Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks  

基于剪枝贝叶斯神经网络的电阻率成像非线性反演（英文）

作　　者：江沸菠 戴前伟[2] 董莉[2,3] 

机构地区：[1]物理与信息科学学院湖南师范大学,长沙410081 [2]地球科学与信息物理学院中南大学,长沙410083 [3]信息科学与工程学院湖南涉外经济学院,长沙410083

出　　处：《Applied Geophysics》2016年第2期267-278,417,共13页应用地球物理（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.41374118);the Research Fund for the Higher Education Doctoral Program of China(Grant No.20120162110015);the China Postdoctoral Science Foundation(Grant No.2015M580700);the Hunan Provincial Natural Science Foundation,the China(Grant No.2016JJ3086);the Hunan Provincial Science and Technology Program,China(Grant No.2015JC3067);the Scientific Research Fund of Hunan Provincial Education Department,China(Grant No.15B138)

摘　　要：Conventional artificial neural networks used to solve electrical resistivity imaging （ERI） inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network （PBNN） nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter αk, which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.针对传统神经网络在电阻率成像反演中存在的过拟合和易陷入局部极值等问题,提出了一种基于剪枝贝叶斯神经网络(PBNN)的非线性反演算法和一种基于K-medoids聚类的样本设计方法。在基于K-medoids聚类的样本设计方法中,利用观测数据的聚类结果提供先验信息构造神经网络的训练样本,从而有针对性地指导神经网络的训练过程;剪枝贝叶斯神经网络是在贝叶斯正则化的基础上,通过评估各隐节点对反演结果的影响来自适应确定神经网络的隐层结构,根据小样本条件下训练样本的先验分布特征,选择了基于广义平均的超参数αk来引导剪枝过程。通过与地球物理领域内其它常用的自适应正则化方法相比较,验证了本文算法的有效性。理论数据和实测数据反演的结果表明:该方法能够较好地抑制神经网络训练过程中噪声的影响,提高网络的泛化能力,其反演结果优于BPNN反演、RBFNN反演和RRBFNN反演以及传统的最小二乘反演。

关 键 词：Electrical resistivity imaging Bayesian neural network REGULARIZATION nonlinear inversion K-medoids clustering 

分 类 号：P631.322[天文地球—地质矿产勘探]