Research And Application Of Metamodel Uncertainty Quantification Based On Bayes' Theorem

In complex engineering systems, approximation models, also called metamodels, are extensively constructed to replace the computationally expensive simulation and analysis codes. With different sample data and metamodeling methods, different metamodels can be constructed to describe the behavior of an engineering system. Due to the lack of data and limited knowledge, metamodel uncertainty will arise from selecting the best metamodel from a set of alternative ones. With delivering and accumulating,such uncertainty will have an important influence on the final performance of the engineering products.This dissertation studies the metamodel uncertainty from the selection course, a method based on Bayes' theorem is proposed to quantify this metamodel uncertainty. To reduce the effect of this metamodel uncertainty, an approach based on Bayes' theorem and adjustment factor is further put forward to improve the robust of metamodel. These methods are well proved by the shape optimization design case study of a deepsea submersible.Firstly, For the metamodel uncertainty involved in choosing, the uncertainty quantification method based on Bayes' theorem is proposed.The metamodel probability is computed by using Bayes' theorem, which can quantify such model uncertainty. In this study, two cases of metamodel uncertainty quantification are conducted: quantifying uncertainty of metamodels constructed by different metamodeling methods and quantifying uncertainty of metamodels created under different sampling methods. The quantification information of metamodel uncertainty will be useful for the choices of a suitable metamodeling method in the approximation of a problem.Secondly, to reduce the influence of this kind of metamodel uncertainty, an approach based on Bayes' theorem and Adjustment factor is proposed. In this approach, we select the best metamodel from a set of alternative ones, and metamodel uncertainty is accounted for by an adjustment factor which is added to the best one. Selecting the best metamodel w ithout ignoring the effcet from those of alternate metamodels, metamodel uncertainty involved in metamodel-selection can be reduced.Finally, the methods proposed in this dissertation are employed in the shape design optimization of a deepsea submersible. For the constructing metamodels of the drag and surrounded volume problem, the influence of this metamodel uncertainty is quantified by the method. Results indicate that the proposed methods can effectively quantify and final reduce the metamodel uncertainty and results in a more robust metamodel.