Lag-Specific Transfer Entropy for Root Cause Diagnosis and Delay Estimation in Industrial Sensor Networks

Chen, Rui; Liang, Shu; Wang, Jian-Guo; Yao, Yuan; Su, Jing-Ru; Liu, Li-Lan

doi:10.3390/s25133980

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Open AccessArticle

Lag-Specific Transfer Entropy for Root Cause Diagnosis and Delay Estimation in Industrial Sensor Networks

by

Rui Chen

¹

,

Shu Liang

¹

,

Jian-Guo Wang

^2,*,

Yuan Yao

^3,*

,

Jing-Ru Su

² and

Li-Lan Liu

²

¹

College of Electronic and Information Engineering, Tongji University, Shanghai 200092, China

²

School of Mechatronical Engineering and Automation, Shanghai University, Shanghai 200072, China

³

Department of Chemical Engineering, National Tsing Hua University, Hsinchu 300044, Taiwan

^*

Authors to whom correspondence should be addressed.

Sensors 2025, 25(13), 3980; https://doi.org/10.3390/s25133980

Submission received: 28 April 2025 / Revised: 17 June 2025 / Accepted: 24 June 2025 / Published: 26 June 2025

(This article belongs to the Special Issue Advances in Sensors for Online Condition Monitoring and Fault Diagnosis)

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Abstract

Industrial plants now stream thousands of temperature, pressure, flow rate, and composition measurements at minute-level intervals. These multi-sensor records often contain variable transport or residence time delays that hinder accurate disturbance analysis. This study applies lag-specific transfer entropy (LSTE) to historical sensor logs to identify the instrument that first deviates from normal operation and the time required for that deviation to appear at downstream points. A self-prediction optimization step removes each sensor’s own information storage, after which LSTE is computed at candidate lags and tested against time-shifted surrogates for statistical significance. The method is benchmarked on a nonlinear simulation, the Tennessee Eastman plant, a three-phase separator test rig, and a full-scale blast furnace line. Across all cases, LSTE locates the disturbance origin and reports propagation times that match known process physics, while significantly reducing false links compared to classical transfer entropy.

Keywords: industrial sensors; lag-specific transfer entropy; root cause diagnosis; time delay; causality analysis

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MDPI and ACS Style

Chen, R.; Liang, S.; Wang, J.-G.; Yao, Y.; Su, J.-R.; Liu, L.-L. Lag-Specific Transfer Entropy for Root Cause Diagnosis and Delay Estimation in Industrial Sensor Networks. Sensors 2025, 25, 3980. https://doi.org/10.3390/s25133980

AMA Style

Chen R, Liang S, Wang J-G, Yao Y, Su J-R, Liu L-L. Lag-Specific Transfer Entropy for Root Cause Diagnosis and Delay Estimation in Industrial Sensor Networks. Sensors. 2025; 25(13):3980. https://doi.org/10.3390/s25133980

Chicago/Turabian Style

Chen, Rui, Shu Liang, Jian-Guo Wang, Yuan Yao, Jing-Ru Su, and Li-Lan Liu. 2025. "Lag-Specific Transfer Entropy for Root Cause Diagnosis and Delay Estimation in Industrial Sensor Networks" Sensors 25, no. 13: 3980. https://doi.org/10.3390/s25133980

APA Style

Chen, R., Liang, S., Wang, J.-G., Yao, Y., Su, J.-R., & Liu, L.-L. (2025). Lag-Specific Transfer Entropy for Root Cause Diagnosis and Delay Estimation in Industrial Sensor Networks. Sensors, 25(13), 3980. https://doi.org/10.3390/s25133980

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Lag-Specific Transfer Entropy for Root Cause Diagnosis and Delay Estimation in Industrial Sensor Networks

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