New sampling scheme for neural network-based meta- modelling with application to air pollutant estimation

Purpose A new method for the design of experiments (DOE) or sampling technique is proposed, using a distance weight function and the k-means theory. The radial basis function neural network metamodelling approach is used to evaluate the performance of the proposed DOE by using an n-degree of test function, applied to the complex nonlinear problem of spatial distribution of air pollutants. A comparison study is included to analyse the performance of the proposed technique against available methods such as the n-level full fractional design method and the Latin Hypercube Design method. Method For one design objective and n number of input design variables, a set of input-output training dataset are { } n j m i x x x x x x X i j j j i ,.., 1 , ,.., 1 ) ,.., , ;....; ,..., , ) ( ) 2 ( ) 1 ( ) ( 1 ) 2 ( 1 ) 1 ( 1 = = = and { } m i y y y Y i ,..., 2 , 1 ,..., , ) ( ) 2 ( ) 1 ( = = , where m is the