Design of experiments and global modeling approach based on sub-domains significance for complicated relationship process
Cui Qing-a · Systems Engineering - Theory & Practice · 2013
For the parameter optimization of process featured with multi-extreme quality characteristics and complicated relationship between parameters and quality characteristics,a sequential experimental design and global modelling approach is proposed considering the significance of changing of quality characteristics in the sub-domains of the process.First,a succession of design sets and appending sets are derived from a certain set of design.Second,a support vector regression(SVR) model is set up based on the initial design set.Then the whole process domain is partitioned into several sub-domains after Ward's clustering of the sample points.Furthermore,the significance of quality characteristics' changing is measured by the corresponding support vector(SV) rate in each sub-domain.Third,each point in the appending set is allocated into a sub-domain according to the Euclidean distance discriminant analysis. Based on the principle of non-uniformity among different sub-domains and uniformity within a single sub-domain,the number of appended points to each sub-domain are adjusted by the corresponding SV rate,with more points appended to sub-domains with higher SV rates,and less points appended to subdomains with low SV rates.Finally,the above steps are iterated until termination condition is reached and consequently,the final SVR model is set up.The simulation studies show that,comparing with traditional design and Latin hypercube sampling(LHS) which are based on the principle of uniform dispersion,experimental design efficiency and model performance of the proposed approach are improved. Design points of the approach congregate in the sub-domains correspondingly to the significance of changing of quality characteristic,and the model prediction error decline at least 29.8%as well.Moreover,the approach can find multi-extreme of the process and therefore get better optimization of parameters by using a smaller sample size.