A critical comparison of four stochastic (PEM, 2SLS, LMS, IV) and three deterministic (LS, Prony, ERA) methods for the parametric time-domain identi"cation of vibrating structures from random excitation and noise-corrupted response signals is presented. Concise summaries of the methods, highlighting their principles and realisations, are provided, while the study is based upon a six-degree-of-freedom structural model characterised by two closely spaced modes, two weak modes and a wide range of modal damping. Monte-Carlo experiments under two di!erent (wideband/narrowband) noise environments are performed, along with comparisons with non-parametric frequency domain identi"cation.
The stochastic methods*most notably PEM, LMS and IV*are, at the price of increased complexity, shown to lead to potential advantages in non-negligible noise cases, while deterministic methods*most notably Prony and ERA*may su$ce under negligible noise. In addition: (a) Model order estimation is shown not to be straightforward, and signi"cant overdetermination is required (especially by the LS). (b) A weak closely spaced mode is hard to identify, while being completely missed by the deterministic methods and the 2SLS. (c) A highly damped mode presents some di$culty as well (mainly for the LS). (d) False modes are exhibited, primarily by the LS (wideband noise) and the ERA (narrowband noise). (e) The achievable estimation accuracy is generally high for the natural frequencies, lower for the damping ratios, and even more so for the residues (mode shapes). Furthermore, accuracy is somewhat lower for the closely spaced modes and signi"cantly lower for the two highly damped modes. (f ) PEM, LMS and IV achieve lower bias errors and good overall accuracy, followed by the 2SLS, Prony, ERA and, "nally, LS. (g) Unstable modes are mainly exhibited by the IV and ERA. (h) All methods appear sensitive to the selected model order and design parameters, and user expertise is necessary.