多層感知器結合基因演算法與粒子群演算法於井測資料之反推

Abstract

井測資料的地層視導電率為真實地層導電率與其鄰近的地層的作用，具有非線性的對應關係。而類神經網路中的多層感知器的輸入與輸出也具有非線性的對應關係，因此我們採用此一模型於井測資料的反推。不過，通常我們用訓練類神經網路的梯度下降法做調整網路的係數，會有陷入區域最佳解的問題。為解決此一問題，我們提出具有全域最佳化的演算法於類神經網路係數的求解。我們採用四種全域最佳化的演算法: 二進位基因演算法、實數型基因演算法、粒子群演算法、和突變式粒子群演算法，四種演算法於兩層感知器網路的係數的調整，在基因演算法內的一個個體或粒子群演算法內的一個粒子表示為一個網路的係數，我們會有多個個體或粒子進行演算。 我們採用兩層的感知器，此一模型為一監督式的訓練系統。在訓練的過程中，輸入為視導電率，期望輸出為理論上計算出來的真實地層的導電率。我們將應用理論，根據輸入資料的長度與樣本數來決定網路中隱藏層的節點個數。再藉由所採用的四種演算法，做網路係數的調整，使得反推的地層導電率與理論的地層真實導電率的誤差為最小，達成訓練的目的。 我們有31口井的模擬資料，為由電學與模型的方法計算得到的。我們利用這31口井的資料分析出兩層感知器的最佳的輸入長度與隱藏層節點數，並且利用循序性的方法決定四種演算法中的最佳參數。我們對25口井做訓練，6口井做測試，得到四種演算法於網路係數的調整的最佳網路模型。 在實驗的部份，分為模擬井測資料的反推與一個實際的井測資料反推。由模擬的實驗的結果，在調整網路係數的四種演算法中，以突變式粒子群演算法於兩層感知器網路訓練得到的測試誤差為最小，為最佳的網路模型。而在基因演算法的比較上，實數型基因演算法於兩層感知器網路訓練比二進位基因演算法得到的測試誤差較小，因為二進位基因演算的位元串限制了網路係數的範圍，所以有較大的測試誤差。 在實際應用方面，在模擬的訓練之後，我們應用最佳的突變式粒子群演算法得出的兩層感知器於實際井測資料的反推，得出的結果是可接受的，表示突變式粒子群演算法於兩層感知器網路的係數的調整用於井測資料的反推是可行的。

The apparent conductivity is from true layer conductivity and effect of its neighboring layers in well log data. It is a non-linear relationship. Also multilayer perceptron (MLP) has the property of non-linear mapping between inputs and outputs. So we adopt MLP to the inversion of well log data. However, in conventional method the MLP using gradient descent learning rule to find the weighting coefficients may converge to a local minimum. In order to solve the problem, we use four global optimization algorithms including binary genetic algorithm (GA), real number GA, particle swarm optimization (PSO), and PSO with mutation (MPSO) to get the global optimized weighting coefficients in MLP. We use many individuals or particles to adjust the weights in the MLP where an individual in GA or a particle in PSO is a set of the weighting coefficients in MLP. We use two layer perceptron. It is a supervised training model. In the training procedure, the input of the network is the apparent conductivity (Ca) and the desired output is the true formation conductivity (Ct). By theorem, the hidden node number of two-layer MLP is determined by the input data length and the number of training patterns. Then we use four methods to train the weights in MLP and minimize the error between inverted conductivity and the desired true conductivity. We have 31 simulated well log data. They are acquired from the calculation of electrical and model-based method. We use the 31 simulated well log data to analyze the best input length and number of hidden nodes in MLP. We get the best parameters in four algorithms by sequential method. We do the training on 25 simulated well log data and the testing on 6 simulated well log data to get the best MLP model of four algorithms in MLP weight learning. We have experiments on simulation and real field data application. From the experimental results in simulation, MPSO in MLP weight learning has the smallest test error and is selected as the best MLP model. For comparison in GA, real number GA has lower error than that of binary GA. That is because the bit string in binary GA limits the range of weighting coefficient and has higher error. In real field data application, after training in the simulation, we apply the best MLP model, MPSO, to the inversion of real field well log data. The result is acceptable. It shows that MPSO in MLP weight learning can work on well log data inversion.