Causal feature selection framework for stable soft sensor modeling based on time-delayed cross mapping

📅 2026-01-20
🏛️ Advanced Engineering Informatics
📈 Citations: 0
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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

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Problem

Research questions and friction points this paper is trying to address.

causal feature selection
soft sensor modeling
time delay
interdependent variables
causal inference
Innovation

Methods, ideas, or system contributions that make the work stand out.

time-delayed cross mapping
causal feature selection
soft sensor modeling
convergent cross mapping
partial cross mapping
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Shi-Shun Chen
School of Reliability and Systems Engineering, Beihang University, Beijing, China
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Xiao-Yang Li
School of Reliability and Systems Engineering, Beihang University, Beijing, China
Enrico Zio
Enrico Zio
Professor Mines Paris/PSL and Politecnico di. Milano
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