| 摘要: | 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。
;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. |
