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

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.