Enhancement of robustness in observer-based fault detection†

A prerequisite for the feasibility of the technique of observer-based fault detection and isolation (FDI) in dynamic systems is a satisfactory robustness with respect to modelling uncertainties. This paper surveys the most relevant methods to increase the robustness in both the stage of residual generation and residual evaluation. Among these methods are the generalized observer scheme, the robust parity space check, the unknown input and H _∞ observer scheme, the decorrelation filter, and the concept of adaptive threshold selection. It is pointed out that the unknown input observer concept, which provides perfect decoupling from the modelling errors or its optimal approximation with the aid of H _∞ techniques, constitutes a general framework of robust residual generation that generalizes and unifies numerous other approaches, among them the parity space and detection filter approach. It is further shown that this FDI method can even be applied to a certain class of nonlinear systems.     

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.     

Full-order observer-based actuator fault detection and reduced-order observer-based fault reconstruction for a class of uncertain nonlinear systems

This paper considers observer-based actuator fault detection and reconstruction problems for uncertain nonlinear systems. Based on a kind of full-order observer which is robust to disturbances but sensitive to actuator faults, a single detection observer is constructed to produce a residual which can be used to alarm the occurrence of the actuator faults when at least one actuator fault occurs indeed. The full-order observer is adaptive one because an adaptation law which can adjust the Lipschitz constant of Lipschitz term is introduced. For this reason, the Lipschitz constant can be unknown in our design. After this, a kind of reduced-order observer is developed by choosing a special observer gain matrix. Based on the reduced-order observer, we provide a kind of unknown information estimating method which can be used to not only reconstruct the actuator faults but also estimate the disturbances of the system. In simulation, a real model of the seventh-order aircraft is used to illustrate the effectiveness of the proposed methods.     

基于观测器的非线性不确定系统鲁棒故障检测新方法

针对非线性不确定系统的鲁棒故障检测问题,提出了一种采用统计理论的新方法.通过设计全阶故障观测器产生残差信号,将鲁棒故障检测观测器设计问题转化为H∞优化问题;利用H∞范数描述故障检测的鲁棒性,保证系统的抗干扰能力,同时引入H_范数,确保对故障信号的灵敏度;应用线性矩阵不等式技术给出了该设计问题解存在的条件和求解方法.将统计理论用于故障检测阈值的确定,充分考虑了残差信号的随机特性,使故障决策更加准确和可靠.最后通过仿真实例验证了本文方法的有效性.     

基于区间观测器的执行器故障检测

针对同时具有未知非线性函数(包括系统不确定性、外部干扰等) 和执行器故障的非线性系统, 提出基于区间观测器的故障检测方法. 首先, 在假定执行器故障不出现的前提下, 基于未知非线性函数的上下界信息, 提出两种区间观测器设计方法; 然后, 利用这两种区间观测器的输出和系统的真实输出, 构造可以对执行器故障进行检测的残差, 以此实现基于区间观测器的执行器故障检测. 最后, 通过两个仿真例子验证了所提出方法的正确性和有效性.

     

Survey of robust residual generation and evaluation methods in observer-based fault detection systems

The paper outlines recent advances of the theory of observer-based fault diagnosis in dynamic systems towards the design of robust techniques of residual generation and residual evaluation. Emphasis will be placed upon the latest contributions using frequency domain techniques including H_∞ theory, nonlinear unknown input observer theory, adaptive observer theory, artificial intelligence including fuzzy logic, knowledge-based techniques and the natural intelligence of the human operator. Two representative examples illustrate the efficiency of the observer-based approach.     

Bumpless transfer between observer-based gain scheduled controllers

This paper deals with bumpless transfer between a number of observer-based controllers in a gain scheduling architecture. Linear observer-based controllers are designed for a number of linear approximations of a non-linear system in a set of operating points, and gain scheduling control can subsequently be achieved by interpolating between each controller. The Youla-Jabr-Bongiorno-Kucera (YJBK) parameterization is used to achieve a smooth scheduling between the controllers. This approach produces a scheduled controller as a linear fractional transformation between a fixed controller and a scheduling parameter. The approach is tested on a simple, but highly non-linear model of a fossil fuel power plant.     

Actuator fault detection and isolation in linear systems

A scheme for the detection and isolation of actuator faults in linear systems is proposed. A bank of unknown input observers is constructed to generate residual signals which will deviate in characteristic ways in the presence of actuator faults. Residual signals are unaffected by the unknown inputs acting on the system and this decreases the false alarm and miss probabilities. The results are illustrated through a simulation study of actuator fault detection and isolation in a pilot plant doubleeffect evaporator.     

Disturbance decoupling in fault detection of linear periodic systems

This paper studies fault detection problems of linear discrete-time periodic systems. The aim is to design residual generators, which deliver a residual signal fully decoupled from unknown disturbances. First, a periodic parity relation based full decoupling residual generator with a periodically varying parity vector is established. Then, the relation between periodic parity vectors and periodic observer-based residual generators is investigated. It is shown that a periodic observer-based full decoupling residual generator can be obtained from a periodic full decoupling parity vector. Finally, the condition of disturbance decoupling is discussed and an example is given to illustrate the proposed approaches.     

Observer and observer-based H∞ control of generalized Hamiltonian systems

This paper deals with observer design for generalized Hamiltonian systems and its applications. First, by using the systems' structural properties, a new observer design method called Augment Plus Feedback is provided and two kinds of observers are obtained: non-adaptive and adaptive ones. Then, based on the obtained observer, H∞ control design is investigated for generalized Hamiltonian systems, and an observer-based control design is proposed. Finally, as an application to power systems, an observer and an observer-based H∞ control law are designed for single-machine infinite-bus systems.Simulations show that both the observer and controller obtained in this paper work very well.     

