Dynamic threshold generators for robust fault detection

Abstract: Detection of faults, such as clogged valves, broken bearings or biased sensors, has been brought more and more into focus during the last few decades. There are two main reasons why faults are important to detect at an early stage. Firstly, faults in safety critical applications, such as aircraft, nuclear reactors, cars and trains, may create risks of personal injuries. Secondly, faults in the manufacturing or process industry, e.g. flotation processes and steel plants, may cause decrease in quality or interruptions of production. A fault detection algorithm consists of two parts, the residual generator, which generates a residual, and the residual evaluator, which compares the residual, or a function of it, with a threshold to determine if a fault is present. The residual generation contains a process model and the residual can be described as a filtered difference between the measured and estimated process outputs. When no fault is present, the residual will be nonzero due to residual disturbances, i.e. measurement disturbances, process disturbances and model uncertainties. Therefore, the residual evaluation must be robust against these disturbances to avoid false alarms. Due to the model uncertainties, the residual is affected by the known input signals, which are, in general, time varying. To achieve a threshold that is as tight to the residual as possible, the threshold should also depend on the known input signals. To make this possible, parametric uncertainty in the process model is considered in this thesis. The dynamic threshold generator is introduced, a dynamic system whose output is the threshold and the inputs are the known process inputs. A dynamic threshold generator is developed for full-state measurement systems, assuming that the residual disturbances are constant and unknown but bounded. This dynamic threshold generator is then generalized to non-full state measurement systems with time-varying but bounded residual disturbances. Both generators depend on the unknown upper bounds of the residual disturbances. These upper bounds are replaced by design parameters, which are determined by minimizing the threshold for a set of fault free data. A nonlinear optimization solution is discussed. It is also shown that the residual generator state vector can always be parameterized such that the designing of the parameters can be done by linear optimization. A part of the generalized dynamic threshold generator is a system whose impulse response is an upper bound to another impulse response. Automatic methods to find realizable upper bounds are derived. To validate the methods in this thesis, two applications have been considered, detection of clogging in the valves of a flotation process and detection of faults in the compressor inlet temperature sensor of a jet engine.