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    题名: 線性混合效果模式在剛性鋪面道路試驗資料之初步分析
    其它题名: Preliminary analysis of linear mixed-effects models of aasho road test rigid pavement data
    作者: 黃自強;Huang, Tze-Chiang
    贡献者: 淡江大學土木工程學系碩士班
    李英豪;Lee, Ying-Haur
    关键词: 剛性鋪面;道路試驗;多層次資料;線性混合效果模式;軸重當量因子;現況服務能力指標值;非線性迴歸模式;Rigid Pavement;AASHO Road Test;Linear Mixed-Effects models;present serviceability index;multilevel data;nonlinear regression
    日期: 2011
    上传时间: 2011-06-16 22:05:54 (UTC+8)
    摘要: 多層次資料在各個領域中相當普遍,而鋪面績效資料即是一種極為常見的多層次資料。當利用傳統迴歸方法來分析此種資料時,常會發現違反了對隨機誤差所做的常態分配與固定變異數的假設。因這類型的資料具有層級性,現在通常是採用線性混合效果(LME)模式來分析。線性混合效果模式在資料探索分析、統計模式構建、模式評估與驗證等方面通常會較傳統迴歸分析來得複雜。
    本研究將建立一個視覺圖技術與線性混合效果模式之系統化分析流程,並以美國AASHO 道路試驗的剛性鋪面原始資料來作為案例進行分析。主要的分析程序包括:探索群組層級與個體層級之成長趨勢、辨識重要參數、慎選適當的統計模式、選擇一個初始的固定效果模式、選擇具隨機效果的參數和共變異矩陣、建立殘差結構、簡化模式、和模式評估與驗證等。
    資料探索分析指出部份的個體(迴圈/車道)在開始時有較高的現況服務能力指標值(PSI),但PSI 值會隨著時間的增加而降低。此外,亦可由分析中發現個體間之明顯差異。在所構建的初始PSI 線性混合效果預測模式中,發現面層厚度之參數估計值為正,代表當鋪面的面層厚度增加時,平均PSI 值也會跟著提高。未經季節性調整因子修正過之原始交通荷重次數的參數估計值為負,代表平均PSI 值會因原始交通荷重次數增加而降低。結果亦顯示個體的預測值較母體的預測值更接近其觀察值,表示此線性混合效果模式能對資料做較適當的解釋。
    此外於本研究中,亦利用非線性迴歸分析,分開建立單軸與雙軸之剛性鋪面設計公式,以修正原AASHO剛性鋪面設計公式中不合理之問題。而新建的單軸與雙軸鋪面設計公式所計算之軸重當量因子均有符合工程常理。但若與原AASHO剛性鋪面設計公式所得之軸重當量因子相比,是有其差異存在。而此差異是由於本研究所得之軸重當量因子並不近似於四次方經驗法則。因此針對四次方經驗法則之適用性,應該是一個可以再深入研究與探討之課題。
    Multilevel data are very common in many fields. Pavement performance data is a very common example of multilevel data. While analyzing this type of data using conventional regression techniques, the normality assumptions with random errors and constant variance were often violated. Because of its hierarchical data structure, multilevel data are often analyzed using Linear Mixed-Effects (LME) models. The exploratory analysis, statistical modeling, and the examination of model-fit of LME models are more complicated than those of standard multiple regressions.
    A systematic modeling approach using visual-graphical techniques and LME models was proposed and demonstrated using the original AASHO road test rigid pavement data. The proposed approach including exploring the growth patterns at both group and individual levels, identifying the important predictors and unusual subjects, choosing suitable statistical models, selecting a preliminary mean structure, selecting a random structure, selecting a residual covariance structure, model reduction, and the examination of the model fit was further discussed.
    Exploratory analysis of the data indicated that most subjects (loop/lane) have higher mean PSIs at the beginning of the observation period, and they tend to decrease over time. The spread among the subjects is substantially smaller at the beginning than that at the end. In addition, there exist noticeable variations among subjects. A preliminary LME model for PSI prediction was developed. The positive parameter estimate for slab thickness indicates that higher mean PSI values tend to occur on thicker pavements. The parameter estimate of unweighted applications is negative indicating that lower PSI values for higher load applications. The prediction line of the within-group predictions follows the observed values more closely than that of the population predictions indicating the proposed LME model provides better explanation to the data.
    Furthermore, nonlinear regression technique was also adopted in an attempt to develop modified rigid pavement design equations for single- and tandem- axle loads separately. The derived equivalent axle load factors (EALF) or load equivalency factors (LEF) using different design equations were compared to the existing LEFs. Even though reasonable results have been obtained, the newly derived LEFs representing quite a departure from the well-known fourth-power rule should be cautioned and further investigated.
    显示于类别:[土木工程學系暨研究所] 學位論文

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