Insensitivity-induced potential non-uniqueness in system identification of Bouc-Wen models

During system identification of hysteretic structural systems with the popular Bouc-Wen (BW) restoring force mechanisms, the BW parameters may often be incorrectly estimated. For the same model, the estimated BW parameters may be different for different sets of input-output measurements, indicating potential non-uniqueness in the parameter estimates. Nonetheless, the non-unique and incorrectly estimated BW parameters may still result in dynamic responses and hysteretic restoring force-deformation behaviours, which are very similar to those obtained for the correct system. In this work, it is shown that alternate sets of BW parameters with significant deviations from a set of "true" BW parameters may exist, which result in the rate of change of the hysteretic force, and consequently, the restoring force behaviour and the dynamic responses, to remain very similar to that obtained with the "true" BW parameters. The existence of these alternate parameters results in potential non-uniqueness of the BW parameter estimates, despite satisfying analytical identifiability requirements. The deviations of the alternate BW parameters are also shown to be dependent on the input excitation as well as the magnitudes of the "true" BW parameters. The systems with these alternate parameters also exhibit very similar inelastic response spectra as well as damage estimates. These results are illustrated using different inputs: sinusoidal, El Centro motion, and a suite of ground motions compatible with the Kanai-Tajimi spectrum. The results of this work contribute to a better understanding of the potential non-uniqueness issues associated with the estimation of the BW parameters from measured responses using any system identification technique, which is caused by the insensitivity of these parameters towards the dynamic responses of the structure.