Fault Diagnosis of Distributed Parameter Systems Modeled by Linear Parabolic Partial Differential Equations with State Faults


In this paper, the problem of fault diagnosis in distributed parameter systems (DPS) is investigated. The behavior of DPS is best described by partial differential equation (PDE) models. In contrast to transforming the DPS into a finite set of ordinary differential equations (ODE) prior to the design of control or fault detection schemes by using significant approximations, thus reducing the accuracy and reliability of the overall system, in this paper, the PDE representation of the system is directly utilized to construct a fault detection observer. A fault is detected by comparing the detection residual, which is the difference between measured and estimated outputs, with a predefined detection threshold. Once the fault is detected, an adaptive approximator is activated to learn the fault function. The estimated fault parameters are then compared with their failure thresholds to provide an estimate of the remaining useful life of the system. The scheme is verified in simulations on a heat system which is described by parabolic PDEs.


Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center

Keywords and Phrases

Equations of state; Failure analysis; Ordinary differential equations; Partial differential equations; Detection threshold; Distributed parameter systems; Failure thresholds; Fault detection schemes; Linear-parabolic; Ordinary differential equation (ODE); Partial differential equations (PDE); Remaining useful lives; Fault detection

International Standard Serial Number (ISSN)

0022-0434; 1528-9028

Document Type

Article - Journal

Document Version


File Type





© 2018 American Society of Mechanical Engineers (ASME), All rights reserved.

Publication Date

01 Jan 2018