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NExT-ERA

version 1.0.0 (8.68 KB) by Ayad Al-Rumaithi
Natural Excitation Technique (NExT) with Eigensystem Realization Algorithm (ERA)

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Updated 17 Jul 2019

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Natural Excitation Technique (NExT) with Eigensystem Realization Algorithm (ERA) using time domain NExT and frequency domain NExT.
Example file is provided for the identification of 2DOF system subject to gaussian white noise excitation with added uncertainty (also gaussian white noise) to both excitation and response.

1-NExT-ERA with time domain NExT
---------------------------------------------------------
[Result] = NExTTERA(data,refch,maxlags,fs,ncols,nrows,cut,shift,EMAC_option)

Inputs :
data: An array that contains response data.its dimensions are (nch,Ndata) where nch is the number of channels. Ndata is the total length of the data
refch: A vecor of reference channels .its dimensions (numref,1) where numref is number of reference channels
maxlags: Number of lags in cross-correlation function
fs: Sampling frequency
ncols: The number of columns in hankel matrix (more than 2/3*numref*(maxlags+1) )
nrows: The number of rows in hankel matrix (more than 20 * number of modes)
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

2-NExT-ERA with frequency domain NExT
---------------------------------------------------------
[Result] = NExTFERA(data,refch,window,N,p,fs,ncols,nrows,cut,shift,EMAC_option)

Inputs :

data: An array that contains response data.its dimensions are (nch,Ndata) where nch is the number of channels. Ndata is the total length of the data
refch: A vecor of reference channels .its dimensions (numref,1) where numref is number of reference channels
window: window size to get spectral density
N: Number of windows
p: overlap ratio between windows. from 0 to 1
fs: Sampling frequency
ncols: The number of columns in hankel matrix (more than 2/3*numref*(ceil(window/2+1)-1) )
nrows: The number of rows in hankel matrix (more than 20 * number of modes)
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] James, G. H., Thomas G. Carne, and James P. Lauffer. "The natural excitation technique (NExT) for modal parameter extraction from operating structures." Modal Analysis-the International Journal of Analytical and Experimental Modal Analysis 10.4 (1995): 260.

[4] 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

[5] 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). NExT-ERA (https://www.mathworks.com/matlabcentral/fileexchange/72170-next-era), MATLAB Central File Exchange. Retrieved .

Comments and Ratings (5)

Ayad Al-Rumaithi

Please check these references for guidelines:-
-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.

Vitor Martini

I'd like the know about the number of rows and columns of the Hankel matrix: the suggestions you made are personal or did you get them from another author?

Ayad Al-Rumaithi

If you increase mass 200 times. The natural period of the structure increases more than 10 times. So it requires longer time length of data to identify natural frequency.

Ayad Al-Rumaithi

If you increase mass 200 times. The natural period of the structure increases more than 10 times. So it requires longer time length of data to identify natural frequency especially for higher modes.

Vitor Martini

If I change the mass values to 200 instead of 1 the code does not work, why is that?

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