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Title: Developing quantitative validation metrics to assess quality of computational mechanics models relative to reality
Author: Dvurecenska, K.
ISNI:       0000 0004 7964 2304
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2019
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Computational models are widely used to assess and predict behaviour of engineering systems. It is desirable that simulation correctly represents the real behaviour of the system's intended use and thus establishment of the level of quality for obtained results through validation is vital. The focus of the research presented in this thesis is the development and implementation of a novel generic validation metric for quantifying the quality of simulation results. The choice of the validation metric is governed by the data available, the outcome required and the model's range of use. Three categories of metrics have been identified: Hypothesis testing, Frequentist and Bayesian. In general, Frequentist methods, in comparison to Hypothesis testing, allow a better understanding of the quality of the current model, through quantifying the differences between the predicted and measured results; whereas Bayesian analysis is typically used for the model parameter calibration. The work presented in this thesis concentrates on developing a Frequentist validation metric, and two novel metrics are proposed, i.e. based on a Theil's inequality coefficient and a new relative error metric. Previously in solid mechanics validation has been applied to data points obtained from strain gauge measurements; in the present work the application is extended to data fields obtained with the aid of optical measurement techniques, e.g. displacement fields. By incorporating orthogonal decomposition the dimensionality of data fields can be reduced to coefficients in the feature vector, while preserving the key information about the deformation of the entire surface, and equivalent measured and predicted data sets can be obtained, which is essential for validation purposes. Utilising the feature vectors, both of the novel metrics provide a measure of quality of the model's predictions relative to reality. The outcome of the Theil's inequality coefficient is a value between 0 and 1, i.e. from excellent to poor correlation of predictions with measured data. Whereas the novel relative error metric combines the use of a threshold based on the uncertainty in the measurement data with a normalised relative error, and the quality of predictions is expressed in terms of a probability statement. Such outcome obtained with the new relative error metric is more quantitative and informative than the previous validation procedures but qualitatively equivalent. Three previously published case studies were successfully employed to demonstrate the efficacy of the novel methodologies.
Supervisor: Patterson, Eann A. ; Patelli, Edoardo ; Graham, Steve Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral