Amir Baniamerian

Fault detection and isolation of dissipative parabolic PDEs: Finite-dimensional geometric approach

In this paper, a nonlinear geometric fault detection and isolation (FDI) method is developed for a system that is governed by a dissipative parabolic partial differential equation (PDE) and that can be approximated by a finite-dimensional ordinary differential equations (ODE). The Galerkin method is employed to derive an approximate ODE which is utilized to design a geometric FDI system. Using singular perturbation theory, it is shown that under certain conditions the designed FDI system can detect and isolate faults corresponding to the original PDE. In addition, the Approximate Inertial Manifold (AIM) concept is used to improve the performance of the designed FDI filter. It is shown that by using the AIM-based approach, one can accomplish fault detection to an arbitrary degree of accuracy, although this technique cannot improve the fault isolation problem.

Geometric fault detection and isolation of two-dimensional (2D) systems

This work is concerned with development of a fault detection and isolation (FDI) scheme for discrete-time two-dimensional (2D) systems represented by the Roesser model. This is accomplished by generalizing the geometric approach of one-dimensional (1D) systems to this 2D model. The basic conditioned invariant and unobservabilty subspaces of 1D systems are extended, and algorithms to compute these subspaces are introduced. Moreover, sufficient conditions for solvability of the FDI problem are provided, and capability of the proposed method is emphasized through numerical simulation results.

A hybrid prognosis and health monitoring strategy by integrating particle filters and neural networks for gas turbine engines

In this paper, a novel hybrid structure is proposed for the development of health monitoring techniques of nonlinear systems by integration of model-based and computationally intelligent and data-driven techniques. In our proposed health monitoring framework, the well-known particle filtering method is utilized to estimate the states as well as the health parameters of the system. Simultaneously, the system observations are predicted through an observation forecasting scheme which is developed based on artificial neural networks to construct observation profiles for future time horizons. As a case study, the proposed approach is applied to predict the health condition of a gas turbine engine when it is affected by degradation damage.

Fault detection and isolation of Riesz spectral systems: A geometric approach

The Riesz spectral (RS) systems represent a large class of parabolic and hyperbolic partial differential equations (PDE) in infinite-dimensional systems. In this work, a fault detection and isolation (FDI) methodology for real diagonalizable RS systems is investigated by using a geometric approach. This paper is mainly concerned with the equivalency of different types of invariant subspaces defined for the RS systems and the necessary and sufficient conditions for solvability of the FDI problem. Moreover, for a subclass of RS systems, we first provide algorithms (for computing the invariant subspaces) that converge in a finite and known number of steps and then derive the necessary and sufficient conditions for solvability of the FDI problem.

Prognosis and Health Monitoring of Nonlinear Systems Using a Hybrid Scheme Through Integration of PFs and Neural Networks

In this paper, a novel hybrid architecture is proposed for developing a prognosis and health monitoring methodology for nonlinear systems through integration of model-based and computationally intelligent-based techniques. In our proposed framework, the well-known particle filters (PFs) method is utilized to estimate the states as well as the health parameters of the system. Simultaneously, the system observations are predicted through an observation forecasting scheme that is developed based on neural networks (NNs) paradigms. The objective is to construct observation profiles that are to be used in future time horizons. Our proposed online training that is utilized for observation forecasting enables the NNs models to track nonergodic changes in the profiles that are present due to presence of hidden damage affecting the system health parameters. The forecasted observations are then utilized in the PFs to predict the evolution of the system states as well as the health parameters (which are considered to be time-varying due to effects of degradation and damage) into future time horizons. Our proposed hybrid architecture enables one to select health signatures for determining the remaining useful life of the system or its components not only based on the system observations but also by taking into account the system health parameters that are not physically measurable. Our proposed hybrid health monitoring methodology is constructed and developed by invoking a special framework where implementation of the observation forecasting scheme is not dependent on the structure of the utilized NNs model. In other words, changing the network structure will not significantly affect the prediction accuracy associated with the entire health prediction scheme. To verify and validate the above results and as a case study, our proposed hybrid approach is applied to predict the health condition of a gas turbine engine when it is affected by and subjected to fouling and erosion degradation and fault damages.

