Adaptable Functional Series TARMA Models for Non-Stationary Signal Representation & Their Application to Mechanical Random Vibration Modelling M.D. Spiridonakos, S.D. Fassois ∗ Stochastic Mechanical Systems & Automation (SMSA) Laboratory, Department of Mechanical Engineering & Aeronautics, University of Patras, GR 265 04 Patras, Greece http://www.smsa.upatras.gr Abstract Functional Series Time-dependent Autoregressive Moving Average (FS-TARMA) models are characterized by time varying parameters which are projected onto selected functional subspaces. They offer parsimo- nious and effective representations for a wide range of non-stationary random signals where the evolution in the dynamics is of deterministic nature. Yet, their identification remains challenging, with a main difficulty pertaining to the determination of the functional subspaces. In this study the problem is overcome via the introduction of the novel class of Adaptable FS-TARMA (AFS-TARMA) models, that is models with basis functions properly parametrized and directly estimated based on the modelled signal. Model identification is effectively dealt with through a Separable Non-linear Least Squares (SNLS) based estimation procedure that decomposes the problem into two simpler subproblems: a quadratic one and a reduced-dimensionality non-quadratic constrained optimization one. The identification method also includes procedures for model order and subspace dimensionality selection. Its effectiveness is demonstrated via a Monte Carlo study, plus its application to the modelling of the non-stationary random mechanical vibration of an experimental pick-and-place mechanism. Comparisons with conventional FS-TARMA modelling, as well as additional alternatives, are used to illustrate the method’s performance and potential advantages. Keywords: Non-stationary signals, time-frequency methods, non-stationary random vibration, functional series models, separable non-linear least squares, adaptable basis functions, time-varying mechanical structures. ∗ Corresponding author, Tel/Fax: (++ 30) 2610 969 495 (direct); (++ 30) 2610 969 492 (central) Email address: fassois@mech.upatras.gr (S.D. Fassois) Preprint submitted to Signal Processing April 26, 2013 Signal Processing, Vol. 96(A), pp. 63-79, 2014. http:/ / dx.doi.org/ 10.1016/ j.sigpro.2013.05.012