Simulation-Based Design Using Variable Fidelity Optimization

Simulation-based design optimization is playing an increasingly prominent role in the design of everything from spacecraft to consumer products. Applying nonlinear optimization techniques to simulation-based design becomes prohibitively expensive as computer models become more complex and increase in fidelity. A common engineering practice is to drive the preliminary design process using lower fidelity models as surrogates of expensive high fidelity simulations. Higher fidelity models are then used in the final design stages to refine the design. However, using automated optimization methods at this stage may still require enormous computational resources. Recently, variable fidelity schemes have been developed to address this problem by incorporating both models into one optimization framework. In these methods the low fidelity models are scaled to approximate the high fidelity simulations. This scaling allows the optimization to be performed using mainly low fidelity function calls, reducing the overall computational cost, while requiring only a few high fidelity evaluations to update the scaling function. Currently, two main scaling varieties are used: first order multiplicative and first order additive. In the multiplicative approach the low fidelity model is multiplied by a scaling function to approximate the high fidelity model; similarly, in the additive approach a scaling function is added to the low fidelity model.

The focus of this dissertation is on improving the efficiency and applicability of variable fidelity optimization algorithms. Highlights of original contributions made in this research include: (1) An adaptive hybrid scaling method that relieves designers from having to choose emph{a priori} which scaling method, multiplicative or additive, is most suitable to their problem with limited information. (2) Second order scaling methods which use approximate Hessian information, resulting in super-linear convergence rates. (3) A kriging-based global scaling method, which uses past design information to improve the global accuracy of the scaling model and was shown to reduce the computational cost of optimization by over 60% compared to single fidelity methods. (4) A metamodel update management strategy to reduce the cost of using kriging metamodels sequentially in large design problems. (5) Extension of the variable fidelity framework to solve reliability based design problems, which significantly lowers the computational cost, compared to traditional methods.