Observer-based Fault Detection Systems Research Articles

Adaptive Threshold-based Fault Detection for Systems Exposed to Model Uncertainty and Deterministic Disturbance

The fault detection problem is investigated for discrete-time linear uncertain systems. Instead of designing a fault detection system from the viewpoint of observer design for robust residual generation, an adaptive threshold approach is proposed to attain robustness against disturbance and norm-bounded model uncertainty. The main goal of the research is to develop a threshold design method that could establish an appropriate trade-off between false alarms and missed fault detection in the presence of model uncertainty. For this purpose, the H∞ optimization technique is adopted in the linear matrix inequality framework to compute the unknown parameters of an adaptive threshold. It is shown that the proposed fault detection system based on an adaptive threshold depends only on the system parameters and the control input of the monitored system. It is independent of robust residual generator designs in traditional observer-based fault detection systems. The effectiveness of the proposed approach is verified on two well-known benchmark systems: a direct-current motor and three tank systems. Several types of faults are successfully detected in both applications.

Optimal Detection Schemes for Multiplicative Faults in Uncertain Systems With Application to Rolling Mill Processes

In rolling mill processes, changes of operation conditions, mismatching of controller parameters, and aging of system components will cause multiplicative faults, which may considerably affect the system operation and the quality of steel products. The main objective of this paper is to address optimal design approaches for detecting multiplicative faults in uncertain industrial systems. To be specific, the design schemes of observer-based fault detection (FD) systems, including residual generators and threshold setting, are investigated first in the closed-loop system setup, aiming at enhancing fault detectability and system robustness against model uncertainties simultaneously. Then, an optimal design scheme of observer-based FD systems for open-loop processes is investigated. The application to an industrial rolling mill benchmark is given to demonstrate the efficiency of the proposed approaches. The task involves the detection of the parameter faults in hydraulic reduction devices in both the closed-loop and open-loop configurations.

Application of randomized algorithms to assessment and design of observer-based fault detection systems

This work is an attempt to establish a probabilistic framework for the assessment and design of observer-based fault detection systems. The fundament of our study is randomized algorithms methods which are successfully applied to deal with uncertainty issues in robust control. For our purpose, probabilistic parameter models for faults and model uncertainties are first introduced. The main focus of our work is on the development of randomized algorithms for the assessment of false alarm rate, fault detection rate and mean time to detection as well as for the design of observer-based fault detection systems. To illustrate the potential applications of the proposed algorithms and methods, benchmark study on a real three-tank system is included.

Fault Detection and Reconstruction for Discrete Nonlinear Systems via Takagi-Sugeno Fuzzy Models

Observer-based actuator fault detection and sensor fault reconstruction for a class of discrete-time nonlinear systems with actuator and sensor faults are investigated in this paper. A descriptor Takagi-Sugeno (T-S) fuzzy model is employed to construct observer-based systems for the purpose of fault detection and sensor fault reconstruction. Two methods for observer design are proposed. In the first method, the observer gains are computed off-line. In the second method, the observer gains are computed on-line at each iteration. The observer designs are formulated using linear matrix inequalities. Sufficient conditions for the existence of the observer-based fault detection and sensor fault reconstruction systems are provided. Comparative simulation study to illustrate the validity of the proposed methods is performed.

Diagnostic Observer Design for T–S Fuzzy Systems: Application to Real-Time-Weighted Fault-Detection Approach

This paper deals with a real-time-weighted observer-based fault-detection (FD) scheme for Takagi–Sugeno (T–S) fuzzy systems. The essential idea is to develop a weighted diagnostic observer-based FD system to optimize the worst case robustness and fault sensitivity simultaneously by using the information provided by each local system. To achieve an early detection of potential fault, the robustness issue is investigated in the $\mathcal {L}_{\infty }/\mathcal {L}_2$ observer-based FD context. Meanwhile, the $\mathcal {L}_-$ fault sensitivity condition is addressed to optimize the fault detectability. Using fuzzy Lyapunov functions, sufficient conditions on the FD system design are studied. Two examples are given in the end to show the efficiency of the proposed results.

Observer-based fault detection for uncertain nonlinear systems

This paper addresses L2 observer-based fault detection issues for a class of nonlinear systems in the presence of parametric and dynamic uncertainties, respectively. To this end, three different types of uncertain affine nonlinear system models studied in this paper are described first. Then, the integrated design schemes of L2 observer-based fault detection systems are derived with the aid of Hamilton–Jacobi inequalities (HJIs), respectively. Numerical examples are also provided in the end to demonstrate the effectiveness of the proposed results.

