A novel method for estimating the failure possibility by combining the adaptive Kriging model with the Markov chain simulation

Under the condition of fuzzy inputs, the structure safety level is generally measured by the failure possibility. Differing from the level cut optimization method and the fuzzy simulation method, a novel method for estimating the failure possibility is proposed in this paper by combining the adaptive Kriging surrogate model with the Markov chain simulation. Based on the principle of fuzzy simulation, the fuzzy design point is defined as the failure point with the maximal joint membership function in the fuzzy simulation sample pool, and the problem of estimating the failure possibility can be transformed into that of searching the fuzzy design point. Then the Markov chain simulation which can quickly simulate the samples in the interest region is employed to search the fuzzy design point by a designed transfer criteria. To efficiently recognize the candidate states of the Markov chain, the Kriging surrogate model is adaptively trained in the candidate sample pool generated by the Markov chain states. By replacing the actual performance function with the convergent Kriging model, the efficiency of Markov chain simulation can be improved greatly. The presented examples are used to prove the rationality and high efficiency of the proposed method.