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研究生:林詩偉
研究生(外文):Lin,Shih-Wei
論文名稱:運用幾何特徵描述詮釋資料特性之研究
論文名稱(外文):Geometric Characterization for Data Interpretation
指導教授:周碩彥周碩彥引用關係
指導教授(外文):Chou,Shuo-Yan
學位類別:博士
校院名稱:國立臺灣科技大學
系所名稱:工業管理系
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:89
中文關鍵詞:幾何演算法資料分析真圓度量測凸出多邊形平行座標系統多度空間旋轉多向度評量法工廠佈置
外文關鍵詞:Geometric algorithmsData AnalysisCircularity AssessmentConvex PolygonParallel Coordinate SystemMultidimensional RotationMulti-Dimensional ScalingFacility Layout
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實務的問題在加以模式化後,在求解的過程中經常可被轉換成幾何問題,再針對幾何問題發展有效率之演算法求得相對應之答案。本研究透過幾何特徵描述之詮釋分析,針對特定實務問題發展出相關演算法求解,所解決的問題包括真圓度之量測問題、轉換成幾何問題之缺點分類、多度空間中之集群、多度空間之旋轉、工廠佈置、施工架配置等不同領域的問題。
本研究將上述問題分為三類。第一類的探討主題與幾何形狀推估有關。對於真圓度量測,本研究依據圓柱中心軸傾斜時,可能造成的影響,而發展出一補正程序。此補正程序可修正因為圓柱中心軸的傾斜,而使得量測點座標資料產生偏差。使用經過補正程序修正之後的量測點來評量真圓度,可降低拒收合格品的機率。對於轉換成幾何問題的鋁箔缺點分類,本研究透過凸出多邊形的特性,將有缺點的鋁箔作一分類,判斷缺點是屬於常見的四種缺點中的哪一種。
第二類要解決的是高度空間之幾何問題。對於高度空間中接近於一條線的點集群之問題,本研究發展scan-line演算法,將資料以平行座標系統顯現後,找出接近於一條線之點集群。對於高度空間之旋轉,本研究以直交正規化矩陣的概念,提出一個N度空間之旋轉方法,將N度空間中之旋轉問題轉換為一個有N(N+1)/2個變數的問題。最後,並搭配模擬退火法來解決多向度評量法之旋轉問題。
第三類要探討之主題為使用幾何結構方式來解決問題。對於工廠佈置問題,本研究使用多向度評量法搭配隔間結構以及模擬退火法,建構出一個可接受的工廠佈置。本演算法首先計算出部門在二度空間中的建議位置,如此可以將佈置問題轉移到二度空間中。然後再用隔間結構方式來計算出建議的工廠佈置。最後透過模擬退火法找出多向度評量法分析資料之旋轉角度以及產生不同的隔間結構,以建立一個較佳的工廠佈置。對於框式施工架配置之問題,本研究針對建築物外框之幾何結構,先作一分析與假設,再發展一循序分析式演算法,計算出建議之框式旋工架配置。
Geometric algorithms can be used to solve research problems modeled by geometric means. In this research, geometric characterization is used for solving geometric problems appeared in areas such as circularity assessment, the categorization of defects, multidimensional clusters, multidimensional rotation, facility layout and scaffold layout problems.
The first class of problems is solved with the shape classification. For the circularity measurement in three dimensions, the characterization of oblique of cylinder is considered, and a compensation procedure is therefore developed for solving the circularity measurement problems where the cylinder is oblique. After the compensation procedure, the compensated measured point can be used for measuring circularity. Thus, the probability of rejecting in-tolerance product will decrease. For the problem of categorization of defective aluminum foils, the properties of convex polygon are used to determine the defective belongs to what kind of the defectives.
The second class of problems is solved in the higher dimensional space. For a cluster of points close to a line problem, a scan-line approach is developed to find a cluster of points close to a line when data points are displayed in the parallel coordinate system. For the N-dimensional rotation problem, orthonormal matrix is used to translate the rotation problem into a dealing with N(N+1)/2 variables problem. Finally, the Simulated Annealing (SA) is used to find a satisfactory N-dimension rotation.
