A Modular Approach to Large-scale Design Optimization of Aerospace Systems.

Gradient-based optimization and the adjoint method form a synergistic combination that enables the efficient solution of large-scale optimization problems. Though the gradient-based approach struggles with non-smooth or multi-modal problems, the capability to efficiently optimize up to tens of thousands of design variables provides a valuable design tool for exploring complex tradeoffs and finding unintuitive designs. However, the widespread adoption of gradient-based optimization is limited by the implementation challenges for computing derivatives efficiently and accurately, particularly in multidisciplinary and shape design problems. This thesis addresses these difficulties in two ways. First, to deal with the heterogeneity and integration challenges of multidisciplinary problems, this thesis presents a computational modeling framework that solves multidisciplinary systems and computes their derivatives in a semi-automated fashion. This framework is built upon a new mathematical formulation developed in this thesis that expresses any computational model as a system of algebraic equations and unifies all methods for computing derivatives using a single equation. The framework is applied to two engineering problems: the optimization of a nanosatellite with 7 disciplines and over 25,000 design variables; and simultaneous allocation and mission optimization for commercial aircraft involving 330 design variables, 12 of which are integer variables handled using the branch-and-bound method. In both cases, the framework makes large-scale optimization possible by reducing the implementation effort and code complexity. The second half of this thesis presents a differentiable parametrization of aircraft geometries and structures for high-fidelity shape optimization. Existing geometry parametrizations are not differentiable, or they are limited in the types of shape changes they allow. This is addressed by a novel parametrization that smoothly interpolates aircraft components, providing differentiability. An unstructured quadrilateral mesh generation algorithm is also developed to automate the creation of detailed meshes for aircraft structures, and a mesh convergence study is performed to verify that the quality of the mesh is maintained as it is refined. As a demonstration, high-fidelity aerostructural analysis is performed for two unconventional configurations with detailed structures included, and aerodynamic shape optimization is applied to the truss-braced wing, which finds and eliminates a shock in the region bounded by the struts and the wing.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111567/1/hwangjt_1.pd

Multi-level and hybrid modelling approaches for systems biology

During the last decades, high-throughput techniques allowed for the extraction of a huge amount of data from biological systems, unveiling more of their underling complexity. Biological systems encompass a wide range of space and time scales, functioning according to flexible hierarchies of mechanisms making an intertwined and dynamic interplay of regulations. This becomes particularly evident in processes such as ontogenesis, where regulative assets change according to process context and timing, making structural phenotype and architectural complexities emerge from a single cell, through local interactions. The informa- tion collected from biological systems are naturally organized according to the functional levels composing the system itself. In systems biology, biological information often comes from overlapping but different scientific domains, each one having its own way of representing phenomena under study. That is, the dif- ferent parts of the system to be modelled may be described with different formalisms. For a model to have improved accuracy and capability for making a good knowledge base, it is good to comprise different sys- tem levels, suitably handling the relative formalisms. Models which are both multi-level and hybrid satisfy both these requirements, making a very useful tool in computational systems biology. This paper reviews some of the main contributions in this field