Abstract: Aiming at the poor prediction performance of Radial Basis Function（RBF） metamodel technology when approximating high-dimensional problems, an improved technology based on Hybrid kernel function Radial Basis Function（HRBF） is proposed. In the case of the uneven distribution of samples of the Latin Hypercube Sampling（LHS）, an Uniform Latin Hypercube Sampling（ULHS）design is proposed by defining an auxiliary function and distance evaluation criteria and used in the construction of RBF. To improve model prediction accuracy and computational efficiency, modeling technology based on Multi Strategy Radial Basis Function（MSRBF） composed of local intensive adding-points, global uniform sampling and minimum distance filtering strategy is used to construct model considering sample point factor; meanwhile, to avoid structural risk when MSRBF is used to approximating high-dimensional problems, considering the influence of structural factors, the weighted hybrid of inverse multiquadratic and cubic kernel functions is performed, and an improved RBF metamodel based on fusion kernel function is constructed. Simulation experiments are carried out using numerical and engineering examples, results show that HRBF not only meets the accuracy requirements, but also significantly improves the computational efficiency and has higher prediction stability.

Key words: radial basis function metamodel technology, Latin hypercube sampling design, modeling technology based on multi strategy, hybrid kernel function, simulation analysis

摘要： 针对径向基代理模型技术在近似高维问题时预测性能较差的不足，提出一种基于融合核函数的改进径向基代理模型技术。在拉丁超立方设计抽样不均匀的情况下，通过定义一种辅助函数与距离评判标准，提出基于均匀抽样的拉丁超立方设计，并应用于代理模型的构建中；为提高模型预测精度与计算效率，考虑样本点因素，采用局部密集加点、全局均匀选点和最小距离筛选的多策略建模技术构建径向基代理模型；同时，为避免该技术在近似高维问题时可能产生的结构风险，考虑结构因素对预测精度的影响，对逆多二次和立方核函数进行了权重式的融合，构建了基于融合核函数的改进径向基代理模型。利用数值和工程算例进行测试仿真，结果表明该技术不仅满足精度要求，且明显提高计算效率，具有更高的预测稳定性。

关键词: 径向基代理模型技术, 拉丁超立方设计, 多策略建模技术, 融合核函数, 仿真分析