Non-Stationary Functional Series Tarma Vibration Modelling and Analysis in a Planar Manipulator

Functional series TARMA modelling and simulation of earthquake ground motion

“…They also avoid the 'artiÿcial' overspeciÿcation of the AR order necessitated in pure TAR models, which may cause di culties such as the loss of model stability and parsimony (note that the estimated models are expected to be stable as the ground motion signals modelled decay to zero; yet, estimated model stability is not guaranteed, and instability may be occasionally observed). For a demonstration of the advantages of full TARMA models the interested reader is referred to Petsounis and Fassois [21].…”

“…representing frequency in rads=time unit, | · | complex magnitude, j the imaginary unit, and T s the employed sampling period. In addition, physically signiÿcant parameters (such as time-varying predominant periods and corresponding damping ratios) of the ground motion signal modelled, which may be used in establishing relationships between the estimated model and seismological variables [6; 8], may be obtained directly from the TAR=TARMA model parameters in a 'time-frozen' sense (see Reference [21]). TARMA-based earthquake ground motion simulation is ÿnally performed by driving the estimated model [Equations (1)- (2)] by non-stationary innovations (w[t]) obtained through Equation (4) and computer-generated independently identically distributed (i.i.d) N(0; 1) (Gaussian with zero mean and unit variance) realizations of variance-stabilized innovations (e[t]).…”

“…The motivation for this generalization stems from the fact that full TARMA models constitute more complete representations capable of modelling both resonances and antiresonances (the latter term referring to frequencies at which the response is sharply attenuated), and thus having the potential for superior capturing of the underlying dynamics as well as parsimony (see Reference [21]). Yet, TARMA modelling is considerably more di cult than pure TAR modelling.…”

Multi-channel output-only identification of an extendable arm structure under random excitation: A comparison of parametric methods

“…Moreover, time-varying identification methods may be classified as either non-parametric or parametric, with the latter offering advantages in terms of compactness of representation (parsimony), as well as in terms of achievable accuracy and resolution. Parametric models are also generally better suited to dynamic analysis and characterization, the refinement of analytical models, design modifications, simulation, excitation characterization, as well as prediction and control [4], [5].…”

Moving Kriging shape function modeling of vector TARMA models for modal identification of linear time-varying structural systems

“…In the second category, after Rao [22] first used a finite number of time functions in the time-dependent AR parameters, Grenier [23] made use of time-dependent ARMA for modeling non-stationary signals. Poulimenos and Fassois [24] surveyed several methods of TARMA-based non-stationary random vibration modeling and classified them into three categories: unstructured parameter evolution methods (such as, recursive TARMA method [25] and short-time TARMA [26]), stochastic parameter evolution methods (smoothness priors TARMA [27]) and deterministic parameter evolution methods (functional series (vector) TARMA [28][29][30][31]). Compared with the first two methods, deterministic parameter evolution methods impose deterministic structure on the time-varying parameters, which are projected onto the selected functional subspaces.…”