NExT-ERA

Natural Excitation Technique (NExT) with Eigensystem Realization Algorithm (ERA)

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
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[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
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[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:
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[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.