績效預測模式普遍應用於鋪面設計、評估、維修及路網管理各個方面。當鋪面設計從純經驗法向力學經驗法發展時，估計交通荷重之單軸軸重當量(ESAL)概念在力學經驗法設計手冊中已不再採用。新的設計手冊成功與否有相當大的程度需要依賴準確的鋪面績效預測模式。因此本研究中利用美國長程鋪面績效(LTPP)資料庫(http://www.datapave.com)來探討與驗證現有鋪面糙度預測模式並改善之。
    針對反應變數進行資料探索分析(EDA)時發現，由常態分配對於隨機誤差與連續變異情形，可能不適用傳統統計迴歸方法來構建預測模式。因此，本研究於後續分析時採用廣義線性模式(GLM)與廣義相加模式(GAM)對於反應變數的分佈情形均不給予任何假設，而是採用以概似估計法的方式測試分配適用度,其中以柏松分配之適用性較良好。並配合Box-Cox冪次轉換法、視覺圖的技術，以及李英豪教授建議的系統化之統計與工程分析方法應用於構建預測模式中。
    經過多方嘗試，預測模式中將保留具有顯著影響與合理闡明物理現象之變數。本研究將構建完成之預測模式檢定其適合度及針對相關的參數進行敏感度分析，最後建構之模式其適用情形與過去模式相比，有的到良好的改善。對目前建立之模式於未來亦可作更進一步之改進，使其更為完善。

Performance predictive models have been used in various pavement design, evaluation, rehabilitation, and network management activities. As pavement design evolves from traditional empirically based methods toward mechanistic-empirical, the equivalent single axle load (ESAL) concept used for traffic loads estimation is no longer adopted in the recommended Mechanistic-Empirical Pavement Design Guide. The success of the new design guide considerably depends upon the accuracy of pavement performance predictions. Thus, this study will first investigate its goodness of fit and strive to develop improved performance prediction models for pavement roughness using the Long-Term Pavement Performance (LTPP) database (http://www.datapave.com or LTPP DataPave Online).
Exploratory data analysis (EDA) of the response variables indicated that the normality assumption with random errors and constant variance using conventional regression techniques might not be appropriate for prediction modeling. Therefore, generalized linear model (GLM) and general additive model (GAM) along with Poisson distribution were adopted in the subsequent analysis. Box-Cox power transformation technique, visual graphical techniques, as well as the systematic statistical and engineering approach proposed by Lee were frequently adopted during the prediction modeling process.
By keeping only those parameters with significant effects and reasonable physical interpretations in the model, various tentative performance prediction models were developed. The goodness of the model fit was further examined through the significant testing and various sensitivity analyses of pertinent explanatory parameters. The tentatively proposed predictive models appeared to reasonably agree with the pavement performance data, although their further enhancements are possible and recommended.

目錄
頁次
目錄.....................................................................................................................................I
圖目錄............................................................................................................................... III
表目錄...............................................................................................................................VI
第1 章 緒論....................................................................................................................... 1
1.1 研究背景.............................................................................................................. 1
1.2 研究目的.............................................................................................................. 1
1.3 研究範圍與研究方法.......................................................................................... 2
1.4 論文組織架構與研究流程.................................................................................. 3
第2 章 文獻回顧............................................................................................................... 5
2.1 鋪面指標.............................................................................................................. 5
2.1.1 功能性指標............................................................................................... 5
2.1.2 結構性指標............................................................................................... 6
2.2 鋪面糙度指標...................................................................................................... 7
2.2.1 PSI 與鋪面糙度關係................................................................................. 7
2.2.2 PSI 之後續發展......................................................................................... 9
2.2.3 PSI 與國際糙度指標............................................................................... 12
2.3 美國長程鋪面績效研究計畫簡介.................................................................... 14
2.4 鋪面糙度績效預測模式發展歷程.................................................................... 17
