Testing Homogeneity of Coefficients in Distributed Systems With Application to Quality Monitoring

The problem of testing homogeneity of coefficients in distributed parameter systems (DPS) is stated and motivated by an example from the quality monitoring of the copper hot rolling process. When a system described by partial differential equation(s) (PDE) is observed using sensors or digital camera...

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Bibliographic Details
Published in:IEEE transactions on control systems technology 2008-03, Vol.16 (2), p.314-321
Main Author: Rafajlowicz, E.
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Condition monitoring
Control theory. Systems
Copper
Differential equations
Digital cameras
Distributed parameter systems
Distributed parameter systems (DPS)
Estimates
Exact sciences and technology
Homogeneity
Hot rolling
identification
Modelling and identification
Monitoring
parameter estimation
Partial differential equations
quality control
Sensor phenomena and characterization
Sensor systems
State estimation
Statistics
Studies
System testing
testing homogeneity
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Description
Summary:The problem of testing homogeneity of coefficients in distributed parameter systems (DPS) is stated and motivated by an example from the quality monitoring of the copper hot rolling process. When a system described by partial differential equation(s) (PDE) is observed using sensors or digital cameras and its coefficients are suspected to be inhomogeneous in space, then it is rather difficult to estimate them from noisy observations. Such observations can however be sufficient to test whether these coefficients are constant in space. The test for homogeneity is proposed, which is computationally simple and applicable online. The main idea for its construction is based on the expansion of a PDE solution into a series of eigenfunctions. Then, coefficients of this series are estimated from the observations of the process state: directly and indirectly, through estimates of PDE parameters, provided that they are constant. Finally, the squared differences between these two sets of coefficients are used to form the test statistic. The results of verification of the test on simulated and experimental data are also provided.
ISSN:1063-6536
1558-0865
DOI:10.1109/TCST.2007.903398