A Fault Detection Scheme for Uncertain Switched Systems Under Asynchronous Switching

The main focus of this paper is on analysis and design issues concerning with fault detection in asynchronous switching systems with uncertainties. To this end, the existence conditions for the application of observer-based fault detection systems are first derived. Based on these conditions, an observer-based fault detection scheme is proposed both for the matched and unmatched switching operations. The core of this scheme is a dynamic threshold. The theoretical results are finally illustrated by a numerical example.

Fault detection for piecewise affine systems with application to ship propulsion systems

In this paper, the design approach of non-synchronized diagnostic observer-based fault detection (FD) systems is investigated for piecewise affine processes via continuous piecewise Lyapunov functions. Considering that the dynamics of piecewise affine systems in different regions can be considerably different, the weighting matrices are used to weight the residual of each region, so as to optimize the fault detectability. A numerical example and a case study on a ship propulsion system are presented in the end to demonstrate the effectiveness of the proposed results.

Fuzzy Observer-Based Fault Detection Design Approach for Nonlinear Processes

This paper is concerned with the analysis and integrated design of a type of observer-based fault detection (FD) system for general nonlinear processes. To this end, the existence and design condition for this type of nonlinear observer-based FD systems is first introduced. In this context, the integrated design scheme is investigated by dealing with the design condition with the aid of Takagi–Sugeno (T–S) fuzzy dynamic modeling technique. To be specific, the universal T–S fuzzy observer-based residual generator is developed via fuzzy Lyapunov functions. Subsequently, an integrated observer-based FD scheme is proposed with an embedded dynamic threshold, which is generated to meet the real-time FD requirements from industrial processes. In the end, a numerical example and case simulation study on a continuous stirred tank heater process are performed to show the application of the proposed method.

Weighted Fuzzy Observer-Based Fault Detection Approach for Discrete-Time Nonlinear Systems via Piecewise-Fuzzy Lyapunov Functions

The main focus of this paper is on the analysis and integrated design of $\mathcal {L}_2$ observer-based fault detection (FD) systems for discrete-time nonlinear industrial processes. To gain a deeper insight into this FD framework, the existence condition is introduced first. Then, an integrated design of $\mathcal {L}_2$ observer-based FD approach is realized by solving the proposed existence condition with the aid of Takagi–Sugeno fuzzy dynamic modeling technique and piecewise-fuzzy Lyapunov functions. Most importantly, a weighted piecewise-fuzzy observer-based residual generator is proposed, aiming at achieving an optimal integration of residual evaluation and threshold computation into FD systems. The core of this approach is to make use of the knowledge provided by fuzzy models of each local region and then to weight the local residual signal by means of different weighting factors. In comparison with the standard norm-based fuzzy observer-based FD methods, the proposed scheme may lead to a significant improvement of the FD performance. In the end, the effectiveness of the proposed method is verified by a numerical example and a case study on the laboratory setup of continuous stirred tank heater plant.

Parameterization of Nonlinear Observer-Based Fault Detection Systems

This note addresses parameterization issues of nonlinear observer-based fault detection (FD) systems which are composed of a residual generator, a residual evaluator and a threshold. Our study consists of two steps. In the first step, with the aid of nonlinear factorization and input-output operator techniques, we prove that any stable residual generator can be parameterized by a cascade connection of the process kernel representation and a post-filter that represents the parameter system. In the second step, based on the state-space representation of the parameterized residual generators, we investigate the so-called ${\mathcal L}_{\infty}$ - and ${\mathcal L}_{2}$ - classes of observer-based FD systems. This leads to the parameterization of the threshold settings for both classes of FD systems and, associated with them, to the characterization of the existence conditions.

Real-Time Fault Detection Approach for Nonlinear Systems and its Asynchronous T-S Fuzzy Observer-Based Implementation.

This paper is concerned with a real-time observer-based fault detection (FD) approach for a general type of nonlinear systems in the presence of external disturbances. To this end, in the first part of this paper, we deal with the definition and the design condition for an L ∞ / L 2 type of nonlinear observer-based FD systems. This analytical framework is fundamental for the development of real-time nonlinear FD systems with the aid of some well-established techniques. In the second part, we address the integrated design of the L ∞ / L 2 observer-based FD systems by applying Takagi-Sugeno (T-S) fuzzy dynamic modeling technique as the solution tool. This fuzzy observer-based FD approach is developed via piecewise Lyapunov functions, and can be applied to the case that the premise variables of the FD system is nonsynchronous with the premise variables of the fuzzy model of the plant. In the end, a case study on the laboratory setup of three-tank system is given to show the efficiency of the proposed results.

