多層感知器偏微分靈敏度分析及應用—以砂性土壤液化潛能辨識為例

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熊大綱(Ta-Kang Hsiung) 查詢紙本館藏

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論文名稱

多層感知器偏微分靈敏度分析及應用—以砂性土壤液化潛能辨識為例
(Sensitivity Analysis with Partial Derivative Approach for Multi-layer perceptrons (MLP) and Its Application on Seismic Liquefaction Potential Identification)

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至系統瀏覽論文 (2027-7-27以後開放)

摘要(中)

本研究針對多層感知器（Multilayer Perceptrons, MLP）神經網路模式應用在兩類別型態識別（2-class Pattern Recognition）時，探討各輸入參數對系統辨識結果之影響程度。首先推導偏微分靈敏度解析方程式，並定義靈敏度指標（Sensitivity Factor of Index, SFi），進一步量化神經網路輸入層各輸入參數對系統整體辨識決策之影響程度及關鍵參數之間相對重要程度之差異。
為了公平客觀地評估前人文獻所提出的各類型靈敏度指標、相對重要度指標及本研究所提出的SFi指標的適用性，本研究創新提出一套數學模擬驗證方法，利用已知數學曲面分類決策邊界函數，在人為有效控制一定程度雜訊比的情況下，隨機產生大量人工資料集，用以訓練多層感知器，而後針對訓練成功的多層感知器，應用諸多學者所提出的靈敏度指標、相對重要度指標等逐一驗證與比較。經比較分析發現，本研究所提指標SFI(%)不論在客觀性、推廣性、可靠性、強健性等方面均具有優異性能，適合快速擷取出一個訓練完成後的多層感知器各項輸入參數相對重要性。而過去文獻常見的相對重要度指標，無法正確解析各項輸入變數對高度非線性或多維度空間的決策邊界的影響程度。
而後，本研究並廣泛蒐集整理全世界地震液化/非液化案例資料共計644筆，實際依據NCEER(1997)法所需的參數將案例資料整理成九維資料，各維度資料並經值域範圍的最大、最小值進行線性正規化至0～1之間後，應用在具有不同網路架構(不同隱藏層神經元個數)的液化潛能感知器的訓練/測試，並從中找出訓練成功且具最佳性能的液化潛能感知器。結果顯示，整體案例辨識率約96.6%，對於液化案例與非液化案例的辨識率相當，被誤判案例呈現隨機分佈。
本研究並進行靈敏度指標SFi(%)之計算，分析結果顯示：最大地表加速度PGA為最靈敏的參數，其次為總覆土應力，再其次為地震規模與SPT-N值，相對而言，細料含量參數FC對液化判識結果反應並不靈敏，只與應力折減因子相當。倘若將九個影響參數歸類為地震參數、土層應力狀態參數與土壤抗液化強度等三類，則它們對液化案例辨識之影響程度也約略相等。倘若從土壤抗液化強度參數與地震引致的地盤之平均反覆剪應力比參數觀點看，相對而言，平均反覆剪應力比參數影響液化/非液化辨識決策邊界的程度大於土壤抗液化強度參數的影響。

摘要(英)

In this study, the sensitivity analysis study of multilayer perceptrons, MLP, with partial derivative approach was carried out. An analytical equation was derived to calibrate the partial sensitivity of all the input parameters on neural network output when using MLP in 2-class pattern recognition problem. A novel vector index, called sensitivity factor of index, SFi, was defined to quantify the total influence of the input-layer parameters upon the recognition output of well-trained MLP.
A set of procedures of verification was proposed by this study to check the index, SFi, and to check other indexes proposed by previous literatures as well. A large number of mathematical simulation dataset of different noise ratio was randomly generated, in which the pattern classification curve had been well-defined and well-known. By using the simulation dataset, many MLP models were well-trained and tested. One of them with the best performance was then picked up to calculate various sensitivity indexes and soon be maked comparison with those calculated from the derivatives of well-defined pattern classification curve. These check could give a chance to understanding the objectivity, reliability, capability of generalization and the robustness against noise of the sensitivity index. The result of verification shows that the SFi index has pretty good performance on objectivity, reliability, capability of generalization and the robustness against noise. The index, SFi was useful to capture the sensitivity or relative importance between those input parameters of well-trained MLP model in pattern recognition problem.
Then a well-trained MLP model is developed to discriminate between the cases of liquefaction and non-liquefaction with totally 644 worldwide cases of seismic liquefaction or non-liquefaction. Excellent performance and good generalization is achieved, with the higher recognition rate 96.6% on the overall cases. Using this model, the SFi values are then calculated and reveal that the peak ground acceleration (PGA) is the most sensitive factor in both the liquefaction and non-liquefaction cases. Earthquake parameters, the stress state parameters of the soil layer, and the soil resistance parameters play approximately equal roles. The factors of cyclic stress ratio are more sensitive than the liquefaction resistance capacity factors in the two-class pattern recognition problem of seismic liquefaction or non-liquefaction.

