Mathematical Problems in Engineering / 2016 / Article / Tab 3

Research Article

An Improved Approach for Estimating the Hyperparameters of the Kriging Model for High-Dimensional Problems through the Partial Least Squares Method

Table 3

Results of the Griewank function in 60D over the interval . Ten trials are done for each test (50, 100, 200, and 300 training points). Best results of the relative error are highlighted in bold type for each case.

SurrogateStatistic50 points100 points
Error (%)CPU timeError (%)CPU time

KrigingMean1.39560.19 s1.04920.41 s
std0.15200.27 s0.05231.34 s
KPLSMean0.920.07 s0.870.10 s
std0.020.02 s0.020.007 s
KPLSMean0.910.43 s0.870.66 s
std0.030.54 s0.021.06 s
KPLSMean0.921.57 s0.863.87 s
std0.041.98 s0.025.34 s
KPLS+K Mean0.992.14 s0.902.90 s
std0.030.72 s0.030.03 s
KPLS+K Mean0.982.44 s0.883.44 s
std0.040.63 s0.021.06 s
KPLS+K Mean0.993.82 s0.886.68 s
std0.052.33 s0.035.34 s

SurrogateStatistic200 points300 points
Error (%)CPU timeError (%)CPU time

KrigingMean0.832015.39 s0.652894.56 s
std0.04239.11 s0.03728.48 s
KPLSMean0.820.37 s0.790.86 s
std0.020.02 s0.030.04 s
KPLSMean0.782.92 s0.741.85 s
std0.022.57 s0.030.51 s
KPLSMean0.786.73 s0.7020.01 s
std0.0210.94 s0.0326.59 s
KPLS+K Mean0.769.88 s0.6622.00 s
std0.030.06 s0.020.15 s
KPLS+K Mean0.7512.38 s0.6023.03 s
std0.032.56 s0.030.50 s
KPLS+K Mean0.7416.18 s0.6141.13 s
std0.0310.95 s0.0326.59 s