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

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.

Parallel study of seismic reliability analysis of water supply pipe network based on quasi-Monte Carlo method

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.