2.5 統計方法應用.................................................................................................... 23
2.5.1 假設檢定................................................................................................. 23
2.5.2 變異數分析............................................................................................. 24
2.5.3 迴歸分析................................................................................................. 24
2.5.4 其它迴歸技術......................................................................................... 25
2.5.5 統計軟體S-Plus 介紹............................................................................. 26
2.6 綜合討論............................................................................................................ 27
第3 章 資料擷取與驗證................................................................................................. 28
3.1 DataPave Online 版的使用介紹......................................................................... 28
3.2 鋪面績效預測模式............................................................................................ 32
3.2.1 SHRP P-020 糙度績效預測模式............................................................ 33
3.2.1.1 剛性鋪面...................................................................................... 33
3.2.1.2 柔性鋪面...................................................................................... 34
3.2.2 NCHRP Project 20-50 .............................................................................. 36
3.2.2.1 剛性鋪面...................................................................................... 36
3.2.2.2 柔性鋪面...................................................................................... 37
3.2.3 DG 2002 暫行手冊.................................................................................. 41
3.3 模式參數資料擷取............................................................................................ 43
3.4 國際糙度指標驗證............................................................................................ 49
3.5 問題與討論........................................................................................................ 55
第4 章 剛性鋪面糙度績效預測模式............................................................................. 57
4.1 IRI 分佈情形....................................................................................................... 57
4.2 剛性預測模式驗證............................................................................................ 62
4.2.1 SHRP P-020.............................................................................................. 62
4.2.2 NCHRP Project 20-50 .............................................................................. 72
4.2.3 DG2002 程式結果................................................................................... 75
4.3 剛性鋪面IRI 績效預測模式之構建................................................................. 77
4.3.1 選取相關參數......................................................................................... 77
4.3.2 線性迴歸結果......................................................................................... 80
4.3.3 構建預測模式......................................................................................... 85
4.3.4 預測模式之敏感度分析......................................................................... 91
4.4 問題與討論........................................................................................................ 92
第5 章 柔性鋪面糙度績效預測模式............................................................................. 96
5.1 IRI 分佈情形....................................................................................................... 96
5.2 柔性預測模式驗證.......................................................................................... 100
5.2.1 SHRP P-020............................................................................................ 100
5.2.2 NCHRP Project 20-50 ............................................................................ 105
5.2.3 DG2002 程式結果................................................................................. 107
5.3 柔性鋪面IRI 績效預測模式之構建............................................................... 110
5.3.1 選取相關參數....................................................................................... 110
5.3.2 線性迴歸結果....................................................................................... 115
5.3.3 構建預測模式....................................................................................... 120
5.3.4 預測模式之敏感度分析....................................................................... 127
