基于汉南-奎因信息准则的电阻率层析成像径向基神经网络反演

径向基神经网络（RBFNN）具有结构简单、学习速度快、不易陷入局部极小等优点，能够有效地提高电阻率层析成像反演的收敛速度和求解质量.本文针对电阻率层析成像反演的非线性特征，提出了一种基于汉南-奎因信息准则（HQC）的正交最小二乘法（OLS）学习算法（HQOLS）.该算法通过计算HQC的最优值来自动选择RBFNN的网络结构，避免了传统OLS学习算法中阈值参数的设定，保证了网络的泛化性能.通过比较聚类法、梯度法、OLS和HQOLS等学习算法的反演性能，构建了基于RBFNN的电阻率层析成像反演模型.数值仿真和模型反演的结果表明，该方法实现简单，在准确性上优于BP反演，成像质量优于传统最小二乘法反演.

RBFNN inversion for electrical resistivity tomography based on Hannan-Quinn criterion

The radial basis function neural network has advantages in aspects of simple structure, fast learning rate and improved global search ability,which can effectively improve the convergence speed and quality of resistivity tomography inversion. This paper presents an improved OLS learning algorithm based on Hannan-Quinn criterion (HQOLS) for RBFNN nonlinear inversion, which can adaptively select the hidden layer structure by calculating the optimal HQC value. The proposed algorithm avoids the parameter setting and guarantees the generalization performance. The inversion performances of the k-means clustering algorithm, gradient algorithm, OLS and HQOLS algorithm are compared and a model of RBFNN inversion is given. Data simulation and model inversion show that the HQOLS-RBFNN has better performance than BPNN in accuracy and has higher imaging quality than the traditional least square inversion.