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Eigensystem Realization Algorithm (ERA)

version 1.0.5 (5.17 KB) by Ayad Al-Rumaithi
Eigensystem realization algorithm with modal indicators including consistent mode indicator and modal participation factor

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Updated 15 Jul 2019

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Eigensystem realization algorithm with modal indicators including consistent mode indicator and modal participation factor.
Example file is provided for the identification of 2DOF system subject to impulse excitation with added uncertainty (gaussian white noise) to the response.

function [Result]=ERA(Y,fs,ncols,nrows,inputs,cut,shift,EMAC_option)

Inputs :

Y: Free vibration output data in a form of Y=[Y1 Y2 ... Y_Ndata] Yi is Markov Parameter of size (outputs,inputs) and the total size is (outputs,inputs*Ndata) where outputs is the number of output channels, inputs is the number of inputs which equals to 1 unless free vibration data comes from Multi-reference channels NExT. Ndata is the length of the data samples
fs: Sampling frequency
ncols: The number of columns in hankel matrix (more than 2/3 of No. of data)
nrows: The number of rows in hankel matrix (more than 20 * number of modes)
inputs: The number of inputs which equals to 1 unless free vibration data comes from Multi-reference channels NExT
cut: cutoff value=2*no of modes
shift: Shift value in the final row and column blocks (Increase EMAC sensitivity) usually =10
EMAC_option: if this value equals to 1, EMAC will be independent of the number of columns (calculated only from observability matrix not from controllability)

Outputs :

Result: A structure consist of the below components
Parameters: NaFreq : Natural frequencies vector
DampRatio: Damping ratios vector
ModeShape: Mode shape matrix
Indicators: MAmC : Modal Amplitude Coherence
EMAC: Extended Modal Amplitude Coherence
MPC: Modal Phase Collinearity
CMI: Consistent Mode Indicator
partfac: Participation factor
Matrices A,B,C: Discrete A,B and C matrices

References:
---------------------
[1] R. Pappa, K. Elliott, and A. Schenk, “A consistent-mode indicator for the eigensystem realization algorithm,” Journal of Guidance Control and Dynamics (1993), 1993.

[2] R. S. Pappa, G. H. James, and D. C. Zimmerman, “Autonomous modal identification of the space shuttle tail rudder,” Journal of Spacecraft and Rockets, vol. 35, no. 2, pp. 163–169, 1998.

[3] Al Rumaithi, Ayad, "Characterization of Dynamic Structures Using Parametric and Non-parametric System Identification Methods" (2014). Electronic Theses and Dissertations. 1325.
https://stars.library.ucf.edu/etd/1325

[4] Al-Rumaithi, Ayad, Hae-Bum Yun, and Sami F. Masri. "A Comparative Study of Mode Decomposition to Relate Next-ERA, PCA, and ICA Modes." Model Validation and Uncertainty Quantification, Volume 3. Springer, Cham, 2015. 113-133.

Cite As

Ayad Al-Rumaithi (2020). Eigensystem Realization Algorithm (ERA) (https://www.mathworks.com/matlabcentral/fileexchange/69494-eigensystem-realization-algorithm-era), MATLAB Central File Exchange. Retrieved .

Comments and Ratings (4)

Dear Raakulan. Please check the following references for guidelines on the practical implementation of ERA:

Nayeri, Reza D., et al. "Study of time-domain techniques for modal parameter identification of a long suspension bridge with dense sensor arrays." Journal of engineering mechanics 135.7 (2009): 669-683.
Caicedo, Juan M. "Practical guidelines for the natural excitation technique (NExT) and the eigensystem realization algorithm (ERA) for modal identification using ambient vibration." Experimental Techniques 35.4 (2011): 52-58.

How to select the dimension of hankel matrix. Can you please explain it further more .............

dear Rahul. I added comments with example. I hope it will be clear

Rahul Kumar

What should be the parameter values to pass in this function???

Updates

1.0.5

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1.0.4

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1.0.3

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1.0.2

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1.0.1

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MATLAB Release Compatibility
Created with R2017b
Compatible with any release
Platform Compatibility
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