ARMAX modal parameter identification in the presence of unmeasured excitation—I: Theoretical background

This study investigates the performance of a time-domain parameter estimation algorithm aimed at identifying modal parameters from excitation and response data corrupted with significant measurement noise and unmeasured sources of periodic and random excitation. The parameters of an autoregressive moving average with exogenous excitation (ARMAX) model are estimated using an iterative multistage estimation algorithm. The use of backwards autoregressive with exogenous excitation (ARX) models in the multistage algorithm allows vibrational modes to be distinguished from spurious numerical poles and is also the basis of a model selection criterion. A diagonal parameterisation of the autoregressive (AR) polynomial matrices allows the MIMO ARMAX model to be separated into a number of MISO systems, and permits simple manipulation and stabilisation of the estimated model. Measurement noise and sources of unmeasured random and periodic excitations are accounted for by the ARMAX model structure. In this paper, the theory and algorithm of the ARMAX model is given.