Efficient Global Optimization of Multidisciplinary System using Variable Fidelity Analysis and Dynamic Sampling Method
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Work in this dissertation is motivated by reducing the design cost at the early design stage while maintaining high design accuracy throughout all design stages. It presents four key design methods to improve the performance of Efficient Global Optimization for multidisciplinary problems. First, a fidelity-calibration method is developed and applied to lower-fidelity samples. Function values analyzed by lower fidelity analysis methods are updated to have equivalent accuracy to that of the highest fidelity samples, and these calibrated data sets are used to construct a variable-fidelity Kriging model. For the design of experiment (DOE), a dynamic sampling method is developed and includes filtering and infilling data based on mathematical criteria on the model accuracy. In the sample infilling process, multi-objective optimization for exploitation and exploration of design space is carried out. To indicate the fidelity of function analysis for additional samples in the variable-fidelity Kriging model, a dynamic fidelity indicator with the overlapping coefficient is proposed. For the multidisciplinary design problems, where multiple physics are tightly coupled with different coupling strengths, multi-response Kriging model is introduced and utilizes the method of iterative Maximum Likelihood Estimation (iMLE). Through the iMLE process, a large number of hyper-parameters in multi-response Kriging can be calculated with great accuracy and improved numerical stability. The optimization methods developed in the study are validated with analytic functions and showed considerable performance improvement. Consequentially, three practical design optimization problems of NACA0012 airfoil, Multi-element NLR 7301 airfoil, and all-moving-wingtip control surface of tailless aircraft are performed, respectively. The results are compared with those of existing methods, and it is concluded that these methods guarantee the equivalent design accuracy at computational cost reduced significantly.
General Audience Abstract
In recent years, as the cost of aircraft design is growing rapidly, and aviation industry is interested in saving time and cost for the design, an accurate design result during the early design stages is particularly important to reduce overall life cycle cost. The purpose of the work to reducing the design cost at the early design stage with design accuracy as high as that of the detailed design. The method of an efficient global optimization (EGO) with variable-fidelity analysis and multidisciplinary design is proposed. Using the variable-fidelity analysis for the function evaluation, high fidelity function evaluations can be replaced by low-fidelity analyses of equivalent accuracy, which leads to considerable cost reduction. As the aircraft system has sub-disciplines coupled by multiple physics, including aerodynamics, structures, and thermodynamics, the accuracy of an individual discipline affects that of all others, and thus the design accuracy during in the early design states. Four distinctive design methods are developed and implemented into the standard Efficient Global Optimization (EGO) framework: 1) the variable-fidelity analysis based on error approximation and calibration of low-fidelity samples, 2) dynamic sampling criteria for both filtering and infilling samples, 3) a dynamic fidelity indicator (DFI) for the selection of analysis fidelity for infilled samples, and 4) Multi-response Kriging model with an iterative Maximum Likelihood estimation (iMLE). The methods are validated with analytic functions, and the improvement in cost efficiency through the overall design process is observed, while maintaining the design accuracy, by a comparison with existing design methods. For the practical applications, the methods are applied to the design optimization of airfoil and complete aircraft configuration, respectively. The design results are compared with those by existing methods, and it is found the method results design results of accuracies equivalent to or higher than high-fidelity analysis-alone design at cost reduced by orders of magnitude.
- Doctoral Dissertations