臺灣博碩士論文加值系統

由於氣膠微粒的粒徑與氣膠動力與捕集具有相當密切的關係，因此使用統計方法得到氣膠粒徑分佈或其分佈參數是基本的氣膠分析工作。由於計算工具的限制，以往對氣膠微粒粒徑分佈的分析大多採用區間代表粒徑或對數粒徑對累積分率百分位尺度迴歸法，然而這兩種方法均有其限制，特別是當分徑區間過大或分徑範圍未充分涵蓋所有粒徑時。
目前被普遍使用的微軟 Excel 試算表程式均內含可進行優化計算與求解非線性方程式的規劃求解功能，可以對粒徑分佈函數或累積分佈函數在線性尺度上進行非線性迴歸，而且具有更大的彈性。
本研究探討不同的微粒分徑區間與分徑範圍探討對非線性迴歸所得粒徑分佈參數的影響。以實驗室所產生的微粒粒徑，利用氣動粒徑分徑器得到粒徑分佈後，以逐步群組與截斷方式分別模擬較大的分徑區間與較小的分徑範圍。假設粒徑成對數常態分佈，以非線性迴歸方式得到在不同分徑區間與範圍所得到的中位數與幾何標準差。所使用的計算方式包括：分佈函數最小平方差和、區間分率最小平方差和、累積分率最小平方差和以及最大概似性，並評估各種方法對各種問題的適用性。
研究結果顯示，無論使用何種方式，粒徑區間大小應小於粒徑幾何標準差才能得到準確的中位數粒徑與幾何標準差。在所有方式中，根據粒徑累積分率建立方差式的最小方差法最適合使用於分徑範圍未涵蓋所有粒徑的微粒樣本分析，但在分徑範圍的微粒分率仍應佔 40% 至 60% 以上才能確保得到準確的結果。當分徑器可以得到小於分徑範圍微粒分率是用於前一個下限值；當分徑器無法得到小於分徑範圍微粒分率時則適用後一個下限值。
本研究成果可應用於在使用粒徑區間較大儀器或儀器量測範圍無法涵蓋所有粒徑分佈範圍時，可以使用後端數據處理突破裝置既有的性能限制。

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 perform a nonlinear regression and determine a size distribution function which has the sum of least square error or maximum likelihood 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.
This study concerned the effects of bin width and sizer range to the distribution parameters, such as CMD （Count Median Diameter）and geometrical standard deviation, determined by the nonlinear regression. The aerosol generated in the laboratory was analyzed by an aerodynamic particle size and the distribution was determined. The size bins were grouped and truncated to simulate the phenomena of greater bin width and the under-coverage. The size distribution was assumed to be log-normal. The methods included the sum of least square error on distribution function, fraction, and cumulative fraction, as well as maximum likelihood.
The results showed that the bin width should be smaller than the particle diameter geometrical standard deviation for an accurate determination of the distribution parameters. This result is independent on the method to be used. This study also showed the least square error on the fraction and cumulative fraction distributions are suitable for the determination of the distribution parameters when the particle size is partially covered by a particle sizers. However, the fraction of the particle to be covered by the sizer should be greater than 40 to 60%. The former lower limit is valid while the particle fraction below the sizing range is available; the latter is valid while the particle fraction outside the sizing range is totally unavailable.
The results of this study can provide a post-processing method to overcome the limitation of apparatus and sampling.

致謝 I
摘要 II
Abstract IV
目錄 VI
圖目錄 VIII
表目錄 XII
符號說明 XIII
第一章 緒論 1
1-1 氣膠粒徑分佈參數 3
1-2 接近對數常態分佈的粒徑分佈 8
1-3 非線性迴歸分析 12
1-3-1 最小方差和 13
1-3-2 最大概似性迴歸 17
1-3-3 最小平方差與最大概似性 19
1-4 粒徑範圍涵蓋不足 20
1-5 優化問題規劃求解 24
1-6 文獻回顧 30
1-7 研究目的 38
第二章 研究方法與步驟 39
第三章 結果與討論 44
3-1 實驗室氣膠樣本 44
3-2 各種粒徑分佈參數分析方式對實驗室氣膠的分析結果 45
3-3 粒徑區間大小對各種粒徑分佈參數分析方式的影響 47
3-4 粒徑涵蓋範圍對各種粒徑分佈參數分析方式的影響 52
第四章 結論與建議 57
參考文獻 59

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