The third class of problems is solved with the aid of geometric patterns. For the facility problem, the combination of Multidimensional Scaling (MDS), Bay structure and SA is used to construct a satisfactory layout. First, MDS is used to compute the relative position of facilities in two-dimensions, and bay structure is used to derive the layout. Finally, SA is used to search the rotation degree of MDS and construct different bay structure in order to derive a satisfactory layout. For the scaffold layout problem, the profile of building is analyzed under some assumptions, and a sequence analytic approach is developed to derive the scaffold layout.
摘要…………………………………………………………………………i
英文摘要……………………………………………………………………ii
誌謝…………………………………………………………………………iii
目錄…………………………………………………………………………iv
圖目錄………………………………………………………………………vii
表目錄………………………………………………………………………x
第一章 緒論………………………………………………………………1
1.1 研究動機與目的……………………………………………………1
1.2 研究範圍……………………………………………………………2
1.3 論文架構……………………………………………………………3
第二章 特徵推估…………………………………………………………5
2.1 圓特徵推估…………………………………………………………5
2.1.1 量測補正之原因………………………………………………7
2.1.2 補正程序………………………………………………………10
2.1.3 實作與比較……………………………………………………14
2.1.4 結論……………………………………………………………16
2.2 不規則物件之凸出多邊形(Convex polygon)推估………………17
2.2.1 凸出多邊形之幾何特徵………………………………………18
2.2.2 問題描述………………………………………………………18
2.2.3 計算凸出多邊形幾何特徵之演算法…………………………19
2.2.4 實驗結果………………………………………………………22
2.2.5 結論……………………………………………………………24
第三章 多度空間幾何問題………………………………………………25
3.1 多度空間資料描述…………………………………………………25
3.2 平行座標系統………………………………………………………27
3.2.1 平行座標系統與基本特性……………………………………27
3.2.2 Scan-Line Approach…………………………………………32
3.2.3 討論與結論……………………………………………………34
3.3 多度空間旋轉-運用於多向度評量法……………………………35
3.3.1 多向度評量法簡介……………………………………………35
3.3.2 多向度評量法之旋轉問題……………………………………36
3.3.2.1 向度詮釋與認知空間之旋轉……………………………36
3.3.2.2 相似性與偏好性認知空間之旋轉………………………37
3.3.3 多度空間旋轉…………………………………………………38
3.3.3.1 傳統旋轉矩陣……………………………………………38
3.3.3.2 直交正規化矩陣…………………………………………38
3.3.4 最佳值函數之判斷……………………………………………39
3.3.5 用直交正規化矩陣來處理二度以上之旋轉問題……………40
3.3.6 運用模擬退火法尋找最佳旋轉角度…………………………41
3.3.7 應用實例………………………………………………………43
3.3.8 結論……………………………………………………………48
第四章 幾何結構運用……………………………………………………49
4.1 用幾何特性觀點來解決工廠佈置問題……………………………49
4.1.1 相關程度在工廠佈置之運用-多向度評量法………………50
4.1.2 用隔間結構 (bay structure)來建構佈置之程……………51
4.1.3 用模擬退火法求解工廠佈置問題……………………………54
4.1.4 實驗結果………………………………………………………57
4.1.5 結論……………………………………………………………60
4.2 運用建築物外框之幾何結構來作框式施工架配置規劃…………61
4.2.1 系統假設與規則定義…………………………………………61
4.2.2 系統演算法流程………………………………………………70
4.2.3 實例……………………………………………………………77
4.2.4 結論……………………………………………………………78
第五章 結論與未來研究方向……………………………………………80
5.1 結論…………………………………………………………………80
5.2 未來研究方向………………………………………………………81
參考文獻……………………………………………………………………82
附錄一………………………………………………………………………87
附錄二………………………………………………………………………88
附錄三………………………………………………………………………89
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