Spectral identification of nonlinear multi-degree-of-freedom structural systems with fractional derivative terms based on incomplete non-stationary data

A novel spectral identification technique is developed for determining the parameters of nonlinear and time-variant multi-degree-of-freedom (MDOF) structural systems based on available input-output (excitation-response) realizations. A significant advantage of the technique relates to the fact that it can readily account for the presence of fractional derivative terms in the system governing equations, as well as for the cases of non-stationary, incomplete and/or noise corrupted data. Specifically, the technique relies on recasting the governing equations as a set of multiple-input/multiple-output systems in the wavelet domain. Next, an l₁-norm minimization procedure based on compressive sampling theory is employed for determining the wavelet coefficients of the available incomplete non-stationary input-output data. Finally, these wavelet coefficients are utilized to reconstruct the non-stationary incomplete signals, and consequently, to determine system related time- and frequency-dependent wavelet-based frequency response functions and associated parameters. Two illustrative MDOF systems are considered in the numerical examples for demonstrating the reliability of technique. The first refers to a nonlinear time-variant system with fractional derivative terms, while the second addresses a nonlinear offshore structural system subjected to flow-induced forces. It is worth noting that for the offshore system, a novel recently proposed evolutionary version of the widely used JONSWAP spectrum is employed for modeling the non-stationary free-surface elevation in cases of time-dependent sea states.