Filter-Based Fault Detection and Isolation in Distributed Parameter Systems Modeled by Parabolic Partial Differential Equations

Abstract

This paper covers model-based fault detection and isolation for linear and nonlinear distributed parameter systems (DPS). The first part mainly deals with actuator, sensor and state fault detection and isolation for a class of DPS represented by a set of coupled linear partial differential equations (PDE). A filter based observer is designed based on the linear PDE representation using which a detection residual is generated. A fault is detected when the magnitude of the detection residual exceeds a detection threshold. Upon detection, several isolation estimators are designed using filters whose output residuals are compared with predefined isolation thresholds. A fault on a linear DPS is declared to be of certain type if the corresponding isolation estimator output residual is below its isolation threshold while the other fault isolation estimator output residual is above its threshold. Next, the fault location is determined when a state fault is identified. The second part of this paper focuses on fault detection and isolation of nonlinear DPS by using a Luenberger type observer. Here fault isolation framework is introduced to isolate actuator, sensor and state faults with isolability condition by using additional boundary measurements and without filters. Finally, the effectiveness of the proposed fault detection and isolation schemes for both linear and nonlinear DPS are demonstrated through simulation.

A model‐based failure times identification for a system governed by a 2D parabolic partial differential equation

“…The finite-dimensional approximation often leads to the loss of essential intrinsic characteristics present in the original PDEs model. On the other hand, "late lumping" methods based on PDEs observer-based fault diagnosis schemes have been successfully applied to parabolic systems in various research projects, such as those mentioned in references [12][13][14][15][16][17][18]. These approaches aim to address the drawbacks of early lumping methods and provide more accurate fault diagnosis by directly considering the inherent characteristics of the PDEs model.…”