Uncertainty in structural dynamic models.

Modelling of uncertainty increases trust in analysis tools by providing predictions with confidence levels, produces more robust designs, and reduces design cycle time/cost by reducing the amount of experimental verification and validation that is required. However, uncertainty-based methods are more complex and compu-tationally expensive than their deterministic counterparts, the characterisation of uncertainties is a non-trivial task, and the industry feels comfortable with the traditional design methods. In this work the three most popular uncertainty propagation methods (Monte Carlo simulation, perturbation, and fuzzy) are extensively benchmarked in structural dynamics applications. The main focus of the benchmark is accuracy, simplicity , and scalability. Some general guidelines for choosing the adequate uncertainty propagation method for an application are given. Since direct measurement is often prohibitively costly or even impossible, a novel method to characterise uncertainty sources from indirect measurements is presented. This method can accurately estimate the probability distribution of uncertain parameters by maximising the likelihood of the measurements. The likelihood is estimated using efficient variations of the Monte Carlo simulation and perturbation methods, which shift the computational burden to the outside of the optimisation loop, achieving a substantial time-saving without compromising accuracy. The approach was verified experimentally in several applications with promising results. A novel probabilistic procedure for robust design is proposed. It is based on reweighting of the Monte Carlo samples to avoid the numerical inefficiencies of re-sampling for every candidate design. Although not globally convergent, the proposed method is able to quickly estimate with high accuracy the optimum design. The method is applied to a numerical example, and the obtained designs are verified with regular Monte Carlo. The main focus of this work was on structural dynamics, but care was taken to make the approach general enough to allow other kinds of structural and non-structural analyses. DECLARATION This work has not previously been accepted in substance for any degree and is not being concurrently submitted in candidature for any degree. Signed Date STATEMENT 1 This thesis is the result of my own investigations, except where otherwise stated. Other sources are acknowledged by explicit references. A bibliography is appended. Signed Date STATEMENT 2 I hereby give my consent for my thesis, if accepted, to be available for photocopying and for interlibrary loan, and for the title and summary to be made available to outside organisations.