NON-STATIONARY FUNCTIONAL SERIES TARMA VIBRATION MODELLING AND ANALYSIS IN A PLANAR MANIPULATOR

The problem of non-stationary stochastic vibration modelling and analysis is considered through a paradigm involving vibration analysis in a periodically varying manipulator. A parametric Functional Series method based upon time-dependent autoregressive moving average (TARMA) models is applied for the first time within the vibration analysis context, and comparisons with both pure TAR and non-parametric Fourier-based analysis are made. These focus on achievable time-dependent spectrum accuracy, resolution, and tracking, as well as on estimated modal parameter accuracy. The Functional Series TARMA method is shown to lead unambiguously to a physically meaningful TARMA(4, 5)p=3representation, while the pure TAR method leads to a TAR(12)p=3representation. The TARMA(4, 5)p=3model is shown to achieve superior spectral and modal parameter accuracy, while avoiding the problem of estimated false modal modes of its TAR(12)p=3counterpart. The TARMA(4, 5)p=3model also attains lower parametric complexity and superior values of the model fit criteria. The study demonstrates the facets and capabilities of the Functional Series TARMA method for non-stationary vibration analysis, indicating that the TARMA modelʹs direct relationship with the underlying physical system constitutes an important asset of the method.