When estimating very small failure probability

the methods based on active learning Kriging (ALK) model usually need too many candidate points and time-consuming calculation. To address this problem

this paper proposes a two-stage surrogate model method

ALK-SS

2

which combines the ALK model and subset simulation(SS). Firstly

based on the constructed surrogate model in the first stage

the method uses a small number of SS last layer samples as candidate samples to complete the rough approximation of the limit state surface

and then in the second stage

it selects the SS last layer samples witha

larger sample size to refine the surrogate model in the first stage

so as to obtain higher accuracy. In addition

considering the conventional stopping criteria are too conservative. based on the failure probabilitv evaluated by ALK-SS

2

a new stopping criterion based on failure probability error is proposed

which further improves the efficiency of the method. From the investigation of four examples and the comparison with relative methods

it is proved that the proposed method has high calculation accuracy and efficiency

and is suitable for dealing with small failure probability problems and time-consuming implicit function problems.