Comparison of Advanced Set-Based Fault Detection Methods with Classical Data-Driven and Observer-Based Methods for Nonlinear and Uncertain Chemical Processes

Abnormal events in chemical processes can cause significant safety, economic and environmental problems. Faults like equipment malfunctions are quite common and cost society billions of dollars each year [1]. Therefore, there is a strong need for fault detection and diagnosis (FDD) methods with the ability to detect faults early and accurately. Classical data-driven methods such as those based on principle component analysis (PCA) are relatively easy to implement in large-scale processes and are effective in many cases. However, such approaches are highly dependent on the quantity and quality of the available historical data. For example, operating at points that are even slightly different than the operating point of the historical data can lead to frequent false alarms, and first-of-kind faults that are not represented in the historical data may not be detected effectively. In contrast, observer-based methods aim to overcome these limitations by incorporating a detailed mathematical process model. These methods generate residuals based on the difference between model predictions and measurements, and then apply them for fault detection. However, it is difficult to set residual thresholds that effectively differentiate faults from disturbances. In principle, this issue is addressed by set-based fault detection methods, which compute an enclosure of all possible states consistent with the process model, past measurements, and bounded set of admissible disturbances, and detect a fault whenever a measurement lies outside this set. This eliminates the possibility of false alarms. However, if the computed enclosures are too conservative, then faults often go undetected. Although numerous papers have presented set-based fault detection methods and established attractive theoretical properties, very few comparisons between set-based methods and more conventional data-driven and observer-based methods have ever been published.

In this poster, we will provide a comprehensive comparison of advanced set-based fault detection methods with conventional methods using several nonlinear chemical process models with large uncertainties. Specifically, methods based on PCA [2] and the extended Kalman filter (EKF) [3] are selected as representatives of the current state-of-practice in data-driven and observer-based fault detection, respectively. Multiple set-based methods based on interval arithmetic, zonotopes [4,5], and differential inequalities (DI) [6] are compared. For each example, several key performance metrics are compared, including the frequency of false alarms in fault-free scenarios and detection speed and missed faults in faulty scenarios. Our results indicate that set-based methods have a major advantage in terms of false alarms. However, most set-based methods suffer from conservative enclosures for nonlinear systems, leading to low fault sensitivity (i.e., missed faults or slow detection). In contrast, recently developed set-based methods using DI do provide accurate enclosures for many problems, and as a result offer a significantly better trade-off between false alarms and fault sensitivity than conventional methods.

References Cited

[1] Venkatasubramanian, V., et al., “A Review of Process Fault Detection and Diagnosis: Part I: Quantitative Model-based Methods,” Computers & Chemical Engineering, 27, pp. 293–311 (2003).

[2] Qin, J., “Statistical Process Monitoring: Basics and Beyond,” Journal of Chemometrics, 17, pp. 480–502 (2003).

[3] Fathi, Z., et al., “Analytical and Knowledge-Based Redundancy for Fault Diagnosis in Process Plants,” AIChE Journal, 26, pp. 42–56 (1993)

[4] Combastel, C., “A State Bounding Observer for Uncertain Non-linear Continuous-time Systems based on Zonotopes,” Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, pp. 7228–7234 (2005).

[5] Alamo, T., et al., “Guaranteed State Estimation by Zonotopes,” Automatica, 41, pp. 1035–1043 (2005).

[6] Yang, X. and Scott, J. K., “Efficient Reachability Bounds for Discrete-Time Nonlinear Systems by Extending the Continuous-Time Theory of Differential Inequalities," presented at the 2018 Annual American Control Conference (ACC), Milwaukee, WI, pp. 6242–6247 (2018).