Random Vibration Analysis using Quasi-Random Bootstrapping

Paper #:
  • 2018-01-1104

Published:
  • 2018-04-03
Abstract:
The estimation of probabilities of rare events is computationally expensive. Suppose one wants to estimate a probability that is approximately 10-3 so that the standard of the estimate is 10-4. This calculation requires 100,000 calls of the performance function. The standard deviation of the estimator is proportional to the inverse of the square root of the of the number of calls, n^(-1/2) . Therefore, in order to reduce the standard deviation to one half of the above value (i.e. decrease it to 0.5 10-4) one needs 400,000 calls. Methods that use quasi-random sequences converge at a rate that could be approximately proportional the n^(-1) , Niederreiter (1978). This paper presents and demonstrates a method that simultaneously employs quasi-random sequences and bootstrapping to reduce the computational cost of the calculation of a probability
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