Sparse and Time-Varying Predictive Relation Extraction for Root Cause Quantification of Nonstationary Process Faults

Abstract

Root cause diagnosis (RCD) is an important technique for maintaining process safety, which infers the causalities between faulty measurements to locate the root cause of the fault. However, process nonstationarity brings time-varying data properties, preventing RCD models from accurately revealing causality. Although existing models can capture time-varying predictive relations among nonstationary variables to characterize causalities, they cannot apply nonsmooth sparsity constraints to the variable selection during parameter updating, leading to redundancy relations. To overcome this challenge, a novel sparse and time-varying predictive relation extraction method is proposed for the RCD of nonstationary processes. First, a time-varying causal matrix is constructed to guide information fusion among variables in the prediction task under sparsity constraints, thus capturing significant causal dependencies. Second, a novel parameter updating algorithm enhanced by the Taylor expansion and subgradient techniques is designed for the causal matrix. Theoretical verification shows that the designed algorithm can obtain sparse and closed-form solutions, overcoming the non-smoothness challenge and ensuring the causal significance. Finally, a causal stability metric is developed to screen reliable causalities from time-varying relations, further eliminating redundant causalities by considering both average strength and variability information. The validity of the proposed method is illustrated through both the Tennessee Eastman benchmark example and a real industrial process.