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Research Papers

# Full- and Reduced-Order Fault Detection Filter Design With Application in Flow Transmission Lines

[+] Author and Article Information
Saeed Salavati

Department of Mechanical Engineering,
University of Houston,
Houston, TX 77004
e-mail: ssalavatidezfuli@uh.edu

Department of Mechanical Engineering,
University of Houston,
Houston, TX 77004

Reza Tafreshi

Department of Mechanical Engineering,
Texas A&M University at Qatar,
Doha, Qatar

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received March 7, 2018; final manuscript received August 30, 2018; published online October 10, 2018. Assoc. Editor: Shankar Coimbatore Subramanian.

J. Dyn. Sys., Meas., Control 141(2), 021010 (Oct 10, 2018) (12 pages) Paper No: DS-18-1114; doi: 10.1115/1.4041383 History: Received March 07, 2018; Revised August 30, 2018

## Abstract

The full- and reduced-order fault detection filter design is examined for fault diagnosis in linear time-invariant (LTI) systems in the presence of noise and disturbances. The fault detection filter design problem is formulated as an $H∞$ problem using a linear fractional transformation (LFT) framework and the solution is based on the bounded real lemma (BRL). Necessary and sufficient conditions for the existence of the fault detection filter are presented in the form of linear matrix inequalities (LMIs) resulting in a convex problem for the full-order filter design and a rank-constrained nonconvex problem for the reduced-order filter design. By minimizing the sensitivity of the filter residuals to noise and disturbances, the fault detection objective is fulfilled. A reference model can be incorporated in the design in order to shape the desired performance of the fault detection filter. The proposed fault detection and isolation (FDI) framework is applied to detect instrumentation and sensor faults in fluid transmission and pipeline systems. To this end, a lumped parameter framework for modeling infinite-dimensional fluid transient systems is utilized and a low-order model is obtained to pursue the instrumentation fault diagnosis objective. Full- and reduced-order filters are designed for sensor FDI. Simulations are conducted to assess the effectiveness of the proposed fault detection approach.

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## Figures

Fig. 1

Block diagram of the proposed fault detection filter scheme

Fig. 2

Linear fractional transformation scheme for the fault detection filter

Fig. 3

Inputs to system u(t)=[Pin(t) Qout(t)]T

Fig. 4

Outputs of fault free system yp(t)=[Pout(t) Qin(t)]T

Fig. 5

Residual signals r(t)=[r1(t) r2(t)]T for fault free system

Fig. 6

Outputs of system with pressure sensor and flow rate sensor faults

Fig. 7

Comparison of fault and residual signals using the full-order fault detection filter

Fig. 8

Comparison of fault and residual signals for the reduced-order fault detection filter

## Errata

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