Fault diagnosis robust

J. Chen and R.J. Patton. Robust model-based fault diagnosis for dynamic systems. Kluwer Academic Publishers, 1999. 

The literature focused on model-based FD presents a few applications of observers to chemical plants. In [10] an unknown input observer is adopted for a CSTR, while in [7] and [21] an Extended Kalman Filter is used in [9] and [28] Extended Kalman Filters are used for a distillation column and a CSTR, respectively in [45] a generalized Luenberger observer is presented in [24] a geometric approach for a class of nonlinear systems is presented and applied to a polymerization process in [38] a robust observer is used for sensor faults detection and isolation in chemical batch reactors, while in [37] the robust approach is compared with an adaptive observer for actuator fault diagnosis. 

In fault diagnosis and in robust control of systems with parameter uncertainties (1.2a, 1.2b) is commonly used in a form in which the matrices are decomposed into the sum of two matrices [9-11]. One of them only depends on the nominal system parameters 0 , the other one accounts for parametric faults or for model parameter uncertainties A and may be constant or time varying. 

Bloch, G., Ouladine, M., Thomas, P. (1995). On-line fault Diagnosis of dynmic systems via robust parameter estimation. Control Engineering Practice. 12(3), 1709-1711. 

Djeziii, M. A., Merzouki, R., Quid Bouamama, B., Dauphin-Tanguy, G. (2007). Robust fault diagnosis by using bond graph approach. lEEE/ASME Transactions on Mechatronics, 12(6), 599-611. 

M. A. Djeziri, R. Merzouki, B. Quid Bouamama, G. Dauphin Tanguy (2007). Bond graph model based for robust fault diagnosis . Proceeding of the 2007 American Control Conference New York City, USA. pp. 3017-3022. 

Adaptive thresholds are designed to achieve robustness in fault diagnosis. The robustness is particularly required with respect to parameter and measurement uncertainties (sensor noise) so that misdetections and false alarms are both minimized. The active approach to robustness is based on generating residuals that are insensitive to uncertainties, but sensitive to faults. The passive approach tries to accomplish robustness in the decision-making stage. Adaptive threshold is a passive approach. 

To measure the diagnostic performance, three parameters are used. Accuracy is 1 if the diagnosis is accurate, that is, a true fault is involved in the final fault candidates set. Otherwise, accuracy is 0. Robustness is the number of wrong detected symptoms independent to the true faults. When accuracy is 1 and robustness is 0, resolution denotes the number of final fault candidates. 

Though 33 cases among 36 cases show the robustness of 0, three cases (1, 15, and 28) detect a variable independent to the true solution in short periods. This wrong detection is due to that smaller CUSUM parameters than necessary were used. In order to prevent wrong detection, CUSUM parameters are doubled for the diagnosis. With the new parameters, the wrong detection of two cases is not occurred. And, fault detection for most cases is delayed for 5-30 s. However, diagnosis accuracy and resolution for 33 cases are not effected to be same with the previous parameters. 

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