| Περίληψη: | The main topic of discussion of this PhD dissertation is the output-only identification of the vibration response of structures with time-dependent dynamics under uncertainty, and its application to the diagnosis of structural damage, referred to as vibration-based Structural Health Monitoring (SHM). This is of relevance to several classes of modern structures, including bridges with moving vehicles, structures with changing geometry, cranes, robotic manipulators, and so on. However, the main focus of application on this dissertation are wind turbines, for which the non-stationary vibration response stems from the time-dependent structural dynamics, as well as the randomness and variability of the wind excitation and other operational and environmental variables.
The development of effective methods for the identification and analysis of non-stationary vibration response is of pertinence for the improved understanding of the dynamic behavior of engineering structures during normal operation, as well for achieving effective representations of complex non-stationary behavior, which may be subsequently used with the purpose of SHM. Moreover, effective SHM methods are useful for early detection of damage, and thus for the reduction of maintenance and repair costs, and more importantly, for safeguarding the structure from catastrophic failure.
Among several other non-stationary modeling methods, Time-dependent ARMA (TARMA) models are characterized by several advantages that make them strong candidates for the problem discussed in this thesis. These include the modeling parsimony, referring to the capacity of representing very complex phenomena within a reduced set of parameters, improved tracking abilities, improved representation accuracy, and several more. However, these models have several limitations regarding to the proper modeling of non-stationary dynamics with uncertainty, the lack of analytical quantities that can serve to understand with precision the dynamic characteristics of fast-evolving non-stationary processes, and the lack of damage diagnosis methods that can deal also with significant uncertainties in the dynamics.
Therefore, this PhD dissertation deals with three issues regarding to the application of TARMA models for the purpose of solving the main problem stated before: (i) the development of non-stationary vibration response modeling methods able to represent both time-dependent dynamics and the effects of uncertainty, (ii) the construction of enhanced analysis methods that can lead to better understanding of fast-evolving non-stationary dynamics featuring in the vibration response, and (iii) the development of robust SHM methods that can deal with non-stationary dynamics and uncertainty in the vibration response.
This thesis is divided in six chapters, each one devoted to the development of methods aiming at solving specific parts of the problem discussed before. Chapter 2 is devoted to the comparison of stationary and non-stationary analysis methods for the vibration response of an operating wind turbine, where it is demonstrated the necessity of non-stationary modeling and the benefit of TARMA representations on this particular identification problem. Besides, it shows the necessity of several improvements on the modeling and analysis methods that are addressed in posterior chapters. In that sense, Chapter 3 addresses the problem of finding a Stochastic Parameter Evolution TARMA modeling method with improved flexibility and accuracy. For that purpose, the class of Generalized linear Stochastic Constraint TARMA (GSC-TARMA) models is introduced, which is characterized by Gaussian AR parameter evolutions. Consequently, the postulated GSC-TARMA models are fully linear and Gaussian, thus facilitating the identification process. Moreover, different identification methods, including Maximum Likelihood and Bayesian methods, are analyzed and adapted to the GSC-TARMA model type. The proposed methods are evaluated on several Monte Carlo simulations and on the identification of in-operation wind turbine vibration response.
Chapter 4 is devoted to the development of enhanced TARMA model-based methods for the analysis of non-stationary dynamics. On this sense, the concepts of Harmonic Impulse Response and Harmonic Frequency Response Function (FRF) are adapted to the TARMA case, from which input-output relations in the time-variant system can be derived, and from which the spectral correlation and some types of time-varying spectral densities can be calculated. The derivation of this quantities is of importance for improved analysis of the dynamics of fast-evolving non-stationary processes that can be represented with TARMA models. This is revealed through the analysis of the dynamic response of simulated LTV models, and on the analysis of the vibration response of an operating wind turbine identified with TARMA models.
Chapters 5 and 6 are devoted to the health monitoring of structures with non-stationary vibration response and operating under significant uncertainty. The representation of both types of effects cannot be simply accomplished with conventional models. Hence, for that purpose, the SHM problem is postulated in terms of a Multiple Model (MM) representation of each structural state. The MM representation is actually a collection of similar models (of the TARMA type), where each model represents the vibration response of the structure under particular uncertainty conditions. This yields a simple but yet effective representation of non-stationary dynamics and uncertainty. Furthermore, two types of damage diagnosis methods (damage detection and damage identification) are defined based on the MM representation, which are fully explained and evaluated in two SHM application examples, the first one based on the simulated vibration response of a time-varying suspension system where uncertainties are introduced by variability in the parameters of the governing differential equation, and the second one based on the simulated vibration response of an operating wind turbine, where uncertainty is introduced by variable wind speed and turbulence. The results demonstrate the robustness of the MM approach, stemming from its simple but effective representation of uncertainty, and its superiority in comparison with other SHM methods in terms of diagnostic accuracy.
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