A maximum entropy method using fractional moments and deep learning for geotechnical reliability analysis

The spatial variability of the properties of natural soils is one of the major sources of uncertainties that can influence the performance of geotechnical structures. The direct Monte-Carlo simulation (MCS) method, although robust and versatile, may incur prohibitively high computational burdens, especially for cases involving low failure probability levels. In this paper, a hybrid strategy that fuses convolutional neural networks (CNNs) and maximum entropy distribution with fractional moments (MaxEnt-FM) is proposed. MaxEnt-FM is a post-processing technique that fits a probability distribution to a set of sample data. The proposed hybrid strategy starts by training a CNN as the metamodel of the time-demanding random field finite element model. The trained CNN is then used to generate sample data, which is subsequently processed using the MaxEnt-FM technique to obtain failure probability. The use of a CNN allows MaxEnt-FM to be carried out without explicit calls to the finite element model. Therefore, the proposed hybrid strategy has the potential to provide a computationally efficient technique to calculate failure probability. For the illustrative slope stability example that has a failure probability of 3 x 10(-4), the proposed hybrid strategy yields a less than 10% error in the predicted failure probability with only hundreds of finite element simulations.