臺灣博碩士論文加值系統

風速在風工程領域扮演著重要角色，使得風速的預測與模擬一直是該領域中的熱門主題。數種數值技巧（如自回歸移動平均模型、類神經網路等）被發展及應用於風速的相關研究。由於風速本身具有隨機性質，本文以一全機率模型–高斯過程模型來考量風速的不確定性，並由貝氏分析與漸變型馬可夫鍊蒙地卡羅法找出合適的高斯過程模型參數。
在本文中，我們由三種不同的數值案例分析（分別為風場風速回歸分析、風速時間序列分析、颱風期間地面風速變化分析），驗證高斯過程模型在風速回歸與模擬的可行性：在風場風速回歸分析中，我們採用主成份分析法降低空間之維度，並利用高斯過程模型配合常態轉換法進行分析，研究對象為數個氣象測站的月平均風速，高斯過程模型表現出良好的回歸能力（內插與外插結果與觀測資料有相似的變化趨勢）；在風速時間序列分析中，我們採用高斯過程模型配合常態轉換法，研究對象為無劇烈氣候變化的測站風速，數值模擬結果顯示高斯過程模型模擬人造風速之統計特性（包括日最大風速平均值及標準偏差、風速超越機率及自相關性函數）與訓練及預測的風速統計特性相近；在颱風期間地面風速變化分析中，我們考慮颱風期間的數種因素（包括颱風與測站的相對距離、颱風與測站方向的夾角、颱風中心氣壓、颱風行進速度、颱風中心最大風速、颱風瞬間最大陣風與七級風半徑），研究對象為地面測站對應颱風警報單時刻的每小時平均風速，高斯過程模型表現出良好的回歸能力（獲得對訓練資料與測試資料一致之趨勢）；除此之外，高斯過程模型的訓練結果有助使用者辨識輸入資料的重要性。根據案例的分析結果，可證明高斯過程模型能合理內插回歸風速與產生與訓練資料統計特性一致的人造風速。本文所提之方法應可作為建立耐風設計、風能評估或節能分析時所需之風速模型；在資料量不足、遺失或誤謬情況嚴重時，更能彰顯所提模型之效用。

Wind speed prediction and simulation are ardent topics all the time because of its stochastic properties and significance in wind engineering. Several numerical techniques, e.g. auto-regressive moving average model, artificial intelligence technique etc., were developed for solving the related problems in recent years. In this research, a probabilistic model, named Gaussian process model, is proposed to consider the uncertainties of wind speed. Moreover, Bayesian analysis and transitional Markov Chain Monte Carlo method are employed to find the model hyper-parameters. Three examples for different issues are presented to demonstrate its practicability and satisfactory interpolation performance. Furthermore, the results also show that the various statistic properties, including exceedance probability, data correlation and distribution, of simulated wind speed are consistent with them of the training wind speed data.

第一章 緒論 1
1.1 研究動機與目的 1
1.2 研究方法 2
1.3 論文架構 2
參考文獻 4

第二章 文獻回顧 5
2.1 前言 5
2.2 機率密度函數模型 5
2.3 自回歸移動平均模型 8
2.4 類神經網路模型 10
參考文獻 13

第三章 風的性質 19
3.1 前言 19
3.2 大氣邊界層與平均風速的垂直分布模式介紹 19
3.3 平均風速與高度之關係 20
3.3.1 指數律下的風速剖面 20
3.3.2 對數律下的風速剖面 20
3.4 平均風速與地表粗糙度之關係 21
3.4.1 指數律下的平均風速剖面轉換 22
3.4.2 對數律下的平均風速剖面轉換 22
3.5 平均風速與平均時間之關係 23
3.6 大氣紊流與風場特性 23
參考文獻 25

第四章 貝氏分析 27
4.1 前言 27
4.2 貝氏分析與資料模型建立 27
4.2.1 貝氏分析的發展歷史 28
4.2.2 貝氏分析的規則 29
4.2.3 貝氏分析於資料模型建立時可能遭遇的問題 33
4.3 於模型選擇時之考量 33
4.3.1 複雜性的考量 34
4.3.2 參數化的考量 35
4.3.3 解釋性的考量 36
4.4 小結 36
參考文獻 38

第五章 高斯過程模型與回歸分析 45
5.1 前言 45
5.2 貝氏回歸 45
5.3 高斯過程模型 47
5.4 互變異函數 48
5.4.1 穩態的互變異函數 48
5.4.2 非穩態的互變異函數 52
5.4.3 互變異函數的產生 54
參考文獻 55

第六章 高斯過程模型參數之決定 58
6.1 前言 58
6.2 證據最大化近似法 58
6.3 拉普拉斯近似法 59
6.4 隨機取樣法 60
6.4.1 混合蒙地卡羅法 62
6.4.2 漸變型馬可夫鍊蒙地卡羅法 64
參考文獻 68

第七章 風場之風速回歸模型 73
7.1 前言 73
7.2 案例說明與資料一致化 74
7.3 主成份分析法 76
7.4 趨勢的移除與變異性的正規化 77
7.5 正常態轉換與逆常態轉換 78
7.6 模型設定 80
7.7 資料分析與討論 82
7.8 風能密度分析 86
7.9 小結 87
參考文獻 90

第八章 風速時間序列模型 110
8.1 前言 110
8.2 案例說明 111
8.3 案例八之一–無劇烈氣候變化測站風速案例分析 112
8.3.1 資料一致化與逐日最大風速之決定 112
8.3.2 趨勢的移除與變異性的正規化 113
8.3.3 正常態轉換與逆常態轉換 114
8.3.4 模型設定 116
8.3.5 模型訓練成果及人造風速資料之隨機數值模擬 117
8.3.6 觀測風速與人造風速之資料統計特性比較 119
8.4 案例八之二–無劇烈氣候變化測站的風速與風向案例分析 122
8.4.1 考慮多輸出變數相關性的聯合高斯過程模型 122
8.4.2 觀測風速與風向的資料前處理 125
8.4.3 模型設定 129
8.4.4 模型訓練成果及人造風速與風向之隨機數值模擬 131
8.4.5 觀測風速與風向和人造風速與風向之統計特性比較 134
8.5 小結 136
參考文獻 139

第九章 颱風時期地面風速變化模型 175
9.1 前言 175
9.2 案例說明與資料前處理 177
9.3 模型設定 179
9.4 資料分析與討論 180
9.5 颱風時期地面風速變化之合成模擬與分析 182
9.6 小結 186
參考文獻 189

第十章 結論與未來展望 211
10.1 結論 211
10.2 未來展望 212

符號索引 214

中英對照表 223

附錄A 基本高斯過程模型函數 A-1

附錄B 主成份分析法 B-1

附錄C 颱風行徑路線圖 C-1

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