供水管网概率水力模型线性化求解方法

Probabilistic hydraulic simulation of water supply network by linearized deterministic hydraulic model

针对确定性水力模型无法模拟节点流量的随机变化对于节点水压、管段流量的影响,只能获得某一工况下的计算结果的问题,通过将确定性水力模型在节点流量取数学期望时进行线性化,将节点水压与管段流量用节点流量的线性组合进行表达,从而利用节点流量的数学期望和标准差,求得节点水压与管段流量的概率分布.随机试验验证表明,概率水力模型的线性化求解方法,求解结果与随机试验方法计算结果吻合良好.这说明在节点流量数学期望值附近,可以利用线性化确定性水力模型进行供水管网的概率水力模拟.

Since many parameters in a water supply network hydraulic model are random variables,and deterministic hydraulic models cannot simulate the fluctuation of nodal heads and pipe flows according to the fluctuation of these random parameters,hydraulic simulation can only obtain results according to certain input parameters.Through linearizing the deterministic hydraulic model at the expected values of nodal flows,the nodal heads and pipe flows can be formulated as linear combinations of nodal flows.The probability density curves of nodal heads and pipe flows can be calculated using the expected values and variances of nodal flows.Example verification shows that the results of probabilistic hydraulic simulation are accordant with those of Monte Carlo simulation.This indicates that near the expected values of nodal flows,the linearized deterministic hydraulic models can be used for probabilistic hydraulic simulation of water supply networks.