類神經網路與基因演算法於井測資料反推

Abstract

在井測資料的反推問題中，井測合成資料與地層真實導電率之間是一種非線性的映對關係，而類神經網路能夠避免複雜的理論計算，經由訓練過程來調整權重值，以逼近輸入輸出值之間的映對關係，因此本研究以類神經網路為基礎，發展高階特徵值類神經網路架構，以應用於井測資料的反推。 由於常用以訓練類神經網路的梯度下降法，有易於陷入區域最小值的缺點，因此，我們以結合基因演算法來改善網路學習的效率。另外，梯度下降法的收斂較為緩慢，因此使用共軛梯度法來增進學習速率。為了加強網路的非線性映對能力，我們提出高階特徵值類神經網路，其特性為使用次方函數來增加輸入特徵值的高階項。此外，為了提高訓練樣本的數量以增進收斂效率，我們測試了不同輸入神經元數量的網路架構。另外，經由實驗結果比較得知，含有1層隱藏層的網路比不含隱藏層的網路有較好的收斂效果，因此我們採用含有1層隱藏層的網路。研究資料一共是31口井的井測合成資料，每一口井含有200點的輸入與期望輸出值資料。實驗以網路的實際輸出值與期望輸出值之間的平均絕對值誤差來評估網路的效能，以Leave-one-out的方式做31次試驗，每次試驗用30組資料做訓練，訓練完成的網路以剩下的1組資料做測試，經過31次的試驗，取其平均值做為該次實驗的結果。 為了驗證高階特徵值類神經網路的有效性，我們以合成的資料作為輸入特徵值來訓練網路，採用的網路架構為30-36-10 (不含bias)，使用共軛梯度法為訓練法則，網路訓練完成後輸入真實的井測資料，以測試網路的反推結果。實驗顯示，我們所提出的高階特徵值類神經網路，能夠有效的應用於井測資料的反推問題。在以類神經網路應用於井測資料的反推問題上，我們的研究結果提供了一個良好的網路架構。

In well logging inversion problem, a non-linear mapping exists between the synthetic logging measurements and the true formation conductivity. Without complexity of theoretic computation, neural network is able to approximate the input-output mapping through training with the iterative adjustment of connection weights. In our study, we develop the higher-order feature neural nets on the basis of neural network, and then apply on well logging inversion. The usually used training algorithm for neural network is gradient descent, which is easy to get trapped at local minimum, so we adopt a method that combine with genetic algorithm to improve the training efficiency. In addition, the convergence of gradient descent is slow, so we adopt the conjugate gradient to speed up the convergence. In order to make network more non-linear, we proposed higher-order feature neural nets that use functions to expand the input feature to higher degree. In order to use more training patterns and increase the convergence efficiency, we test various network architectures that use different number of input nodes. Besides, the experimental results show that the convergence efficiency of the network with 1 hidden layer is better than that without hidden layer, so we adopt the network with 1 hidden layer. We use 31 synthetic logging datasets. Each has 200 input features and corresponding outputs. The performance of network is evaluated by comparing the mean absolute error between the actual outputs and desired outputs. Leave-one-out validation method is used in experiments. Each time 30 datasets are used in training, the trained network is then tested with the left 1 dataset. After 31 trials, the network performance is computed by averaging these testing results. To validate the effectiveness of higher-order feature neural nets, the network size is 30-36-10 (not include bias), we train the network using conjugate gradient with synthetic logging datasets, and the trained network is then tested with real field logs. Results obtained from our experiments have shown that the proposed higher-order feature neural nets can be used effectively to process the well logging inversion. Our study shows an effective architecture of neural network to apply on well logging data inversion.