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姓名 陳士文(Shih-Wen Chen) 查詢紙本館藏 畢業系所 土木工程學系 論文名稱 橋梁動態載重識別之直接正規化法
(Dynamic Loadings Identification of Bridge by the Direct Regularization Method)相關論文 檔案 [Endnote RIS 格式]
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摘要(中) 傳統上獲取卡車總重與各軸軸重的方法是將車輛停置於地磅站測重，此方法費時且占地，故關於測量車輛載重衍生出許多動態載重識別法（Weight-In-Motion）的研究，其中有一部份是著重於橋樑與車輛間互制行為的載重識別研究，稱作為橋梁動態載重識別（Bridge Weight-In-Motion），特色是由橋梁的力學反應來反算出通過車輛的總重與軸重，而本文的研究引用到工程學反算理論，研究目的是以橋梁的應變來反算出移動荷載，其中橋梁結構是用有限元素法來模擬分析，分階段從單純的二維梁元素模型，到三維梁以及版元素模擬；反算理論則是將傳統的結構動力方程式求解，藉由引入應用數學中動態程序化(Dynamic Programming)討論的近似解數列誤差量觀念、線性離散時間系統(Linear Discrete-Time System)裡面的狀態空間系統(State-Space System)和線性代數求解近似值用到的其中一種直接正規化法，如Tikhonov正規化，以建立出完整的橋梁動態載重識別法來反算識別出梁上移動載重。
另外本論文除了利用數值模擬分析來觀察整個動態載重識別法可行性外，也實際進行實驗室單跨簡支梁的實驗分析案例，由分析結果探討加入許多不可抗拒之外在影響因素後，移動軸重識別結果精確度的變化，以下會概略介紹本文的研究主軸。摘要(英) In structural dynamics the forward problem is concerned with estimating the
response of the structure with respect to time to a known forcing function. The inverse
problem is concerned with estimating the forcing functions that cause the system to best
match the known or measured response. The procedure utilised to solve this type of
inverse problem is known as the method of general inverse theory and uses three areas of
mathematics. These are least squares minimisation with regularisation such as Tikhonov
regularisation, dynamic programming which provides an efficient solution to the least
squares problem and finally the L-curve method to calculate the optimal regularisation
parameter.
In the numerical simulation, the inverse system is already useful to identify the
passing loads clearly on the simulate beam model. The system uses the strain reactions of
each girder to calculate and monitor the bridge safety and maintenance. With this system,
we’ll have a clear and accurate data about all the passing trucks’ loading.關鍵字(中) ★ 動態程序化
★ 狀態空間系統
★ Tikhonov正規化
★ L曲線法
★ 動態載重識別系統關鍵字(英) ★ least square method
★ Tikhonov regularization
★ L-curve
★ dynamic programming
★ weight-in-motion論文目次 目錄
摘要..................................................................................................................................... I
Dynamic Loadings Identification of Bridge by the Direct Regularization Method ........... II
誌謝................................................................................................................................... III
目錄................................................................................................................................... IV
表目錄............................................................................................................................. VIII
圖目錄............................................................................................................................... IX
第一章 緒論................................................................................................................... - 1 -
1.1 研究動機與目的 ...................................................................................................- 1 -
1.2 論文架構 ...............................................................................................................- 2 -
第二章 文獻回顧........................................................................................................... - 4 -
第三章 結構動力學反算求解..................................................................................... - 12 -
3.1 狀態空間方程式 ................................................................................................ - 12 -
3.1.1 理論背景 ..................................................................................................... - 12 -
3.1.2 連續方程式之離散數列 ............................................................................. - 12 -
3.1.3 結構動力方程式之狀態空間系統之轉換 ................................................. - 19 -
3.2 應變與節點自由度關係 .................................................................................... - 27 -
3.2.1 前言 ............................................................................................................. - 27 -
V
3.2.2 二維梁元素彎矩應變方程式 ..................................................................... - 28 -
3.2.3 二維梁元素剪力應變方程式 ..................................................................... - 30 -
3.2.4 Grid 梁元素應變方程式 .............................................................................. - 32 -
3.2.5 板元素應變方程式 ..................................................................................... - 35 -
3.3 多軸移動力位置追蹤 ........................................................................................ - 41 -
第四章 正規化法則..................................................................................................... - 44 -
4.1 方程解析之正規化 ............................................................................................ - 44 -
4.1.1 離散問題直接正規化法 ............................................................................. - 44 -
4.1.2 正規化參數 ................................................................................................. - 48 -
4.1.3 小結 ............................................................................................................. - 50 -
4.2 動態問題最小化程序 ........................................................................................ - 52 -
4.2.1 前言 ............................................................................................................. - 52 -
4.2.2 動態程序化基礎理論 ................................................................................. - 52 -
4.2.3 正規誤差最小化程序應用 ......................................................................... - 63 -
4.2.4 一階正規最小化程序 ................................................................................. - 71 -
4.2.5 數值分析應用案例 ..................................................................................... - 73 -
4.2.6 正規化參數選擇 ......................................................................................... - 79 -
第五章 數值模擬與分析............................................................................................. - 83 -
5.1 單跨簡支梁元素模型 ........................................................................................ - 83 -
5.1.1 梁構件分析模型 ......................................................................................... - 83 -
VI
5.1.2 梁元素參數 ................................................................................................. - 85 -
5.1.3 移動力量加載形式 ..................................................................................... - 87 -
5.1.4 動態力量識別結果 ..................................................................................... - 88 -
5.2 三維Grid 梁元素結構模擬 ............................................................................... - 93 -
5.2.1 單跨雙大梁與橫梁結構分析模型 ............................................................. - 93 -
5.2.2 移動力量加載形式 ..................................................................................... - 94 -
5.2.3 參考彎矩應變之動態力量識別結果 ......................................................... - 95 -
5.2.4 參考彎矩應變與剪應變之動態力量識別結果 ....................................... - 100 -
5.3 三維板元素結構模擬 ...................................................................................... - 108 -
5.3.1 單跨板元素結構分析模型 ....................................................................... - 108 -
5.3.2 板元素參數 ............................................................................................... - 110 -
5.3.3 移動力量加載形式 ................................................................................... - 111 -
5.3.4 速度識別結果 ........................................................................................... - 112 -
5.3.5 動態力量識別結果 ................................................................................... - 116 -
第六章 實驗室試驗................................................................................................... - 118 -
6.1 實驗室試驗試體與儀器設備 .......................................................................... - 118 -
6.2 自然振動頻率量測 .......................................................................................... - 124 -
6.3 彎曲剛度識別 .................................................................................................. - 125 -
6.4 阻尼比識別 ...................................................................................................... - 126 -
6.5 單軸荷重識別 .................................................................................................. - 127 -
VII
6.5.1 單軸荷重識別結果 ................................................................................... - 128 -
6.6 雙軸荷重識別 .................................................................................................. - 134 -
6.6.1 雙軸荷重識別結果 ................................................................................... - 135 -
6.6.2 識別結果曲線平化度控制 ....................................................................... - 150 -
6.7 小結 .................................................................................................................. - 155 -
第七章 結論與建議................................................................................................... - 156 -
7.1 結論 .................................................................................................................. - 156 -
7.2 建議 .................................................................................................................. - 157 -
參考文獻..................................................................................................................... - 159 -
附錄 A ........................................................................................................................ - 163 -
附錄 B ........................................................................................................................ - 165 -參考文獻 Bellman, R. & Dreyfus, S. E., (1962). Applied DynamicP programming. The
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