(16c) Fault Detection in Uncertain Nonlinear Chemical Systems: A Comparison of Advanced Set-Based Methods with Conventional Data-Driven and Observer-Based Methods

Modern chemical plants suffer from frequent component malfunctions, control system errors, and other abnormal events, collectively termed faults. When faults are not quickly detected and addressed, they can have serious deleterious effects on process economics, emissions, and safety. To address this challenge, many researchers are pursuing fault detection methods with the ability to detect faults early and accurately. Within this broad literature, at least three distinct approaches have been developed based on quite different ideas. We refer to these as the data-driven methods, observer-based methods, and set-based methods, as described in more detail below. Although each of these approaches has distinct advantages and disadvantages, there are very few published comparisons of these different paradigms. In this talk, we will present a comprehensive comparison of representative methods from these three categories for several challenging examples of nonlinear and uncertain chemical processes.

Data-driven fault detection methods, which have been widely implemented in large-scale industrial processes, work by comparing measured plant data with historical datasets in real time. A fault is indicated whenever the current data is inconsistent with the historical data as measured by certain statistical tests. While these methods are simple and broadly applicable, they require a large amount of historical data, and may suffer from frequent false alarms if the current operating point differs from the operating points represented in historical data. In contrast, observer-based methods use a detailed mathematical model of the system rather than using historical data, and indicate a fault whenever the difference between the model predictions and measurements exceeds an empirical threshold. Using a model eliminates many of the difficulties caused by using insufficient or inappropriate historical data. However, both data-driven and observer-based methods often struggle to effectively distinguish faults from disturbances, primarily because both depend on empirical thresholds that are difficult to tune. This issue is rigorously addressed by set-based fault detection methods. In these methods, all disturbances and measurement noises are assumed to be bounded within compact sets. Then, set-based arithmetics are used to compute an enclosure of all possible measurements consistent with the system model, the past measurements, and the disturbances and measurement noises each step. A fault is indicated whenever a real measurement lies outside this set. These methods guarantee zero false alarm rates, but they often fail to detect faults quickly or at all if the computed enclosures are too conservative.

In this presentation, we select a representative data-driven method based on principle component analysis (PCA) [1] and a representative observer-based method based on the extended Kalman filter (EKF) [2] and compare them against different set-based fault detection methods for several simulated nonlinear chemical systems under uncertainty. The compared set-based methods include a standard interval method [3], two methods based on zonotopic enclosures [4,5], and a recent method developed in our research group based on discrete-time differential inequalities (DI) [6]. To the best of our knowledge, no comprehensive comparison between these three distinct approaches has previously been presented. The performance of these methods is compared in several fault-free and faulty scenarios and quantified in terms of false alarm rate, detection speed, missed fault rate, and robustness to different uncertainty distributions. Our results elucidate several key advantages and disadvantages of each method and have clear implications for when and why each class of method should be applied. In particular, we demonstrate that recent advances in set-based methods have made this approach competitive with, and in some respects superior to, the classical data-driven and observer-based approaches. Moreover, our results suggest several important areas of future research that could address key limitations of methods in each category.

References Cited

[1] Qin, J., J. Chemom, 17, pp. 480–502 (2003).

[2] Fathi, Z., et al., AIChE J., 26, pp. 42–56 (1993)

[3] Moore E., et al., SIAM, (2009)

[4] Combastel, C., Proc. IEEE Conf. Decis. Control, pp. 7228–7234 (2005).

[5] Alamo, T., et al., Automatica, 41, pp. 1035–1043 (2005).

[6] Yang, X. and Scott, J. K., 2018 Conf. Decis. Control, pp. 680-685 (2018).