Using wavelet packet denoising and ANFIS networks based on COSFLA optimization for electrical resistivity imaging inversion

Electrical resistivity imaging (ERI) inversion is a complicated non-linear inversion problem, which is high dimensional and non-convex. Using traditional neural networks to solve the ERI inversion problem has an over-fitting phenomenon and easily falls into local minima. Moreover, the artificial neural network (ANN) model is a black box; its relationships between the inputs and outputs are not easy to interpret. In order to solve these problems, a wavelet packet denoising (WPD) procedure and an improved adaptive neuro-fuzzy inference system (ANFIS) based on Cauchy oscillation shuffled frog leaping algorithm (COSFLA) are proposed in this paper. The wavelet packet denoising methodology is based on soft thresholding and Shannon entropy using a Db10 wavelet which is applied to remove the noise component from the measured apparent resistivity data. Meanwhile, COSFLA is introduced for updating the premise parameters of the ANFIS to improve the learning ability and prediction accuracy of the algorithm. The development of the proposed method and the total inversion process are also presented. The inversion of the synthetic and field examples are provided to demonstrate the feasibility and validity of the proposed method. Additionally, the introduced method is transparent and its if-then rules are easy to understand and interpret.