SSI with Mode Condensation

Stochastic Subspace Identification with Mode Condensation Algorithm

Stochastic Subspace Identification with Mode Condensation Algorithm. This function does not use system identification toolbox function n4sid. 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.

function [Result] = SSID_CONDENSED(output,fs,ncols,nrows,initialcut,maxcut,LimCMI,LimMAC,LimFreq,Plot_option)

Inputs :

output: reaponse data of size (No. output channels, No. of data)
fs: Sampling frequency
ncols: The number of columns in hankel matrix (more than 2/3 of No. of data)
nows: The number of rows in hankel matrix (more than 20 * number of modes)
initialcut: initial cutoff value of mode order
maxcut: maximium cutoff value of mode order
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
Parameters.DampRatio : Damping ratios vector
Parameters.ModeShape : Mode shape matrix

Indicators.EMAC : Extended Modal Amplitude Coherence
Indicators.MPC : Modal Phase Collinearity
Indicators.CMI : Consistent Mode Indicator
Indicators.partfac : Participation factor

References
[1] Van Overschee, Peter, and B. L. De Moor. Subspace identification for linear systems: Theory—Implementation—Applications. Springer Science & Business Media, 2012.

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

[3] 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.

[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