Nonlinear fault detection based on locally linear embedding

In this paper, a new nonlinear fault detection technique based on locally linear embedding （LLE） is developed. LLE can efficiently compute the low-dimensional embedding of the data with the local neighborhood structure information preserved. In this method, a data-dependent kernel matrix which can reflect the nonlinear data structure is defined. Based on the kernel matrix, the Nystrrm formula makes the mapping extended to the testing data possible. With the kernel view of the LLE, two monitoring statistics are constructed. Together with the out of sample extensions, LLE is used for nonlinear fault detection. Simulation cases were studied to demonstrate the performance of the proposed method.     

线性随机系统的微小传感器故障检测

针对一类线性随机系统,研究了其微小传感器故障检测问题.基于Kalman滤波算法构造状态估计器,利用移动加权平均方法设计残差与评价函数.根据非中心卡方分布的性质,分析了故障幅值、窗口长度、误报率和漏报率之间的关系.采用不等式技术,得到了确保在统计意义下微小故障可检测性的最优权值和最小窗口长度.最后,通过一个仿真实例验证了所提方法的有效性.     

Optimal fault detection for linear discrete time-varying systems

This paper deals with the problem of observer-based fault detection for linear discrete time-varying (LDTV) systems. A problem formulation is first proposed to address the optimization of the fault detection filter (FDF) design, which is expressed in terms of maximizing a finite horizon H_∞/H_∞ or H₋/H_∞ performance index. This formulation can be applied to FDF design of LDTV systems subject to l₂-norm bounded unknown inputs or stochastic noise sequences. It is shown that a unified optimal solution to the FDF can be obtained by solving the discrete time Riccati equation and the optimal FDF is not unique. A numerical example is given to illustrate the proposed method.     

Timely robust fault detection for multirate linear systems

This paper presents a fault detection and isolation scheme for multirate systems with a fast input sampling rate and slower output sampling rates. We design a separate observer for each set of simultaneous measurements with the observer operating at their sampling rate. We use an unknown input observer design to allow state estimation in the presence of disturbances and modelling errors. The observer allows us to estimate the system state and obtain a residual vector to be used in fault detection. Furthermore, we are able to use single-rate methodologies for fault diagnosis. We provide necessary and sufficient conditions for the existence of the observer and the detection of the fault vector. An example is given to illustrate the new fault detection approach and another to demonstrate fault isolation.     

Robust sliding mode observer-based actuator fault detection and isolation for a class of nonlinear systems

In this article, an actuator fault detection and isolation scheme for a class of nonlinear systems with uncertainty is considered. The uncertainty is allowed to have a nonlinear bound which is a general function of the state variables. A sliding mode observer is first established based on a constrained Lyapunov equation. Then, the equivalent output error injection is employed to reconstruct the fault signal using the characteristics of the sliding mode observer and the structure of the uncertainty. The reconstructed signal can approximate the system fault signal to any accuracy even in the presence of a class of uncertainty. Finally, a simulation study on a nonlinear aircraft system is presented to show the effectiveness of the scheme.     

Constrained observer-based controller for linear continuous-time systems

The observer-based controller design in the presence of inequality constraints on the system input is considered. The solution is obtained by an adequate use of the positive invariance concept     

Actuator fault diagnosis: an adaptive observer-based technique

This paper presents a novel approach for the fault diagnosis of actuators in known deterministic dynamic systems by using an adaptive observer technique. Systems without model uncertainty are initially considered, followed by a discussion of a general situation where the system is subjected to either model uncertainty or external disturbance. Under the assumption that the system state observer can be designed such that the observation error is strictly positive real (SPR), an adaptive diagnostic algorithm is developed to diagnose the fault, and a modified version is proposed for the general system to improve robustness. The method is demonstrated through its application to a simulated second-order system     

Dynamic observer-based controllers for linear uncertain systems

This paper addresses robust controller design for uncertain linear systems via a dynamic observer-based controller. A dynamic observer is an alternative structure for a classical observer which can be regarded as a general form of a usual observer and has additional degrees of freedom in the observer structure. Using this new observer structure, a new observer-based controller for linear systems is proposed. Some strict linear matrix inequalities (LMIs) have been given to find the dynamic observer parameters and controller gain. It is shown that dynamic observer can be used effectively for tackling the drawbacks of the classical observer-based robust controller design methods. As an advantage, LMIs are derived even in the presence of uncertainties in system, input and output matrices simultaneously, whereas by using the traditional observer, bilinear matrix inequalities (BMIs) are given in the presence of such uncertainties. Moreover, the proposed LMIs do not imply the equality constraint. Simulation results are used to illustrate the effectiveness of the proposed design technique.     

Robust fault detection in linear systems based on PI observers

A parametric approach for robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order proportional-integral (PI) observers. The approach is based on a result for PI observer design recently proposed. In terms of the design degrees of freedom provided by the parametric PI observer design and a group of introduced parameter vectors, a sufficient and necessary condition for PI observer design with disturbance decoupling is established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance to the residual signal is decoupled, and a simple algorithm is presented. The presented approach offers all the degrees of design freedom. A numerical example illustrates the effect of the proposed approach.     

Robust fault detection of uncertain linear systems via quasi-LMIs

A novel H_∞ deconvolution filter design method is discussed for fault detection of uncertain polytopic linear systems subject to unknown inputs. The enhancement of fault sensitivity is characterized in terms of an H_- index. By means of the Projection Lemma and Congruence Transformations, a quasi-convex LMI formulation of the design problem is obtained. The effectiveness of the filter is illustrated via a numerical example.