Phase space interrogation of the empirical response modes for seismically excited structures

Abstract

Conventional Phase Space Interrogation (PSI) for structural damage assessment relies on exciting the structure with low dimensional chaotic waveform, thereby, significantly limiting their applicability to large structures. The PSI technique is presently extended for structure subjected to seismic excitations. The high dimensionality of the phase space for seismic response(s) are overcome by the Empirical Mode Decomposition (EMD), decomposing the responses to a number of intrinsic low dimensional oscillatory modes, referred as Intrinsic Mode Functions (IMFs). Along with their low dimensionality, a few IMFs, retain sufficient information of the system dynamics to reflect the damage induced changes. The mutually conflicting nature of low-dimensionality and the sufficiency of dynamic information are taken care by the optimal choice of the IMF(s), which is shown to be the third/fourth IMFs. The optimal IMF(s) are employed for the reconstruction of the Phase space attractor following Taken’s embedding theorem. The widely referred Changes in Phase Space Topology (CPST) feature is then employed on these Phase portrait(s) to derive the damage sensitive feature, referred as the CPST of the IMFs (CPST-IMF). The legitimacy of the CPST-IMF is established as a damage sensitive feature by assessing its variation with a number of damage scenarios benchmarked in the IASC-ASCE building. The damage localization capability, remarkable tolerance to noise contamination and the robustness under different seismic excitations of the feature are demonstrated.