A reliability index extrapolation method for separable limit states

When the limit state function (or performance function) of a structure can be written as the difference of a capacity function and a response function that are expressed in terms of independent sets of random variables (i.e., when the limit state function has a separable form), efficient simulation based techniques (e.g., Separable Monte Carlo Simulation method) can be used to predict the reliability of the structure. The accuracies of these simulation based techniques, on the other hand, diminishes as the structural reliability increases. This paper proposes a reliability index extrapolation method to predict reliability of a highly safe structure that has a separable limit state function. In this method, the standard deviations of the random variables that contribute to the capacity function are artificially inflated by using a scale parameter to obtain various (smaller) scaled reliability index values (that can be predicted accurately with small number of samples). The standard deviations of the random variables that contribute to the response function are kept unchanged in order to use the same response values in prediction of various scaled reliability indices. Then, least square regression is used to build a relationship between the standard deviation scale parameter and scaled reliability index values. Finally, an extrapolation is performed to estimate the actual (higher) reliability index. The accuracy of the proposed method is evaluated through reliability assessment of mathematical and structural mechanics example problems as well as a reliability based design optimization problem. It is found that the proposed method can provide reasonable accuracy for high reliability index estimations with only 1000 response function evaluations