ARMAX identification of vibrating structures: model and model order estimation

The determination of the model characteristics, number and values of natural frequencies, damping ratios, and mode shapes of a vibrating structure from records of its excitation and its response is investigated. First, a multistage eXogeneous Autoregressive Moving Average (ARMAX) procedure, recently employed in a single response measurement format is reviewed and extended to yield not only estimates of the natural frequencies and damping ratios but also of the mode shapes of a structure. The reliability of this technique, even in the presence of strong measurement noise, led to the introduction of a simple and efficient model order determination technique that relies on identification results obtained with different sets of data. Four examples of application are presented that demonstrate the reliability of the proposed model and model order estimation technique for both simulated and experimental data.