🤖 AI Summary
This study addresses the limitations of existing causal feature selection methods, which often neglect time delays and dynamic dependencies among variables in industrial processes, leading to insufficient accuracy and robustness in soft sensor models. To overcome this, we propose a delay-aware causal feature selection framework based on time-delayed cross-mapping. By reconstructing state spaces to capture lagged interdependencies, the framework introduces Time-Delayed Convergent Cross-Mapping (TDCCM) and Time-Delayed Partial Cross-Mapping (TDPCM) for inferring overall and direct causal relationships, respectively. An adaptive strategy is further developed to automatically determine causal thresholds based on validation set performance, enabling data-driven feature selection. Evaluated on two real-world industrial datasets, the proposed approach significantly improves prediction accuracy, with TDCC