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研究生:林廷謙
研究生(外文):Ting-Chien Lin
論文名稱:使用基因演算法結合稀疏回歸進行結構變位角估計的方程式探索
論文名稱(外文):Equation Discovery for Structural Drift Estimation Using Genetic Algorithm with Sparse Regression
指導教授:吳日騰
指導教授(外文):Rih-Teng Wu
口試委員:朴艾雪張國鎮歐昱辰
口試委員(外文):Aishwarya PuranamKuo-Chun ChangYu-Chen Ou
口試日期:2024-01-26
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:土木工程學系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2024
畢業學年度:112
論文頁數:111
中文關鍵詞:基因演算法稀疏回歸變位角估計方程探索數據驅動
外文關鍵詞:Genetic algorithmSparse regressionDrift estimationEquation discoveryData-driven
DOI:10.6342/NTU202400575
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本研究採用基因演算法,結合了Rudy、Samuel H.等人(2017)提出的稀疏回歸算法,以發現結構數據中的方程式。結構位移估算方程中的參數被重組成多個候選方程式,利用基因演算法中基因的排列組合形成候選方程式,並且加入稀疏回歸進行重要方程式的搜索,以發現位移估算的方程。旨在使用此方法發現新的位移估算方程。

新的位移估算方程中的參數數據來自Shah(2021)中整理計算而得的數值。這些參數被使用於計算Sozen,M. A.(2003)提出的位移估算方程和FEMA 440(2005)中的系數法提出的位移估算方程。利用這些參數構建多元的方程式組合(基因組合),並且經過演算法後發現方程式組合中的重要方程式,並找到新的位移估算方程。

基因演算法可以利用演化的方式發現多元的基因組合(方程式組合),但在此多元的組合中並不一定所有的組合都適用於目標函數,因此在透過稀疏回歸的演算後,進而找到新的漂移估算方程式,並對於發現的方程與先前提出的方程進行討論與比較。
This study adopts a genetic algorithm combined with the sparse regression algorithm proposed by Rudy, Samuel H., et al.(2017) to discover equations in structural data. The parameters in the structural displacement estimation equations are rearranged into multiple candidate equations using the permutation and combination of genes in the genetic algorithm. Sparse regression is integrated to search for important equations within the candidate equations, aiming to discover new displacement estimation equations.

The parameter data for the new displacement estimation equation is compiled from Shah (2021). These parameters are used to compute the displacement estimation equations proposed by Sozen, M. A. (2003) and the Coefficient Method presented in FEMA 440 (2005). By utilizing these parameters to construct a multivariate set of equations (genetic combination), and through algorithmic analysis, significant equations within the combination are identified, leading to the discovery of a new displacement estimation equation.

Genetic algorithms can utilize evolution to discover diverse sets of gene combinations (equation combinations). However, not all combinations within this diversity are necessarily suitable for the objective function. Therefore, through the algorithm of sparse regression, new drift estimation equations are identified. Subsequently, a discussion and comparison are carried out between the discovered equations and the previously proposed equations.
Verification Letter from the Oral Examination Committee . . . . . . . . . . . i
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Denotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Chapter 1 INTRODUCTION 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Research Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2 LITERATURE REVIEW 5
2.1 Method for estimating drift demands . . . . . . . . . . . . . . . . . . 5
2.1.1 Sozen, M. A. (2003).[30] . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Coefficient Method . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Method for data-driven discovery . . . . . . . . . . . . . . . . . . . 7
Chapter 3 BASELINE EQUATIONS 9
3.1 Sozen, M. A. (2003).[30] . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1.1 Velocity Amplification Factor . . . . . . . . . . . . . . . . . . . . . 11
3.1.2 Effective Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Coefficient Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2.1 C0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2.2 C1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2.3 C2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter 4 METHODOLOGY 17
4.1 Genetic algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.1.1 Customized genes . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.1.2 Fitness function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1.3 Crossover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1.4 Mutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1.5 Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2.1 Sparse regression . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.2 Ridge regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.3 STRidge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.3 Algorithm description . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.4 Selection of parameters and candidate functions . . . . . . . . . . . . 27
4.4.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4.2 Selection of candidate functions . . . . . . . . . . . . . . . . . . . 28
Chapter 5 RESULTS 31
5.1 Hyperparameter in GA . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.2 Discovered equation . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.2.1 Effective period . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.2.2 Peak ground acceleration (PGA) . . . . . . . . . . . . . . . . . . . 35
5.2.3 Spectral acceleration . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2.4 Discussion about discovered equation . . . . . . . . . . . . . . . . 36
5.2.5 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.3 Comparison with baseline equations . . . . . . . . . . . . . . . . . . 40
5.3.1 Roof drift ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.3.2 Maximum story drift ratio . . . . . . . . . . . . . . . . . . . . . . . 44
5.4 Performance in low-rise and high-rise structures . . . . . . . . . . . 45
5.4.1 High-rise structures . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.4.2 Low-rise structures . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.4.3 Conclusion of high-rise and low-rise structures . . . . . . . . . . . 50
Chapter 6 Conclusions 69
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
References 73
Appendix A — Algorithm 79
Appendix B — Database 83
B.1 Aristizabal and Sozen, 1976 . . . . . . . . . . . . . . . . . . . . . . 83
B.2 Healey and Sozen, 1978 . . . . . . . . . . . . . . . . . . . . . . . . 84
B.3 Moehle and Sozen, 1978 . . . . . . . . . . . . . . . . . . . . . . . . 84
B.4 Abrams and Sozen, 1979 . . . . . . . . . . . . . . . . . . . . . . . . 85
B.5 Cecen, 1979 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
B.6 Moehle and Sozen, 1980 . . . . . . . . . . . . . . . . . . . . . . . . 86
B.7 Wolfgram, 1984 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
B.8 Wood, 1985 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
B.9 Schultz, 1985 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
B.10 Shahrooz and Moehle, 1987 . . . . . . . . . . . . . . . . . . . . . . 89
B.11 Bonacci, 1989 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
B.12 Eberhard and Sozen, 1989 . . . . . . . . . . . . . . . . . . . . . . . 90
B.13 Van Nuys Holiday Inn, 1994 . . . . . . . . . . . . . . . . . . . . . . 91
B.14 UCSD Bridge Column, 2012 . . . . . . . . . . . . . . . . . . . . . . 91
B.15 Laughery, 2016 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
B.16 10F E-Defense RC Building, 2015/2018 . . . . . . . . . . . . . . . . 93
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