(588f) An Advanced Set-Based Fault Diagnosis Approach for Uncertain Nonlinear Chemical Systems

Due to the increase of complexity, automation, and integration in chemical processes in recent years, abnormal events like system malfunctions and control errors occur frequently. These events are termed faults. If not dealt with properly, faults are harmful for process economics and safety. To tackle this problem, numerous fault detection and diagnosis (FDD) approaches have been developed. Set-based methods are a particular class of model-based methods that assume the uncertainties (disturbances, measurement noises, etc.) are bounded and can make rigorous guarantees that every alarm is a real fault. Compared with conventional data-driven and observer-based methods, set-based methods offer several potential advantages including the guarantee of zero false alarm rate and robust performance in different fault-free and faulty scenarios [1,2].

Current set-based FDD approaches can be categorized into two main classes. The first class uses set-based observers. At each sampling time, a set-based observer computes a set that contains all possible outputs at the next sampling time that are consistent with the system model, the past measurements, and known bounds on the disturbances and measurement noises. This set is called an output enclosure. For fault detection, this is done with a fault-free process model and a fault is declared if the real output falls outside the enclosure. For fault diagnosis, multiple set-based observers are used for a library of candidate fault models. A candidate model is excluded if the real output falls outside the output enclosure for that model. The current challenge for this class of methods is how to compute output enclosures without introducing too much conservatism. The second class of set-based methods detects and diagnoses faults by solving a series of feasibility optimization problems in a moving horizon framework. A predetermined length is selected for the time window. All system parameters, states, outputs, disturbances, and noises within the given time window are regarded as decision variables, while the system model, past measurements, and uncertainty bounds serve as constraints. Fault detection is done using a fault-free model and a fault is declared if the problem is not feasible. Otherwise, the time window moves one step forward. This is executed iteratively. For fault diagnosis, a library of fault candidate models is again required, and a candidate model is excluded if the problem is infeasible for that model. The limitations of these include high computational cost, the need for long time horizons, and sometimes the need to relax the feasibility problem for easier online solution.

At the 2021 AIChE Meeting, we presented an effective set-based fault detection method using a new set-based observer based on so-called discrete-time differential inequalities (DTDI) [3]. Compared with other set-based observers like the standard interval and zonotopic observers in [4,5,6], the DTDI observer provides output enclosures with significantly less conservatism, and hence detects faults earlier [1]. In this presentation, we extend this method to fault diagnosis. We present a generalization of the DTDI observer with wider applicability [7], a new fault diagnosis algorithm based on this observer, and comparisons with two state-of-the-art feasibility-based fault diagnosis methods [8]. The proposed method is shown to invalidate inconsistent models much more quickly. In addition, the computational time is often tens or hundreds of times shorter than solving feasibility problems, making it more suitable for online application. Finally, our results suggest several important directions for improvements in future research.

References Cited

[1] https://aiche.confex.com/aiche/2021/meetingapp.cgi/Paper/627905

[2] Yang, X., Doctoral dissertation, Georgia Institute of Technology (2020).

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

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

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

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

[7] Mu, B., Yang, X., and Scott, J. K., 2021 Proc. Am. Control Conf., pp. 3664-3669 (2021).

[8] Rumschinski, P., Richter, J., Savchenko, A., et al., IFAC Proc., 43(5): 127-132 (2010).