A Deep Learning Approach for Stochastic Structural Plane Generation Based on Denoising Diffusion Probabilistic Models

• Published in: Mathematics
• Main Authors: Han Meng, Xiaoyu Qi, Gang Mei
• Format: Article in Journal/Newspaper
• Language: English
• Published: MDPI AG 2024
• Subjects: rock mass; stochastic structural planes; Monte Carlo method; deep learning; denoising diffusion probabilistic model (DDPM); Mathematics; QA1-939; Nordland
• Online Access: https://doi.org/10.3390/math12131997; https://doaj.org/article/0b08ca1d879f45eaaeca8bf71a9d563b

The stochastic structural plane of a rock mass is the key factor controlling the stability of rock mass. Obtaining the distribution of stochastic structural planes within a rock mass is crucial for analyzing rock mass stability and supporting rock slopes effectively. The conventional Monte Carlo method generates each parameter of stochastic structural planes separately without considering the correlation between the parameters. To address the above problem, this study novelly uses the denoising diffusion probabilistic model (DDPM) to generate stochastic structural planes. DDPM belongs to the deep generative model, which can generate stochastic structural planes without assuming the probability distribution of stochastic structural planes in advance. It takes structural plane parameters as an integral input into the model and can automatically capture the correlations between structural plane parameters during generation. This idea has been used for stochastic structural plane generation of the Oernlia slope in the eastern part of Straumsvatnet Lake, Nordland County, north-central Norway. The accuracy was verified by descriptive statistics (i.e., histogram, box plot, cumulative distribution curve), similarity measures (i.e., mean square error, KL divergence, JS divergence, Wasserstein distance, Euclidean distance), error analysis, and the linear regression plot. Moreover, the linear regression plots between the dip direction and the dip angle verified that DDPM can effectively and automatically capture the correlation between parameters.