Khashayar Khorasani

Esmaeil Naderi, Khashayar Khorasani

In this work, we propose explicit state-space based fault detection, isolation and estimation filters that are data-driven and are directly identified and constructed from only the system input-output (I/O) measurements and through estimating the system Markov parameters. The proposed methodology does not involve a reduction step and does not require identification of the system extended observability matrix or its left null space. The performance of our proposed filters is directly connected to and linearly dependent on the errors in the Markov parameters identification process. The estimation filters operate with a subset of the system I/O data that is selected by the designer. It is shown that the proposed filters provide asymptotically unbiased estimates by invoking low order filters as long as the selected subsystem has a stable inverse. We have derived the estimation error dynamics in terms of the Markov parameters identification errors and have shown that they can be directly synthesized from the healthy system I/O data. Consequently, the estimation errors can be effectively compensated for. Finally, we have provided several illustrative case study simulations that demonstrate and confirm the merits of our proposed schemes as compared to methodologies that are available in the literature.

Zahra Gallehdari, Nader Meskin, Khashayar Khorasani

In this work, an $H_{\infty}$ performance fault recovery control problem for a team of multi-agent systems that is subject to actuator faults is studied. Our main objective is to design a distributed control reconfiguration strategy such that \textbf{a)} in absence of disturbances the state consensus errors either remain bounded or converge to zero asymptotically, \textbf{b)} in presence of actuator fault the output of the faulty system behaves exactly the same as that of the healthy system, and \textbf{c)} the specified $H_{\infty}$ performance bound is guaranteed to be minimized in presence of bounded energy disturbances. The gains of the reconfigured control laws are selected first by employing a geometric approach where a set of controllers guarantees that the output of the faulty agent imitates that of the healthy agent and the consensus achievement objectives are satisfied. Next, the remaining degrees of freedom in the selection of the control law gains are used to minimize the bound on a specified $H_{\infty}$ performance index. The effects of uncertainties and imperfections in the FDI module decision in correctly estimating the fault severity as well as delays in invoking the reconfigured control laws are investigated and a bound on the maximum tolerable estimation uncertainties and time delays are obtained. Our proposed distributed and cooperative control recovery approach is applied to a team of five autonomous underwater vehicles to demonstrate its capabilities and effectiveness in accomplishing the overall team requirements subject to various actuator faults, delays in invoking the recovery control, fault estimation and isolation imperfections and unreliabilities under different control recovery scenarios.

Najmeh Daroogheh, Nader Meskin, Khashayar Khorasani

In this paper, we propose and develop a methodology for nonlinear systems health monitoring by modeling the damage and degradation mechanism dynamics as "slow" states that are augmented with the system "fast" dynamical states. This augmentation results in a two-time scale nonlinear system that is utilized for development of health estimation and prediction modules within a health monitoring framework. Towards this end, a two-time scale filtering approach is developed based on the ensemble Kalman filtering (EnKF) approach by taking advantage of the model reduction concept. The performance of our proposed two-time scale ensemble Kalman filters is shown to be superior and less computationally intensive in terms of the equivalent flop (EF) complexity metric when compared to well-known particle filtering (PF) approaches. Our proposed methodology is then applied to a gas turbine engine that is affected by erosion of the turbine as the degradation phenomenon and damage mechanism. Extensive comparative studies are conducted to validate and demonstrate the advantages and capabilities of our proposed framework and methodology.

Esmaeil Naderi, Khashayar Khorasani

We propose a framework for inversion-based estimation of certain categories of faults in discrete-time linear systems. The fault signal, as an unknown input, is reconstructed from its projections onto two subspaces. One projection is achieved through an algebraic operation, whereas the other is given by a dynamic filter whose poles coincide with the transmission zeros of the system. A feedback is then introduced to stabilize the above filter as well as to provide an unbiased estimate of the unknown input. Our solution has two distinctive and practical advantages. First, it represents a unified approach to the problem of inversion of both minimum and non-minimum phase systems as well as systems having transmission zeros on the unit circle. Second, the feedback structure makes the proposed scheme robust to noise. We have shown that the proposed inversion filter is unbiased for certain categories of faults. Finally, we have illustrated the performance of our proposed methodologies through numerous simulation studies.

