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Modeling the Water Recycling System

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.

Figure 3: Simplified Schematic of the Water Recycling System

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 pWT, pFT1, pFT2, and pProd, respectively. The FO (resp. RO) module is modeled as two tanks, FO1 and FO2 (resp. RO1 and RO2), with pressures pFO1 and pFO2 (resp. pRO1 and pRO2), are separated by the FO (resp. RO) membrane, and pFO (resp. pRO) 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, pPipe1 and pPipe2, respectively. The outflow rate of Pump 1, Pump 2, Pump 4, and RO Pump are denoted by qPump1, qPump2, qPump4, and qROPump, respectively. The flow through Filter 1 and Filter 2 are denoted by qFilt1 and qFilt2, respectively, and qProd denotes the rate of flow of clean water into the Product Tank from the RO Module. qFO1FT2 denotes the flow of water from the FO module to Feed Tank 2, and qRO1FO2 denotes the flow of water from the RO module to the FO module.

We model both the nominal and faulty behavior of the WRS.

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