5.4 問題與討論...................................................................................................... 128
第6 章 結論與建議....................................................................................................... 131
6.1 結論.................................................................................................................. 131
6.2 建議.................................................................................................................. 132
參考文獻......................................................................................................................... 133

圖目錄
頁次
圖1-1 研究流程圖............................................................................................. 4
圖2-1 國際糙度指標範圍[Sayers & Karamihas, 1998] ................................. 13
圖2-2 歷年鋪面績效預測模式的發展與推論空間的擴展方式[Lee, 1993] 18
圖2-3 模式構建的方法[Lee, 1993] ................................................................ 19
圖2-4 2002 年暫行設計手冊建議設計流程................................................... 20
圖2-5 2002 年暫行設計手冊JPCP 建議設計流程........................................ 21
圖2-6 DG2002 設計軟體的使用介面[ARA, 2004] ........................................ 22
圖2-7 顏色編碼[ARA, 2004].......................................................................... 22
圖2-8 DG2002 程式設計程序[ARA, 2004] .................................................... 23
圖3-1 依據所在位置選擇路段....................................................................... 29
圖3-2 選取特定路段之詳細報告................................................................... 29
圖3-3 依據準則選擇路段............................................................................... 30
圖3-4 選取路段之歷年破壞調查數據........................................................... 30
圖3-5 執行搜尋與降雨量相關之資料表與欄位........................................... 31
圖3-6 資料敘述的三種層級........................................................................... 31
圖3-7 查詢土壤分類指數之代碼說明........................................................... 32
圖3-8 資料庫單位問題................................................................................... 48
圖3-9 計算國際糙度指標之四分車模型[Shahin, 1994] ............................... 50
圖3-10 GPS1 潮濕結冰區 SG200 < 20 % [Perera, & Kohn, 2001] ............... 56
圖4-1 部份剛性鋪面歷年IRI 趨勢圖............................................................. 58
圖4-2 剛性鋪面現地IRI 資料分佈................................................................ 59
圖4-3 地理位置對剛性鋪面現地IRI 影響.................................................... 59
圖4-4 鋪面種類對剛性鋪面現地IRI 影響.................................................... 60
圖4-5 車道寬度對剛性鋪面現地IRI 影響.................................................... 60
圖4-6 氣候因素對剛性鋪面現地IRI 影響.................................................... 61
圖4-7 路肩型式對剛性鋪面現地IRI 影響.................................................... 61
圖4-8 底層型式對剛性鋪面現地IRI 影響.................................................... 62
圖4-9 IRI 調查值與P-020 預測模式之相關參數.......................................... 63
圖4-10 IRI 調查值與P-020 預測模式交通參數............................................ 64
圖4-11 IRI 調查值與P-020 預測模式氣候參數............................................ 64
圖4-12 P-020 IRI 預測結果與現地比較圖.................................................... 65
圖4-13 不同鋪面種類之P-020 IRI 預測結果................................................ 66
圖4-14 不同地理位置之P-020 IRI 預測結果............................................... 67
圖4-15 P-020 IRI 預測結果依照鋪面氣候區域分......................................... 68
圖4-16 P-020 IRI 預測結果與底層型式......................................................... 69
圖4-17 P-020 IRI 預測結果與車道加寬......................................................... 69
圖4-18 P-020 IRI JPCPND 預測結果............................................................. 70
圖4-19 P-020 IRI JPCPND 預測結果與交通的關係..................................... 70
圖4-20 P-020 IRI JPCPND 預測結果與氣候的關係..................................... 70
圖4-21 P-020 IRI JPCPND 預測結果............................................................. 71
圖4-22 為P-020 JPCPND 預測結果與版厚的關係...................................... 71
圖4-23 NCHRP project 20-50 預測結果與現地比較圖................................. 72
圖4-24 NCHRP project 20-50 預測結果依照鋪面種類分............................. 73
圖4-25 NCHRP project 20-50 預測結果依照鋪面地理位置區分................. 74
圖4-26 NCHRP project 20-50 預測結果依照鋪面氣候位置區分................. 74
圖4-27 DG2002 程式分析結果....................................................................... 76
圖4-28 DG2002 程式分析結果依氣候區分類............................................... 77
圖4-29 LMS 迴歸分析結果(JPCPND)........................................................... 83
