基于Pareto定律参数优化的径向基近似建模

针对传统留一交叉验证法计算量大不适用于大规模复杂系统的问题,借鉴经济学中的Pareto定律,选择对全局误差大小起决定性作用的样本点作为关键点,对留一交叉验证法进行了改进,提出了基于Pareto定律的留一交叉验证方法。针对径向基模型形状参数的优化选择问题,将基于Pareto定律的留一交叉验证方法应用于形状参数的优化,提出了基于Pareto定律参数优化的径向基模型构造方法。测试表明,该方法构造的径向基模型具有良好的近似精度和较高的计算效率,具有推广的价值。

Optimal parameter based on Pareto law for radial basis function approximation modeling

The traditional leave one out method confronts the difficulty of large calculation scale and is not applicable to a large scale complex system. Learning from the Pareto law in the economic science, sample points which play dominant roles in the global errors are chose as key points. Accordingly, a new leave one out method is proposed to improve the traditional one. To obtain the shape parameter of the radial basis function, the method of the optimal parameter based on the Pareto law for radial basis function approximation modeling is proposed by combining the new leave one out method and shape parameter optimization. Numerical tests show that the method is accurate and efficient, and deserves to be promoted.