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曲線擬合在數(shù)學(xué)建模中的應(yīng)用
目錄
摘 要 1
Abstract 2
前言 3
1 數(shù)學(xué)建模簡(jiǎn)介 4
1.1 數(shù)學(xué)建模的概念 4
1.2 數(shù)學(xué)建模的1般方法和步驟 4
1.3 數(shù)學(xué)建模的重要意義 4
2 MATLAB簡(jiǎn)介 5
2.1 組成 5
2.2 MATLAB語(yǔ)言 6
3 曲線擬合 8
3.1 曲線擬合理論 8
3.2 曲線擬合的最小2乘法 8
3.3 線性最小2乘法 9
3.4 直線擬合 10
3.5 多項(xiàng)式擬合 10
3.6 用MATLAB作線形最小2乘擬合 11
4 MATLAB與曲線擬合在水塔流量估計(jì)模型中的應(yīng)用 14
4.1 問題的提出 14
4.2 問題分析 14
4.3 模型假設(shè) 14
4.4 流量估計(jì)的解題思路 15
4.5 算法設(shè)計(jì)與編程 15
4.6 分析與改進(jìn) 23
5 結(jié)束語(yǔ) 24
參考文獻(xiàn) 25
致謝 26
摘 要
數(shù)學(xué)建模方法是處理科學(xué)理論的1種經(jīng)典方法，也是解決各類實(shí)際問題的常用方法。通過抽象、簡(jiǎn)化、假設(shè)、引進(jìn)變量等處理過程后，將實(shí)際問題用數(shù)學(xué)方式表達(dá)，建立起數(shù)學(xué)模型，然后運(yùn)用先進(jìn)的數(shù)學(xué)方法及計(jì)算機(jī)技術(shù)進(jìn)行求解。曲線擬合通俗地講就是用1條(或1族)適當(dāng)?shù)那�去模擬1組(或多組)實(shí)驗(yàn)數(shù)據(jù)，從而得到較好地符合實(shí)驗(yàn)事實(shí)的數(shù)學(xué)關(guān)系式。MATLAB是1種廣泛應(yīng)用于工程計(jì)算及數(shù)值分析領(lǐng)域的新型高級(jí)語(yǔ)言。本文探討了MATLAB這1強(qiáng)而有力的工具在實(shí)驗(yàn)數(shù)據(jù)分析和處理中的應(yīng)用。將測(cè)量中得到的水塔流量的相關(guān)數(shù)據(jù)運(yùn)用最小2乘法，通過編寫程序?qū)崿F(xiàn)向計(jì)算機(jī)輸入實(shí)驗(yàn)測(cè)量數(shù)據(jù)，由MATLAB計(jì)算求出其函數(shù)表達(dá)式，明確表示出各物理量之間的關(guān)系。同時(shí)在屏幕上作出函數(shù)表達(dá)式的曲線，實(shí)現(xiàn)了數(shù)據(jù)分析和處理的快捷、準(zhǔn)確和直觀。計(jì)算結(jié)果與實(shí)際記錄基本吻合。
關(guān)鍵詞：數(shù)學(xué)建模；曲線擬合；水塔流量
Abstract
Mathematics modelling is a classical method to the process scientific theory . Also, it’s a common method to solve all kinds of actual problems. Through the processing of abstract, simplification, supposition and introduction variable, we can express the actual problem with mathematics, establish the mathematical model, and adopt the advanced mathematics method and computer technology to carry on the solution . Generally speaking, the curve fitting is to use a suitable curve imitating, a group with (or multi-groups) the empirical datum, and then abtain mathematics relationship in line with the fact well. MATLAB is a new advanced language applying in the field of engineering calculation and the numerical analysis . This article will discuss MATLAB —— this powerful tool applying in the empirical datum analysis and processing. Utilize the relevant data about the flow of the water tower acquired in survey to realize the input of survey data for erperient into the computer ,first by way of the lowese square metheod and later through programming; then, the function expression will be worked out through MATLAB computation ,and the relationship between various physical volume can be showed clearly. Meanwhile the curve of function expression on the screen makes it quick, accurate and direct for figures analying and processing. The computed result corresponds to the real record basically.
Key words：mathematics modeling; curve fitting ; water tank current capacity
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