Active Machine Learning for Computational Design and Analysis under Uncertainties

Abstract

Computational design has become a predominant element of various engineering tasks. However, the ever increasing complexity of numerical models creates the need for efficient methodologies. Specifically, computational design under uncertainties remains sparsely used in engineering settings due to its computational cost. This dissertation proposes a coherent framework for various branches of computational design under uncertainties, including model update, reliability assessment and reliability-based design optimization. Through the use of machine learning techniques, computationally inexpensive approximations of the constraints, limit states, and objective functions are constructed. Specifically, a novel adaptive sampling strategy allowing for the refinement of any approximation only in relevant regions has been developed, referred to as generalized max-min. This technique presents various computational advantages such as ease of parallelization and applicability to any metamodel. Three approaches tailored for computational design under uncertainties are derived from the previous approximation technique. An algorithm for reliability assessment is proposed and its efficiency is demonstrated for different probabilistic settings including dependent variables using copulas. Additionally, the notion of fidelity map is introduced for model update settings with large number of dependent responses to be matched. Finally, a new reliability-based design optimization method with local refinement has been developed. A derivation of sampling-based probability of failure derivatives is also provided along with a discussion on numerical estimates. This derivation brings additional flexibility to the field of computational design. The knowledge acquired and techniques developed during this Ph.D. have been synthesized in an object-oriented MATLAB toolbox. The help and ergonomics of the toolbox have been designed so as to be accessible by a large audience.