關鍵字(中)

★ 多層感知器
★ 靈敏度分析
★ 靈敏度指標
★ 土壤液化
★ 數值模擬驗證
★ 簡易液化評估法
★ 案例分析

關鍵字(英)

★ multilayer perceptrons
★ sensitivity analysis
★ sensitivity of index
★ seismic liquefaction
★ verification of numerical simulation
★ simplified evaluation of liquefaction
★ case analysis

論文目次

摘要 I
ABSTRACT III
目錄 V
圖目錄 IX
表目錄 XVI
符號說明 XXIII
第一章、緒論 1
1-1 前言 1
1-2 研究動機 2
1-3 研究範圍、方法與架構 2
1-4 論文內容大綱 5
第二章、文獻回顧 6
2-1 多層感知器概述 6
2-1-1 感知器發展簡史 6
2-1-2 多層感知器的架構 9
2-1-3 多層感知器的倒傳遞演算法 11
2-1-4 應用多層感知器的注意事項 15
2-1-5 多層感知器的數學特性 18
2-2 多層感知器輸入參數相對重要度分析 19
2-2-1 Garson的相對重要度指標 20
2-2-2神經網路闡釋圖 22
2-2-3鍵結值法 24
2-3 多層感知器靈敏度分析 26
2-3-1簡介靈敏度分析法 26
2-3-2偏微分靈敏度指標分析 28
2-3-3偏微分靈敏度分析與應用 30
2-3-4偏微分法與其他方法比較研究 35
2-4 砂性土壤液化潛能簡易評估法 36
2-5 多層感知器分析液化潛能 40
第三章、多層感知器偏微分靈敏度指標 63
3-1 偏微分靈敏度解析方程式 63
3-1-1 基本假設 63
3-1-2 單一隱藏層架構的偏微分靈敏度解析方程式 63
3-1-3 多隱藏層架構的偏微分靈敏度解析方程式 66
3-2 本研究靈敏度指標的定義 68
3-2-1 適用於型態識別問題的靈敏度指標 68
3-2-1 適用於連續數值模擬預測問題的靈敏度指標 70
3-3 本章綜合討論 71
第四章、靈敏度指標數值模擬驗證 73
4-1 數值模擬驗證概述 73
4-2 三維空間圓球體曲面資料集的驗證 79
4-2-1 圓球體曲面無雜訊資料集與理論指標值 79
4-2-2 圓球體曲面無雜訊資料集訓練/測試MLP 84
4-2-3 圓球體曲面有雜訊資料集的驗證 87
4-3 三維空間橢球體曲面驗證 89
4-3-1橢球體曲面無雜訊資料集與理論指標值 89
4-3-2 橢球體曲面無雜訊資料集訓練/測試MLP 91
4-3-3橢球體曲面有雜訊資料集的驗證 94
4-4 三維空間圓柱體曲面驗證 95
4-4-1 圓柱體曲面無雜訊資料集與理論指標值 95
4-4-2 圓柱體曲面無雜訊資料集訓練/測試MLP 97
4-4-3圓柱體曲面有雜訊資料集的驗證 100
4-5 八維空間廣義球體曲面資料的驗證 102
4-5-1廣義球體曲面無雜訊資料集與理論指標 102
4-5-2廣義球體曲面無雜訊資料集訓練/測試MLP 104
4-5-3廣義球體曲面有雜訊資料集的驗證 107
4-6 八維空間高次多項式資料集的驗證 108
4-6-1 高次多項式無雜訊資料集與理論指標 108
4-6-2高次多項式無雜訊資料集訓練/測試MLP 110
4-6-3高次多項式有雜訊資料集的驗證 114
4-7 本章綜合討論 116
第五章、液化潛能感知器靈敏度分析 229
5-1 地震液化案例 229
5-1-1 案例蒐集與整理 229
5-1-2 案例資料分佈情形 233
5-2 SPT-N值簡易液化潛能評估 234
5-2-1 NCEER(1997)簡易液化潛能評估 234
5-2-2 本土HBF簡易液化潛能評估 236
5-3 液化潛能感知器訓練與測試 239
5-4 靈敏度分析結果 242
5-5 本章綜合討論 243
第六章、結論與建議 265
6-1 結論 265
6-2 建議 268
參考文獻 270
附錄A、Levenberg-Marquardt演算法簡介 278
附錄B、本研究蒐集整理的地震液化案例資料 281

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指導教授

李崇正

審核日期

2017-7-28

推文