Abstract
Subspace based algorithms for estimating modal parameter have now become common within modal analysis domain. This is especially true for Operational Modal Analysis, where Stochastic Subspace Identification (SSI) algorithm is a well-known and commonly used algorithm. Despite their increasing use and popularity, one often encounters basic questions such as (and not limited to)
-
1.
How are these algorithms related to (or different from) traditional matrix polynomial coefficient based algorithms like Polyreference Time Domain (PTD) etc.?
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2.
What is the link between covariance and data driven approaches to SSI?
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3.
What is the need for having different variants of SSI (Covariance-driven and Data-driven)?
In fact, even before addressing the questions listed above, there is a fundamental need to look at these algorithms from the perspective of modal parameter estimation, whose requirements and demands differ from those of system identification within Control Systems Engineering, where these algorithms originated.
This paper aims at addressing these issues and examine subspace algorithms from a purely modal parameter estimation perspective. The author expects that this paper will provide readers with a simple and clear understanding of these algorithms towards their utilization for modal parameter estimation.
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Abbreviations
- ERA:
-
Eigensystem realization algorithm
- ITD:
-
Ibrahim time domain
- OMA:
-
Operational modal analysis
- SSI:
-
Stochastic subspace identification
- SSI-Cov:
-
Covariance-driven SSI
- SSI-Data:
-
Data-driven SSI
- SVD:
-
Singular value decomposition
- x :
-
State vector
- y :
-
Response vector
- A :
-
State transition matrix
- C :
-
Output matrix
- w and v :
-
Process and measurement noise vectors
- Y :
-
Hankel data matrix
- H :
-
Hankel matrix of covariance matrices
- Λ :
-
Covariance matrix
- \( \overline{\mathbf{O}} \) :
-
Extended observability matrix
- \( \overline{\mathbf{C}} \) :
-
Extended controllability matrix
- Σ :
-
State covariance matrix
- \( \overline{\boldsymbol{\upalpha}} \) :
-
Matrix polynomial coefficients
- P fp :
-
Projection of future output responses on past output responses
- \( {\widehat{\mathbf{X}}}_i \) :
-
Kalman filter state estimate
References
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© 2016 The Society for Experimental Mechanics, Inc.
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Chauhan, S. (2016). Subspace Algorithms in Modal Parameter Estimation for Operational Modal Analysis: Perspectives and Practices. In: De Clerck, J., Epp, D. (eds) Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics & Laser Vibrometry, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-30084-9_27
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DOI: https://doi.org/10.1007/978-3-319-30084-9_27
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