Multiscale Partial Symbolic Transfer Entropy for Time-Delay Root Cause Diagnosis in Nonstationary Industrial Processes

Nonstationary characteristics and lack of time delays analysis remain two large obstacles to diagnosing fault root cause in industrial processes. However, ignoring these two issues, many traditional methods tend to introduce some spurious or indirect causal relationships that interfere with root cause judgments. In this article, multiscale partial symbolic transfer entropy (MPSTE) is proposed to handle the above-mentioned problems. On the one hand, a multivariate multiscale filter module of MPSTE is designed to estimate the information transfer on multiple time scales and detect time delays while considering the indirect causality of the multivariate industrial system. On the other hand, to capture the causal information from the nonstationary processes, MPSTE introduces a segmental symbolization procedure and maps time series into finite rank vectors, overcoming the limitation of stationarity. Moreover, two causal criteria for MPSTE are constructed to identify the direction and significance level of causality correspondingly. MPSTE can thus provide sufficient information for causal relationships and exclude spurious causality. Finally, a causal diagram construction strategy with time delay based on MPSTE is established to diagnose the root cause and trace the fault propagation path. The results of experimental verification in a coal mill rig prove the effectiveness of the proposed strategy.