Abstract
This thesis concentrates on the development and validation of methods for identifying dynamic models of complex structures as well as predicting fatigue damage accumulation by exploiting measured vibration information. The identified models refer to mathematical modal models as well as linear finite element models of structures, while the applications cover mainly ground/air vehicles and civil structures. The thesis is divided into three interrelated parts. Part A: Least-squares optimization methods are introduced for identifying non-classically damped modal models of complex structures using (1) output response measurements obtained from measured excitations at multiple support, and (2) output-only ambient vibration measurements. In the first case, a common structure of the time and frequency formulations is revealed and exploited to develop an identification software common for both formulations. The measure of fit represents the difference between the measured response time historie ...
This thesis concentrates on the development and validation of methods for identifying dynamic models of complex structures as well as predicting fatigue damage accumulation by exploiting measured vibration information. The identified models refer to mathematical modal models as well as linear finite element models of structures, while the applications cover mainly ground/air vehicles and civil structures. The thesis is divided into three interrelated parts. Part A: Least-squares optimization methods are introduced for identifying non-classically damped modal models of complex structures using (1) output response measurements obtained from measured excitations at multiple support, and (2) output-only ambient vibration measurements. In the first case, a common structure of the time and frequency formulations is revealed and exploited to develop an identification software common for both formulations. The measure of fit represents the difference between the measured response time histories (or their Fourier transform) and the response time histories (or their Fourier transforms) predicted by a modal model when subjected to multiple support measured excitations. In the second case, the measure of fit represents the difference between measured and modal model predicted cross power spectral density functions. Computationally efficient two-step and three-step algorithms are developed to solve the resulting highly non-convex nonlinear optimization problems and identify the modal characteristics such as number of contributing models, modal frequencies, modal damping ratios, modeshapes and modal participation factors or operational reference vectors. The two-step approach is a very fast and accurate non-iterative algorithm, involving solution of two linear systems and singular value decomposition operations for estimating the modal characteristics. The third step solves the original nonlinear optimization problem using the estimates from the two-step approach to notably accelerate convergence of gradient based optimization algorithms. It is demonstrated that the third step is required only for closely spaced and overlapping modes to improve the estimates of the modal characteristics. The proposed methodology automates the estimation of the modal characteristics without, or with minimal, user interference and thus is especially applicable to continuous, real-time, structural health monitoring purposes. Part B: The problem of finite element structural model updating and response prediction variability based on measured modal characteristics is revisited. The correspondence between the recently proposed multi-objective identification, the conventional single-objective weighted residuals identification and the Bayesian statistical identification is established. These methods result in multiple Pareto optimal finite element models. An optimally weighted modal residuals method is also proposed for selecting the most preferred Pareto optimal model. The variability of these optimal models depends on the model and measurement error and affects the variability in the response predictions. In particular, Bayesian statistical identification offers the advantage of quantifying the uncertainty in the Pareto optimal models and the response predictions. Theoretical and computational issues arising in multi-objective and single-objective identification are addressed, including issues related to estimation of global optima, convergence of the xi xii proposed algorithms, and identifiability. Hybrid methods are proposed to identify global optima and the normal boundary intersection method is adopted to efficiently estimate the Pareto front and the Pareto optimal models. Finally, computational efficient algorithms are developed for estimating the gradients and the Hessians of the single and multiple objectives based on Nelson’s method for finding the sensitivity of eigenproperties to model parameters. It is shown that the computation time for estimating the Pareto optimal models is independent of the number of model parameters involved.
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