Stochastic Subspace Identification (SSI)

Stochastic subspace identification with modal indicators including consistent mode indicator and modal participation factor

Stochastic subspace identification with modal indicators including consistent mode indicator and modal participation factor. 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(output,fs,ncols,nrows,cut)

Input:
output: output 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)
cut: cutoff value=2*no of modes

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

Matrices A,C: Discrete A and C matrices

References:
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[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] 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