Robust fuzzy observer-based fault detection for nonlinear systems with disturbances

This paper studies the integrated design of fuzzy observer-based fault detection (FD) for nonlinear systems in the presence of external disturbances. To this end, we first approximate the nonlinear systems by a set of Takagi–Sugeno (T–S) fuzzy models. Then, the observer-based FD systems are studied with the aid of L2 stability theory. In the end, a numerical example is given to show the efficiency of the proposed method.

On observer-based fault detection for nonlinear systems

This paper addresses analysis and integrated design of observer-based fault detection (FD) for nonlinear systems. To gain a deeper insight into the observer-based FD framework, definitions and existence conditions for nonlinear observer-based FD systems are studied first. Then, a scheme for an integrated design of observer-based FD systems for affine nonlinear systems is proposed. Our work is considerably inspired by the study on input–output stability and stabilization of nonlinear systems. Examples are given at the end of the paper to illustrate the theoretical results.

Data-driven realizations of kernel and image representations and their application to fault detection and control system design

This paper deals with the data-driven design of observer-based fault detection and control systems. We first introduce the definitions of the data-driven forms of kernel and image representations. It is followed by the study of their identification. In the context of a fault-tolerant architecture, the design of observer-based fault detection, feed-forward and feedback control systems are addressed based on the data-driven realization of the kernel and image representations. Finally, the main results are demonstrated on the laboratory continuous stirred tank heater (CSTH) system.

Residual Fault Detection Filter Design in the Finite Frequency Domain Based on LMI Optimization

In the observer based fault detection methods, the parameter be designed and optimized is the observer gain matrix. However, an observer cannot be optimized to achieve all the expected performances. A novel fault detection filter designed method is presented in this paper, where the filter is cascaded after the observer based fault detection system. The filter is designed to be sensitive to the faults but robust to the disturbances and model uncertainties in the finite frequency domain. For the proposed filter, there are four matrices need to be optimized and the performance would be enhanced significantly. The effectiveness of the proposed method is demonstrated by applying it to a railway suspension system.

Data-Driven Design of Observers and Its Applications

AbstractIn this paper, we address the data-driven design of observers for the process monitoring and control purposes. Instead of identifying a standard state space model, our design schemes are based on the identification of the so-called parity subspace. Two design schemes are developed, which allow a direct design of (a) observer-based fault detection systems (b) a full order observer for the estimation of the process state variables. The achieved results are illustrated by a benchmark example.

Subspace based identification of diagnostic observer for Wiener systems

A subspace identification technique based design of observer is developed in this paper. Verhaegen and Westwick [1995] provided a subspace algorithm to identify state space matrices for LTI system with nonlinearity on the output side, or the so called Wiener systems. Their results were based on Bussgang's theorem on crosscorrelation functions of amplitude distorted Gaussian signals. We have combined these two important results in order to develop an observer based fault detection system that is identified directly from the test data generated by nonlinear dynamic systems.

Fault Diagnosis for LTI Systems Based on Subspace Identification Technique

This paper concerns the fault estimation for a class of systems in an innovation form. We propose a new fault diagnosis strategy based on the well-known subspace model identification technique. The underlying faults, mainly sensor bias and actuator additive bias, are parameterized in the model which is estimated in two stages. In the first stage, the contribution of the fault, similar to the residual in classical observer based fault detection system, is estimated. In the second stage, the faults are recovered from the residual. For the component faults, we use online parameter identification to monitor the fault. Recursive online monitoring algorithms are derived. One example is given to illustrate the effectiveness of the proposed method.

Report on the European Control Conference ECC 2007

This paper addresses analysis and integrated design of observer-based fault detection (FD) for nonlinear systems. To gain a deeper insight into the observer-based FD framework, definitions and existence conditions for nonlinear observer-based FD systems are studied first. Then, a scheme for an integrated design of observer-based FD systems for affine nonlinear systems is proposed. Our work is considerably inspired by the study on input–output stability and stabilization of nonlinear systems. Examples are given at the end of the paper to illustrate the theoretical results.