Structural Health Monitoring via Phase Space Warping and Time-Delay Embedding

The state of a structure’s health can be determined by investigating its vibration characteristics. Vibration-based structural health monitoring (SHM) enables early detection and diagnosis of damage as well as extension of service life. Herein, linear and nonlinear tracking metrics are proposed to track deterioration in the condition of multistory structures and assess their instantaneous health in real-time via measurement of floor accelerations. The linear metrics, the amplitude damage index ${\mathrm{ADI}}^n(\overline{t})$ and the frequency damage index ${\mathrm{FDI}}^n(\overline{t})$, are based on tracking the power spectra of floor accelerations. The nonlinear metric $e(\overline{t})$ is based on a novel implementation of the phase-space warping method and obtained from the orbits representing the floors’ motions in pseudo phase-space. A scaled-down model of a four-floor moment-resisting frame building is designed and fabricated to demonstrate and to compare the capabilities of the three damage indices. Structural damage is introduced to individual columns, to mimic damage initiation, by cutting two notches on opposite sides of a column cross-section at midheight. The ${\mathrm{ADI}}^n(\overline{t})$ detected large damage events, fast deterioration beyond them, and the onset of failure using any of the four floor accelerations. The ${\mathrm{FDI}}^n(\overline{t})$ proved insensitive to damage compared with the other two metrics. The nonlinear metric $e(\overline{t})$ detected gradual (fatigue-induced) deterioration in the building’s health before introduction of damage, large damage events, fast deterioration beyond them, and the onset of failure, using any of the four floor accelerations. The $e(\overline{t})$ metric varied slowly and continuously with gradual deterioration and exhibited larger discontinuous jumps with discrete damage events. This was true for all three damage experiments undertaken on the model building. The nonlinear $e(\overline{t})$ metric was also found to be more efficient, in terms of signal utilization, in comparison with the linear ${\mathrm{ADI}}^n(\overline{t})$ metric.