Damage detection using transient trajectories in phase-space with extended random decrement technique under non-stationary excitations

Abstract

This paper proposes a damage detection method based on the geometrical variation of transient trajectories in phase-space, and the proposed methodology is compatible with non-stationary excitations (e.g., earthquake-induced ground motion). The work presented assumes zero-mean non-stationary excitation, and extends the random decrement technique to convert non-stationary response signals of the structure into free-vibration data. Transient trajectories of the structure are reconstructed via the embedding theorem from the converted free-vibration data, and trajectories are mapped successively into phase-space to enhance statistical analysis. Based upon the characterized system dynamics in terms of phase-space, the time prediction error is adopted as the damage index. To identify the presence and severity of damage in a statistically rigorous way, receiver operating characteristic curves and the Bhattacharyya distance are employed. The results from both numerical simulations and experiments validate the proposed framework, when the test structures are subject to non-stationary excitations. The extension achieved in this paper enables the phase-space damage detection approach to be compatible with non-stationary scenarios, such as traffic, wind, and earthquake loadings. Moreover, the results indicate that this phase-state-based method is able to identify damage-induced nonlinearity in response, which is an intrinsic characteristic associated with most structural damage types.