Bayesian operational modal analysis
Bayesian Operational Modal Analysis (BAYOMA) adopts a Bayesian system identification approach for Operational Modal Analysis (OMA). That is, it aims at identifying the modal properties (natural frequencies, damping ratios, mode shapes, etc) of a constructed structure using only its (output) vibration response (e.g., velocity, acceleration) measured under operating conditions. The (input) excitations to the structure are not measured but are assumed to be 'ambient' ('broadband random').
Pros and Cons
In the absence of (input) loading information, the identified modal properties from OMA often have significantly larger uncertainty (or variability) than their counterparts identified using free vibration or forced vibration (known input) tests. Regardless of whether the identification uncertainty has been acknowledged or not, it is always there. Ignoring this fact in the interpretation or presentation of identification results can lead to misrepresentation or over-confidence.
A Bayesian system identification approach is relevant for OMA as it provides a fundamental means for processing the information in the ambient vibration data for making inference on the modal properties in a manner consistent with probability logic and modeling assumptions. In addition to the most probable value, the identification uncertainty of the modal parameters can also be rigourously quantified and calculated.
The potential disadvantage of Bayesian approach is that the theoretical formulation can be more involved and less intuitive than their non-Bayesian counterparts. Algorithms are needed for efficient computation of the statistics (e.g., mean and variance) of the modal parameters from the posterior distribution.
Methods
Bayesian formulations have been developed for OMA in the time domain[1] and in the frequency domain using the spectral density matrix[2] and FFT (Fast Fourier Transform)[3] of ambient vibration data. Based on the formulation for FFT data, fast algorithms have been developed for computing the posterior statistics of modal parameters.[4] The fundamental precision limit of OMA has been investigated and presented as a set of uncertainty laws.[5][6]
See also
References
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Yuen, K.V. (2001). "Bayesian time-domain approach for modal updating using ambient data". Probabilistic Engineering Mechanics. 16 (3): 219–231. doi:10.1016/S0266-8920(01)00004-2.
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Yuen, K.V. (2001). "Bayesian spectral density approach for modal updating using ambient data". Earthquake Engineering and Structural Dynamics. 30: 1103–1123. doi:10.1002/eqe.53.
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Yuen, K.V. (2003). "Bayesian Fast Fourier Transform approach for modal updating using ambient data". Advances in Structural Engineering. 6 (2): 81–95. doi:10.1260/136943303769013183.
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Au, S.K. (2013). "Bayesian operational modal analysis: theory, computation, practice". Computers and Structures. 126: 3–14. doi:10.1016/j.compstruc.2012.12.015.
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Au, S.K. (2013). "Uncertainty law in ambient modal identification. Part I: theory". Mechanical Systems and Signal Processing. doi:10.1016/j.ymssp.2013.07.016.
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Au, S.K. (2013). "Uncertainty law in ambient modal identification. Part II: implication and field verification". Mechanical Systems and Signal Processing. doi:10.1016/j.ymssp.2013.07.017.
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