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Root cause diagnosis of process industry is of significance to ensure safe production and improve production efficiency. Conventional contribution plot methods have challenges in root cause diagnosis due to the smearing effect. Other traditional root cause diagnosis methods, such as Granger causality (GC) and transfer entropy, have unsatisfactory performance in root cause diagnosis for complex industrial processes due to the existence of indirect causality. In this work, a regularization and partial cross mapping (PCM)-based root cause diagnosis framework is proposed for efficient direct causality inference and fault propagation path tracing. First, generalized Lasso-based variable selection is performed. The Hotelling $T^{2}$ statistic is formulated and the Lasso-based fault reconstruction is applied to select candidate root cause variables. Second, the root cause is diagnosed through the PCM and the propagation path is drawn out according to the diagnosis result. The proposed framework is studied in four cases to verify its rationality and effectiveness, including a numerical example, the Tennessee Eastman benchmark process, the wastewater treatment process (WWTP), and the decarburization process of high-speed wire rod spring steel.

Process monitoring and fault root cause analysis of industrial processes play a critical role to inform timely maintenance and ensure safe production. Existing distributed monitoring frameworks are able to determine the fault occurrence units, but often fall short on fault causality analysis for deeper insights. Therefore, it is necessary to conduct further analysis on variable correlations to locate the fault variable. Conventional fault root cause analysis methods, such as Granger causality and transfer entropy, ignore the distinction between indirect and direct causations between variables, resulting in unsatisfactory results of fault root cause analysis. Therefore, this article proposes a distributed process monitoring and fault root cause analysis framework via direct causality analysis based on partial cross mapping (PCM). First, fault units are located through distributed process monitoring. Then, PCM is used to locate the root cause variables hierarchically. This framework makes full use of the fault unit information obtained by a distributed monitoring method so that the number of variables for causality analysis is reduced, which increases computational efficiency as well as accuracy of the PCM method. The validity of the proposed framework is verified on the Tennessee–Eastman process and a wastewater treatment process.