Bayesian operational modal analysis: Difference between revisions

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'''Bayesian Operational Modal Analysis''' (BAYOMA) adopts a [[Bayesian inference|Bayesian]] [[system identification]] approach for [[Operational Modal Analysis]] (OMA). That[[Operational is,Modal itAnalysis]] (OMA) aims at identifying the modal properties ([[natural frequency|natural frequencies]], [[damping ratio|damping ratios]], [[mode shape|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 Vibrations|ambient]]' ('broadband random'). In a Bayesian context, the set of modal parameters are viewed as uncertain parameters or random variables whose probability distribution is updated from the prior distribution (before data) to the posterior disribution (after data). The peak(s) of the posterior distribution represents the most probable value(s) ('''MPV''') suggested by the data, while the spread of the distribution around the MPV reflects the remaining uncertainty of the parameters.

==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. IgnoringQuantifying thisand fact incalculating the interpretationidentification or presentationuncertainty of identification results can leadthe tomodal misrepresentationparameters orbecome over-confidencerelevant.

AThe advantage of a [[Bayesian inference|Bayesian]] [[system identification]] approach is relevant for OMA asis that it provides a fundamental means forvia the Bayes' Theorem to processingprocess the information in the ambient vibration data for making statistical inference on the modal properties in a manner consistent with [[probability]] logic and modeling assumptions. Inand additionprobability to the most probable value, the identification uncertainty of the modal parameters can also be rigorously quantified and calculatedlogic.

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]].

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|doi=10.1016/j.ymssp.2013.07.017

|url=}}</ref>

==Notes==

*See Jaynes<ref name=jaynes>

{{cite book

|first=E.T. |last=Jaynes

|title=Probability Theory: The Logic of Science

|year= 2003

|publisher=Cambridge University Press

|___location=United Kingdom

|isbn=

|url=}}

</ref> and Cox<ref name=cox>

{{cite book

|first=R.T. |last=Cox

|title=The Algebra of Probable Inference

|year= 1961

|publisher=Johns Hopkins University Press

|___location=Baltimore

|isbn=

|url=}}

</ref> for Bayesian inference in general.

*See Beck<ref>

{{cite journal

|last=Beck

|first=J.L.

|coauthors=

|title=Bayesian system identification based on probability logic

|journal=Structural Control and Health Monitoring

|year=2010

|month=

|volume=17

|issue=7

|pages=825–847

|doi=10.1002/stc.424

|url=}}</ref> for Bayesian inference in structural dynamics (relevant for OMA)

*The uncertainty of the modal parameters in OMA can also be quantified and calculated in a non-Bayesian manner. See Pintelon et al.<ref>

{{cite journal

|last=Pintelon

|first=R.

|coauthors=Guillaume, P.; Schoukens, J.

|title=Uncertainty calculation in (operational) modal analysis

|journal=Mechanical Systems and Signal Processing

|year=2007

|month=

|volume=21

|issue=

|pages=2359-2373

|doi=10.1016/j.ymssp.2006.11.007

|url=}}</ref>

==See also==