| Abstract: | 統計迴歸方法被廣泛運用在鋪面工程上已 有三十多年歷史。多元線性迴歸、逐步迴歸及 非線性迴歸是建立鋪面預估模式中最受歡迎的 方法。本文將對這些迴歸方法的優缺及所受限 制詳加探討。 本文採用Friedman和Stuetzle在1981年所發展的 投影追逐迴歸方法(Projection Pursuit Regression,PPR) 來協助選擇合適的函數型式及將多元線性迴歸 、逐步迴歸及非線性迴歸所產生的問題減至最 小。此方法係採用小區域平均(local smoothing)之 技術,將所欲分析之回應表面(response surface)模 擬成一系列非參數性變數的投影函數(projection function)之和。這些投影函數實際上是可以二維 曲線之圖形表示,也可很容易地被識別並加以模式化。因此,本文建議採用一個兩階段的分 析方法,並以一項個案研究(case study)...混凝土 鋪面受輪載重之邊界應力分析...作為實例展示 之用。 本文亦指出要建立可信及完善的預估模式 不應只依賴統計迴歸方法。和主題有關的工程 知識、因次分析原理、適當函數型式的選擇、 及可適用的工程邊界條件均是非常重要的因素 。這些因素的重要性亦將在文中逐一探討。將應用以往傳統的模式構建方法和本文所提議的 方法所發展出的預測模式在預估及外插求值上 作一比較,我們可以明確的看出本文所提議的 方法之可行及優越性。
Statistical regression algorithms have been utilized extensively in pavement engineering for more than three decades. Multiple linear regression, stepwise regression, and nonlinear regression techniques are the most popular ones for pavement predictive modeling. The advantages, the deficiencies, and the limitations of these regression techniques are reviewed. To minimize these problems, the projection pursuit regression (PPR) introduced by Friedman and Stuetzle (1981) was selected to assist in the proper selection of functional forms. Through the use of local smoothing techniques, the PPR attempts to model the response surface as a sum of nonparametric functions of projections of the explanatory variables. The projected terms are essentially two- dimensional curves which can be graphically represented, easily visualized, and properly formulated. As a result, a two-step predictive modeling approach is proposed and demonstrated in a case study for the prediction of edge stress of a pavement slab. This paper also demonstrates that statistical regression techniques should not be used alone to obtain a more reliable and comprehensive predictive model. The importance of subject-related engineering knowledge, the principles of dimensional analysis, the proper selection of functional forms, and applicable engineering boundary conditions are considered essential and are also demonstrated in this paper. A comparison of the predictive models previously developed and the proposed approach to "prediction" and"extrapolation" clearly shows the preference of the proposed approach and the promising features of the PPR algorithm. |
