Fault diagnostics study for linear uncertain systems using dynamic threshold with application to propulsion system

Fault detection and isolation plays a critical role in aircraft engines and the performance of their control systems. A great amount of research on model-based fault detection and isolation of aircraft engines has been studied since the 1970s. Model-based fault detection and isolation methods rely on the accuracy of the model. Model uncertainty, disturbances and noise, etc., all have a great impact on the fault detection and isolation design results. A challenge in the fault detection applications is the design of a scheme which can distinguish between model uncertainties, disturbances and the occurrence of faults. Most of the current approaches use a constant detection threshold. Currently, there are no useful guidelines for constant optimal threshold selection. In the absence of faults, a predetermined constant threshold would lead to more false alarms and missed detections under modeling uncertainties. Hence a technique to accommodate uncertainties and disturbances in the model, help in reducing false alarms and missed detections is essential for the enhancement of aircraft engine operations. In this work, a dynamic threshold algorithm is developed for aircraft engine fault detection and isolation that accommodates parametric uncertainties and disturbances. The algorithm takes the parametric uncertainties into consideration and proposes a dynamic threshold that makes use of the bounds on the parametric uncertainties which can thus distinguish an actual fault from the model uncertainties. First we design Kalman filters or unknown input observers based on the linearized engine model about a given nominal operating point, but the filters or observers use the measurements from the nonlinear engine model which includes uncertainty description. Using the robustness analysis of parametric uncertain systems, we generate upper-bound and lower-bound time response trajectories of the dynamic threshold. The extent of parametric uncertainties is assumed to be such that the perturbed eigenvalues reside in a set of distinct circular regions. A set of "structured" Kalman filters or unknown input observers are used for engine sensor or actuator fault diagnosis design. The residuals are errors between measured outputs and estimated outputs from a set of Kalman filters or a set of unknown input observers. With the dynamic threshold design approach, the residual crossing the upper bound or lower bound of the dynamic threshold indicates the occurrence of fault. Application to an aircraft turbofan engine model illustrates the performance of the proposed method.