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系統識別號 U0026-1107202007483000
論文名稱(中文) 以複合高斯小波產生人工地震新演算法
論文名稱(英文) A New Algorithm of Generating Ground Accelerograms by Compound Gaussian Wavelets
校院名稱 成功大學
系所名稱(中) 土木工程學系
系所名稱(英) Department of Civil Engineering
學年度 108
學期 1
出版年 108
研究生(中文) 黃昱喬
研究生(英文) Yu-Chiau Huang
學號 N68011017
學位類別 博士
語文別 中文
論文頁數 274頁
口試委員 指導教授-洪李陵
口試委員-朱聖浩
口試委員-朱世禹
口試委員-張文忠
口試委員-林其璋
口試委員-黃百誼
口試委員-鍾立來
中文關鍵字 人工地震  反應譜相符  複合高斯小波  單一週期最大偏差修正法 
英文關鍵字 artificial ground accelerogram  spectrum-compatible  compound Gaussian wavelet  single-period maximum-deviation modification method 
學科別分類
中文摘要 重要結構物基於極端水準的耐震需求,進入非線彈性狀態,需要進行動態歷時分析,此時外力輸入即為基底的加速度歷時。設計震譜為結構物耐震設計的依據,其形狀往往是諸多實測地表加速度紀錄的綜合結果,與之相符的地表加速度歷時只能人為產生。目前不論是時域或頻域演算法產生人工地表加速度歷時,其收斂條件以滿足與目標反應譜相符的容許誤差為主,較少考慮PGA的擬合、地動歷時波形的維持,以及基線偏移與否。本文首先理論推導新演算法產生人工地震,包含:(1)以高階高斯小波為基底函數;(2)直接調整反應位移歷時,再微分得地表加速度歷時;(3)加入低階高斯小波以滿足某些因地動延時有限的需求;以及(4)建議最佳需求之設定。接著以各種實例產生人工地震,進行比較,包含:(1)採用平滑或曲折的目標反應譜,一般或近斷層設計震譜;(2)選用等差或等比數列的反應譜擬合週期點,週期點數由23個至1000個不等;(3)針對不同的基底函數和修正對象;以及(4)降低反應譜擬合的容許誤差。經由理論推導與實例驗證,本文利用複合高斯小波逐次直接調整最大偏差的反應位移歷時,皆可在設定的反應譜擬合容許誤差和各項限制條件下,達致收斂,因此本文的人工地震新演算法極具實務應用價值。
英文摘要 Important structures will vibrate inelastically on the seismic demand of extreme level, and then their dynamic time history analyses should be performed under specified base excitation. For the purpose of seismic design, design spectra are usually proposed, where their forms are constituted based on many free-field records. Hence, ground accelerograms compatible with design spectra are generated only artificially. No matter what artificial accelerograms are generated in the time or the frequency domain, the results of convergence is reached as long as the maximum error compared with a target response spectrum is less than a tolerance, without the consideration of PGA matching, wave form maintenance, and baseline drift prevention. At first, this study develops a new algorithm theoretically to generate artificial earthquakes. The algorithm contains: (1) the use of a high-order Gaussian wavelet as the base function, (2) adjusting the response displacement time history corresponding to a single period directly, then obtaining the ground accelerogram by differential, (3) adding several low-order Gaussian wavelets to satisfy some demands due to the finite duration of ground accelerograms, and (4) suggesting the optimal demand setting. Then, the new algorithm are compared and verified through various simulation study and practical cases on generating artificial earthquakes. Those comparisons include: (1) using smooth or piecewise-defined target response spectra, general or near-fault site design spectra, (2) covering 23 to 1000 various matching periods from an arithmetic or a geometric sequence, (3) selecting different base functions and time histories under modification, and (4) reducing tolerance of matching. On the basis of theoretical formulation and practical verification, the new algorithm, which uses compound Gaussian wavelets to directly adjust the response deformation at one period at a time, can achieve convergence in all cases. Therefore, our new algorithm of generating artificial earthquakes is worthy of practical application.
論文目次 目錄
摘要 I
Extended Abstract II
致謝 IX
目錄 X
表目錄 XIV
圖目錄 XV
符號表 XX
第一章 緒論 1
第二章 文獻回顧 5
2.1 隨機訊號修正 6
2.2 頻域修正 12
2.2.1 頻域修正演算法簡介 13
2.2.2 Basu和Gupta (1998)以及Mukherjee和Gupta (2002) 15
2.2.3 Suárez和Montejo (2005) 17
2.3 時域修正 19
2.3.1 時域修正演算法簡介 19
2.3.2 Kual (1978) 22
2.3.3 Lilhanand和Tseng (1987, 1988) 25
2.3.4 Abrahamson (1992) 26
2.3.5 Hancock等人 (2006) 27
2.3.6 Atik和Abrahamson (2010) 29
2.3.7 Hong和Huang (2015) 30
2.4 三種人工地震產生方法的比較 31
2.5 近斷層地表加速度歷時的基線修正 33
2.6 近斷層反應譜 37
2.6.1 建築物耐震設計規範及解說 (2011) 38
2.6.2 洪李陵等人 (2018) 39
第三章 高斯小波應用於人工地震之數學理論推導 47
3.1 高斯小波簡介 47
3.1.1 高斯小波定義 47
3.1.2 小波函數的容許條件 48
3.1.3 赫米特多項式 49
3.2 能量正規化高斯小波及基本性質 50
3.2.1 能量正規化高斯小波 50
3.2.2 能量正規化高斯小波之絕對最大值 52
3.2.3 能量正規化高斯小波之零根 54
3.3 能量正規化高斯小波之進階性質 55
3.3.1 能量正規化高斯小波之微分遞迴公式 55
3.3.2 能量正規化高斯小波之三階遞迴公式式 56
3.3.3 能量正規化高斯小波極值之包絡線 57
3.4 利用能量正規化高斯小波設計基底加速度歷時 58
3.4.1 無限延時之能量正規化高斯小波 58
3.4.2 有限延時之能量正規化高斯小波 63
3.4.3 有限延時能量正規化高斯小波修正項之推導 65
3.4.4 由反應位移歷時推導基底振動歷時 68
3.4.5 滿足地動需求 71
第四章 時域產生人工地震之新演算法 95
4.1 外力線性內插法 95
4.2 單一週期最大偏差修正法 97
4.3 單一週期最大偏差修正法之探討與改良 99
4.3.1 高斯小波簡介 102
4.3.2 高斯小波與其它基底函數之探討 105
4.4 有限延時高斯小波之進一步修正 110
4.5 有限延時高斯小波不同限制條件之案例探討 115
4.6 反應位移極值發生時間之改變 120
4.7 PGA調整方法 122
4.8 人工地震演算法流程圖 125
4.9 小結 127
第五章 人工地震演算法實例應用及探討比較 197
5.1 不同情況產生人工地震的比較 198
5.1.1 情況組合概要 198
5.1.2 Case 1探討 200
5.1.3 Case 2至Case 4探討 202
5.1.4 Case 5至Case 7探討 203
5.1.5 Case 8及Case 9探討 205
5.1.6 Case 10至Case 12探討 205
5.1.7 12個Case小結 206
5.2 台灣海峽風機場址的人工地震 207
5.3 近斷層場址的人工地震 210
5.4 小結 212
第六章 結論與建議 266
6.1 結論 266
6.2 建議 268
參考文獻 270
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