供水管网中节点流量随机性的影响分析

供水管网中节点流量是一个随机变量。首先利用网络矩阵的理论求出了节点压力和管段流量对节点流量的偏导数矩阵。基于正态分布研究了由于节点流量的随机性所导致的节点压力和管段流量的随机性问题,利用概率论的理论求出了节点压力和管段流量的概率密度分布、均值、方差及置信区间。最后以实例说明了节点流量的随机性对管段流量和节点压力的影响。结果表明,节点流量的随机性变化对管网中的节点压力和管段流量有显著影响。

Stochastic analysis of demands at nodes in water distribution network

Demands at nodes are random variables in water distribution network.The partial de- rivative matrix of pressure heads at nodes and flow through pipes to demands at nodes are solved by the theory of network matrix.The randomicity of pressure heads at nodes and flow through pipes due to the randomicity of demands at nodes are developed based on normal distribution.With the theory of probability,the probability density distribution function,mean,variance and confidence limit are solved.At last,an example demonstrates the effect of randomicity of demands at nodes to pressure heads at nodes and flow through pipes.The results show that randomicity of demands at nodes affect pressure heads at nodes and flow through pipes remarkably.