土石流發生潛勢-區別分析的擬合與預測

Potential of Analysis of Debris Flow–Fitting and Prediction of Discriminant Analysis

林裕翔(Yu-Hsiang Lin)

指導教授 ： 林美聆

國立臺灣大學/工學院/土木工程學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.01055

摘要

台灣處於板塊交界帶，地質狀況破碎且複雜，山崩、地滑及土石流等災害屬於正常的自然現象。每當颱風所帶來的豪雨，造成台灣各地多起土石流災害，故有許多對於土石流發生潛勢分析之研究，其中以費雪區別分析法最為常見。本研究搜集土石流之相關資料，針對南投地區被列入92年水保局所公開之1420條土石流潛勢溪流進行研究。

本研究重點在於費雪區別分析之擬合與預測，一開始以南投地區土石流潛勢分析為出發，將其影響因子資料庫加以檢查與修正，同時考慮抽樣溪流樣本其數目與分佈情形，其對於費雪區別函數之影響因子以及區別分析之結果皆有所影響，進而對費雪區別函數之正判率與預測準確率，其穩定性與適用性有所影響，故探討影響因子之重要性。觀察原始函數其正判率與驗證率來決定函數之最終模式，達到簡化函數但可充份反應各區土石流潛勢溪流資訊之目的。本研究將一併使用主成份分分析，採與謝育樺(2007)相異之研究方法，並將研究結果與前人相互比較，想對主成份分析其類別項影響因子萃取效果與對於費雪區別分析之適用性做討論。

進一步探討費雪區別模式之預測可行性，利用南投地區所建立之費雪區別函數預測其相同地質分區，南投以北的台中與南投以下的嘉義地區，討論影響因子之代表性與費雪區別函數之穩定性，並找尋其誤差與影響因子之關係，利用相似性指標(similarity index)來探討預測準確率與影響因子其相似性之關係。希望藉由統計分析的取樣與推論方法，對費雪區別分析之擬合與預測與其適用性加以研究。

關鍵字

土石流 ； 影響因子 ； 主成分分析 ； 費雪區別分析 ； 相似性指標

並列摘要

Taiwan is situated in the junction of tectonic plates, which induces broken and complex geological conditions with freguent, landslides, mudslides and debris flows. The heavy rains carried by typhoon, often caused landslides and debris flows in Taiwan. In this study, the potential analysis of debris flow is intended using the Fisher’s discriminant analysis. This research collects debris flow related data in Nantou County and the debris flow major disaster histories. The debris flow torrents potential analysis was performed based on the 1420 debris flow torrents by Soil-and-Water Conservation-Bureau (2003) in Nantou County.

This study focused on fitting and prediction of the Fisher’s discriminant analysis, beginning with the potential analysis of debris flow in Nantou Area, considering its fitting streams using random sampling, the sample distribution. The Fisher’s discriminant analysis of their assumptive testing results have been different, and the resulting Fisher’s discriminant functions of their influence factors nay be different for fitting and prediction, which affect its stability and applicability. By comparing the fitting and prediction rate, the functions of the final model can be adequately determined. Comparisons were made between this research and previous research using the principal component analysis for the study of influence factors, adopting different methods of subdivision study area, finally the applicability of principal component analysis for the Fisher’s discriminant analysis is discussed.

The discriminant model based on the Nantou district D randomly selected samples are used for predicting the same geological subdivision D in Taichung, and Chiayi areas. The influence factor stability of the Fisher’s discriminant model and the prediction rate associated with the difference in influence factors were discussed using, and used similarity index.

並列關鍵字

debris flow ； influenced factors ； principal component analysis ； similarity index

參考文獻

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