Constrained Kalman Filtering via Density Function Truncation for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This article develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the probability density function (PDF) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but also improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. It is also shown that the truncated Kalman filter may provide a more accurate way of incorporating inequality constraints than other constrained filters (e.g. the projection approach to constrained filtering)

Gas turbine aero-engines real time on-board modelling: A review, research challenges, and exploring the future

On-board real time modelling for gas turbine aero-engines has been extensively used for engine performance improvement and reliability. This has been achieved by the utilization of on-board model for the engine's control and health management. This paper offers a historical review of on-board modelling applied on gas turbine engines and it also establishes its limitations, and consequently the challenges, which should be addressed to apply the on-board real time model to new and the next generation gas turbine aero-engines. For both applications, i.e. engine control and health management, claims and limitations are analysed via numerical simulation and publicly available data. Regarding the former, the methods for modelling clean and degraded engines are comprehensively covered. For the latter, the techniques for the component performance tracking and sensor/actuator diagnosis are critically reviewed. As an outcome of this systematic examination, two remaining research challenges have been identified: firstly, the requirement of a high-fidelity on-board modelling over the engine life cycle, especially for safety-critical control parameters during rapid transients; secondly, the dependability and reliability of on-board model, which is critical for the engine protection in case of on-board model failure. Multiple model-based on-board modelling and runtime assurance are proposed as potential solutions for the identified challenges and their potential and effectiveness are discussed in detail

Kalman Filter Constraint Switching for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints has been shown to generally improve the filter’s estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy. After all, the Kalman filter is theoretically optimal, so the incorporation of heuristic constraints may degrade the optimality of the filter. This paper proposes a way to switch the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high