Enabling Automated, Reliable and Efficient Aerodynamic Shape Optimization With Output-Based Adapted Meshes

Simulation-based aerodynamic shape optimization has been greatly pushed forward during the past several decades, largely due to the developments of computational fluid dynamics (CFD), geometry parameterization methods, mesh deformation techniques, sensitivity computation, and numerical optimization algorithms. Effective integration of these components has made aerodynamic shape optimization a highly automated process, requiring less and less human interference. Mesh generation, on the other hand, has become the main overhead of setting up the optimization problem. Obtaining a good computational mesh is essential in CFD simulations for accurate output predictions, which as a result significantly affects the reliability of optimization results. However, this is in general a nontrivial task, heavily relying on the user’s experience, and it can be worse with the emerging high-fidelity requirements or in the design of novel configurations. On the other hand, mesh quality and the associated numerical errors are typically only studied before and after the optimization, leaving the design search path unveiled to numerical errors. This work tackles these issues by integrating an additional component, output-based mesh adaptation, within traditional aerodynamic shape optimizations. First, we develop a more suitable error estimator for optimization problems by taking into account errors in both the objective and constraint outputs. The localized output errors are then used to drive mesh adaptation to achieve the desired accuracy on both the objective and constraint outputs. With the variable fidelity offered by the adaptive meshes, multi-fidelity optimization frameworks are developed to tightly couple mesh adaptation and shape optimization. The objective functional and its sensitivity are first evaluated on an initial coarse mesh, which is then subsequently adapted as the shape optimization proceeds. The effort to set up the optimization is minimal since the initial mesh can be fairly coarse and easy to generate. Meanwhile, the proposed framework saves computational costs by reducing the mesh size at the early stages of the optimization, when the design is far from optimal, and avoiding exhaustive search on low-fidelity meshes when the outputs are inaccurate. To further improve the computational efficiency, we also introduce new methods to accelerate the error estimation and mesh adaptation using machine learning techniques. Surrogate models are developed to predict the localized output error and optimal mesh anisotropy to guide the adaptation. The proposed machine learning approaches demonstrate good performance in two-dimensional test problems, encouraging more study and developments to incorporate them within aerodynamic optimization techniques. Although CFD has been extensively used in aircraft design and optimization, the design automation, reliability, and efficiency are largely limited by the mesh generation process and the fixed-mesh optimization paradigm. With the emerging high-fidelity requirements and the further developments of unconventional configurations, CFD-based optimization has to be made more accurate and more efficient to achieve higher design reliability and lower computational cost. Furthermore, future aerodynamic optimization needs to avoid unnecessary overhead in mesh generation and optimization setup to further automate the design process. The author expects the methods developed in this work to be the keys to enable more automated, reliable, and efficient aerodynamic shape optimization, making CFD-based optimization a more powerful tool in aircraft design.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163034/1/cgderic_1.pd

Essays in Financial Economics.

The first chapter studies the impact of house price expectations together with securitization, on the magnitude of risky mortgage lending by banks. This chapter first presents a simple model to explore the impact of both house price expectations and the growth of securitization on the extent of subprime lending. The model shows that a high expectation of housing prices not only increases lenders' willingness to lend to riskier borrowers, but, in addition, enhances the attractiveness of the originate-to-distribute (OTD) model of lending. Access to securitization markets also amplifies banks' incentives to lend to sub-prime borrowers and leads to a worsening of mortgage-market credit quality. Thus, when housing prices decline, the extent of defaults is magnified with OTD lending. Empirical findings confirm the model's predictions. In particular, the results show that, in markets with higher housing price growth, banks with higher OTD participation extended mortgages to riskier borrowers, and thus, had larger incidence of defaults once house prices declined. The second chapter models the interaction between lending institutions and credit rating agencies under different economic scenarios, where an originator window dresses claims it issues and a credit rating agency (CRA) screens. Both window dressing and screening efforts are shown to depend on the state of the economy: better states exhibit greater window dressing and less screening. The rating quality and default probability for given ratings also vary with economic conditions, and credit spreads adjust to such variations. The third chapter examines how retirement affects households portfolio choice. Conventional wisdom suggests that when income is substantially reduced after retirement, households should hold more safe assets in their portfolios. The data, however, show that, on average, retirement causes an approximately five to seven percent increase in the share of risky assets in households' portfolios. In addition, this positive shift mostly happens right after retirement immediately and is mainly driven by the fact that households without risky assets start to hold risky assets after retirement. Evidence in support of (a) shifts in risk tolerance and (b) spending additional time tracking the stock market is presented.PHDEconomicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135738/1/gdchen_1.pd

Airfoil Shape Optimization Using Output-Based Adapted Meshes

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143055/1/6.2017-3102.pd

How Cooperation and Competition Arise in Regional Climate Policies: RICE as a Dynamic Game

One of the most widely used models for studying the geographical economics of climate change is the Regional Integrated model of Climate and the Economy (RICE). In this paper, we investigate how cooperation and competition arise in regional climate policies under the RICE framework from the standpoints of game theory and optimal control. First, we show that the RICE model is inherently a dynamic game. Second, we study both cooperative and non-cooperative solutions to this RICE dynamic game. In cooperative settings, we investigate the global social welfare equilibrium that maximizes the weighted and cumulative social welfare across regions. We next divide the regions into two clusters: developed and developing, and look at the social welfare frontier under the notion of Pareto optimality. We also present a receding horizon approach to approximate the global social welfare equilibrium for robustness and computational efficiency. For non-cooperative settings, we study best-response dynamics and open-loop Nash equilibrium of the RICE game. A Recursive Best-response Algorithm for Dynamic Games (RBA-DG) is proposed to describe the sequences of best-response decisions for dynamic games, which indicates convergence to open-loop Nash equilibrium when applied to the RICE game by numerical studies. We also study online receding horizon feedback decisions of the RICE game. A Receding Horizon Feedback Algorithm for Dynamic Games (RHFA-DG) is proposed. All these proposed solution concepts are implemented and open sourced using the latest updated parameters and data. The results reveal how game theory may be used to facilitate international negotiations towards consensus on regional climate-change mitigation policies, as well as how cooperative and competitive regional relations shape climate change for our future

The Past, Present and Future Situation of Mixed Martial Arts (MMA) in China

[EN] China, with a history of more than 5,000 years, has created uncountable splendid civilizations. Chinese folk martial arts..