Sub-Nyquist signal-reconstruction-free operational modal analysis and damage detection in the presence of noise

Abstract

Motivated by a need to reduce energy consumption in wireless sensors for vibration-based structural health monitoring (SHM) associated with data acquisition and transmission, this paper puts forth a novel approach for undertaking operational modal analysis (OMA) and damage localization relying on compressed vibrations measurements sampled at rates well below the Nyquist rate. Specifically, non-uniform deterministic sub-Nyquist multi-coset sampling of response acceleration signals in white noise excited linear structures is considered in conjunction with a power spectrum blind sampling/estimation technique which retrieves/samples the power spectral density matrix from arrays of sensors directly from the sub-Nyquist measurements (i.e., in the compressed domain) without signal reconstruction in the time-domain and without posing any signal sparsity conditions. The frequency domain decomposition algorithm is then applied to the power spectral density matrix to extract natural frequencies and mode shapes as a standard OMA step. Further, the modal strain energy index (MSEI) is considered for damage localization based on the mode shapes extracted directly from the compressed measurements. The effectiveness and accuracy of the proposed approach is numerically assessed by considering simulated vibration data pertaining to a white-noise excited simply supported beam in healthy and in 3 damaged states, contaminated with Gaussian white noise. Good accuracy is achieved in estimating mode shapes (quantified in terms of the modal assurance criterion) and natural frequencies from an array of 15 multi-coset devices sampling at a 70% slower than the Nyquist frequency rate for SNRs as low as 10db. Damage localization of equal level/quality is also achieved by the MSEI applied to mode shapes derived from noisy sub-Nyquist (70% compression) and Nyquist measurements for all damaged states considered. Overall, the furnished numerical results demonstrate that the herein considered sub-Nyquist sampling and multi-sensor power spectral density estimation techniques coupled with standard OMA and damage detection approaches can achieve effective SHM from significantly fewer noisy acceleration measurements.

Output-only Modal Analysis of a Beam Via Frequency Domain Decomposition Method Using Noisy Data

“…As shown in Table 4, by increasing the noise level, the values of the natural frequencies identified using FDD method do not change. The results corroborate with those reported by Gkoktsi et al [31]. In the frequency domain methods such as FDD, the natural frequency of a structure is estimated from the peak values of PSD diagram.…”

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

“…The solution of Eq. (7) relies on the weighted least square criterion (7) is treated by the FDD algorithm to extract mode shapes and natural frequencies 14 .…”

“…In fact, one may note that even the consideration of 14 M  channels may be unrealistic in practice. However, this is a setting that has been used before in pertinent theoretical studies 14,30,32 , while recent advancements in the hardware implementation of multi-coset samplers provide CRs independently of the number of interleaved ADCs 37 .…”

“…To this end, it has been recently recognized that OMA relying on non-uniform in time data sampling/acquisition techniques [9][10][11][12][13][14] at sub-Nyquist rates (i.e., average sampling rates below an assumed application-dependent Nyquist rate) is a viable alternative to off-line data compression in reducing data transmission payloads. These techniques involve simultaneous signal acquisition and compression at the sensor front-end.…”

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

“…In this respect, the PSBS approach does not return the time-histories of acceleration response signals but, on the positive side, it is purely signal agnostic in terms of signal structure in the frequency domain and, therefore, indifferent to signal sparsity attributes and/or to additive noise. In this regard, it was shown that the PSBS approach achieves quality mode shape extraction and robust modal strain-based damage detection from response acceleration measurements corrupted by additive noise (Gkoktsi et al, 2016) at rates as low as 80% below Nyquist leading to significant energy consumption gains in wireless sensors (Gkoktsi and Giaralis, 2019).…”