Addressing Heterogeneous Time-Frequency Causality: Source Consistency Exploring for Industrial Root Cause Alignment and Diagnosis

Process variables may exhibit both temporal trends and periodic responses, with their fault propagation pathways manifesting in time-domain and frequency-domain causalities, respectively. However, the differing causal perspectives of time-domain and frequency-domain methods can lead to distinct causalities, posing the causal heterogeneity challenge for root cause diagnosis (RCD). Thereupon, we reveal the mechanism of source consistency in Granger causality (GC), that is, the root cause variable provides the most significant predictive information in both time and frequency domains. Accordingly, we propose a causal source consistency analytics (CSCA) framework that achieves time-frequency synergy. First, we design a nonlinear enhancement module to extract temporal features for causal inference. Second, to extract time-domain and frequency-domain GC, we develop a parallel causality learning module, where a differentiable frequency-domain expansion operator is designed along with a temporal prediction submodule. Meanwhile, a time-frequency entropy constraint is constructed to ensure causal significance by inducing sparsity. Finally, a root cause alignment module is proposed to ensure source consistency. A predictive information quantification algorithm, formulated as an eigenvalue decomposition problem, is designed to locate the root cause. We develop an approximate exponential transformation to convert the eigenvalue decomposition into a differentiable source alignment loss. Thus, source consistency can be ensured during end-to-end inference. The validity of CSCA is illustrated through the Tennessee Eastman process and a gas turbine application. CSCA identified the root causes in both examples correctly. Furthermore, ablation studies validate that CSCA enables the time-domain and frequency-domain models to identify consistent root causes, thereby overcoming causal heterogeneity.