A performance evaluation method of monitoring systems for inner-basin drainage under imperfect observation

Major issues of urban drainage are coping with flooding caused by torrentia- l downpours and water pollution caused by washing loads from non-point sources. Large-scale trunk sewers and pumping stations are constructed in large Japanese cities. To reduce both types of damage due to floods and water pollution, these sewerage systems should have additional functions of storage and treatment of the washing loads. In such a case, pump operations have a key role for the reduction of damage. However, perfect observation of the state of the system is difficult since continuous observation of water levels and/or water flow in all the points of the sewers is necessary. Hence, we cannot use operation optimization techniques which require perfect observation of the system. In a certain condition, several stochastic optimization techniques only require partial state observations: systems equations and observation equations are both linear, the objective function is quadratic and the time-horizon of the problem is finite. Although there may be cases where these assumptions hold, it is hard to obtain an optimal operation policy of pumping stations in urban inner-drainage systems using these optimization techniques, since observation equations, at least, are non-linear in most situations. This paper focuses on this partial observabi- lity of states for pump operation problems in sewerage systems. A practical method to design pump operation optimization and an evaluation method of the performance on the reduction of damage by implementing another monitoring station to the system are introduced. A numerical example is also presented to illustrate how the proposed method works.