The reliability sensitivity analysis based on saddlepoint approximation and its improved method

The saddlepoint approximation (SA) can directly estimateprobability distribution of linear performance function in non-normalvariables space and then calculate the failure probability of structure.Based on the property of SA, SA based reliability sensitivity analysismethod is developed. For the nonlinear performance function, SA method needsthe linearization of performance function firstly, but they neglect theinfluence of nonlinearity of performance function on the failureprobability. So the reliability sensitivity analysis method based itsimproved method, named as SA based line sampling (LS), is presented. Thereliability sensitivity can be estimated by the average of these partialderivatives of failure probabilities with respect to the distributionparameter of random variables, and the probabilities and sensitivities ofthe linear performance functions can be estimated by the SA in thenon-normal variables space. By comparing basic concepts, implementations andresults of illustrations, the following conclusions can be drawn, (1) SAbased reliability sensitivity method is only acceptable for the linearperformance function. The error mostly results from the linearization of theperformance functions. (2) The SA based LS method can obtain the estimatorsof failure probability and reliability sensitivity, which converge to theactual value along with the increase of sample size. The SA based LS methodconsiders the influence of nonlinearity of performance function on thefailure probability and reliability sensitivity; therefore it has the wideapplicability.