以非線性迴歸評估氣膠粒徑分佈

Evaluating aerosol size distribution by non-linear regression

陳正豐(Jheng-Fong Chen)

指導教授 ： 陳友剛

長榮大學/健康科學學院/職業安全與衛生學系(所)/碩士(2011年)

https://doi.org/10.6833/CJCU.2011.00003

摘要

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。本研究由於傳統氣膠粒徑的分析方法，大多採用區間代表粒徑或對數粒徑對累積百分位尺度迴歸法，而兩種方法都有其限制。所以開發非線性迴歸評估氣膠粒徑分佈的分析方法。

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，具有更大的彈性，可延伸運用在粒徑的密度函數(f) 與累積函數(F)。並在線性尺度上進行非線性迴歸，可以找到更佳的參數組合使迴歸數據值與實測值的平方差和最小。本研究先從較單純的粒徑分佈開始，使用APS採樣器作為粒徑分佈的描述，取得氣膠微粒分佈數據與參數作為推估標準。研究結果顯示判定係數R2在新式分析法皆優於傳統方法。將結果呈現在線性尺度上，傳統方法區間代表粒徑法 (R2f= 0.78, R2F= 0.99) 與對數粒徑對累積百分位尺度迴歸法 (R2f= 0.90, R2F= 1.00) 判定係數R2都比新式方法 (R2f= 0.94, R2F= 1.00) 低。顯見新式方法是有效的氣膠粒徑分析方法。

關鍵字

氣膠粒徑分佈 ； 規畫求解 ； 非線性迴歸

並列摘要

The size of an aerosol particle significantly affects the dynamic and capture properties of the particle. Therefore, analysis of particle size distribution is a basic task in the study of an aerosol sample. Size distribution analysis is usually performed either by statistical calculation using a representative diameter of each size bin, or by a linear regression on a logarithmic plot of particle diameter vs. cumulative fraction (percentile scale). However, both methods have analytical limitations. In an effort to overcome these limitations, this study presents a new method for the analysis of aerosol particle size distribution.

The new method makes use of the Solver tool in Microsoft's Excel spreadsheet software. This tool, which is basically an optimization function, enables a nonlinear regression on a size distribution function (f) or a cumulative distribution function (F). In this study, an aerosol sample obtained by APS was analyzed for particle size distribution using both the new and traditional methods, and the results were compared. The values of the correlation coefficient, R2, obtained by new method (R2f= 0.78, R2F= 0.99) were higher than those obtained by traditional methods (R2f= 0.90, R2F= 1.00) using the representative diameter of each size bin; (R2f= 0.94, R2F= 1.00) using a logarithmic plot of particle diameters vs. cumulative fraction). It is therefore concluded that the new method is a more effective tool for the analysis of the size distribution of an aerosol sample.

並列關鍵字

Aerosol size distribution ； Excel solver ； Nonlinear regression

參考文獻

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