Rapid and Accurate Fault Detection for Uncertain Nonlinear Systems Using Advanced Set-Based State Estimation Techniques

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Yang, Xuejiao
Scott, Joseph K.
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In applications such as wind energy, industrial robotics, and chemical processing, increases in complexity and automation have made component malfunctions and other abnormal events (i.e., faults) an ever-present threat to safety and reliability. Thus, fault detection algorithms have become an essential feature of modern control systems, leading to significant decreases in downtime, maintenance costs, and catastrophic failures. However, while well-established statistical methods are effective in many cases, they often fail to make the critical distinction between faults and normal process disturbances. An attractive alternative is to exploit detailed process models that, at least in principle, can be used to characterize the outputs consistent with normal operation, providing a rigorous basis for fault detection. Methods that furnish a guaranteed enclosure of these outputs (e.g., using set-based state estimators) are particularly attractive because they eliminate the possibility of costly false alarms and provide better trade-offs between false alarms and missed faults. However, such methods are currently impractical for systems with strong nonlinearities or large uncertainties. For such systems, existing set-based estimation techniques often produce enclosures that are far too conservative to be useful for fault detection, or avoid this only at excessive computational cost. Thus, there is a critical need for advanced algorithms that can rapidly detect faults for realistic nonlinear systems, and do so rigorously in the presence of disturbances, measurement noise, and large model uncertainties. In this thesis, we develop an advanced set-based state estimation method for uncertain nonlinear systems, and demonstrate its application to provide fast and accurate fault detection for such systems. Our proposed 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 process 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 continuous-time differential inequalities (DI) method and extends it to discrete-time systems. The DI method uses very efficient interval computations, but is effective at mitigating some key sources of conservatism typically associated with such computations in discrete-time systems by exploiting redundant model equations, which can be easily found in many representative reaction and separation models. Moreover, we make use of past process measurements in a novel way in the prediction step, potentially leading to further improvements in bound accuracy. Our results demonstrate that, for a variety of systems of practical interest, the proposed prediction step in the state estimation algorithm leads to dramatically tighter enclosures of the states, with only modest additional computational cost relative to standard interval methods. Moreover, by combining the proposed correction step with the prediction method, this guaranteed state estimation algorithm largely increases the accuracy of the estimated state sets and is suitable for online applications. The numerical results show that this method produces state estimates with significantly higher accuracy and efficiency than state-of-the-art zonotopic methods for a challenging nonlinear chemical reactor model. Finally, we apply the resulting estimators to achieve significantly faster and more accurate fault detection than is achievable with existing fault detection methods. The proposed approach is demonstrated to achieve high accuracy and eliminate false alarms using a range of examples with comparisons to existing state-of-the-art data-based and model-based fault detection algorithms.
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