Principal Component Analysis for non-linearity detection and linear equivalent transfer function estimation

In this paper the term system identification addresses the process of obtaining useful information to describe the system characteristics from the relationships between the measured input and output data of a physical system in the most efficient way possible. It can be shown that [1] if the model SISO System under investigation is assumed to be linear time-invariant and stable, in the case of uncorrelated additive measurement noise on both the system input and the output, the use of Principal Component Analysis (PCA) as a transfer function estimator gives results which makes it a useful alternate to the conventional estimators. When the input-output relationship is non-linear, PCA leads to a form of linearization of the system and offers a logical and consistent interpretation. The relative strengths (eigenvalues) of the principal components is a direct indicator of the significance of the non-linearity. The eigenvectors give the features of the equivalent linear system.