Adaptable functional series TARMA models for non-stationary signal representation and their application to mechanical random vibration modeling

• Published in: Signal processing Vol. 96; pp. 63 - 79
• Main Authors: Spiridonakos, M.D., Fassois, S.D.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2014
• Subjects: Adaptable basis functions; Basis functions; Computer simulation; Constraints; Functional series models; Monte Carlo methods; Non-stationary random vibration; Non-stationary signals; Nonlinearity; Representations; Separable non-linear least squares; Subspaces; Time-frequency methods; Time-varying mechanical structures; Vibration; Non-stationary random vibration; Separable non-linear least squares; Adaptable basis functions; Functional series models; Time-varying mechanical structures; Time-frequency methods; Non-stationary signals
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2013.05.012

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 parsimonious 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 modeled 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 modeling of the non-stationary random mechanical vibration of an experimental pick-and-place mechanism. Comparisons with conventional FS-TARMA modeling, as well as additional alternatives, are used to illustrate the method's performance and potential advantages. •Non-stationary Adaptable Functional Series TARMA models are introduced.•The models’ basis functions are adaptable to the signal modeled.•An effective identification method is introduced based on separable NLS.•The method's performance is assessed via a Monte Carlo study and comparisons.•The method is applied to the modeling of non-stationary vibration of a mechanism.