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This study aims to develop a novel wavelet neural-network (WNN) model for solving electrical resistivity imaging (ERI) inversion with massive amounts of measured data in control and measurement fields. In the proposed method, we design a mixed multilayer WNN (MMWNN) which uses Morlet and Mexican wavelons as different activation functions in a cascaded hidden layer structure. Meanwhile, a hybrid STGWO-GD learning approach is used to improve the learning ability of the MMWNN, which is a combination of the self-tuning grey wolf optimizer (STGWO) and the gradient descent (GD) algorithm adopting the advantages of each other. Moreover, updating formulas of the GD algorithm are derived, and a Gaussian updating operator with weighted hierarchical hunting, a chaotic oscillation equation, and a nonlinear modulation coefficient are introduced to improve the hierarchical hunting and the control parameter adjustment of the modified STGWO. Five examples are used with the aim of assessing the availability and feasibility of the proposed inversion method. The inversion results are promising and show that the introduced method is superior to other competitors in terms of inversion accuracy and computational efficiency. Furthermore, the effectiveness of the proposed method is demonstrated over a classical benchmark successfully.

One of the great challenges of unconfined seepage through a dam lies in the accurate determination of free surface that depends on the complexity of the seepage model, especially if the model is characterized with complex geometry and sharp variations in permeability distribution. This study presents a practical methodology that combines the adaptive moving-mesh algorithm and the Galerkin finite element method (FEM) to solve an unconfined seepage problem with high efficiency and precision. The methodology employs a set of improvement terms, such as remainder factor, step-size parameter and termination condition, all of which guarantee that the simulation and the refinement fitting can be implemented efficiently until the free surface converges within a given allowable error. In particular, a specialized discussion is presented for the significant relation between the location of the exit point and the corresponding grid fineness. To validate the practicability of the proposed method, a series of examples are performed. Comparing the result with those of other numerical approaches, we conclude that even though the unconfined seepage model may be complicated with arbitrary complex geometry and sharp variations in permeability distribution, the proposed algorithm provides a great improvement in efficiency and accuracy in free-surface searching.

The traditional artificial neural network (ANN) inversion of electrical resistivity imaging (ERI) based on gradient descent algorithm is known to be inept for its low computation efficiency and does not ensure global convergence. In order to solve above problems, a kernel principal component wavelet neural network (KPCWNN) trained by an improved shuffled frog leaping algorithm (ISFLA) method is proposed in this study. An additional kernel principal component (KPC) layer is applied to reduce the dimensionality of apparent resistivity data and increase the computational efficiency of wavelet neural network (WNN). Meanwhile, a novel ISFLA algorithm is adopted for improving the learning ability and inversion quality of WNN. In the proposed ISFLA, a hybrid LC mutation attractor is used to enhance the exploitation ability and a differential updating rule is used to enhance the exploration ability. Four groups of experiments are considered to demonstrate the feasibility of the proposed inversion method. The inversion results of the synthetic and field examples show that the introduced method is superior to other algorithms in terms of prediction accuracy and computational efficiency, which contribute to better inversion results., (Copyright © 2018 Elsevier Ltd. All rights reserved.)