ERA with Mode Condensation

version 1.0.0 (7.95 KB) by Ayad Al-Rumaithi
Eigensystem Realization Algoirthm with Mode Condensation Algorithm


Updated 1 Oct 2019

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Eigensystem Realization Algoirthm with Mode Condensation Algorithm. Example file is provided for the identification of 2DOF system subject to impulse excitation with added uncertainty (gaussian white noise).

function [Result] = ERA_CONDENSED(Y,fs,ncols,nrows,inputs,initialcut,maxcut,shift,EMAC_option,LimCMI,LimMAC,LimFreq,Plot_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
initialcut: initial cutoff value of mode order
maxcut: maximium cutoff value of mode order
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)
LimCMI: Minmium allowable CMI for modes
LimMAC & LimFreq: Minimium value of MAC and maximium value of frequency difference to assume two modes are referring to the same real mode
Plot_option: if 1 plots stabilization diagram

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

[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.

[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 (2022). ERA with Mode Condensation (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2017b
Compatible with any release
Platform Compatibility
Windows macOS Linux
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