3.3. Kriging model (KRG)
KRG is an interpolation technique that SQ109 predicts the value as a combination of two parts, one which captures the large scale variations (f(x)) and a systematic departure (Z(x)). Kriging model is represented mathematically:equation(6)F(x)=f(x)+Z(x)F(x)=f(x)+Z(x)
3.4. Weighted average surrogate (WAS)
WAS is a weighted average technique which uses the basic surrogates to find an ‘average’ function, which is defines as.equation(7)FWAS(x)=∑iNsmwi(x)Fi(x)where, Nsm represents the number of the surrogate models, ith surrogate model at the design point of x produces a weight wi(x) and Fi(x) is the predicted response by the ith surrogate. The weights are calculated from the CV error estimation . The weighting scheme is as follows:equation(8)Ei=1Nsp∑i=1k(Fi−Fii−1)2equation(9)Eavg=∑i=1NsmEiNsmequation(10)wi∗=(EiEavg+α)β,wi=wi∗∑iwi∗,β<0,α<1
The next step is to search the optimal points. Genetic algorithm (GA) tool is used for searching the global optimal point . The GA is based on the generation of random number; each run may report a different result and may even neglect the actual optimal point. The above problem can be reduced by using a sequential quadratic programming (SQP). The SQP is a local search algorithm, which is used to give fine-tune to the results produced by the GA. The combination of the GA and SQP is called hybrid genetic algorithm (HGA). The SQP can be used directly to search local optima. But the non-linear functions may have many local optima and finding right optima requires a right ‘initial guess’ for the SQP function. Normally node of Ranvier is done through inserting several guess values to evaluate the SQP function.