Research Papers

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

[+] Author and Article Information
Hasan Ferdowsi

Electrical Engineering Department,
Texas A&M University—Texarkana,
7101 University Avenue,
Texarkana, TX 75503
e-mail: hfqk6@mst.edu

S. Jagannathan

Department of Electrical and
Computer Engineering,
Missouri University of Science and Technology,
301 West 16th Street,
Rolla, MO 65409
e-mail: sarangap@mst.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 5, 2016; final manuscript received July 10, 2017; published online September 8, 2017. Assoc. Editor: Davide Spinello.

J. Dyn. Sys., Meas., Control 140(1), 011010 (Sep 08, 2017) (6 pages) Paper No: DS-16-1290; doi: 10.1115/1.4037332 History: Received June 05, 2016; Revised July 10, 2017

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.

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Grahic Jump Location
Fig. 2

Estimated distributed temperature

Grahic Jump Location
Fig. 3

Detection residual and threshold

Grahic Jump Location
Fig. 4

Actual and estimated fault magnitude

Grahic Jump Location
Fig. 5

Time-to-failure estimation

Grahic Jump Location
Fig. 1

Actual system response



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