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

Author-Highlights
• 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.

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.