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This paper proposes an observer-based residual generator (OBRG) for diagnosing faults in a continuous non-affine system with polynomial non-linearities up to any finite degree where the fault and an unknown input affect both the system and part of the output. Firstly, given certain assumptions and the use of defined extended vectors, a parameterized polynomial system is considerred for which a compact set of sufficient conditions is given for the existence of a candidate OBRG. Conditions for error stability (by a Lyapunov method) and detectability are given. The calculation steps in the design of the OBRG are shown to involve the solution of three linear equations (with parameterizations) and the calculation of a set of constant matrices (for detectability of faults). A result is then given establishing that the design holds for a much wider class of systems. The residual design is applied to a real three-tank system.

The design of a high-gain observer-based residual is considered for a class of non-linear systems. Input–output maps are derived for use in residual design to increase design flexibility. An invest...

This paper proposes a robust fault detection observer (RFDO) for a continuous non-linear system with polynomial non-linearities up to any finite degree. The observer error and residual are robust with respect to unknown inputs. Sufficient conditions are given, in an efficient algebraic compact form, for a RFDO (observer and residual) to exist. Useable results on detectablility conditions are proved. Numerical prodedures for the design of a RFDO and a sub-optimal RFDO (SORFDO) are given. The theory is illustrated with an application to a (benchmark) three-tank system. One linear and three non-linear models are considered with corresponding RDFOs (including a sub-optimal RFDO), and the performances of the corresponding residuals are compared under two initial conditions for a scenario consisting of a leak (fault) and a disturbance.

two observer-based fault detection designs are considered for detecting a fault in any inaccessible tank which forms part of a larger n-tank system. A subsystem of n – 2 tanks is situated in a hazardous environment and only control and measurements of the outer tanks is possible. Given a set of nonlinear differential equations, several transformations are derived to aid the design of the two problems of control and fault detection. Two nonlinear observer approaches are given and illustrated by an example. Stability and detectability are examined.

This paper proposes a robust fault detection observer for a wide class of nonlinear models. Results are given for existence, error stability and detecability. Special choices of the gain matrices are chosen relating to the time-varying error dynamics. These enable algebraic conditions to be given for detectability of faults. An application example is given demonstrating the use of the theory.

This paper proposes a fault detection observer for classes of nonlinear models which consist of bilinear and polynomial nonlinearies up to degree three and are structured in continuous state space form. A design procedure is presented for calculating the observer matrices and is applied to an industrial application.

This paper proposes an observer-based fault detection method for a class of nonlinear models which have bilinear and quadratic nonlinear terms in their discrete state-space representations. Various other methods proposed in the field are related to this method or are special cases of it. A nonlinear fault detection observer is proposed such that the error dynamics are independent of an unknown disturb ance. A result is proved for the observer error dynamics and a numerical algorithm is given for calculating the observer and residual gain matrices. Sufficient conditions are also stated for fault detectability. An illustrative example is given for the problem of detecting certain faults in a hydraulic system.

A fault detection method is proposed for a fairly wide class of nonlinear systems based on a nonlinear observer. Other methods proposed in the field are related to this method or are special cases of it. The observer is designed such that the error dynamics are independent ofstate, input, output and unknown disturbances. Conditions are given for the observer to exist and to be robust with respect to an unknown input. Applications are made to a hydraulic system.

A fault detection observer is considered for a class of continuous singular bilinear descriptor systems subject to unknown inputs and faults. A member system may be singular and possibly noncausal. Existence of solutions is considered and the initial system is is firstly transformed into a special (causal) form given certain assumptions hold true. The main observer design rests on the solution of a Riccati equation and the use of a quadratic Liapunov function. Two other designs are briefly outlined. A design algorithm is given and applied to the estimation of the states of a flexible joint robot.

