基于SVM与SRM耦合的抗剪强度参数随机场模拟

Random Field Simulation of Soil Shear Strength Parameters Based on SVM and SRM Coupling

摘要:

实验数据表明土体参数具有很大的空间变异性，而随机场理论为模拟土体参数空间变异性提供了有效途径。因为传统的谱表示法（SRM）无法正确模拟多维多元随机场参数间的互相关性，提出支持向量机法（SVM）与SRM耦合的方法。SVM是基于统计学习理论和结构风险最小化原理基础上的通用机器学习方法，它在解决小样本、非线性和高维模式识别问题中表现出诸多优势。以土体抗剪强度参数：黏聚力c和内摩擦角φ为例，通过实验证明二者之间存在天然负相关性，即为二维二元随机场。结果表明，在样本数量较少的条件下，基于耦合算法模拟随机场不仅能有效地描述变量的自相关性，而且能够准确地描述变量间的互相关性，为解决小样本条件下模拟多维多元随机场提供了一种有效的方法。

Abstract:

Previous experimental data show that the soil parameters have great spatial variability, which can be effectively simulated by the random field theory. The traditional spectral representation method (SRM) can not accurately simulate the cross-correlation between the parameters of multidimensional-multivariate random field. A support vector machine (SVM) and SRM coupling method was proposed in this paper. As a general machine learning method based on statistical learning theory and the principle of structural risk minimization, SVM has many advantages in solving the problems such as limited training data, nonlinear and high-dimensional pattern recognition. The shear strength parameters of soil (cohesion c and internal friction angle φ) were taken as an example, and the experiment proved that there is a natural negative correlation between them. The results showed that the proposed method can not only effectively describe the auto-correlation of variables, but also accurately describe the cross-correlation between variables under limited training data. The study provides an effective method to simulate multidimensional-multivariate random fields with a limited training data.