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| 研究生： |
林昱 Lin, Yu |
|---|---|
| 論文名稱： |
混合週期因子的生長曲線建模 The modeling of Logistic Curve by mixing the periodic factor |
| 指導教授： |
曾正男
Tzeng, Jeng-Nan |
| 口試委員: |
李明融
Li, Meng-Rong 薛名成 Shiue, Ming-Cheng |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2017 |
| 畢業學年度： | 105 |
| 語文別： | 中文 |
| 論文頁數： | 102 |
| 中文關鍵詞： | 曲線擬合 、數學模型 、生長曲線 、基因演算法 |
| 外文關鍵詞： | Curve fitting, Mathematical model, Logistic curve, Genetic algorithm |
| 相關次數： | 點閱：209 下載：9 |
| 分享至: |
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在這篇論文中，我們引用“海岸綠提-水筆仔”的資料
。我們的目的是要找到一個合適的函數去擬合這些資料，以及找到一個合適的微分方程式，使得該方程式的解是能夠擬合這些資料的。這樣的函數以及微分方程將能幫助我們更了解這筆資料的性質，並對預測資料未來走向更有幫助。
我們首先藉由生長曲線來建構我們的數學函數，並對這個數學函數的模型加上週期項來改良。藉由Matlab curve fittig tool，我們找到了這個函數的一組參數來擬合原始資料。最後得到的結果如我們的預期，加了週期函數做出來的建模較原本生長曲線的建模更為貼近原始資料。
在尋找微分方程系統的建模上，我們參考了文獻方法，並加以改良。然而這個新的微分方程式在加上週期項來改良之後卻沒辦法找到解析解，所以我們利用基因演算的方法來去尋找適合這個微分方程系統的參數，並搭配Heun's method，RK2 method和RK4 method求出一些數值解。最後得到了一個比原參考文章更好的結果。
In this paper, we focus on the data from the website `Seacoast Green Bank-Kandelia'. There are two things we want to do for these data. First, we want to find a function which graph fits these data. Second, we want to find a differential equation such that its solution fits these data well. By exploring the function and the differential equation, we can understand more properties of these data.
We first build our mathematical function from Logistic curve and improve it by adding a periodic factor. By using Matlab curve fitting tools, we find parameters of this function which fit these data well. The final result is the same as our expectation. The model by adding a periodic factor fits the data better than the model of Logistic function.
To look for a differential equation, we follow the method in \cite{rfspaper} and improve it. However, there is no analytical solution after adding a periodic factor into the model. Thus we use the method of a genetic algorithm to find suitable parameters of this differential equation. Moreover, we find the numerical solution by using Heun's method, RK2 method and RK4 method. Finally, we get a better result than one in Ren-fa, Chen's paper.
Chapter 1 Introduction 1
Chapter 2 Source of Data 4
Section 1 Sources 4
Section 2 Time and Height 7
Chapter 3 Construct Model Function 9
Section 1 Fit by Logistic Curve 9
Section 2 Model 1 10
Section 3 Model 2 11
Section 4 Genetic Algorithm 13
Chapter 4 Construct Differential Equation Model 15
Section 1 Survey from Ren-fa's Paper 15
Section 2 First Order Differential of the Data 20
Section 3 Model 3 22
Subsection 1 Using Regression 23
Subsection 2 Using Finite Difference Method 25
Subsection 3 Using Analytical Solution 29
Section 4 Model 32
Subsection 1 Using Finite Difference Method 32
Subsection 2 Using Genetic Algorithm 35
Subsection 3 Using Matlab Curve Fitting Tool 39
Chapter 5 Conclusion 42
Appendix Code use in paper 44
Appendix 1 Code 01 44
Appendix 2 Code 02 55
Appendix 3 Code 03 65
Appendix 4 Code 04 76
Appendix 5 Code 05 90
Bibliography 102
url
海岸綠提—水筆仔 http://163.20.52.80/stu635/cwpspage/mang/study/index.htm.
book
William E Boyce. Elementary differential equations and boundary value problems. Wiley,9th edition, 2010.
book
Brian Bradie. A friendly introduction to nummerical analysis. Pearson Education, Inc., 2006.
book
Laurence D Hoffmann. Applied calculus for bussiness, economics, and the social and life sciences. McGraw-Hill, eleventh edition, 2014.
url
Tzeng Jeng-nan. 數值微分 http://glophy.com/index.php/2014-02-07-01-06-58/2014-02- 07-01-07-46/79-2014-02-05-07-28-44.
book
David Kincaid. Numerical analysis: Mathematics of scientific computing. Brooks/Cole, third edition, 2002.
paper
Chen Ren-fa. Nonlinear differential equation of second order and its applications. 2015.
