ARMAX modal parameter identification in the presence of unmeasured excitation—II: Numerical and experimental verification

Abstract

The performance of an autoregressive moving average with exogenous excitation (ARMAX) time-domain parameter estimation algorithm is assessed using data simulating the response of a two degree-of-freedom system and also experimental data obtained from a cantilever aluminium beam. The algorithm is aimed at identifying modal parameters in the presence of significant measurement noise and unmeasured sources of periodic and random excitation. The simulated system exhibits lightly damped modes and is excited with measured random excitation as well as unmeasured random and periodic excitation. A second case is considered where the modal frequencies of the simulated system are separated by 0.345 Hz and the frequency of an unmeasured periodic excitation is 0.257 Hz below the first modal frequency. Electrodynamic shakers as well as piezoceramic plates are used to apply multiple independent excitation forces, including measured random noise and also unmeasured random and periodic signals. Successful identification of modal parameters is achieved in the presence of up to 10% random measurement noise, as well as over 200% unmeasured periodic and random excitations. Results showed that the ARMAX algorithm achieved better results than ARX models estimated from experimental data corrupted by the effects of unmeasured excitations. The use of piezoceramic plates for structural excitation was demonstrated in experiments and the ability to excite modes was observed to be dependent on the deflection of a particular mode in the contact area of the piezoceramic plates.