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Faulty System Modeling

Faults are modeled as unexpected changes in the system parameters. We assume the faults are persistent. Typical degradation modes of the WRS include clogged membranes, clogged filters, and sensor faults. In particular, Filter 1, Filter 2, the FO membrane, and the RO membrane all get clogged over time due to buildup of solids. These clogging faults, denoted by RFilt1, RFilt2, AFO, and ARO, respectively, are represented as gradual decrease in the coefficient of flow through the filters, RFilt1 and RFilt2, and the membrane permeabilities AFO and ARO, respectively. Sensors faults can include abrupt bias and gradual drift fault.

Modeling Filter Clogging Fault

For Filter i, the gradual decrease in RFilti is represented as dRFilti/dt = 0 when t\f, and dRFilti/dt = ΔRFilti otherwise, where tf is the time of fault occurrence, and ΔRFilt1 is the fault parameter.

Modeling Membrane Clogging Fault

For membrane j, the gradual decrease in Ai is represented as dAi/dt = 0 when t\f, and dAi/dt = ΔAi otherwise, where ΔAi is the fault parameter.

Modeling Sensor Bias Fault

A bias fault in sensor S is indicated as S(b;ΔS), and is modeled as an abrupt addition of a constant bias b added to the sensor value from the point of fault injection tf , i.e., S = S when t\f, and S = S + ΔS otherwise.

Modeling Sensor Drift Fault

A drift fault in sensor S is indicated as S(d;ΔS), and is modeled as a gradual addition of a constant drift d to the sensor value at each time step from the point of fault injection tf , i.e., dS/dt = 0 when t\f, and dS/dt = ΔS otherwise.

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