An adaptive sequential sampling method based on ANN_MCD and RF: Application in geotechnical problems

In geotechnical engineering, surrogate modeling is a vital technique for enhancing computational efficiency when faced with limited and costly samples. However, most adaptive sequential sampling (ASS) methods use the Kriging model, which directly evaluates the uncertainty of the model at unsampled points, but they are not efficient in solving multiple output problems. A few studies use cross-validation to indirectly evaluate the uncertainty of other surrogate models, which is time-consuming to repeatedly train multiple models. In addition, few methods consider input feature sensitivity, which further reduces the efficiency of ASS methods. To address these issues, this study proposes a hybrid ASS method that combines artificial neural networks with Monte Carlo dropout (ANN_MCD) and random forests (RF). The ANN is suitable for multiple output problems, and the MCD enables the ANN architecture to stochastically transform and efficiently predict uncertainty at unsampled points with a single model training. The RF evaluates input feature sensitivity, assigns weights to the sampling space based on feature sensitivity, and effectively avoids the interference of low-sensitivity features. Furthermore, two active learning functions are proposed to regulate the sampling areas on either a global scale or close to the limit state function, depending on the problem type. The study validates the efficacy of the proposed method through three representative geotechnical engineering examples: system reliability analysis of soil slope, back-analysis of soil constitutive parameters, and estimating the penetration rate in diamond drilling. The outcomes demonstrate that the proposed method has less computational cost than related studies and has more potential in addressing geotechnical sampling. •We proposed an effective adaptive sequential sampling method that combines ANN_MCD and RF.•The ANN_MCD model is used to efficiently predict the uncertainty of the unsampled points.•Weighting the input space allows the model to focus on more important features.•Different geotechnical problems were used to validate the proposed sampling method.