Stochastic response surface method in uncertainly analysis

A stochastic response surface method (SRSM) which has beenpreviously proposed for problems dealing only with random variablesis extended in this paper for problems in which physical propertiesexhibit spatial random variation and may be modeled as random fields.Based on Karhunen-Loève expansion of random field, the paperutilizes Hermite polynomial chaos expansion to build the stochasticresponse surface function, Karhunen–Loeve (K–L) expansion torepresent the input, and polynomial chaos expansion to represent theoutput and the unknown coefficients of the function in the polynomialchaos expansion are calculated using a probabilistic collocationapproach in SRSM. This strategy helps us to decouple the finiteelement and stochastic computations, and the finite element code canbe treated as a black box,. Then, the geometric method can be used tocalculate the structural uncertaily. comparison with Monte Carlosimulation shows that the proposed method can achieve high accuracyand efficiency while analyzing the property of the second-order andthe third-order stochastic response surface.

کلیدواژه ها:

stochastic ، uncertainly ، polynomial chaos ، Karhunen- Loeve expansion