Identification of Time-Varying Modal Models

Modal, decoupled models of linear systems have easily interpreted parameters: gains and poles for independent rate processes, hence time constants and damping ratios. Time-varying modal models can fit a wide range of time-invariant, non-linear systems, and the time variation shows the effects of non-linearity. Modal parameters can be estimated via an ARMAX model, but the calculation is ill conditioned, so direct estimation of time-varying modal parameters is examined. The modal components of the output cannot be observed so must be estimated along with the parameters, a non-linear estimation problem. It is treated as state estimation, using the extended Kalman filter (EKF) and optimal smoothing. The capabilities and limitations of the EKF are investigated by simulation. With care, good results can be obtained even in difficult cases, e.g. with abrupt change in an input or output offset.