Source-Invariant Ordinal Label Distribution Learning for Heterogeneous Rockburst Intensity Prediction

Abstract

Rockburst intensity prediction is commonly formulated as a hard-label classification problem, although rockburst grades are ordered, transitional, and often ambiguous under sparse geomechanical indicators. This study integrates three publicly available datasets to construct a 761-sample heterogeneous rockburst database using three common predictors: Stress Coefficient (SC), Brittleness Coefficient (BC), and Elastic Energy Index (EEI). Diagnostic analysis shows substantial adjacent-grade overlap and source-dependent feature shifts, indicating that conventional one-hot labels and random validation may be insufficient for robust intensity assessment. To address these issues, a Source-Invariant Ordinal Label Distribution Learning (SI-OLDL) framework is proposed. The framework generates neighborhood-adaptive ordinal soft labels to represent local grade ambiguity and introduces a source-confusion branch to reduce source-specific bias during training. Under repeated stratified random validation, SI-OLDL achieved an accuracy of 0.821 and a Macro-F1 of 0.824, showing performance comparable to XGBoost, which achieved 0.819 and 0.823, respectively. Under leave-one-source-out validation, SI-OLDL showed more favorable average cross-source ordinal performance within the tested benchmark, with a Macro-F1 of 0.856 and a severe misclassification rate of 0.020. These results suggest that modeling rockburst intensity as an ordinal risk distribution is a useful representation strategy for heterogeneous small-sample rockburst databases, while independent external validation remains necessary before broader engineering deployment.