《Journal of Computing in Civil Engineering 》杂志刊登“人工神经网络与径向基函数内插法在土坝防渗模型中的整合作用”

作  者：Vahid Nourani, Ali Babakhani

刊  物：《Journal of Computing in Civil Engineering》，第27卷第2期（2013年3月），183-195页

关键词：人工智能技术；多元二次函数；渗流分析；土坝；Sahand 坝

摘  要：本文运用径向基函数空间插值法来估算土坝潜在的水头。利用MQ函数来离散渗流偏微分方程和相关的边界条件，这个函数包含了在模型校正中起重要作用的形状系数c。系数c首先通过Hardy和交叉验证方法进行优化，然后利用最优的系数c建立了两个模型，其中一个考虑内部条件，所得到的的结果与有限差分法的结果进行比较。为了解决FDM和RBF方法在时空模拟上的局限性，同时利用人工神经网络来处理非线性时间变化。然后利用神经网络来处理位于核心的测压计，预测水头潜在的时间序列，所得到的结果作为RBF方法中的内部条件，与边界条件一起得到水头的时空模型。最后利用交叉验证方法证明了系数c是不随时间变化的。结果显示系数c的最优值随时间无显著的变化，因此可得出结论：在MQ函数中形状系数常常取决于几何形状而不是边界条件的时间变化。

Integration of Artificial Neural Networks with Radial Basis Function Interpolation in Earthfill Dam Seepage Modeling

Authors: Vahid Nourani, Ali Babakhani

Journal: 《Journal of Computing in Civil Engineering》,Volume 27, Issue 2 (March 2013),183-195

Keywords: Artificial intelligence technics;Multiquadric function;Seepage analysis;Earthen dam;Sahand dam

Abstract: In this study, the radial basis function (RBF) spatial interpolation method was used to estimate the potential water heads through an earthen dam. The multiquadric (MQ) function was used to discretize the seepage governing partial differential equation and related boundary conditions. The function contains a shape coefficient of c , which plays an important role in model calibration. Therefore, the coefficient of c was first optimized via Hardy and cross validation methods, and then, by employing the optimal c (c _opt ), two scenarios of modeling with and without considering the internal conditions were provided and the results were compared with the results of the finite difference method (FDM). In the next step, an artificial neural network was used for handling the nonlinear time variability of the phenomenon to cope with the limitations of the FDM and RBF methods in temporal modeling. Thus, by training neural networks for the piezometers located in the core, the potential time series of water were predicted and their results were imposed upon the RBF method as the internal conditions, along with the boundary conditions for spatial-temporal modeling of the water heads. Finally, the assumed time-invariant inherency of c was confirmed by the cross-validation method. The results show no notable time variation in time series of c _opt , and therefore, it can be concluded that the value of the shape coefficient in MQ formulations generally depends on the geometry of the problem rather than the temporal variation of the boundary conditions.

原文链接：http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29CP.1943-5487.0000200