圖4-30 ACE 迴歸分析結果(JPCPND) ............................................................ 83
圖4-31 AVAS 迴歸分析結果(JPCPND) .......................................................... 84
圖4-32 GAM 轉換分析結果(JPCPND) .......................................................... 85
圖4-33 JPCPND 建議之Box-Cox 轉換圖...................................................... 86
圖4-34 無綴縫筋JPCP 之IRI 預測結果....................................................... 89
圖4-35 含綴縫筋JPCP 之IRI 預測結果....................................................... 90
圖4-36 JRCP 之IRI 預測結果........................................................................ 90
圖4-37 CRCP 之IRI 預測結果....................................................................... 91
圖4-38 無綴縫筋JPCP 之IRI 敏感度分析.................................................. 92
圖4-39 P-020 NCHRP project 20-50 DG2002 三者比較............................... 93
圖4-40 DG2002 不同鋪面形式結果比較....................................................... 94
圖4-41 DG2002 程式與LTPP 現地高差預測結果[林佳慧，2007].............. 94
圖4-42 DG2002 程式與LTPP 現地橫向裂縫預測結果[林佳慧，2007]...... 95
圖5-1 部份柔性鋪面歷年IRI 趨勢圖............................................................. 96
圖5-2 柔性鋪面現地IRI 資料分佈................................................................ 97
圖5-3 地理位置對柔性鋪面現地IRI 影響.................................................... 98
圖5-4 不同底層型式對柔性鋪面現地IRI 影響............................................ 98
圖5-5 氣候因素對柔性鋪面現地IRI 影響.................................................... 99
圖5-6 IRI 調查值與SHRP P-020 預測模式之相關參數............................. 101
圖5-7 IRI 調查值與SHRP P-020 預測模式交通參數................................. 101
圖5-8 IRI 調查值與P-020 預測模式氣候參數............................................ 102
圖5-9 P-020 預測結果.................................................................................. 103
圖5-10 P-020 依地理區域預測結果............................................................ 103
圖5-11 P-020 依照氣候區預測結果............................................................. 104
圖5-12 P-020 依照底層型式預測結果........................................................ 104
圖5-13 NCHRP project 20-50 預測結果....................................................... 105
圖5-14 依地理區域NCHRP project 20-50 預測結果.................................. 106
圖5-15 依氣候區域NCHRP project 20-50 預測結果.................................. 106
圖5-16 依照底層型式NCHRP project 20-50 預測結果.............................. 107
圖5-17 DG2002 預測結果............................................................................ 108
圖5-18 DG2002 依照地理區域預測結果.................................................... 109
圖5-19 DG2002 依照氣候區預測結果........................................................ 109
圖5-20 DG2002 依底層型式預測結果........................................................ 110
圖5-21 LMS 柔性鋪面全部迴歸分析結果.................................................. 118
圖5-22 ACE 柔性鋪面全部迴歸分析結果.................................................. 118
圖5-23 AVAS 柔性鋪面全部迴歸分析結果................................................. 119
圖5-24 柔性鋪面全部建議之Box-Cox 轉換圖.......................................... 122
圖5-25 柔性鋪面建議之Box-Cox 轉換圖.................................................. 123
圖5-26 柔性鋪面之IRI 全區預測結果........................................................ 126
圖5-27 不同底層型式對柔性鋪面之IRI 預測結果.................................... 126
圖5-28 柔性鋪面之IRI 預測結果................................................................ 127
圖5-29 柔性鋪面全區IRI 敏感度分析....................................................... 128
圖5-30 全部資料P-020 NCHRP project 20-50 DG2002 三者比較........... 129
圖5-31 相同筆數P-020 NCHRP project 20-50 DG2002 三者比較........... 129
圖5-32 DG2002 程式與LTPP 現地車轍預測結果[吳佩樺，2006]............ 130
圖5-33 DG2002 程式與LTPP 現地疲勞裂縫比較圖[吳佩樺，2006]........ 130

表目錄
頁次
表2-1 國外PSI 模式比較[張家瑞, 2001] ........................................................ 8
表2-2 國內PSI 模式比較................................................................................. 9
表2-3 應用Fechner’s 定律的PSI 轉換公式................................................. 11
表2-4 RI 與MPI 指標轉換模式比較[Liu & Herman, 1997].......................... 12
表2-5 IRI 與PSR 指標轉換模式比較[Al-Omari & Darter, 1992] ................. 13
表2-6 LTPP 計劃之鋪面研究定義[FHWA, 2004] .......................................... 16
表3-1 長程鋪面績效之糙度早期分析結果[Simpson et al., 1994] ............... 33
表3-2 全部地區之預測模式所需參數[Simpson et al., 1994] ....................... 34
表3-3 潮濕-不冰凍地區之預測模式所需參數[Simpson et al., 1994].......... 35
表3-4 潮濕-冰凍地區之預測模式所需參數[Simpson et al., 1994].............. 35
表3-5 乾燥-不冰凍地區之預測模式所需參數[Simpson et al., 1994].......... 35
表3-6 乾燥-冰凍地區之預測模式所需參數[Simpson et al., 1994].............. 36