A bilinear fault detection filter (BFDF) is proposed for bilinear systems with unknown inputs. Sufficient conditions are given for the existence of a BFDF and a strict BFDF for which the latter is sensitive to all faults. A particular choice of observer structure is shown to give explicit solutions both for the observer gain matrix and for establishing fault sensitivity. Structured actuator and component faults give rise to residuals with known directions enabling these faults to be easily isolated. A numerical example is used to demonstrate the BFDF design.

A nonlinear observer is considered for a class of discrete nonlinear descriptor systems subject, to unknown inputs and faults. This class is partly characterized by globally Lipschitz nonlinearities, and a member system may be singular and possibly non-causal. The structure proposed for the observer makes it useful for both state estimation for feedback controls and residual generation for fault detection. Results on the existence of solutions are given and some useful bounds are derived which are important in the observer design. The proposed nonlinear observer is based on a transformed system and on the solution of a Riccati equation. The existence, convergence properties and robustness of the observer are investigated by the use of a quadratic Lyapunov function. A design algorithm is given and applied to the estimation of the states of a flexible joint robot.

A simulation study is undertaken on fault diagnosis for a gas-fired high temperature furnace. A single input multi output bilinear model is found to be suitable to represent the furnace. A previously proposed full-order bilinear state observer is used to generate the residual. Two actuator and two sensor faults are simulated and tested using this method.

Observer-based fault detection and modelling are considered for the drive-train of a Jaguar car with an automatic transmission. Test data is used for the modelling and use is made of nonlinear polynomials, where various structures are compared and assessed. A robust fault detection observer (RFDO), consisting of an observer which generates a residual, for the class of nonlinear models emerging from the modelling, is proposed consisting of polynomial nonlinearities up to degree three and a cubic term with respect to the state and input. The observer and the residual are decoupled from unknown inputs. Three fault scenarios are considered, each with a different set of measurements, to test the effectiveness of the RFDO design.

A Jaguar Car engine is used to provide data for modelling the throttle body, engine pumping and manifold body. Based on the gas law of the intake dynamics, input/output variables are identified and used to train a neural network. Various structures are compared and assessed. The best structure is then used for fault detection. A neural network observer is developed and error stability is assessed. Two fault scenarios are considered.

This paper investigates the detection of faults in an hydraulic pipeline for which both laminar and non-laminar flows are present. A fault detection observer is developed for classes of nonlinear models which are structured in continuous state space form. The observer is designed such that the error dynamics are independent of state, input, output and unknown disturbances. The conditions for the observer to exist, and remain robust with respect to unknown inputs, are derived. The approach is applied to a particular pipeline to detect simulated faults. The results presented demonstrate the effectiveness of the nonlinear observer for fault detection.

This paper considers a problem associated with the transportation of oil through a pipeline, possibly from an oil rig. A hydraulic hose, known as a sub-sea umbilical, is used to open or close a valve which controls the oil flow in a larger pipeline. A linear state-space model is described, including model terms for the faults. A general linear unknown input observer is then proposed and an example is given for the rig-system. An input-output model for the lamina case is then derived which facilitates identification of three important parameters. Finally, a nonlinear model for the nonlaminar flow case is proposed which includes certain quadratic nonlinearities. Fault modelling is also included.

Observer approaches for fault diagnosis are reviewed with particular emphasis on bilinear systems. An introduction and an overview are given where the basic methods for linear and nonlinear systems are summarised. Several methods of robust residual generation for bilinear systems are then given, including the bilinear fault detection observer method, the full-order bilinear observer method and the minimal-order bilinear observer method. Robust issues are addressed throughout the paper. Hybrid methods, fault isolation and a bilinear parity-space method are briefly discussed.

The problem of robust residual generation is considered for systems in descriptor or generalized state-space form subject to an unknown disturbance. A class of perturbations is considered for which the perturbed system has the same number of dynamic modes. A two stage design process is proposed for calculating the observer and residual gain matrices and some useful results are given for reducing the norms of certain key matrices.