Abstract

This thesis contributes and provides solutions to the problem of fault diagnosis and estimation from three different perspectives which are i) fault diagnosis of nonlinear systems using nonlinear multiple model approach, ii) inversion-based fault estimation in linear systems, and iii) data-driven fault diagnosis and estimation in linear systems. The above contributions have been demonstrated to the gas turbines as one of the most important engineering systems in the power and aerospace industries.


The proposed multiple model approach is essentially a hierarchy of nonlinear Kalman filters utilized as detection filters. A nonlinear mathematical model for a gas turbines is developed and verified. The fault vector is defined using the Gas Path Analysis approach. The nonlinear Kalman filters that correspond to the defined single or concurrent fault modes provide the conditional probabilities associated with each fault mode using the Bayes' law. The current fault mode is then determined based on the maximum probability criteria. The performance of both Extended Kalman Filters (EKF) and Unscented Kalman Filters (UKF) are investigated and compared which demonstrates that the UKF outperforms the EKF for this particular application.

The problem of fault estimation is increasingly receiving more attention due to its practical importance. Fault estimation is closely related to the problem of linear systems inversion. This thesis includes two contributions for the stable inversion of non-minimum phase systems. First, a novel methodology is proposed for direct estimation of unknown inputs by using only measurements of either minimum or non-minimum phase systems as well as systems with transmission zeros on the unit circle. A dynamic filter is then identified whose poles coincide with the transmission zeros of the system. A feedback is then introduced to stabilize the above filter dynamics as well as provide an unbiased estimation of the unknown input. The methodology is then applied to the problem of fault estimation and has been shown that the proposed inversion filter is unbiased for certain categories of faults. Second, a solution for unbiased reconstruction of general inputs is proposed. It is based on designing an unknown input observer (UIO) that provides unbiased estimation of the minimum phase states of the system. The reconstructed minimum phase states serve then as inputs for reconstruction of the non-minimum phase states. The reconstruction error for non-minimum phase states exponentially decrease as the estimation delay is increased. Therefore, an almost perfect reconstruction can be achieved by selecting the delay to be sufficiently large. The proposed inversion scheme is then applied to the output-tracking control problem.

An important practical challenge is the fact that engineers rarely have a detailed and accurate mathematical model of complex engineering systems such as gas turbines. Consequently, one can find a trend towards data-driven approaches in many disciplines, including fault diagnosis. In this thesis, explicit state-space based fault detection, isolation and estimation filters are proposed that are directly identified from only the system input-output (I/O) measurements and through the system Markov parameters. The proposed procedures do not involve a reduction step and do not require identification of the system extended observability matrix or its left null space. Therefore, the performance of the proposed filters is directly connected to and linearly dependent on the errors in the Markov parameters estimation process. The estimation error dynamics is then derived in terms of the Markov parameters identification errors and directly synthesized from the healthy system I/O data. Consequently, the estimation errors have been effectively compensated for. The proposed data-driven scheme requires the persistently exciting condition for healthy input data which is not practical for certain real life applications and in particular to gas turbine engines. To address this issue, a robust methodology for Markov parameters estimation using frequency response data is developed. Finally, the performance of the proposed data-driven approach is comprehensively evaluated for the fault diagnosis and estimation problems in the gas turbine engines.