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The main challenge in the implementation of long-lasting vibration monitoring systems is to tackle the constantly evolving complexity of modern “mesoscale” structures. Thus, the design of energy-aware solutions is promoted for the joint optimization of data sampling rates, onboard storage requirements, and communication data payloads. In this context, the present work explores the feasibility of the rakeness-based compressed sensing (Rak-CS) approach to tune the sensing mechanism on the second-order statistics of measured data. In particular, a novel model-assisted variant (MRak-CS) is proposed, which is built on a synthetic derivation of the spectral profile of the structure by pivoting on numerical priors. Moreover, a signal-adapted sparsity basis relying on the wavelet packet transform operator is conceived, which aims at maximizing the signal sparsity while allowing for a precise time-frequency localization …