(284h) Rapid and Accurate Fault Detection and Diagnosis for Uncertain Nonlinear Systems Using Advanced Set-Based State Estimation Techniques

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 and diagnosis (FDD) 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 FDD. 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 can even guarantee FDD for certain faults using active inputs (i.e., excitations). However, such methods are currently impractical for systems with strong nonlinearites or large uncertainties. For such systems, existing set-based estimation techniques often produce enclosures that are far too conservative to be useful for FDD, or avoid this only at excessive computational cost. Thus, there is a critical need for advanced algorithms that can rapidly detect and diagnose faults for realistic nonlinear systems, and do so rigorously in the presence of disturbances, measurement noise, and large model uncertainties.

In this contribution, we will present recent advances in set-based state estimation for uncertain nonlinear systems, and demonstrate their application to provide fast and accurate fault detection and diagnosis for such systems. Specifically, these advances are based on a powerful new method for enclosing the reachable sets of nonlinear systems recently developed by the authors. This algorithm achieves high efficiency (necessary for online implementation) by using simple interval enclosures, but overcomes the high conservatism typically associated with interval methods using a technique called the addition of states and invariants (ASI). In ASI, additional state variables are defined as certain linear or nonlinear combinations of the original states, and the original dynamics are augmented with additional differential or difference equations for these new states. By construction, the states of this augmented system satisfy a set of linear or nonlinear equality constraints at all times, called solution invariants. The key idea is then to compute an enclosure of the solutions of the augmented system at each time step using a cheap (and often conservative) interval method, and subsequently refine this enclosure using the solution invariants. Our recent results demonstrate that, for very many systems of practical interest, there exist choices of new state variables that lead to dramatically tighter enclosures of the reachable set through ASI, with only modest additional computational cost relative to standard interval methods. This contribution will discuss a preliminary extension of this technique to set-based state estimation rather than reachability analysis (the former incorporates process measurements), and the application of the resulting estimators to achieve significantly faster and more accurate fault detection and diagnosis than is achievable with existing set-based methods. The proposed approach will be demonstrated using two CSTR and batch reactor case studies (and potentially others), and compared with existing state-of-the-art set-based FDD algorithms based on more complex zonotopic and polytopic set enclosures.