Markov chain Monte Carlo ground‐motion selection algorithms for conditional intensity measure targets

Abstract

SummaryTwo new algorithms are presented for efficiently selecting suites of ground motions that match a target multivariate distribution or conditional intensity measure target. The first algorithm is a Markov chain Monte Carlo (MCMC) approach in which records are sequentially added to a selected set such that the joint probability density function (PDF) of the target distribution is progressively approximated by the discrete distribution of the selected records. The second algorithm derives from the concept of the acceptance ratio within MCMC but does not involve any sampling. The first method takes advantage of MCMC's ability to efficiently explore a sampling distribution through the implementation of a traditional MCMC algorithm. This method is shown to enable very good matches to multivariate targets to be obtained when the numbers of records to be selected is relatively large. A weaker performance for fewer records can be circumvented by the second method that uses greedy optimisation to impose additional constraints upon properties of the target distribution. A preselection approach based upon values of the multivariate PDF is proposed that enables near‐optimal record sets to be identified with a very close match to the target. Both methods are applied for a number response analyses associated with different sizes of record sets and rupture scenarios. Comparisons are made throughout with the Generalised Conditional Intensity Measure (GCIM) approach. The first method provides similar results to GCIM but with slightly worse performance for small record sets, while the second method outperforms method 1 and GCIM for all considered cases.