Mode Decomposition using Principal Component Analysis

Mode shapes identification using principal component analysis

This example file shows mode shapes identifcation using principal component analysis (PCA) of 2DOF system subjected to gaussian white noise excitation with added uncertainty (also gaussian white noise) to the response. However it should be taken into acount:

-Eigenvector of PCA are orthognal due to the symmetry property of covariance matrix.

-Modeshapes are only orthognal if the matrix inv(M)*K is symmetric.

-PCA will identify the real mode shapes only if they are orthognal which means inv(M)*K is symmetric.

By changing mass matrix M=[2 0; 0 1]; instead of identity inv(M)*K will not be symmetric even stiffness matrix is symmetric and PCA will fail to identify the real mode shapes.

References:

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[1] 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

[2] 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.