Fault detection and isolation of Fornasini-Marchesini 2D systems: A geometric approach

The fault detection and isolation (FDI) problem for discrete-time two-dimensional (2D) systems represented by the Fornasini-Marchesini model II is investigated in this work. It is shown that the sufficient conditions for solvability of the FDI problem that we have developed recently for the Roesser model is also applicable to this class of 2D systems. In this paper, we are mainly concerned with the necessary conditions. Two sets of necessary conditions for the solvability of the FDI problem are derived. The first necessary condition involves a new set of invariant subspaces that has no one-dimensional (1D) equivalency. The second set which is consistent with its equivalent 1D case is derived, generically (from the algebraic geometry point of view). A numerical example is also provided to illustrate the application of the results.

Deterioration Detection and Health Monitoring in Aircraft Jet Engines

In this paper the problem of jet engine deterioration detection and health monitoring is investigated by utilizing two methods. The first method is based on the fusion of the modified CUSUM (CUmulative SUM) method with the differential analysis approach. An enhanced differential analysis method is developed through which the degradation is captured from the unsymmetrical performance analysis of both engines on an aircraft. This is achieved by considering the effects of minor maintenance actions that are not reported. In the second approach, a statistical method based on the Hotelling’s T2-test approach is utilized to detect gradual degradations in the engine performance. The performance of our proposed approaches is evaluated by implementing them on a dual spool engine model that is developed by using the GSP software.Copyright

Fault detection and isolation of two-dimensional (2D) systems ☆

This work is concerned with development of a fault detection and isolation (FDI) scheme for discrete-time two-dimensional (2D) systems represented by the Roesser model. This is accomplished by generalizing the geometric approach of one-dimensional (1D) systems to this 2D model. The basic conditioned invariant and unobservabilty subspaces of 1D systems are extended, and algorithms to compute these subspaces are introduced. Moreover, sufficient conditions for solvability of the FDI problem are provided, and capability of the proposed method is emphasized through numerical simulation results.

Joint Kalman Filtering and Recursive Maximum Likelihood Estimation Approaches to Fault Detection and Identification of Boeing 747 Sensors and Actuators

In this paper, a joint state and parameter estimation scheme is applied to address the problem of detection and identification of loss of effectiveness faults in both sensors or the actuators of a Boeing 747 longitudinal model. The Kalman filter and the recursive maximum likelihood schemes are used for the state and the parameter estimations, respectively. Compared to the other simultaneous state and parameter estimation methods, the proposed strategy maintains the linearity of the system and can also be applied to both sensor or actuator faults. In simulation studies conducted, our proposed approach is compared to the adaptive structure multiple-model scheme. In view of the computational resources considerations, the method proposed in this paper is more efficient than the adaptive structure multiple-model technique and also has the potential to detect and identify faults with lower severities as well as concurrent faults.

A geometric approach to fault detection and isolation of multi-dimensional (n-D) systems

In this work, we develop a novel fault detection and isolation (FDI) scheme for discrete-time multi-dimensional (n-D) systems for the first time in the literature. These systems represent as generalization of the Fornasini–Marchesini model II two- and three-dimensional (2-D and 3-D) systems. This is accomplished by extending the geometric FDI approach of one-dimensional (1-D) systems to n-D systems. The basic invariant subspaces including unobservable, conditioned invariant and unobservability subspaces of 1-D systems are generalized to n-D models. These extensions have been achieved and facilitated by representing an n-D model as an infinite dimensional system, and by particularly constructing algorithms that compute these subspaces in a 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 n-D systems using LMI filters are also developed. Moreover, the capabilities and advantages of our proposed approach are demonstrated by performing an analytical comparison with the only currently available 3-D geometric methods in the literature.