Data-driven stochastic modeling of guided wave propagation and robust damage diagnosis

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Ahmed, Shabbir
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Electronic thesis
Mechanical engineering
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Modern day civil, mechanical, and aeronautical structures are transitioning towards a continuous, online, and automated maintenance paradigm in order to ensure increased safety and reliability. The field of structural health monitoring (SHM), which is concerned with online damage detection, localization and quantification, is playing a key role in this respect, and a significant amount of research efforts have been directed towards achieving this maintenance paradigm. Active sensing acousto-ultrasound guided-wave based SHM techniques have shown great promise due to their potential sensitivity to small damages. However, the methods' robustness and diagnosis capability become limited in the presence of environmental and operational variability such as a change in surrounding temperature, different load and boundary conditions, variation in material properties, etc. In addition, the currently used techniques rely on deterministic damage diagnosis schemes rather than probabilistic frameworks, which can account for uncertainty arising from different sources. As such, it is critical to model guided wave propagation in the presence of varying external sources, environments, operating conditions, and material property variations that impose uncertainty on guided wave propagation in order to enable the formulation of a robust, reliable, and probabilistic damage diagnostic scheme. In order to achieve this goal, in this report, a novel stochastic time series based framework was adopted to model guided wave propagation. Different stochastic time-varying time series models, such as Recursive Maximum Likelihood Time-varying Auto-Regressive (RML-TAR) and Functional Series Time-varying Auto-Regressive (FS-TAR) models, and stationary Functionally Pooled (FP) time-series models were put forward to model and capture the uncertainty in guided wave propagation under varying temperature, loads, as well as material property variations based on experimental data. In order to incorporate information from a physics perspective, high-fidelity finite element (FE) models were also established to model the effect of temperature and material property variation on guided wave propagation. The effect of broadband high frequency actuation on guided wave propagation under different temperature was studied with the help of novel Functionally-Pooled Auto-Regressive (FP-AR) models. Finally, surrogate models were formulated through the use of stochastic time-dependent RML-TARX models and compared with the FE models under varying temperatures. The advantages of using surrogate models will be manifested in the future work that has been proposed in this report with the ultimate aim of formulating a probabilistic SHM framework. Once the modeling part is complete, stochastic time series models are invoked to formulate damage diagnosis algorithm. At first, stochastic stationary time series models such as autoregressive models (AR) are used. In addition to using standard AR-based approach, where all the model parameters are used for formulating a statistical characteristic quantity, two other approaches are also introduced, namely: singular value decomposition (SVD) and principal component analysis (PCA)-based method. The performance of these three methods are analyzed and assessed in detail for damage detection and identification in the aluminum as well as the composite plates. It is shown that the AR-based approach works well for aluminum plates but shows poor performance for composite plates in damage identification. As guided wave signals are non-stationary in nature, it is more appropriate to use non-stationary modeling techniques for damage detection and identification. An important class of parametric methods for the effective solution of the modeling of non-stationary problems is based on functional series time-dependent autoregressive moving average (FS-TARMA) models. These models have parameters that explicitly depend upon time, with the dependence described by deterministic functions belonging to specific functional subspaces. The advantages of FS-TARMA models involve improved accuracy, improved tracking of the time-varying dynamics, increased predictive ability, and representation parsimony. In this study, FS-TAR models, which is a subclass of FS-TARMA models, are used for damage detection and identification using non-stationary guided wave signals. When formulating damage detection and identification based algorithms, constant coefficients of projection as well as the time-varying parameters are used. Three types of functional basis functions are investigated, namely: wavelet, Chebyshev and trigonometric basis functions and their performance in terms of damage detection and identification are analyzed and assessed. Lastly, the idea of using a high-frequency broadband white noise actuation instead of a tone-burst actuation for exciting the guided wave signal is investigated. The hypothesis is that the broadband actuation will excite additional vibratory modes of the structure, which are not realized from a traditional tone-burst actuation. This new type of actuating the structure may help formulate a more robust damage diagnosis scheme.
May 2022
School of Engineering
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Rensselaer Polytechnic Institute, Troy, NY
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