A multi-sensor sub-Nyquist power spectrum blind sampling approach for low-power wireless sensors in operational modal analysis applications

Abstract

A novel multi-sensor power spectrum blind sampling (PSBS) approach is proposed supporting low-power wireless sensor networks (WSN) for Operational Modal Analysis (OMA) applications. The developed approach relies on arrays of wireless sensors, employing deterministic non-uniform in time multi-coset sampling to acquire structural response acceleration signals at sub-Nyquist sampling rates, treated as realizations of stationary random processes without making any assumption about the average signal frequency content and spectral support. The acquired compressed measurements are transmitted to a central server and collectively processed via a PSBS technique, herein extended to the multi-sensor case, to estimate the power spectral density matrix of an underlying spatially correlated stationary response acceleration random process directly from the compressed measurements. Structural modal properties are then extracted through standard frequency domain decomposition (FDD). The efficacy of the proposed approach to resolve closelyspaced modes is numerically tested for various data compression levels using noisy response acceleration signals of a white-noise excited finite element model of a space truss as well as fieldrecorded acceleration time-histories of an instrumented bridge under operational loading. It is shown that accurate mode shapes based on the modal assurance criterion can be obtained from as low as 89% less measurements compared to conventional non-compressive FDD at Nyquist sampling rate. Further, significant gains in energy consumption and battery lifetime prolongation of the order of years are estimated, assuming wireless sensors operating on multi-coset sampling at different data compression levels. It is, therefore, concluded that the proposed PSBS approach could provide long-term structural health monitoring systems with low-maintenance cost once wireless sensors with multi-coset sampling capabilities become commercially available.

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

“…In CS-based techniques, the achieved level of data compression (sub-Nyquist rate) for faithful time-series recovery and/or modal properties extraction depends on the acceleration signals sparsity, i.e., non-zero signal coefficients on a given basis. 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].…”

“…At first instance, it benefits from the inherent superresolution and denoising capabilities of the MUSIC algorithm yielding a pseudo-spectrum which is found to outperform conventional Fourier transform-based spectral estimators for extracting natural frequencies in vibrationbased system identification applications using ordinary Nyquist-sampled data (e.g., [16,17]). Further, similar to the multi-coset PSBS method [9], the proposed approach does not rely on any signal sparsity conditions treating the acquired signals as wide-sense stationary stochastic processes in alignment with the OMA framework that assumes stochastic (white noise) excitation and linear structural response [1]. In this context, it is a signal reconstruction-free compressive power spectral estimation approach aiming to estimate the auto-correlation function of stochastic structural response processes directly from noisy co-prime sampled measurements.…”

“…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

“…The "smart" feature of most such wireless platforms, allowing for local processing at the wireless senor (node) level, has been exploited for decentralized autonomous monitoring solutions (Nagayama et al, 2009). Nonetheless, WSNs have so far not enjoyed widespread adoption into practice, largely owing to their limited wireless transmission bandwidth and the maintenance costs related to frequent battery replacement (Klis and Chatzi, 2016a;Gkoktsi and Giaralis, 2019).…”

“…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.…”