基于改进支持向量机的快速稳健代理模型研究

Fast and robust surrogate model research based on improved support vector machine

最小二乘支持向量机代理模型具有较好的泛化能力和强大的非线性处理能力,但其对实际工程中不可避免的异常样本十分敏感,而传统的加权最小二乘支持向量机易产生过度拟合并且未考虑到回归误差分布特性,针对这一问题提出正态分布概率密度函数加权方法,并且采用回归误差的中值作为计算权值的衡量标准,增强了加权算法的稳健性;提出了迭代加权最小二乘支持向量机快速递推算法,利用矩阵关系进行迭代递推计算,减少了计算量,节约了建模时间。通过数值实例验证了该方法的可行性、有效性。

Surrogate model based on Least Squares Support Vector Machine（LS-SVM）has preferable generalization ability and powerful non-linear expression ability, but LS-SVM is very sensitive to outliers which are inevitable in actual projects. Traditional Weighted Least Squares Support Vector Machine（WLS-SVM）often has the problem of over fitting, and it does not consider the regression error distribution characteristic. Aiming at these problems, normal distribution probability density function weighted method is presented, and the median value of regression error is selected as criteria for computing weighted value in order to improve the weighted algorithm robustness. Moreover, fast recursive algorithm for iteratively weighted LS-SVM is proposed. Matrix relation is utilized in this fast algorithm for iteratively recursive calculation, which can reduce computation and save modeling time. Lastly, the results of numerical regression experiment validate the feasibility and effectiveness of this method.