本論文旨在提出一套處理多目標工程問題之變數設計與公差配置的方法。在現有文獻中,大 多數討論的焦點集中於如何在特定的公差配置下進行最佳設計,或是如何針對特定設計點進 行公差配置。若要針對一個系統之設計變數與公差進行同步設計,將導致系統的維度增加, 使得演算更加困難,此情況在多目標工程設計且系統模型相對複雜的問題中尤為明顯。本論 文提出一設計流程來獲得數個多目標設計最佳點,並依據各點性能受不確定因素影響之狀況 定義一影響範圍將其量化。藉由影響範圍量化方法,設計者能得知各個設計點之系統性能變 動情況。透過最佳影響範圍面積之計算,設計者能量化各個設計點之性能變動範圍大小;而 最佳影響範圍中沿多目標Pareto set之方向及遠離Pareto set之方向分別定義為訊號及雜訊, 此訊號/雜訊比能指出設計點在不確定因素的影響下,其性能表現是否仍能符合Pareto set之 趨勢。此外,為了確保各個設計點的性能變動範圍均能在設計者所允許之範圍內,本論文所 提出之設計流程亦整合了公差設計方法。此設計流程也整合傳統的不確定因素分析與解析目 標傳遞法,以解決多層系統之多目標設計與公差配置問題。本論文所提出之方法,並不直接 指出最佳的設計點,而是提供設計者三個量化指標來輔助設計者進行決策。本論文將使用一 數學範例與一工程範例進行演示。透過單一系統與多層系統的多目標最佳化,說明此方法於 實際工程上之應用。

In this work we develop a method to perform simultaneous design and tolerance allocation for engineering problems with multiple objectives. Most studies in existing literature focus on either optimal design with constant tolerances or the optimal tolerance allocation for a given design setup. Simultaneously performing both design and tolerance allocation with multiple objectives for hierarchical systems increases problem dimensions and raises additional com- putational challenges. A design framework is proposed to obtain optimal design alternatives and to rank their performances when variations are present. An optimality influence range is developed to aid design alternatives selections with an influence signal-to-noise ratio that indicates the accordance of objective variations to the Pareto set and an influence area that quantifies the variations of a design . An additional tolerance design scheme is implemented to ensure that design alternatives meet the target tolerance regions. The proposed method is also extended to decomposed multi-level systems by integrating traditional sensitivity analysis for uncertainty propagation with analytical target cascading. This work enables decision-makers to select their best design alternatives on the Pareto set using three measures with different purposes. Examples demonstrate the effectiveness of the method on both single- and multi-level systems.

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