Two accuracy measures of the Kriging model for structural reliability analysis

The Kriging model for structural reliability analysis applications has attracted much attention within recent years. Several Kriging-based strategies of design of experiments are constructed for structural reliability analysis procedure. However, the quantitative accuracy measure of Kriging is still undesirable. Two accuracy measures are introduced. The first one is further studied through derivation and proposed to quantify accuracy of the Kriging-based estimate of the limit state. This paper treats the target failure probability as a variable with epistemic randomness. The second measure is innovatively defined as the standard deviation of the target failure probability. Combining with Chebyshev's inequality, the second measure is available to construct a lower upper bound of the error of the failure-probability estimate. The joint distribution of performance values at untried points of a given Kriging model is derived and proved, which is indeed essential for computing the innovative accuracy measure because it takes the correlation between performance values of untried points into account. Monte Carlo simulation is employed to compute them with acceptable computational cost. To validate the accuracy measures, four benchmark examples are studied. Results demonstrate the availability of them.