application of importance sampling as a variance reduction technique in structural reliability

  in structural reliability analysis, where the probability of failure is generally relatively small, the directmonte carlo (mc) simulation procedure becomes inefficient. in this case many simulations are requiredto estimate a probability and limit the uncertainty in the estimate. in mc simulation to produce defensibleresults for a case with a large number of random variables, a large number of sampling sets is required.thus, there are limitations to obtaining high accuracy for large-scale problems, which require tremendouscomputational time and effort. to improve the rate of convergence, several modifications can beintroduced to mc simulation. in this paper, importance sampling (is) is presented as a well-knownapproach in variance reduction method for mc simulation.

the importance sampling method is a modification of mc simulation in which the simulation is biasedfor greater efficiency. in is, the sampling is done primarily in the tail of the distribution, rather thanspreading it out evenly, in order to ensure that sufficient simulated failures occur. is consist in generatingrandom weighted samples from an auxiliary distribution that named is density function rather than thedistribution of interest. the crucial part of this method is the choice of is density function that should beable to simulate more rare random events. in this paper shifted joint probability distribution function(pdf) of random variables is used for is density function. in this method pdf shifted to the β-point(most probable of point) obtained from first-order reliability method (form) theory. some examples aresolved by this method and results show that the is has smaller variance than mc with same number ofsimulations.