臺灣博碩士論文加值系統

氣膠的粒徑對氣膠動力與捕集具有密切的關係，使用統計方法求得粒徑分佈與粒徑分佈參數是基本的氣膠分析工作。目前普遍使用的微軟 Excel 試算表程式含有優化計算的規劃求解功能，可以求取與給定粒徑分佈型態具最小方差和的氣膠粒徑分佈函數，並得到分佈函數中各不同成分的比例與分佈參數。在以往的研究中，曾與實驗室所產生的氣膠比較，得到相當準確的結果。

然而，在使用於現場狀況下，預期仍會增遇到各種問題，其中最基本的問題就是若兩氣膠粒徑分佈相當接近，上述方法是否仍可以得到正確的結果？如果要使用上述方法得到正確的結果，氣膠分佈函數必須要滿足何種條件。

本研究組合兩組粒徑成對數常態分佈的氣膠，經過各種成分比例與分佈參數組合，得到可以使用規劃求解得到正確結果的範圍。當兩組氣膠具相同的幾何標準差，經過 ANOVA 分析，發現當F< 0.24（在樣本數極大的狀況下，相當於p< 0.6）時，所得到的結果與預期值會相當的差異（以計算結果與預期值的方差何做為指標）。當兩組氣膠具相同的中數粒徑時，使用 Bartlett's 檢驗，發現 Bartlett 係數b非常接近 1 才會得到明顯誤差，也就是當兩組氣膠粒徑幾何標準差相當接近，或份量差異甚大時。

The size of an aerosol particle significantly affects the dynamic and capture properties of the particle. Therefore, analysis of particle size distribution is an essential task in the study of an aerosol sample. Currently, the Solver tool in Microsoft's Excel spreadsheet software can be employed to determine a size distribution function which has the sum of least square error to a given distribution pattern. Hence, the fraction and distribution parameter of each component in an aerosol mixture can be determined. This method has been assessed successfully with the aerosol generated in the laboratory.

However, there is still one major concern. No study has shown the limit of above method to be employed to determine the fractions with similar distributions. With extensive computation, this study has found that limit. While two components have the same geometrical standard deviation, an ANOVA test with F< 0.24(or p< 0.6 with extremely large sample size) above method will obtain a significant error. While two components have the same count median diameter, an Bartlett's test shows that above method will also fail when b is close to 1.

摘要 i
Abstract ii
目錄 iii
圖目錄 iv
表目錄 vi
符號說明 vii
第一章 緒論 1
1-1 氣膠粒徑分佈 2
1-2 非線性迴歸與優化問題 4
1-3 文獻回顧 7
1-4 研究目的 16
第二章 研究方法與步驟 18
2-1 參數誤差的評估方法 20
2-2 Excel 的規劃求解功能 21
2-3 統計分析—變異數分析（ANOVA） 24
2-4 統計分析—Bartlett檢定 27
第三章 結果與討論 28
第四章 結論與建議 39
參考文獻 40
附錄 42

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