高速公路事故時間分佈研究-以函數資料分析方法

Abstract

過去高速公路事故頻次之研究大多以計數模式（例如，卜松模型或負二項模型）檢視各種風險因子（一般採用之變數大致可分成幾何變數、交通量變數、環境變數）對於各分析路段全年發生事故件數之影響，較少進一步探討這些風險因子對於各分析路段事故發生分佈之影響。而事故發生於不同時段（上午、下午或夜間）對於事故防制與救護策略之規劃又至為重要。基此，本研究乃利用函數資料分析方法中之函數型主成份分析、函數型變異數分析，以及函數型線性模式兩種方法，針對各路段事故發生次數之一日24小時時間分佈圖進行模化分析，以了解各路段分佈圖形之差異及其影響因素。其中，函數型主成份分析可以獲得解釋分佈圖形變異的主成份，函數型變異數分析則主要用於檢視各潛在風險因子是否具有影響事故時間分佈型態的效果。至於函數型線性模式則可進一步分析影響各路段事故時間分佈型態之影響因素，藉此提供事故分析的另一種分析觀點與研究方法。 本研究以國道一號為例，並以兩兩交流道所形成之路段作為分析基礎。因此，以交流道劃分62個路段，南下、北上因不互相干擾視為獨立樣本，故共計124個路段，事故時間分佈圖以各路段一年中在各小時之統計次數加以呈現。每路段並收集包含下坡度、曲率、車道數、固定測速點數、年雨量、路段是否鄰近都會區，小型車流量、大客貨車流量、聯結車流量、重車比例等資訊輔以分析。 由函數型主成份分析結果顯示造成分佈圖形變異的三個主成份分別為昏峰時段事故件數增加、晨峰時段事故件數增加，以及白天離峰時間事故件數減少。本研究對於事故件數分佈圖利用函數型變異數分析探討高速公路幾何變數因子(下坡度、曲率、車道數)、環境變數因子(固定測速照相、年雨量、鄰近都會區)對事故時間分佈圖是否存在顯著差異，結果顯示曲率因子、車道數因子、固定測速照相因子顯著影響事故時間分佈圖差異。最後，本研究以同為函數型資料的小型車流量、客貨車流量、聯結車流量及重車比例資料與事故時間分佈進行線性模式分析，結果以小型車流量解釋事故時間分佈圖能力最佳，但其整體解釋能力仍屬偏低，表示仍有其他重要解釋變數未納入分析。

Previous studies in freeway crash frequency modeling mostly used of count models (e.g. Poisson and Negative Binomial models) to investigate the effect of risk factors (commonly adopted factors including geometric variables, traffic variables, and environment variables) on the annual number of accidents on an analytical road segment. Few of them further considered the effect of these factors on the time-of-day distribution of accidents. The time distribution of accidents is essential for proposing strategies for accident prevention and effective emergency rescue. Based on this, this study uses of functional data analysis (FDA) – functional principal components analysis (FPCA), functional analysis of variance (FANOVA) and functional linear model (FLM)- to model and analyze the time-of-day distribution of accidents of analytical road segments. Where the functional principal component analysis can explain the variations of pattern, functional ANOVA helps to identify the effect of each of key factors and functional linear model can investigate how the functional key factors affect the distribution patterns of accidents. A case study on accidents data in Freeway No.1 with a total of 124 road segments formed by two adjacent interchanges and two directions (northbound and southbound) is conducted. The potential factors includes downward slope, curvature, number of lanes, posted speed camera, yearly rainfall, neighboring to metropolitan, traffic flows of small vehicles, large vehicles and trailer-tractors, and percentage of large vehicles and trailer-tractors. The results of FPCA show that three principal components of pattern variations are Increase in crash frequency in the morning peak hours, Increase in crash frequency in evening peak hours, and Decrease in crash frequency in the daytime off-peak hours. The results of FANOVA indicate that curvature, number of lanes and posted speed camera significantly affect the differences in the distribution patterns. At last, the functional linear modeling between functional traffic flows (small vehicles, large vehicles, trailer-tractors, percentage of large vehicles and trailer-tractors) and time-of-day distribution of crash frequency is analyzed. The results show that small vehicles traffic flow has the best explanatory power, suggesting the distribution patterns of accidents are best fitted to the distribution patterns of small vehicle traffic flow. However, the coefficient of determination is low, implying some missing important factors have not been considered in this study.