A Sequential Optimization Sampling Method for Metamodels with Radial Basis Functions

Table 1

Commonly used basis functions.

Name	Radial function 𝑟=‖𝑥−𝑥𝑖‖2
Linear	𝜙(𝑟)=𝑐𝑟
Cubic	𝜙(𝑟)=(𝑟+𝑐)^3
Thin-plate spline	𝜙(𝑟)=𝑟^2log𝑐𝑟^2
Gaussian	𝜙(𝑟)=exp−𝑐𝑟^2
Multiquadric	𝜙(𝑟)=𝑟^2+𝑐^21/2

c is a constant.