Optimal selection of dictionary atoms for sparse dictionary learning of time-varying monitoring data in two-dimensional geotechnical problems

Abstract

Geotechnical monitoring data (e.g., settlement monitoring data) are often sparsely measured at limited locations, but the corresponding geotechnical quantities of interest (e.g., ground settlement) usually vary in both temporal and spatial dimensions. The sparsely measured monitoring data can be efficiently leveraged under a sparse dictionary learning (SDL) framework, which represents a spatio-temporally varying quantity (e.g., settlement) by a weighted summation of dictionary atoms. However, selection of dictionary atoms in SDL greatly affects the SDL performance, and under-fitting or over-fitting problems are frequently encountered, particularly when dealing with limited monitoring data. To tackle these problems, a knee point-based method is proposed in this study to properly select dictionary atoms for optimizing the SDL performance. The proposed method not only automatically determines dictionary atom IDs and weights, but also strikes a balance between the under-fitting and over-fitting. The proposed approach is illustrated using a real case history of embankments constructed on soft clay in Australia. The proposed approach significantly improves the prediction of time-varying settlements that also spatially vary over a two-dimensional (2D) space (e.g., a vertical cross-section), particularly at subsequent time steps and spatial locations without monitoring data. Effects of the dictionary atom quantity on settlement predictions are also investigated.