表3-7 NCHRP Project 20-50 剛性鋪面[Perera, & Kohn, 2001] ..................... 37
表3-8 NCHRP Project 20-50 柔性鋪面[Perera, & Kohn, 2001] ..................... 38
表3-9 國際糙度指標預測公式表................................................................... 39
表3-10 國際糙度指標和現地與結構相關因子係數表................................. 40
表3-11 剛性鋪面DG2002 建議公式表.......................................................... 41
表3-12 柔性鋪面DG2002 建議公式表......................................................... 42
表3-13 一般(Administrative)資料模組.......................................................... 43
表3-14 氣候(Climatic)資料模組.................................................................... 44
表3-15 養護(Maintenance)與維修(Rehabilitation)資料模組........................ 44
表3-16 監測(Monitoring)資料模組................................................................ 45
表3-17 交通(Traffic)資料模組....................................................................... 45
表3-18 基本(Inventory)資料模組................................................................... 46
表3-19 試驗(Testing)資料模組....................................................................... 47
表3-20 DataPave 各層型式編碼之對應表...................................................... 48
表3-21 LTPP Standard Data Release 18 之剖面資料..................................... 49
表3-22 剖面資料匯出檔案............................................................................. 50
表3-23 國際糙指標程式碼............................................................................. 51
表3-23 國際糙指標程式碼（續）................................................................. 52
表3-24 IRI 程式計算結果................................................................................ 53
表3-25 量測間隔係數[Shahin, 1994] ............................................................. 54
表4-1 剛性鋪面各類型資料分佈................................................................... 66
表4-2 剛性鋪面地理區域資料分佈............................................................... 67
表4-3 剛性鋪面氣候區域資料分佈............................................................... 68
表4-4 DG2002 設計軟體所需之輸入參數[林佳慧，2007] .......................... 75
表4-4 DG2002 設計軟體所需之輸入參數（續）[林佳慧，2007] .............. 76
表4-5 剛性鋪面IRI 相關各項單變數分析結果............................................ 78
表4-6 剛性鋪面IRI 各項變數之相關係數分析結果.................................... 79
表4-6 剛性鋪面IRI 各項變數之相關係數分析結果（續）........................ 80
表4-7 相關影響因子對剛性鋪面IRI 之線性迴歸結果................................ 81
表4-8 鋪面型態與綴縫筋對剛性鋪面IRI 迴歸結果之影響........................ 82
表4-9 剛性鋪面建議之Box-Cox 轉換.......................................................... 87
表4-10 剛性鋪面預測模式............................................................................. 87
表4-11 JPCPND 轉換後含綴縫筋模式構建之迴歸結果............................... 88
表4-11 轉換後含綴縫筋模式構建之迴歸結果（續） ................................. 89
表5-1 地理位置與柔性鋪面底層型式數量表............................................... 97
表5-2 氣候區與柔性鋪面底層型式數量表................................................... 99
表5-3 DG2002 所需參數.............................................................................. 107
表5-4 柔性鋪面IRI 相關各項單變數分析結果.......................................... 112
表5-5 柔性鋪面IRI 各項變數之相關係數分析結果.................................. 113
表5-5 柔性鋪面IRI 各項變數之相關係數分析結果（續）...................... 114
表5-6 初步迴歸分析..................................................................................... 115
表5-7 選定參數迴歸分析結果..................................................................... 116
表5-8 選定參數迴歸分析結果..................................................................... 117
表5-9 為不同分配之連結函數與變異數之關係......................................... 120
表5-10 柔性鋪面建議之Box-Cox 轉換...................................................... 123
表5-11 柔性鋪面預測模式........................................................................... 124
表5-12 轉換後柔性鋪面模式構建之迴歸結果........................................... 125

參考文獻
林惠玲、陳正倉，「統計學方法與應用（上、下冊）」，第二版，雙葉
書廊，2001。
劉應興編譯，「類別資料分析導論」，華泰文化事業股份有限公司，2003。
吳政隆，「柔性鋪面現況服務力指標之研究」，台灣大學土木工程學系
碩士論文，1995。
江煌基，「高速公路鋪面服務能力指標建構之研究」，淡江大學土木工
程學系碩士論文，1995。
吳政德，「國際操度指標與梅氏指標關係之初步研究」，淡江大學土木
工程學系碩士論文，1995。
林志棟等，「台灣地區路面結構強度指標模式分析」，第十一屆鋪面工
程學術研討會，2001。
張家瑞，「建立台灣地區瀝青路面網級養護管理系統−以公路局中壢工
務段為例」，中央大學土木工程學系博士論文，2001。
陳克斌，「綜合性指標在鋪面工程之應用」，淡江大學土木工程學系碩
士論文，2002。
吳佩樺，「柔性鋪面績效預測模式之建立」，淡江大學土木工程學系碩
士論文，2006。
林佳慧，「應用LTPP 資料庫於剛性鋪面績效預測模式之建立」，淡江
大學土木工程學系碩士論文，2007。
ARA, Inc. ERES Consultants Division. “Guide for Mechanistic- Empirical
Design of New and Rehabilitated Pavement Structure,” NCHRP 1-37A
Rep., Transportation Research Board, National Research Council,
Washington, D. C., 2004.
