This thesis has focused on novel algorithmic approaches supporting sub-Nyquist data acquisition and processing techniques to reduce the power consumption in wireless sensor networks used for operational modal analysis and data-driven damage detection in civil engineering structures. By exploiting recent theoretical and technological advances, the proposed methods achieve simultaneous data acquisition and compression at the sensor front-end, eliminating the need for local on-sensor data processing. The latter consideration directly translates into minimum sensor complexity with reduced computational, power, and memory requirements, enabling low-cost and power-efficient monitoring deployments in densely instrumented structures. This final section summarises the milestones reached in each chapter and highlights the main contributions of this research, concluding with recommendations for future work.
8.1.
Summary and Main Contributions
The latest advances in sub-Nyquist data acquisition strategies for low-power and reliable wireless VSHM in civil engineering structures have been reviewed in Chapter 2 (§2. Compressive
Sensing: Basic Concepts & Applications in VSHM). These strategies rely on random sampling
schemes and signal reconstruction operations, originating from the theory of compressive sensing (CS). In this respect, Chapter 2 explained the basic principles of the CS theory followed by an extensive literature survey on the state-of-the-art CS-based VSHM approaches and discussed their limitations which are summarised as follows.
• Limitation 1: Time-domain signal reconstruction, sparsity constraints and computational
cost
The aim of CS signal reconstruction operations is to retrieve time-domain response data at Nyquist rate (or above) from a considerably reduced number of measurements. This is an underdetermined problem with increased computational demands that yields a unique solution when subjected to signal’s sparsity constraints.
Limitation 2: Sparsity requirements on a pre-defined vector basis
The signal compression level for which quality CS-based signal reconstruction can be achieved is limited by the sparsity level of the monitored response acceleration signals on a pre- defined vector basis. It was observed that the widely-used discrete Fourier transform (DFT) basis does not provide significantly sparse representations of structural responses due to detrimental noise folding and spectral leakage, while the consideration of alternative expansion bases, such as the discrete Haar wavelet basis, does not significantly improve the underlying signal sparsity. It was recognised that generalised harmonic wavelet bases or over-complete dictionaries may enhance the signals’ sparsity attributes, although such practices depend strongly on the application at hand.
• Limitation 3: Unknown signal sparsity and noise influence in practical applications In practice, field-recorded structural response signals are not strictly sparse on a given domain (i.e., compressible signals) but they can be adequately approximated as sparse representations. Further, the actual sparsity/compressibility level of real-time monitored signals is not known in advance while it is adversely affected by environmental noise. Notably, information on the sparse signal structure can only be retrieved from signal processing operations at the expense of increased computational, power, and memory demands. In the absence of such information, a target sparsity level should be assumed in the CS sparse signal recovery step, the selection of which is not trivial since it is associated with a trade-off between reconstruction accuracy and computation complexity.
Aiming to address Limitation 2 and improve the efficiency of CS-based VSHM approaches,
Chapter 3 (§3. CS-based Damage Detection Using the Relative Wavelet Entropy) examined the
“sparsest” representation of structural acceleration responses on the wavelet transform domain using four energy-preserving wavelet analysis filter banks (i.e., Haar, smooth Daubechies, Meyer, Harmonic) with different frequency domain attributes. The suitability of the adopted wavelet bases was numerically assessed in terms of data-driven structural damage identification results (i.e., damage detection and localisation) considering the relative wavelet entropy (RWE) index – a damage-sensitive quantity that has been efficiently embedded on wireless sensors for VSHM deployments. This comprehensive numerical study was mainly driven by the signal sparsity requirements of the CS theory and motivated by the lack of comparative studies and practical recommendations for the computation of the RWE.
Thus, the conventional RWE approach was numerically tested on full-length response acceleration datasets obtained from a healthy and a damaged state of a benchmark structure subject to broadband excitations, and RWE values were reported vis-à-vis for the four different wavelet filter banks. The reported numerical data confirmed that frequency selectivity and resolution across the scales of the wavelet analysis filter bank are the key for achieving enhanced
RWE-based stationary damage detection/localisation drawing information about damage from multiple mode shapes. It was shown that the widely-used Haar wavelets in conjunction with the standard dyadic discrete wavelet transform suffer from significant energy leakage across scales and may not be able to detect damage based on information carried at relatively high frequencies. It was further confirmed that wavelet filter banks with enhanced frequency selectivity among scales reduce spectral leakage, enabling the detection of damage in the vicinity of structural resonances at the excited modes of vibration. Thus, it was verified that the harmonic wavelets are the most effective for RWE-based stationary damage detection as they are not limited by the dyadic discrete wavelet transform discretisation and can achieve any level of frequency resolution.
An important contribution of Chapter 3 was the development of a novel data-driven damage detection approach that couples the CS theory with the RWE damage index using sparse signal representations on the harmonic wavelet transform. Based on random sub-Nyquist sampling schemes, the proposed method can significantly reduce the number of acquired and wirelessly transmitted measurements. Considering a “partial” harmonic wavelet basis matrix saved at the server, standard CS-reconstruction algorithms (e.g., CoSaMP) can be used to retrieve the underlying harmonic wavelet coefficients and derive the CS-based RWE damage index directly from the received compressed data without recovering the full-length acceleration response signals in time-domain. It was shown that this novel approach yields highly sparse structural response signals on the harmonic wavelet transform, being capable to detect structural damage equally well with the conventional RWE method while drastically reducing the required number of data samples by 80%-90% compared to traditional uniform-in-time sampling schemes. The numerical results suggest that the proposed CS-based RWE is a potent tool for inexpensive data- driven damage detection implementations in civil structures instrumented with wireless sensors of low energy demands.
