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Generating Quantitative Relationships Among Loop Components For characterization of these four relationships through mathematical equations, the GMDH method was applied to the same fault-free database. A coefficient matrix representing each model is generated by the GMDH. This matrix is used to obtain the predicted (or analytical) component value. This predicted value is then later used for fault detection. The main task of the GMDH algorithm is to find the model that best maps the input/output set for given basic functions.

The error (%) between the predicted values and the measurements for the Inlet Flow rate as a function of Bypass MOV and Inlet MOV positions. 7. The GMDH predicted values (“o”) against the test output values (“x”) for the Outlet Flow rate as a function of Water Level and Outlet MOV positions. 8. The GMDH predicted values (“o”) against the training output values (“x”) for the Outlet Flow rate as a function of Water Level and Outlet MOV positions. 9. The error (%) between the predicted values and the measurements for the Outlet Flow rate as a function of Water Level and Outlet MOV positions.

The GMDH predicted values (“o”) against the training output values (“x”) for the Inlet Flow rate as a function of Bypass MOV and Inlet MOV positions. 6. The error (%) between the predicted values and the measurements for the Inlet Flow rate as a function of Bypass MOV and Inlet MOV positions. 7. The GMDH predicted values (“o”) against the test output values (“x”) for the Outlet Flow rate as a function of Water Level and Outlet MOV positions. 8. The GMDH predicted values (“o”) against the training output values (“x”) for the Outlet Flow rate as a function of Water Level and Outlet MOV positions.

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