Low dimensional modeling of Double T-junctions in water distribution networks using Kriging interpolation and Delaunay triangulation

Pacific Journal of Mathematics for Industry

Table 3 Result of optimization of the Kriging parameters by resolving the log-likelihood function with respect to the shape parameter theta and the regularization parameter for no polynomial and polynomial degree equals to 0, 1, 2 and 3

Polynomial degree	No polynomial	k = 0	k = 1	k = 2	k = 3
\( \tilde{\uptheta} \)	2.76	2.81	2.85	3.13	3.63
α	0.5	0.5	0.5	0.5	0.5
\( \mathrm{f}\left(\tilde{\uptheta},\upalpha \right) \) initial	2902.92	2895.64	2891.3	2855.29	2806.2
\( \mathrm{f}\left(\tilde{\uptheta},\upalpha \right) \) optimal	2866.93	2864.77	2863.32	2841.27	2804.62
average error		1.75	1.94	1.86	1.82
standard deviation		3.40	3.24	2.83	2.37
min		0.02	0	0	0
max		35.19	34.09	31.4	26.86