Dynamic process monitoring method based on recursive generalized eigenvalue decomposition using temporal covariance matrix

2008 ◽  
Author(s):  
Xiang Gao ◽  
Fei Liu
Keyword(s):  
Covariance Matrix ◽  
Process Monitoring ◽  
Dynamic Process ◽  
Eigenvalue Decomposition ◽  
Monitoring Method ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Decomposition

Generalized Eigenvalue Decomposition in Time Domain Modal Parameter Identification

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Wenliang Zhou ◽  
David Chelidze
Keyword(s):  
Time Domain ◽  
Hankel Matrix ◽  
Eigenvalue Decomposition ◽  
Modal Parameter ◽  
Current Time ◽  
Modal Parameter Identification ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Decomposition ◽  
Single Input ◽  
Complex Exponential

This paper is intended to point out the relationship among current time domain modal analysis methods by employing generalized eigenvalue decomposition. Ibrahim time domain (ITD), least-squares complex exponential (LSCE) and eigensystem realization algorithm (ERA) methods are reviewed and chosen to do the comparison. Reformulation to their original forms shows these three methods can all be attributed to a generalized eigenvalue problem with different matrix pairs. With this general format, we can see that single-input multioutput (SIMO) methods can easily be extended to multi-input multioutput (MIMO) cases by taking advantage of a generalized Hankel matrix or a generalized Toeplitz matrix.

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