Vibration monitoring via spectro-temporal compressive sensing for wireless sensor networks

Assessment of sub-Nyquist deterministic and random data sampling techniques for operational modal analysis

“…In practice, a range of different KT values should be tested (off-line) to strike a good balance between accuracy and computational complexity. It thus becomes obvious that both M and KT parameters depend on the signal sparsity level K which is adversely affected by broadband environmental noise while it is unknown, unless a priori knowledge becomes available through conventional uniform-in-time sampling and signal processing 11,[23][24][25] ; a scenario that is not addressed in this paper. In the next section, an alternative spectral estimation approach relying on low-rate (sub-Nyquist) measurements is reviewed which does not depend on signal sparsity.…”

“…This rather unfavorable condition can be explained through Figure 5, where it is numerically shown that higher CS reconstruction errors occurs at larger KT values for CR=11%, having a profound impact on the accuracy of the obtained CS modal results. In this case, if a priori knowledge of the signal sparsity was known 11,[21][22][23][24] , then one should normally opt to increase the average random sampling rate (i.e., obtain a larger number of measurements, M, within the same time frame). Nevertheless, the signal agnostic PSBS approach is capable to extract structural mode shapes associated with the local peaks of the spectrum even for CR=11% and signals with lower sparsity (at SNR=10dB) as long as they are not completely "buried" in noise.…”

“…Importantly, in the above CS-based approach, as in all CS-based approaches for OMA [9][10][11][12][13] and, more generally, for structural health monitoring 8,[21][22][23][24] , the minimum average random sampling rate for which quality signal recovery can be achieved depends strongly on and is limited by the actual sparsity/compressibility of the monitored response acceleration signals on a pre-specified/assumed basis or frame 25,26 . At the same time, discrete-time versions of such signals, as recorded in the field, may not be significantly sparse on a DFT basis 8,9,23 partly due to unknown environmental excitation 23 and partly due to spectral leakage 27,28 associated with the fact that the assumed grid of the DFT frequencies may not coincide with the (unknown) resonant structural natural frequencies.…”

“…Furthermore, the fairness of the comparison in relation to up-front and/or operational monitoring costs is safeguarded by the fact that neither of the approaches consider on-sensor data processing before transmission, while no prior knowledge on the properties (i.e., the sparsity) of the acquired signals is assumed available. The latter would theoretically benefit the CS-based approach but would require either the use of an additional complementary network of wired sensors 11 incurring additional monitoring costs, or increased energy demands due to fast (conventional) uniform-in-time sampling and heavy data post-processing on the wireless sensors [21][22][23][24] . Instead, this study assumes the availability of sensors that acquire and transmit signals directly in the compressed domain supporting low-power WNSs 9 .…”

A Sub-Nyquist Co-Prime Sampling MUSIC Spectral Approach for Natural Frequency Identification of White-noise Excited Structures

“…Nonetheless, wireless sensors are constrained by frequent battery replacement requirements leading to increase maintenance costs while their bandwidth limitations pose restrictions to the amount of data that can be reliably transmitted. It has been established that the above disadvantages may be alleviated by considering system identification techniques using measurements sampled at low rates, significantly below the nominal application-dependent Nyquist rate [4][5][6][7][8][9].…”