臺灣博碩士論文加值系統

在動態限制的條件下，桁架結構尺寸及形狀質量最佳化設計是個高度非線性問題。在多個自然頻率限制下，會導致動態靈敏度分析困難，由於減少質量與頻率限制是相互抵觸的，加上形狀變化容易造成振動模式的改變顯得更加困難，因此使用的最佳化演算法格外重要。於是本文提出新式的和聲搜尋演算法( New Harmony Search , 下稱NHS )，使用改良式和聲搜尋演算法(Improved Harmony Search , 下稱IHS)，並混合全域最佳和聲搜尋演算法( Global-best Harmony Search , 下稱GHS )再加入三點改進策略，分別為改進GHS音高微調方式、強迫調音與兩階段和聲改善，使NHS能更加完善的包含IHS與GHS的優點，發展出多樣性與集中性並重的啟發式演算法。而本文將介紹四種桁架結構的尺寸與形狀隨頻率限制條件最佳化的例子，這些例子在許多的文獻中被提出，並被當作基準。在此使用新式和聲演算法與原始和聲演算法和改良式和聲演算法比較，而後再將新式和聲演算法與相關文獻的案例進行比較，其NHS的結果可以得到接近甚至更佳的解，並且有著良好的穩定度，證明NHS為一有效的啟發式演算法。

Mass optimization on shape and sizing with dynamic constraints are a highly nonlinear problem. Since truss structure mass reducing contradict frequency constraint, multiple natural frequency constraints are difficult for dynamic sensitivity analysis, besides, shape modifications may easily cause vibration modes switch. Thus the choice of the appropriated method is important. Therefore, this paper presents a New Harmony Search (NHS) algorithm, this algorithm is a hybridization of the Improved Harmony Search (IHS) algorithm and the Global-best Harmony Search (GHS) algorithm then add 3 enhanced strategies. These strategies are (1) Improve the way of GHS' "pitch adjustment" (2) Compelling pitch adjust (3) Two-step harmony improve. These strategies make NHS perfectly include IHS and GHS' advantage then developed into a heuristic algorithm that diversification and intensification are in great balance. There are four remarkable examples which are widely reported and used in the related literature. NHS will compare with HS and IHS, and also compare with others method in the related literature. The results show that NHS performed similar to other methods and even better in some cases.

摘要 i
Abstract ii
誌謝 iii
目錄 iv
表目錄 vi
圖目錄 viii

第一章　緒論 1
1.1 研究背景與動機 1
1.2 研究目的 1
1.3 論文架構 2

第二章 理論及文獻回顧 3
2.1 最佳化設計簡介 3
2.2 頻率限制的桁架尺寸及形狀最佳化設計 3
2.3 桁架結構動力分析 4
2.3.1 桁架單位勁度矩陣 4
2.3.2 桁架單位質量矩陣 6
2.3.3 頻率方程式 9
2.4 最佳化演算法 9
2.5 和聲搜尋演算法(Harmony Search，HS) 10
2.6 改良和聲搜尋演算法 14
2.6.1 改良式和聲搜尋演算法(Improved Harmony Search ,IHS) 14
2.6.2 全域最佳和聲搜尋演算法(Global-best Harmony Search ,GHS) 15
2.6.3 IHS與GHS的比較 16

第三章　研究方法 17
3.1 目標函數 17
3.2 新式和聲搜尋演算法( New Harmony Search , NHS ) 18

第四章　案例與結果 21
4.1 桁架結構尺寸最佳化 21
4.1.1 10桿平面桁架結構 21
4.1.2 72桿空間桁架結構 22
4.2 桁架結構尺寸及形狀最佳化 24
4.2.1 37桿平面桁架結構 24
4.2.2 52桿空間桁架結構 26

第五章 結論與未來展望 28
5.1 結論 28
5.2 未來展望 28

參考文獻 29
附表 31
附圖 47

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