Multidisciplinary and Dynamic Decisions in Simulation-Based Design

Tao, Siyu

doi:https://doi.org/10.21985/n2-z008-wp17

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Multidisciplinary and Dynamic Decisions in Simulation-Based Design

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Modern design practices rely more and more on computer simulations due to their low cost compared with physical experiments. However, it is still an elusive task to fully unleash the advantages of the simulation models while mitigating their disadvantages for designing complex engineering systems. In simulation-based design, computer simulation models play a central role in assessing the performance of alternative designs of an engineering product and identifying its best design. When the simulation runs are costly, it is usually most efficient to sequentially evaluate the simulation model on alternative designs, so that decisions on which alternative design to evaluate next can be best made under the guidance of past evaluation results. Such decisions hence must be dynamically made in response to the latest information about past evaluations. This dissertation addresses the issues on fidelity improvement of a simulation model, information synthesis for a simulation model, and dynamic decision-making in simulation-based multidisciplinary design. The fidelity of simulation models can be improved through model calibration. The paradigm of model calibration is to adjust the low-fidelity (LF) models against high-fidelity (HF) models or HF data based on a statistical calibration formula. Although most existing model calibration techniques assume LF and HF models have identical inputs, in some engineering applications, e.g., wing aerodynamics computations, inputs to LF and HF models are often defined differently due to different levels of abstraction in modeling or simulation. For such problems, a new model calibration method is proposed to calibrate a mapping from HF model inputs to LF inputs by matching HF and LF model outputs. The advantages of the proposed method on calibration accuracy, parameter selection, and insights-drawing are demonstrated through an application of calibrating aerodynamic simulation models. Perhaps the best way to synthesize the information from a simulation model with its evaluation data is to fit an emulator to it. Gaussian process (GP) models are the most popular types of emulators for this purpose. GP models have been extended to emulate computer models with both qualitative and quantitative/continuous variables. Two recent GP models map each qualitative variable to some underlying numerical latent variables (LVs) and have achieved promising performance. Despite their success, the effects of their different LV structures on the models are still poorly understood. In this dissertation, a theorem is developed that reveals the effect of the ranks of the qualitative factor correlation matrices (QFCM) of mixed-variable GP models. Based on the insights obtained from the theorem, an alternative model is proposed that outperform the existing two by having better model flexibility. Extensive case studies show that the new model achieves higher accuracy on average. For multidisciplinary design optimization, the most efficient type of approach depends on the cost of evaluating the simulation models for the system. To design multidisciplinary systems using expensive simulation models, a commonly used approach is to treat the whole system as a single expensive model and apply Bayesian optimization (BO) , a class of methods for efficiently finding the global optimum of an expensive and often highly nonlinear function. This single-model approach is inefficient due to the need of evaluating all the component models at once in each iteration. A multi-model BO approach is proposed that dynamically decides to evaluate one component model per iteration based on the uncertainty quantification of linked emulators (metamodels) and the so-called “knowledge gradient” of system response as the acquisition function. This approach also solves problems with constraints and feedback couplings by penalizing the objective emulator and reformulating the original problem into a decoupled one. The superior efficiency of the proposed approach is demonstrated by solving two analytical problems and optimizing a multidisciplinary electronic packaging system design. To design multidisciplinary systems using inexpensive simulation models, various multidisciplinary design optimization (MDO) methods have been proposed to achieve the best efficiency. Enhanced collaborative optimization (ECO) is a recently developed method in the family of collaborative optimization (CO). While ECO achieves better optimization performance than its predecessors, its formulation is much more complex and incurs higher computation and communication costs, mainly due to the use of linear models of nonlocal constraints (LMNC). A new method named “ECO-ADMM” is proposed, which introduces the alternating direction method of multipliers (ADMM) to ECO. With the aid of Lagrangian multipliers, ECO-ADMM increases each discipline’s “awareness” of global constraint conditions and search history at a negligible cost of updating Lagrangian multipliers. A simplified version of ECO-ADMM is also proposed, which removes LMNC from the original ECO-ADMM. Advantages of ECO-ADMM over ECO on convergence properties are evidenced through case studies of two analytic test problems and an industrial vehicle suspension design problem.

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