An active learning method based on Monte Carlo dropout neural network for high-dimensional reliability analysis

In structural reliability analysis, the AK-MCS method, which combines Kriging and Monte Carlo Simulation, is well-acknowledged for its effectiveness but struggles with accuracy and efficiency in high-dimensional and nonlinear scenarios. To leverage the advantages and circumvent the limitations of AK-MCS, an active learning method based on the Monte Carlo dropout (MC-dropout) neural network is proposed. The MC-dropout neural network-based surrogate model provides both predictive mean and standard deviation in complex scenarios with a limited number of samples. By identifying candidate samples and utilizing a learning function that considers predictive mean and standard deviation, the method selects new samples close to the limit state surface with significant uncertainties to update the surrogate model. An ensemble of MC-dropout neural networks is then used to obtain a reliable failure probability. Two convergence criteria are introduced to determine the termination of the active learning process. Two numerical examples, a cantilever beam and an actual cable-stayed bridge are used to demonstrate the efficacy of the proposed method. The results show that the MC-dropout neural network-based surrogate model exhibits adaptivity and flexibility in handling high-dimensional and nonlinear scenarios and the proposed method achieves a relatively accurate failure probability with a limited number of samples.