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| Line sampling method based on saddlepoint approximation for reliability analysis with non-normal random variables |
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Abstract For reliability analysis of non-linear limit state function with non-normal random variables, a novel saddlepoint based line sampling method is presented on the combination of saddlepoint approximation and line sampling. For the structural reliability problem with non-normal variables, traditional line sampling reliability analysis method requires the transformation from the original non-normal variable space into the equivalent standard normal space. This transformation is nonlinear, which tends to increase the nonlinearity of the performance function and difficulty of estimating the failure probability. The presented saddlepoint based line sampling method does not require this nonlinear transformation. By use of saddlepoint approximation to estimate the probability distribution directly for the linear performance function with non-normal variables, and the traditional line sampling method expressing the failure probability of nonlinear performance function as the arithmetic average of a set of failure probabilities of the linear performance functions. The presented method can realize the high precision estimation of the failure probability of non-linear limit state function with non-normal variables. Before employing the saddlepoint based line sampling method, the linear standardized transformation is needed to eliminate the dimensions of variables. The theoretical derivation verifies that the saddlepoint based line sampling method degenerates into traditional line sampling when all the random variables are normally distributed. The results of the illustrations show that the presented method has higher precision than the direct saddlepoint approximation for non-linearperformance function reliability problem.
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Received: 12 January 2009
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2010, Vol. 31 
