For diagnosis and prognosis, we model only a subset of the complete WRS shown in __Fig. 2__ . This subset is shown in Fig. 3 below, and consists of all components of the complete WRS except the Antiscale Supply Tank, pH Adjust Tank, the NaCl Supply Tank, and Pumps 5 - 7.

In the hydraulic domain, we denote volumetric flow rate as q and hydraulic pressure as p. The pressures are the state variables in our model. As shown in Fig. 3, the pressures at the bottom of the Waste Water Tank, Feed Tank 1, Feed Tank 2, and Product Tank are denoted by p_{WT}, p_{FT1}, p_{FT2}, and p_{Prod}, respectively. The FO (resp. RO) module is modeled as two tanks, FO1 and FO2 (resp. RO1 and RO2), with pressures p_{FO1} and p_{FO2} (resp. p_{RO1} and p_{RO2}), are separated by the FO (resp. RO) membrane, and p_{FO} (resp. p_{RO}) denotes the volumetric flow rate of water across the FO (resp. RO) membrane. The pipe segments Pipe 1 and Pipe 2, between Pump 2 and Filter 1, and Pump 4 and Filter 2, respectively, are also modeled as very small tanks, with pressures, p_{Pipe1} and p_{Pipe2}, respectively. The outflow rate of Pump 1, Pump 2, Pump 4, and RO Pump are denoted by q_{Pump1}, q_{Pump2}, q_{Pump4}, and q_{ROPump}, respectively. The flow through Filter 1 and Filter 2 are denoted by q_{Filt1} and q_{Filt2}, respectively, and q_{Prod} denotes the rate of flow of clean water into the Product Tank from the RO Module. q_{FO1FT2} denotes the flow of water from the FO module to Feed Tank 2, and q_{RO1FO2} denotes the flow of water from the RO module to the FO module.