(456g) An Improved Set-Based State Estimation Method for Fault Detection and Diagnosis in Highly Nonlinear and Uncertain Chemical Processes

Due to the level complexity, integration, and automation in modern chemical processes, abnormal events such as equipment malfunctions and failures pose a serious threat to safe and profitable operation. Therefore, there is an urgent need for algorithms that can achieve early and accurate fault detection and diagnosis (FDD), which can effectively mitigate the safety risks associated with abnormal operations, as well as the associated economic losses caused by off-spec production, maintenance, and downtime. Classical data-based FDD methods have proven to be effective in many industrial chemical processes. However, the lack of high quality historical data that is relevant to current operating conditions (e.g., under a novel fault or abnormal disturbance) often leads to false alarms, missed faults, and misdiagnoses. This is a significant limitation, especially for systems with large uncertainties. A promising alternative is to exploit first principles process models, which are available at least at the level of individual process units and subsystems in many applications of interest. In the model-based approach, faults are detected and diagnosed by comparing the set of process outputs that are consistent with the model (under all relevant uncertainties) to the outputs observed from the real process. This talk specifically considers the set-based FDD approach, where this comparison is done using rigorous enclosures of the possible model outputs computed through a set-based state estimation method. The set-based approach is advantageous because it eliminates the possibility of false alarms and can even guarantee the detection of certain faults using active excitations. However, existing set-based estimation methods are either too computationally demanding for online FDD or produce bounds that are too conservative for effective FDD, especially for highly nonlinear and uncertain systems.

In this talk, we will present an improved set-based state estimation method for nonlinear discrete-time systems with large uncertainties. This method extends a novel reachability analysis algorithm based on discrete-time differential inequalities that we presented in last year's AIChE meeting. Our estimation method is performed recursively in two steps. First, the prediction step computes an enclosure of the possible model outputs under uncertainty over one discrete time step. Next, the correction step uses the processes measurements to update this enclosure by eliminating regions that are not consistent with the measurements. In contrast to existing set-based estimation methods, our prediction step makes use of our previously developed discrete-time differential inequalities method, which uses very efficient interval computations, but is effective at mitigating some key sources of conservatism typically associated with such computations in discrete-time systems. This approach also enables the use of redundant model equations to tighten the prediction bounds, which is not possible using existing approaches and has been shown to lead to much tighter enclosures for many representative reaction and separation models. Finally, we show that this reachability approach can be modified in the context of set-based state estimation to exploit past process measurement in a novel way even in the prediction step, leading to further improvements in bound accuracy. Numerical examples will be provided demonstrating the effectiveness of this approach for quickly and accurately detecting and diagnosing faults. Moreover, the advantages of our approach will be highlighted through comparisons with existing set-based FDD methods and more conventional data-based approaches.