The presentation is manly based on the reach contributions collected for the recent issue of MSSP [1] on time varying systems. This issue has been devoted to share and spread the knowledge on the main techniques recently developed for the identification of those systems where the parameter invariability assumption leads to important errors and misleading interpretations. Independently on the model adopted, these methods can be generically classified as time-frequency methods because they can follow the parameter evolution along the time ; they are usually classed as non-parametric when directly adopting time-frequency methods, while are classed as parametric, such as a type of TARMA (Time dependent ARMA) or TVSSI (Time Variant Stochastic Subspace) when using structured equations. Quite often they are adopted for output only measurements, which is the case by far more frequent in real structures analysis such as for bridges, robots, deploying systems, rockets and aircraft wings.

Apart the cited time-frequency methods and TARMA, TVSSI techniques, some other techniques adopting wavelets, Hilbert or windowed Hilbert-Huang transform, as well as some Least Square methods, have been approached by authors in the recent past to better fit the models in case of time variant behaviour.

The speech is trying to underline the basic differences and assumptions among these techniques, highlighting the advantages, the drawbacks and the limits of applicability.

One of the final goal of these procedures remains the capability of detecting and enhancing damage discovering and incipient fault localisation for SHM applications.

References

[1] Mechanical Systems and Signal Processing
Special Issue on the Identification of Time Varying Structures and Systems
Volume 47, Issues 1–2, Pages 1-286 (3 August 2014)
Edited by Luigi Garibaldi and Spilios Fassois