Non-stationary random vibration modeling and analysis: kernel versus adaptable Functional Series TAR methods

Functional Series Time-dependent AutoRegressive, FS-TAR, modeling constitutes a powerful tool for the effective representation and analysis of zero-mean non-stationary random vibration. Yet, a main difficulty pertains to the need for determining the specific functional subspaces upon which the model parameters and innovations variance are to be projected. This study focuses on kernel based versions of the models, aiming at alleviating this problem while also allowing for infinite dimensional functional subspaces. This leads to improved modeling flexibility at the expense of reduced model parsimony. A batch estimation method is presented, and is subsequently successfully assessed via its application to the modeling and analysis of a non-stationary random vibration signal measured on an operating fan. Critical comparisons with an alternative, Adaptable FS-TAR, method and certain simpler approaches are also made.