Geometric Fault Detection and Isolation of Infinite Dimensional Systems

A broad class of dynamical systems from chemical processes to flexible mechanical structures, heat transfer and compression processes in gas turbine engines are represented by a set of partial differential equations (PDE). These systems are known as infinite dimensional (Inf-D) systems. Most of Inf-D systems, including PDEs and time-delayed systems can be represented by a differential equation in an appropriate Hilbert space. These Hilbert spaces are essentially Inf-D vector spaces, and therefore, they are utilized to represent Inf-D dynamical systems. Inf-D systems have been investigated by invoking two schemes, namely approximate and exact methods. Both approaches extend the control theory of ordinary differential equation (ODE) systems to Inf-D systems, however by utilizing two different methodologies. In the former approach, one needs to first approximate the original Inf-D system by an ODE system (e.g. by using finite element or finite difference methods) and then apply the established control theory of ODEs to the approximated model. On the other hand, in the exact approach, one investigates the Inf-D system without using any approximation. In other words, one first represents the system as an Inf-D system and then investigates it in the corresponding Inf-D Hilbert space by extending and generalizing the available results of finite-dimensional (Fin-D) control theory. It is well-known that one of the challenging issues in control theory is development of algorithms such that the controlled system can maintain the required performance even in presence of faults. In the literature, this property is known as fault tolerant control. The fault detection and isolation (FDI) analysis is the first step in order to achieve this goal. For Inf-D systems, the currently available results on the FDI problem are quite limited and restricted. This thesis is mainly concerned with the FDI problem of the linear Inf-D systems by using both approximate and exact approaches based on the geometric control theory of Fin-D and Inf-D systems. This thesis addresses this problem by developing a geometric FDI framework for Inf-D systems. Moreover, we implement and demonstrate a methodology for applying our results to mathematical models of a heat transfer and a two-component reaction-diffusion processes. In this thesis, we first investigate the development of an FDI scheme for discrete-time multi-dimensional (nD) systems that represent approximate models for Inf-D systems. The basic invariant subspaces including unobservable and unobservability subspaces of one-dimensional (1D) systems are extended to nD models. Sufficient conditions for solvability of the FDI problem are provided, where an LMI-based approach is also derived for the observer design. The capability of our proposed FDI methodology is demonstrated through numerical simulation results to an approximation of a hyperbolic partial differential equation system of a heat exchanger that is represented as a two-dimensional (2D) system. In the second part, an FDI methodology for the Riesz spectral (RS) system is investigated. RS systems represent a large class of parabolic and hyperbolic PDE in Inf-D systems framework. This part is mainly concerned with the equivalence of different types of invariant subspaces as defined for RS systems. Necessary and sufficient conditions for solvability of the FDI problem are developed. 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. Finally, by generalizing the results that are developed for RS systems necessary and sufficient conditions for solvability of the FDI problem in a general Inf-D system are derived. Particularly, we first address invariant subspaces of Fin-D systems from a new point of view by invoking resolvent operators. This approach enables one to extend the previous Fin-D results to Inf-D systems. Particularly, necessary and sufficient conditions for equivalence of various types of conditioned and controlled invariant subspaces of Inf-D systems are obtained. Duality properties of Inf-D systems are then investigated. By introducing unobservability subspaces for Inf-D systems the FDI problem is formally formulated, and necessary and sufficient conditions for solvability of the FDI problem are provided

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.NPRP grant No. 4-195-2-065 from the Qatar National Research Fund (a member of Qatar Foundation)Scopu

Fault detection of infinite dimensional systems in presence of disturbances

In this brief paper we are concerned with the fault detection (FD) problem of single-input multi-output infinite dimensional (Inf-D) systems. We develop a geometric methodology to detect a fault in presence of a disturbance signal. In other words, the detection decision making process is decoupled from the disturbance signal. Specifically, we first consider the invariant subspaces of Inf-D systems and derive sufficient conditions for convergence of the computing algorithm corresponding to conditioned invariant subspaces. Then, by using the developed methodology necessary and sufficient conditions for solvability of the FD problem are provided.Scopu

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. 1 2016, Springer Science+Business Media New York.This publication was made possible by NPRP Grant No. 4-195-2-065 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.Scopu

Effects of pressurization on the Enthalpy of vaporization for the SiO2 nanofluid

A microchannel heatsink is an advanced cooling technique to meet the cooling needs of electronic devices installed with high-power integrated circuit packages (microchips). These heat sinks utilize microchannel heat exchangers (MCHEs) with boiling-mode cooling (BMC) and nanofluids. Such MCHEs usually have high operating pressures (3-13 bar). In spite of a large number of studies on other thermo-physical properties of nanofluids, few studies have been carried out on the latent heat of evaporation (LHE) of nanofluids. The limited published literature, all report the LHE at atmospheric conditions which are outside of the operating range of MCHEs. The precise estimation of the LHE is essential for the appropriate design of the MCHEs. In the present study, a novel experimental setup is applied for the measurement of LHE in high operating pressures and temperatures (90-180°C and 80-880 kPa) and investigating the effects of pressure on LHE. It is shown that by exposing a nanofluid under pressure some new hydrogen bonds form and increase the LHE which can significantly improve the performance of boiling cooling of MCHEs. Based on the obtained results by pressurizing a 2 vol.% (4.6 wt%) SiO2 nanofluid the LHE can be increased by about 17% in comparison with a similar non-pressurized sample. On the other hand, pressurization can improve nanofluid stability. Finally, a correlation is proposed for the calculation of enthalpy of evaporation of SiO2 nanofluids

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.Manuscript received June 1, 2016; accepted July 27, 2016. Date of publication August 15, 2016; date of current version July 17, 2017. This work was supported by the Qatar National Research Fund (a member of Qatar Foundation) under NPRP Grant 4-195-2-065. This paper was recommended by Associate Editor G. Provan.Scopu