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Most incidents in complex systems such as process plants are not-chance events and weak signals emerge for a long time before incidents occur. It is necessary to identify and respond to the weak signals as early as possible for preventing incidents. However, in the era of Industry 4.0, recognizing weak signals from the abundance of data is challenging. Since the terminology “weak signal” was not precisely defined, the study first proposed a formal definition of “weak signal” and discussed its characteristics. Additionally, a framework was developed to address the challenges of observing, evaluating, and responding to weak signals in complex systems. The framework first utilized Function Resonance Analysis Method (FRAM) to determine the information to be collected for observing weak signals. Then, the relevance of weak signals and the corresponding responses were evaluated by utilizing Balanced Random Forest (BRF), Weighted Random Forest (WRF) and Decision Tree (DT) classification models. The case study of a hypothetical batch process showed great potentials for applying the framework in real operations. Based on the potential weak signals that were indicated by FRAM, probabilities of temperature deviations in the process were predicted with high accuracy by the optimal BRF model. Underlying weak signals and the corresponding responses to reduce the probabilities were identified from the DT.

This work deals with the problem of designing functional observers for fault diagnosis in nonlinear systems in the presence of noises. It follows up previous work of the authors on design of functional observers (residual generators) for deterministic systems from the point of view of observer error linearization. Here, we consider the effect of noises on residual generation. The effect of sensor noises on the residuals is studied analytically and the associated probability distributions are derived. Following this, a well-known statistical hypothesis testing approach, Generalized Likelihood Ratio, is used to track changes in the mean of the residual to enable robust fault detection. The approach is also extended to process noises (plant-model mismatch) numerically. Throughout the study the methods presented are tested on a non-isothermal CSTR case study. The results show that the fault diagnosis scheme is able to quickly and accurately detect faults in the presence of both sensor and process noises.

Hazardous scenarios emerging from complex system where number of functions are large and corresponding function coupling are humongous, are very difficult if not impossible to identify humanly. Today’s complex systems generate a very large dataset every minute and dynamic nature of the generated data makes it difficult to track such couplings. The Functional Resonance Analysis Method (FRAM) got success in recent years to understand hazards emerging from function couplings in complex systems, however, challenges remain to estimate aggregated couplings appropriately without quantitative analysis. The current study developed a data-driven approach to quantify function couplings using lift confidence intervals of association rules. Later, association rules were merged to identify the paths leading to a potential hazardous scenario. The paths were presented graphically and equipped with quantified coupling information and capable of providing guidance to prevent the emerging hazard scenario. The approach has been demonstrated with a case study of a polymerization process in process industry for which function couplings are represented by a very large dataset.