基于主成分-正则化极限学习机的超高密度电法非线性反演

超高密度电法是一种新的地球物理探测技术,它通过多通道数据采集和多装置数据联合反演,极大地提高了电法勘探的成像精度.本文提出一种主成分-正则化极限学习机(PC-RELM)非线性反演方法,该方法针对超高密度电法所获取的高维勘探数据进行反演建模,通过随机设定隐层参数来简化模型的学习过程,通过主成分分析方法来进行高维数据降维,最后引入正则化因子提高反演模型的泛化能力.论文给出了超高密度电法的原理、样本构造方法和非线性反演流程,使用交叉验证方法获得了优化的隐节点数目和正则化参数,构造了优化的反演模型.通过两个经典的超高密度模型的反演结果表明,该方法能够较好地解决超高密度电法反演的高维数据非线性建模问题,能够弥补单一装置数据反演的不足,同时相较其他的非线性反演方法(ELM,BPNN和GRNN)具有更加准确的反演结果.

Ultra-high density resistivity nonlinear inversion based on principal component-regularized ELM

Ultra-high density resistivity inversion is a complicated non-linear inversion problem, which is high dimensional and non-convex. The traditional approaches suffer from some common drawbacks: they are mostly linear approximations of nonlinear problems and critically depend on the initial models chosen for them. A principal component-regularized extreme learning machine (PC-RELM) nonlinear inversion method for high dimensional ultra-high density resistivity data is analyzed. An additional principal component analysis layer is used for dimensionality reduction of the data to increase the computational efficiency of ELM inversion. Then, random hidden layer parameters are used to simplify the learning process of ELM. Additionally, the regularization factor is introduced to improve the generalization ability of the inversion model. The experimental results demonstrate that the proposed method exhibits high inversion accuracy and can solve the ultra-high density resistivity inversion problem efficiently: (1) The effect of using PCA for reducing the dimensions of ultra-high density resistivity data is obvious, and variance contribution rate of the first principal component reaches up to 40% or more. The ultra-high density resistivity data are reduced to 19 dimensions through the PCA layer with little information loss. (2) Optimized number of hidden nodes and value of regularization factor are obtained by cross validation. ELM with Sigmoid kernel, which reaches the lowest training MSE 28.3762 and testing MSE 83.9386, is used for inversion modeling. (3) The proposed inversion method reconstructs the size, location and sharpness of the anomalous body better than Least-squares inversion results of Wenner, Wenner-Schlumberger and Dipole-Dipole configurations with the same electrode number. (4) The proposed inversion method is also compared with BPNN, RBFNN and GRNN for nonlinear inversion. The results show that the proposed method reaches the lowest testing MSE 128.1303, and achieves the highest testing R² 0.8508. In this study an implementation framework of PCA dimension compression and ELM modeling with regularization for ultra-high density resistivity inversion is proposed. PCA layer is used for dimension compression and principal component selection, and then an improved RELM with Sigmoid kernel is used for ultra-high density resistivity inversion. The proposed method is accurate, fast, and easy for implementation. Another advantage of our proposed method is the direct approach to the nonlinear task, which avoids linearization and the choice of appropriate starting models necessary for classical minimization methods. Despite this contribution, there are many remaining challenges for the future work. Firstly, the way to optimize the parameters of ELM with optimal structure could be studied more deeply including the examination of theoretical implications of the associated choices. Secondly, the extension of the method to more complex field data set could be of interest, both from theoretical and practical viewpoints. Finally, GPU parallel computation will be introduced to the proposed inversion method to improve calculation efficiency. Our future research will be directed toward the development of fast and effective inversion algorithm for large-scale ultra-high density resistivity data inference.