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

Abstract

This article assesses numerically the potential of two different spectral estimation approaches supporting non-uniformin-time data sampling at sub-Nyquist average rates (i.e. below the Nyquist frequency) to reduce data transmission payloads in wireless sensor networks for operational modal analysis of civil engineering structures. This consideration relaxes transmission bandwidth constraints in wireless sensor networks and prolongs sensor battery life since wireless transmission is the most energy-hungry on-sensor operation. Both the approaches assume acquisition of sub-Nyquist structural response acceleration measurements and transmission to a base station without on-sensor processing. The response acceleration power spectral density matrix is estimated directly from the sub-Nyquist measurements, and structural mode shapes are extracted using the frequency-domain decomposition algorithm. The first approach relies on the compressive sensing theory to treat sub-Nyquist randomly sampled data assuming that the acceleration signals are sparse/compressible in the frequency domain (i.e. have a small number of Fourier coefficients with significant magnitude). The second approach is based on a power spectrum blind sampling technique considering periodic deterministic sub-Nyquist ''multi-coset'' sampling and treating the acceleration signals as wide-sense stationary stochastic processes without posing any sparsity conditions. The modal assurance criterion is adopted to quantify the quality of mode shapes derived by the two approaches at different sub-Nyquist compression rates using computer-generated signals of different sparsity and field-recorded stationary data pertaining to an overpass in Zurich, Switzerland. It is shown that for a given compression rate, the performance of the compressive sensing-based approach is detrimentally affected by signal sparsity, while the power spectrum blind sampling-based approach achieves modal assurance criterion .0.96 independently of signal sparsity for compression ratios as low as 22% the Nyquist rate. It is concluded that the power spectrum blind sampling-based approach reduces effectively data transmission requirements in wireless sensor networks for operational modal analysis, without being limited by signal sparsity and without requiring a priori assumptions or knowledge of signal sparsity.

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

“…Alternatively, the authors developed a power spectrum blind sampling (PSBS) approach [9] which relies on sub-Nyquist non-uniform in time deterministic multi-coset data acquisition to estimate the power spectral density (PSD) matrix of response acceleration signals treated as realizations of a multi-dimensional stationary stochastic process without imposing any sparsity conditions. Whilst the latter approach does not return the acceleration timeseries, it achieves quality mode shape estimation via standard frequency domain OMA techniques at lower (sub-Nyquist) sampling rates compared to standard CS techniques even for noisy signals [8].…”

“…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].…”

Output-Only Vibration-Based Monitoring of Civil Infrastructure via Sub-Nyquist/Compressive Measurements Supporting Reduced Wireless Data Transmission

“…Aiming to circumvent the signal sparsity requirement for the identification of modal characteristics (natural frequencies and modal shapes) from sub-Nyquist sampled response acceleration data, Gkoktsi and Giaralis (2017), Gkoktsi and Giaralis (2019) developed an alternative to the former CS-based approaches. The latter approach couples the sub-Nyquist non-uniform-in-time deterministic multi-coset sampling strategy (Venkataramani and Bresler, 2001), with a Power Spectrum Blind Sampling (PSBS) technique (Ariananda and Leus, 2012;Tausiesakul and González-Prelcic, 2013) extended to the multi-channel case by Gkoktsi et al (2015) to estimate the response acceleration PSD matrix (second order statistics) from correlation sequences of the sub-Nyquist measurements.…”

“…The latter approach couples the sub-Nyquist non-uniform-in-time deterministic multi-coset sampling strategy (Venkataramani and Bresler, 2001), with a Power Spectrum Blind Sampling (PSBS) technique (Ariananda and Leus, 2012;Tausiesakul and González-Prelcic, 2013) extended to the multi-channel case by Gkoktsi et al (2015) to estimate the response acceleration PSD matrix (second order statistics) from correlation sequences of the sub-Nyquist measurements. Ultimately, the considered PSBS approach derives structural modal properties by application of the FDD algorithm to the estimated PSD matrix without response acceleration signal recovery in the time domain and without making an a priori assumption on signal sparsity in the DFT or in any other domain (Gkoktsi and Giaralis, 2017). In doing so, measured response signals are assumed as stationary correlated stochastic processes in alignment with OMA theory (Brincker and Ventura, 2015).…”

“…Previously, the PSBS approach has been compared to standard BPDN CS-based approach in terms of quality mode shape extraction (Gkoktsi and Giaralis, 2017). Herein, we comparatively assess the PSBS-based scheme (Gkoktsi andGiaralis, 2017, 2019) and the STCS approach (Klis and Chatzi, 2016a,b) in an effort to demonstrate their readiness levels for output-only modal identification supported by low-power wireless sensors which is the first step toward cost-effective SHM.…”