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    Title: 技術先進的三點近似法工程最佳化研究
    Other Titles: Technologically Advanced Three-Point Approximation Method for Engineering Design Optimization
    Authors: 史建中
    Contributors: 淡江大學機械與機電工程學系
    Keywords: 結構最佳化;近似函數;近似法最佳化;工程設計最佳化;奇異性;電腦輔助設計;structural optimization;function of approximation;optimization of approximation method;engineering design optimization;singularity;computer-aided design
    Date: 2011
    Issue Date: 2012-05-30 22:42:23 (UTC+8)
    Abstract: 在現代實用的工程結構最佳化設計中,由於系統的複雜及大型,經常需用套裝的大量有限元素 進行分析及最佳化設計程序。除了耗費時間與數值運算資源外,亦增加解題的複雜性及非線性程度, 使得求解不穩定,也增加偏離最佳解的可能性。前述問題可以近似法最佳化尋求改善,三點近似法最 佳化為近代近似法最佳化發展的主流,求解過程中,尚缺乏完整有效的策略。 本研究擬開發先進(advanced)的新型三點近似法及最佳化策略,旨在改善三點近似法指數不可調 整的缺點,提升準確性,擴大近似空間,並研訂兼具有效性及合理性之最佳化策略。但因建構近似函 數趨向複雜化。常使得在最佳化求解時,違反限制條件,造成不穩定收斂,增加迭代計算及誤差。本 研究即是加入保守度(conservation)的考量,提出保守三點指數近似法及最佳化策略,達到較能穩當收 斂,提升最佳化效率及精確度。本研究的第三項主題為去除求解過程裡的奇異(singularity)現象。不論 是欲探討的先進新型三點近似法及最佳化略,或三點保守點指數近似法及最佳化策略,在某些最佳化 求解情況下,使指數展開近似函數在奇異點的附近誤差過大。本研究引入提昇水準(shifting level)的中 介變數,改善先進新型三點近似法產生奇異現象的缺點,擴大近似範圍,提升準確度。研究中將發展 去除奇異性的先進新型三點近似法最佳化策略,及去除奇異性的三點保守點指數近似法最佳化策略。 在研發過程中,除了應用理論發展外,並應用於大量有限元分析的結構應用設計。其中的案例將 應用於高精度自動光學檢測精密機器(high precision automatic optical inspection (AOI) machine) 的有限 元分析結構設計上,這是第四個研究特點。第五個研究特點是開發以實用最佳化設計分析計算軟體 -Visual DOC- 與有限元素分析軟體 -ANSYS- 的合併使用程序,其中的核心技術就是本研究欲探討開 發的去除奇異性的先進三點近似法函數及最佳化演算流程;及三點保守點指數近似法的最佳化策略, 可提升實際應用的價值。
    Some optimization and finite element software are well-developed during last two decades that provide very efficient tools for engineering design and analysis. Although individual software has specific function; however, it is not convenient to cooperate those two in one phase for engineering application. This project will explore the integration of those two specialized software for engineering design optimization. Particularly, a structural optimization problem requires a large amount computation of finite element analysis. Somehow, it increases the nonlinearity of problem characteristic. A general recognized strategy is to adopt the approximation technique that transforms implicitly to explicitly mathematical behavior functions. Three-point approximation technique is relatively superior to other approaches in precision and optimization performance, as recognized the main stream in this research field.. The most recent development is called the new three-point approximation. This project applies the approximation to 2nd order term in Taylor series where only the diagonal items are included, as called advanced new three point approximation. The feature of this project includes the computation of a set of parameters using intervening variable. This project describes the complete mathematical modeling and the error analysis with several numerical problems. The proposed approach is then applied to engineering design optimization. By considering the characteristic, an efficient optimization process is consequently developed and presented. For dealing the robustness during optimization process, conservative computation and avoid singularity are two important considerations during the development of three-point approximation technique. Thus, this project proposes a conservative three-point approximation optimization and enhanced methodology for both advanced new three-point and conservative three-point approximate optimization. A research problem consists of large scale finite element analysis and design optimization is the high precision automatic optical inspection (AOI) machine. Including some critical dimension are required to design, structural weight and critical displacement are two design goals for this problem. Not only the proposed research method can be applied for practical usage, but also the innovative approximation methodology is integrated into engineering optimization process as the important academic contribution.
    Appears in Collections:[機械與機電工程學系暨研究所] 研究報告

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