从内存、执行配置和指令等方面优化并行算法. 以某城市供水管网系统为例,对比串行和并行计算方法的精度及效率,分析Sobol点列和伪随机数序列对管网可靠性分析的影响. 结果表明,并行和串行方法计算结果的误差最大为0.52%,并行方法最高加速比为串行算法的96倍,在保证结果精度的同时大幅度提高计算效率. 基于Sobol点列进行1 000次并行模拟及基于伪随机数序列进行5 000次并行模拟,2种模拟结果与基于模糊数学法的解析值的最大误差分别为0.2%、0.4%,表明基于拟Monte Carlo的并行方法具有更高的精确度,更快的收敛速度.

关键词: 供水管网统一计算设备架构(CUDA)宽度优先搜索并行计算网络可靠性分析拟Monte Carlo方法    
Abstract:

In order to improve the seismic reliability analysis efficiency of water supply pipe network based on Monte Carlo simulation, the failure probabilities of water supply pipe network nodes and pipes were sampled by using low discrepancy Sobol sequence instead of pseudo-random number sequence. Combined with the breadth-first search algorithm, a parallel algorithm for seismic reliability analysis of water supply pipe network based on quasi-Monte Carlo method and compute unified device architecture (CUDA) was proposed. The parallel algorithm was optimized from the aspects of memory, execution configuration and instructions. A city water supply pipe network was taken as the computational example, the accuracy and efficiency of serial and parallel computing methods were compared, and the influence of Sobol sequence and pseudo-random number sequence on the reliability analysis of pipe network was analyzed. Results show that the maximum error of the parallel and serial methods is 0.52%. The maximum acceleration ratio of the parallel method is 96 times that of the serial method, and the parallel method significantly improves the computational efficiency while ensuring the accuracy of results. 1 000 parallel simulations were performed based on Sobol sequences and 5 000 parallel simulations were performed based on pseudo-random number sequences, and the maximum errors between the two simulation results and the analytical value based on fuzzy mathematics were 0.2% and 0.4%, respectively. It indicates that the parallel method based on quasi-Monte Carlo has higher accuracy and faster convergence speed.

Key words: water supply pipe network    compute unified device architecture (CUDA)    breadth-first search    parallel computing    network reliability analysis    quasi-Monte Carlo method
收稿日期: 2019-07-30 出版日期: 2020-03-10
CLC:  TU 990  
基金资助: 国家自然科学基金资助项目(51678475);国家科技支撑计划资助项目(2013BAJ08B03);陕西省重点研发计划资助项目(2017ZDXM-SF-093);陕西省教育厅产业化资助项目(18JC020)
通讯作者: 郑山锁     E-mail: longliforever@163.com;zhengshansuo@263.net
作者简介: 龙立(1992—),男,博士生,从事城市生命线工程地震灾害损失评估. orcid.org/0000-0001-8429-5608. E-mail: longliforever@163.com
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引用本文:

龙立,郑山锁,周炎,贺金川,孟宏立,蔡永龙. 基于拟蒙特卡罗方法的供水管网抗震可靠性分析并行化研究[J]. 浙江大学学报(工学版), 2020, 54(2): 241-247.

Li LONG,Shan-suo ZHENG,Yan ZHOU,Jin-chuan HE,Hong-li MENG,Yong-long CAI. Parallel study of seismic reliability analysis of water supply pipe network based on quasi-Monte Carlo method. Journal of ZheJiang University (Engineering Science), 2020, 54(2): 241-247.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.02.004        http://www.zjujournals.com/eng/CN/Y2020/V54/I2/241

图 1  CUDA设备上的内存空间
图 2  基于CUDA的管网抗震可靠性分析并行计算流程
图 3  某城市区域管网平面布置图
图 4  某城市区域供水管网在不同地震作用下的连通概率
k Ts/s Tp/s Rs
1 000 9.260 0.116 80
3 000 28.351 0.313 91
5 000 47.333 0.498 95
10 000 93.723 0.972 96
表 1  串行和并行计算时间对比
序列 T/s
伪随机数 0.258
Sobol序列 0.256
表 2  抽样点生成计算时间
图 5  Monte Carlo与拟Monte Carlo在7度地震作用下的模拟结果对比
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