Al-Omari, B., and Darter, M.I., ”Relationships Between IRI and PSR ”,
Transportation Engineering Series No.69,civil Engineering Studies,
University of Illinois at Urbana-Champaign, July 1992.
Carey. W.N., and Irick. P.E., ”The Pavement Serviceability Performance
Concept”, Highway Research Board Bulletin No.250, 1960.
Chou, C. P., and Wu, C. L., “Evaluation of Panel Characteristics and
User-Based Pavement Serviceability” Transportation Research Record
1592, 1997, pp. 98-106.
Feighan, K.J., Shahin, M.Y., Sinha, K.C., and White, T.D., “A Prioritization
Scheme for the MicroPAVER Pavement Management System”,
Transportation Research Record 1215, 1989.
Gulan, S. R., Woods, J. W., and Anderson, V. L., ”Correlation of Present
Serviceability Ratings with International Roughness Index”,
Transportation Research Record 1435, TRB, 1994.
Highway Research Board . The AASHO Road Test, Report 5, Pavement
Research, Special Report 61E, Publication No. 954, National Academy
of Science, National Research Council, Washington, D.C., 1962.
Huang, Y.H. Pavement Analysis and Design, 2nd Edition, Prentice Hall,
Englewood Cliffs, New Jersey., 2003
Ker, H.S. Application of regression spline in multilevel longitudinal
modeling. Ph.D. dissertation, University of Illinois, Urbana, Illinois.
2002
Lee, Y.H. Development of Pavement Prediction Models, Ph.D. dissertation,
University of Illinois, Urbana., 1993
Liu, C., and Herman, R., “New Approach to Roadway Performance Indices”
Journal of Transportation Engineering, 1996, pp. 329-336.
Liu, C., and Herman, R., “Roadway-Vehicle Interaction, Physical Indexes,
and Human Judgment of Ride Quality” Transportation Research
Record 1570, 1997, pp. 55-59.
Liu, C., and Herman, R., “Road Profiles, Vehicle Dynamics, and Human
Judgment of Serviceability of Roads: Spectral Frequency Domain
Analysis” Journal of Transportation Engineering, 1998, pp. 106-111.
Liu, C., and Herman, R., “Road Profiles, Vehicle Dynamics, and Ride
Quality Rating” Journal of Transportation Engineering, 1999, pp.
123-128.
Mohseni, A., Darter, M.I., and Hall, J.P., “Illinois Pavement Network
Rehabilitation Management Program”, Transportation Research
Records 1272, 1990.
Perera, R.W., Kohn, S.D. “LTPP Data Analysis: Factors Affecting Pavement
Smoothness”, NCHRP Project 20-50, National Research Council, 2001
Nelder, J.A. and R.W.M. Wedderburn, “Generalized Linear Models”,
Journal of the Royal Statistical Society (Series A) 135, 370-384, 1972.
Pinheiro, J. C., and Bate, D. M,. Mixed-effects models in S and S-Plus, New
York: Springer-Verlag., 2000
Shahin, M.Y. Pavement Management for Airports, Roads, and Parking Lots,
Chapman & Hall., 1994
Simpson, A.L., Rauhut, J.B., Jordhal, P.R., Owusu-Antwi, E., Darter, .M.I,
Ahmad, R., Pendleton, O.J., Lee, Y.H. “Sensitivity Analyses for
Selected Pavement Distresses”, SHRP-P-393, Contract No. P-020,
National Research Council, 1994
S-Plus 61 Guide Statistics volume 1.