Chapter 4 (§ 4. Proposed Multi-Sensor Power Spectrum Blind Sampling Approach for OMA: Theory) provided the theoretical development of a multi-sensor power spectrum blind sampling
(PSBS) approach capable to circumvent the CS limitations detailed above. This innovative approach extends a previously considered PSBS technique supporting single sensor deployments and it was proposed herein, for the first time, as a viable alternative for low-power WSNs used for operational modal analysis (OMA) and data-drive damage detection in civil structures. This is a fundamentally different approach that enjoys numerous advantages over the current CS-based approaches, in that:
• It relies on a common deterministic multi-coset sampling pattern among sensors, capable to acquire signals at sub-Nyquist rates (i.e., compression) without imposing sparsity conditions;
• It is genuinely signal agnostic, theoretically and numerically, and, therefore, it does not require any a priori knowledge of the signal structure (e.g., sparsity);
• It only requires that signals be wide-sense stationary which is in alignment with OMA theory;
• It retrieves auto/cross power-spectral density estimates directly from compressed data by solving a least-squares optimisation problem while by-passing signal reconstruction operations in time-domain;
• It attains a computationally efficient and relatively fast algorithm that mathematically relies on overdetermined systems of linear equations that can be easily solved;
• It can be fused with standard OMA algorithms (e.g., FDD algorithm) for structural natural frequency and mode shape estimation, and combined further with data-driven damage detection strategies based on the extracted modal information (e.g., the modal strain energy damage index).
The efficacy of the developed PSBS approach was numerically assessed in Chapter 5 (§5.
Proposed Multi-Sensor Power Spectrum Blind Sampling Approach for OMA: Applications) while
its superiority over a recently proposed CS-based approach (e.g., O’Connor et al. (2014)) was numerically verified in Chapter 6 (§6. Assessment of the Proposed PSBS Approach vis-à-vis CS-
based Approach for OMA). The numerical evaluation was performed with wide-sense stationary
acceleration response signals measured on structures under low-amplitude ambient excitations. The considered datasets involved both synthetic (computer-simulated) data – generated either by linear analyses in white-noise excited finite element models or by white-noise sequences coloured via ARMA filters – and field-recorded acceleration responses originating from actual monitoring campaigns (i.e., an operational wind turbine in Lübbenau, Germany, and an overpass in Zurich, Switzerland). By adopting an optimal multi-coset sampling scheme in the mean square error sense, simulated compressed acceleration data were derived at various compression ratios (CRs) ranging between 11% and 50% (i.e., 89% and 50% fewer measurements compared to conventional uniform-in-time sampling schemes).
In this study, the primary focus was on extracting quality modal estimates (natural frequencies and mode shapes) from a significantly reduced number of measurements with special attention drawn on identifying closely-spaced and poorly excited modes of vibration in noisy environments pertaining to signal-to-noise-ratios (SNRs) as low as zero decibel (i.e., 0 dB – extreme noise case yielding equal power in signal and noise components). The identification of local structural damage has also been addressed within the OMA context, using sub-Nyquist noisy acceleration response datasets at various structural states (i.e., reference/healthy and damaged states).
It was observed that the accuracy of the proposed method depends on the power spectral recovery performance of the PSBS strategy. The latter was found to be a function of the acquired number of compressed measurements, controlled by the adopted CR value in a fixed observation time-window. It was further confirmed that the PSBS method can efficiently recover power spectral densities (PSDs) directly from sub-Nyquist-sampled acceleration data even in cases of closely-spaced structural vibrating modes whose resonant frequencies are spaced less than 1 Hz apart (i.e., 20rad/s and 25rad/s). This novel spectral estimation method was shown to be practically insensitive to additive noise for SNRs as low as 10dB. At higher noise levels, though, of the order of 0 dB, larger errors were observed on the recovered PSDs estimates. However, such extreme noise cases may not be encountered in practical VSHM deployments.
Overall, it was confirmed that multi-sensor PSBS approach can retrieve quality modal estimates even for the lowest considered CR value at 11% pertaining to 89% fewer data compared to conventional uniform-in-time sampling schemes (at Nyquist rate or above), yielding natural frequency estimates with small errors of the order of 1-5% (depending on the application), and modal deflected shapes with MAC values well above 0.9 (i.e., the established modal assurance criterion for accurate mode shape extraction).
The damage detection capabilities of the PSBS method were tested for CR=31% and a wide range of SNR values. The numerical results demonstrated that the proposed multi-sensor PSBS technique coupled with standard OMA and damage detection approaches can identify the location of light structural damage of equal quality compared to conventional approaches at Nyquist rate, using less than 69% of data samples buried in high level noise with SNR at 10 dB. Thus, it was confirmed that the PSBS approach can infer structural damage directly from the recovered PSDs in the compressed domain without returning the monitored signals deterministically in time domain.
The comparison against the CS-based approach by O’Connor et al. (2014) revealed that the inherent signal agnostic attributes of the proposed multi-sensor PSBS-based approach renders the latter method more advantageous in cases where high signal compression levels are desired to address sensor power consumption and wireless bandwidth transmission limitations. In fact, it has been numerically shown and theoretically justified, that, for a given sub-Nyquist sampling rate, the capability of the CS-based approach to extract faithful estimates of the mode shapes depends heavily on the target sparsity level, ST, which needs to be assumed in the CS signal
reconstruction step. It has also been demonstrated that the accuracy of the CS-based approach improves at larger ST values at the cost of higher computational effort reflected on the increased
required runtime of the adopted CS sparse signal recovery algorithm. However, no increase to the assumed ST value can compensate for the acquisition of an excessively small number of
compressed measurements which is the case for CR=11% for all the sets of acceleration signals considered in this work. In this regard, it is concluded that conservative compression ratios should