Improved dimension reduction method (DRM) in uncertainty analysis using kriging interpolation

Abstract

Uncertainty or reliability analysis is to investigate the stochastic behavior of response variables due to the randomness of input parameters, and evaluate the probabilistic values of the responses against the failure, which is known as reliability. While the major research for decades has been made on the most probable point (MPP) search methods, the dimension reduction method (DRM) has recently emerged as a new alternative in this field due to its sensitivity-free nature and efficiency. In the recent implementation of the DRM, however, the method was found to have some drawbacks which counteract its efficiency. It can be inaccurate for strong nonlinear response and is numerically instable when calculating integration points. In this study, the response function is approximated by the Kriging interpolation technique, which is known to be more accurate for nonlinear functions. The integration is carried out with this meta-model to prevent the numerical instability while improving the accuracy. The Kriging based DRM is applied and compared with the other methods in a number of mathematical examples. Effectiveness and accuracy of this method are discussed in comparison with the other existing methods.