Parity Equations


For parity equations, a process model with fixed parameters is run in parallel to the process. The difference between the process output and the model output is termed residual.

In the fault free case, the model output and the process output should be similar - provided the model is of sufficient fidelity. Thus the difference between the process otuput and the model output should be close to zero.

In the case of a fault, the process behavior will be different from the model behavior, since the model has been designed solely to mimic the fault-free case. Thus, in case of a fault, the residual will deviate more or less strongly from zero, then the residual is termed a deflected residual.


In the video, you can see how the parity based fault detection and diagnosis system detects increased leakage in the hydraulic cylinder. The increased leakage has been simulated by means of an external bypass valve with sufficiently small hydraulic flow in the open position.

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Related Publications
14Marco Muenchhof and Rolf Isermann: Zustandsüberwachung für hydraulische Proportionalwegeventile. Proceedings of the 2ter Paderborner Workshop Intelligente mechatronische Systeme, Heinz Nixdorf Institut, 2004. Language: Deutsch
15Marco Muenchhof and Rolf Isermann: Fault Detection and Diagnosis of a Linear Hydraulic Servo Axis. Proceedings of the 16th IFAC Symposium on Automatic Control in Aerospace (ACA), International Federation of Automatic Control, 2004. Language: Englisch
16Marco Muenchhof and Rolf Isermann: Comparison of Change Detection Methods for a Residual of a Hydraulic Servo Axis. Proceedings of the 16th IFAC World Congress, International Federation of Automatic Control, 2005. Language: Englisch
19Marco Muenchhof: Model-Based Fault Management for a Hydraulic Servo Axis. Proceedings of the 5. Internationales Fluidtechnisches Kolloquium, IFAS Aachen, 2006. Language: Englisch
21Marco Muenchhof: Model-Based Fault Detection for a Hydraulic Servo Axis: Fortschrittberichte Reihe 8, Nr. 1105. VDI-Verlag, 2006. Language: Englisch
23Marco Muenchhof: Modellbasierte Hydraulik-Überwwachung. O+P Zeitschrift für Fluidtechnik, 4, 2007. Language: Deutsch
24Marco Muenchhof: Fehlerdiagnose für hydraulische Servo-Achsen. at Automatisierungstechnik, 2, 2007. Language: Deutsch
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