A Reconstruction-Free Sub-Nyquist Sensing Approach for Earthquake Damage Detection Using the Music Algorithm

Abstract eng:
Motivated by a need to reduce energy consumption in wireless sensors used for Vibration-based Structural Health Monitoring (V-SHM) in seismically prone areas, this paper explores the potential of a recently established sampling scheme, termed co-prime sampling, in conjunction with the multiple signal classification (MUSIC) pseudo-spectrum for earthquake-induced structural damage detection. Firstly, co-prime sampling is adopted to acquire noise-corrupted response acceleration measurements of low-amplitude white-noise excited structures before and after an earthquake, treated as stationary stochastic processes in agreement with the operational modal analysis theory. The obtained measurements are acquired by two different samplers per recording channel operating at different uniform sampling rates, 1/(N1T) and 1/(N2T), where N1 and N2 are co-prime numbers and 1/T is the Nyquist frequency rate used in conventional sampling schemes. The adopted sampling strategy accumulates samples at an average sub-Nyquist rate (i.e., 1/(N1T)+1/(N2T) < 1/T), supporting the use of arrays of wireless sensors of reduced power consumption associated with data acquisition and wireless transmission rate. Secondly, the MUSIC super-resolution spectral estimator is used to identify up to N1N2 structural natural frequencies with resolution 1/(N1N2T) from the auto-correlation function of the sub-Nyquist measurements without taking any (typically computationally expensive) signal reconstruction step in the time-domain, as required by various recently proposed in the literature sub-Nyquist compressive sensing-based approaches for structural health monitoring, while filtering out any broadband noise added during data acquisition. It is assumed that within the short pre- and post- earthquake time interval, the environmental conditions remain the same and thus any (likely to be slight) change to the natural frequencies detected by the proposed approach can be related to damage due to the input seismic action to the structure. The applicability of the proposed approach is numerically illustrated using a white-noise excited linear reinforced concrete 3-story frame in a healthy and two damaged states caused by ground motions of increased intensity. The damaged states are represented by linear finite element models with reduced effective flexural rigidities at plastic hinge zones, computed by non-linear response history analysis and the Takeda hysteretic model. The furnished numerical results demonstrate that the considered approach can detect structural damage manifested by changes to the natural frequencies as minor as 1% directly from the sub-Nyquist measurements even for additive white noise of SNR=10dB. These results suggest that the adopted approach makes a dependable noise-immune structural damage detection technique that can be potentially embedded within arrays of wireless sensors for cost-efficient (in terms of data sampling and wireless transmission rates) vibration-based structural health monitoring in seismically prone regions.

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