稳态流体管网的灵敏度

Sensitivity of steady fluid piping networks

引入微分灵敏度和大变化灵敏度的数学原理,导出了它们在稳态流体网络中的计算公式和求解方法,从而在流体网络中当某些分支参数产生微小变化或任意变化时,能分别利用微分灵敏度和大变化灵敏度来反映这些参数变化对网络响应的影响.通过对加热管网算例的比较分析,证明了流体网络中某些参数任意改变后,采用大变化灵敏度分析方法,可以获得网络响应的准确解.网络中m个分支参数的较大变化会引起n个分支流量的变化,将它们对整个网络的影响分开考虑,易于区分开网络系统的故障区域和流量的正常波动区域,有利于评估流体管网的实际特性,实现在线模拟和故障诊断等.

Mathematical theories about the differential sensitivity （DS） and large change sensitivity （LCS） are introduced, and relevant computing expressions and solving methods about steady fluid piping network are also given. Therefore when parameter changes of some branches in fluid network are small or large, it is convenient to measure the variation in network output using the DS and LCS, respectively. An example of a heating network is computed and analyzed. The result suggests that an exact solution of the network output could be obtained using the LCS method when some branch parameters are subjected to arbitrary variations. Considering a network with large changes of m branches which cause a flux variations of n branches, calculating their impact on the whole network separately will differentiate the fault part of the network from the natural fluctuating region, and the work of evaluating the real characteristic of the network, online simulating and fault diagnosing will be easier.