Najmeh Daroogheh, Nader Meskin, Khashayar Khorasani

In this paper, a dual estimation methodology is developed for both time-varying parameters and states of a nonlinear stochastic system based on the Particle Filtering (PF) scheme. Our developed methodology is based on a concurrent implementation of state and parameter estimation filters as opposed to using a single filter for simultaneously estimating the augmented states and parameters. The convergence and stability of our proposed dual estimation strategy are shown formally to be guaranteed under certain conditions. The ability of our developed dual estimation method is testified to handle simultaneously and efficiently the states and time-varying parameters of a nonlinear system in a context of health monitoring which employs a unified approach to fault detection, isolation and identification is a single algorithm. The performance capabilities of our proposed fault diagnosis methodology is demonstrated and evaluated by its application to a gas turbine engine through accomplishing state and parameter estimation under simultaneous and concurrent component fault scenarios. Extensive simulation results are provided to substantiate and justify the superiority of our proposed fault diagnosis methodology when compared with another well-known alternative diagnostic technique that is available in the literature.

Esmaeil Naderi, Khashayar Khorasani

In this paper, we propose a framework for output tracking control of both minimum phase (MP) and non-minimum phase (NMP) systems {as well as systems with transmission zeros on the unit circle}. Towards this end, we first address the problem of unknown state and input reconstruction of non-minimum phase systems. An unknown input observer (UIO) is designed that accurately reconstructs the minimum phase states of the system. The reconstructed minimum phase states serve as inputs to an FIR filter for a delayed non-minimum phase state reconstruction. It is shown that a quantified upper bound of the reconstruction error exponentially decreases as the estimation delay is increased. Therefore, an almost perfect reconstruction can be achieved by selecting the delay to be sufficiently large. Our proposed inversion scheme is then applied to solve the output-tracking control problem. {We have also proposed a methodology to handle the output tracking problem of systems that have transmission zeros on the unit circle in addition to MP and NMP zeros.} Simulation case studies are also presented that demonstrate the merits and capabilities of our proposed methodologies.

Amir Baniamerian, Nader Meskin, Khashayar Khorasani

In this work, we develop a novel fault detection and isolation (FDI) scheme for discrete-time two-dimensional (2D) systems that are represented by the Fornasini-Marchesini model II (FMII). This is accomplished by generalizing the basic invariant subspaces including unobservable, conditioned invariant and unobservability subspaces of 1D systems to 2D models. These extensions have been achieved and facilitated by representing a 2D model as an infinite dimensional (Inf-D) system on a Banach vector space, and by particularly constructing algorithms that compute these subspaces in a \emph{finite and known} number of steps. By utilizing the introduced subspaces the FDI problem is formulated and necessary and sufficient conditions for its solvability are provided. Sufficient conditions for solvability of the FDI problem for 2D systems using both deadbeat and LMI filters are also developed. Moreover, the capabilities and advantages of our proposed approach are demonstrated by performing an analytical comparison with the currently available 2D geometric methods in the literature. Finally, numerical simulations corresponding to an approximation of a hyperbolic partial differential equation (PDE) system of a heat exchanger, that is mathematically represented as a 2D model, have also been provided.

Bahareh Pourbabaee, Nader Meskin, Khashayar Khorasani

In this paper, a novel sensor fault detection, isolation and identification (FDII) strategy is proposed by using the multiple model (MM) approach. The scheme is based on multiple hybrid Kalman filters (HKF) which represents an integration of a nonlinear mathematical model of the system with a number of piecewise linear (PWL) models. The proposed fault detection and isolation (FDI) scheme is capable of detecting and isolating sensor faults during the entire operational regime of the system by interpolating the PWL models using a Bayesian approach. Moreover, the proposed multiple HKF-based FDI scheme is extended to identify the magnitude of a sensor fault by using a modified generalized likelihood ratio (GLR) method which relies on the healthy operational mode of the system. To illustrate the capabilities of our proposed FDII methodology, extensive simulation studies are conducted for a nonlinear gas turbine engine. Various single and concurrent sensor fault scenarios are considered to demonstrate the effectiveness of our proposed on-line hierarchical multiple HKF-based FDII scheme under different flight modes. Finally, our proposed HKF-based FDI approach is compared with various filtering methods such as the linear, extended, unscented and cubature Kalman filters (LKF, EKF, UKF and CKF, respectively) corresponding to both interacting and non-interacting multiple model (MM) based schemes. Our comparative studies confirm the superiority of our proposed HKF method in terms of promptness of the fault detection, lower false alarm rates, as well as robustness with respect to the engine health parameters degradations.