The Stretching Method for Vibration-Based Structural Health Monitoring of Civil Structures

This article newly proposes the application of the stretching method, that is used in geophysics for detecting variations in the velocity with which waves propagate in the earth’s crust from seismic noise recordings, in the context of vibration-based Structural Health Monitoring (SHM) of civil structures. The result is a computationally efficient long-term vibration-based SHM tool, that follows the current trend of using a very limited number of sensors permanently installed on site to measure operational structural responses for the purpose of damage detection. In the SHM setting, the proposed method aims at a direct identification of small permanent shifts in the natural frequencies of the structure in a changing environment, which is achieved by maximizing the correlation coefficient between a reference waveform, computed in a training reference period in which the structure is assumed to be undamaged, and a stretched version of the same waveform evaluated at the current time. The comparison is performed in the frequency domain and the waveform of interest is obtained from cross-correlations of the ambient vibration measurements. More specifically, in the case of multiple sensors, the waveform can be either the cross-power spectral density of the signals recorded by a pair of sensors, or the largest singular value of the spectral matrix of the measurements. It follows that the method can be regarded as an extension of the classic Frequency Domain Decomposition (FDD). A key feature of the proposed stretching method is mitigating the effects of environmental fluctuations by time domain averaging of cross-correlations over a proper period of time, before taking their Fourier transform to estimate the spectral densities. Such a time domain averaging is carried out in a relatively long period of time for estimating the reference waveform, whereas it is carried out in a shorter time for estimating the current waveform. The main features of the proposed methodology are its very low sensitivity to environmental fluctuations, resulting in a quite short training period length, and its low computational cost, which could be compatible with a direct integration within smart sensors with embedded electronics. The performance of the method is illustrated in the case study of an Italian historical monumental bell tower that has been monitored by the authors for more than 1 year.