Multi-channel sub-Nyquist cross-spectral estimation for modal analysis of vibrating structures

Operational modal analysis (OMA) is a widely used construction verification and structural health monitoring technique aiming to obtain the modal properties of vibrating civil engineering structures subject to ambient dynamic loads by collecting and processing structural response acceleration signals. Motivated by the need for cost-efficient OMA using wireless sensor networks which acquire and transmit measurements at a lower than the Nyquist rate, a novel OMA approach is put forth to derive modal properties directly from sub-Nyquist sampled (compressed) acceleration measurements from arrays of sensors. This is achieved by adopting sub-Nyquist deterministic non-uniform multi-coset sampling devices and by extending a previously proposed in the literature power spectrum blind sampling method for single-channel spectral estimation of stochastic processes to treat the case of multiple channel cross-spectral estimation. The standard frequency domain decomposition is used to obtain the modal properties from the cross-spectral matrix derived directly from the sub-Nyquist measurements. The applicability and efficiency of the proposed approach is exemplified by retrieving mode shapes of a white-noise excited simply supported steel beam with good accuracy according to the widely used modal assurance criterion using 70% less than the Nyquist rate measurements.