Designing fault detection observers for linear systems with mismatched unknown inputs

Algebraic unknown input observers (UIOs) that have been previously reported in the literature can be constructed under the assumption that linear systems with unknown inputs satisfy the so-called observer matching condition. This condition restricts practical applications of UIOs for fault detection and isolation (FDI). We present an algebraic design for fault detection observers (FDOs) for the case in which the observer matching condition is not satisfied. To loosen the restriction imposed by the observer matching condition, the UIO design method combined with the unknown input modeling technique is proposed to design an FDO that decouples the effect of mismatched unknown inputs. To do this, first, unknown inputs that denote the faults of no interest and process disturbances are decomposed into algebraically rejectable unknown inputs and modeled unknown inputs such that the observer matching condition is satisfied. Under the assumption that mismatched unknown inputs are deterministic and can be expressed as the responses of fictitious autonomous dynamical systems, an augmented system is obtained by combining the original system model with the unknown input model. Finally, through the design technique of a UIO for the augmented system, a reduced-order FDO is constructed to estimate an augmented state vector that consists of both the original state variables and the augmentative state variables. The estimated state is then used to generate the residual, which should be designed to be insensitive to unknown inputs while being sensitive to the faults of interest. Two numerical examples are provided to show the usefulness and the feasibility of the presented approach.     

A gain-varying UIO approach with adaptive threshold for FDI of nonlinear F16 systems

A discrete gain-varying unknown input observer (UIO) method is presented for actuator fault detection and isolation (FDI) problems in this paper. A novel residual scheme together with a moving horizon threshold is proposed. This design methodology is applied to a nonlinear F16 system with polynomial aerodynamics coefficient expressions, where the coefficient expressions for the F16 system and UIOs may be slightly different. The simulation results illustrate that a satisfactory FDI performance can be achieved even when the F16 system is under the environment of model uncertainties, exogenous noise and measurement errors.     

Unified model-based fault diagnosis for three industrial application studies

This paper proposes a unified scheme for fault detection and isolation (FDI) that integrates model-based and multivariate statistical methods. For creating suitable models, subspace model identification is utilized together with state-observers to track the measured process operation. To describe and analyze the impact of fault conditions, the scheme utilizes input reconstruction and unknown input estimation to generate multivariate residual-based statistics. In contrast to existing work, the paper presents three industrial application studies involving sensor faults, as well as process and actuator faults which result from measured and unmeasured disturbances.     

Design of unknown input functional observers for nonlinear systems with application to fault diagnosis

This paper considers the design of low-order unknown input functional observers for robust fault detection and isolation of a class of nonlinear Lipschitz systems subject to unknown inputs. The proposed functional observers can be used to generate residual signals to detect and isolate actuator faults. By using the generalized inverse approach, the effect of the unknown inputs can be decoupled completely from the residual signals. Conditions for the existence and stability of reduced-order unknown input functional observer are derived. A design procedure for the generation of residual signals to detect and isolate actuator faults is presented using the proposed unknown-input observer-based approach. A numerical example is given to illustrate the proposed fault diagnosis scheme in nonlinear systems subject to unknown inputs.     

UIO design for singular delayed LPV systems with application to actuator fault detection and isolation

In this paper, the unknown input observer (UIO) design for singular delayed linear parameter varying (LPV) systems is considered regarding its application to actuator fault detection and isolation. The design procedure assumes that the LPV system is represented in the polytopic framework. Existence and convergence conditions for the UIO are established. The design procedure is formulated by means of linear matrix inequalities (LMIs). Actuator fault detection and isolation is based on using the UIO approach for designing a residual generator that is completely decoupled from unknown inputs and exclusively sensitive to faults. Fault isolation is addressed considering two different strategies: dedicated and generalised bank of observers’ schemes. The applicability of these two schemes for the fault isolation is discussed. An open flow canal system is considered as a case study to illustrate the performance and usefulness of the proposed fault detection and isolation method in different fault scenarios.     

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.     

Optimal stochastic fault detection filter

A fault detection and identification algorithm, called optimal stochastic fault detection filter, is determined. The objective of the filter is to detect a single fault, called the target fault, and block other faults, called the nuisance faults, in the presence of the process and sensor noises. The filter is derived by maximizing the transmission from the target fault to the projected output error while minimizing the transmission from the nuisance faults. Therefore, the residual is affected primarily by the target fault and minimally by the nuisance faults. The transmission from the process and sensor noises is also minimized so that the filter is robust with respect to these disturbances. It is shown that the filter recovers the geometric structure of the unknown input observer in the limit where the weighting on the nuisance fault transmission goes to infinity. Further, the asymptotic behavior of the filter near the limit is determined by using a perturbation method. Filter designs can be obtained for both time-invariant and time-varying systems.     

Canonical correlation analysis-based fault detection methods with application to alumina evaporation process

In this paper, canonical correlation analysis (CCA)-based fault detection methods are proposed for both static and dynamic processes. Different from the well-established process monitoring and fault diagnosis systems based on multivariate analysis techniques like principal component analysis and partial least squares, the core of the proposed methods is to build residual signals by means of the CCA technique for the fault detection purpose. The proposed methods are applied to an alumina evaporation process, and the achieved results show that both methods are applicable for fault detection, while the dynamic one delivers better detection performance.     

High-gain observation with disturbance attenuation and application to robust fault detection

One approach to the problem of residual generation in a purpose of fault detection is to use an observer. One particular difficulty is to distinguish between faults and disturbances. Various observers have already been inspected in that direction, generally based on exact decoupling w.r.t. unknown disturbances. Here the use of high-gain observer techniques is inspected, with a purpose of attenuation of disturbances rather than exact decoupling: conditions allowing some “robust partial estimation” are first presented, and their possible use in fault detection is then discussed.     

Analysis of performance criteria in sampled-data fault detection

Sampled-data control systems are widely used in industry. In this paper the problem of fault detection and isolation (FDI) in sampled-data systems is studied. Many existing methods to design a robust sampled-data FDI are based on optimization of a norm based performance index. Our focus in this study is on the selection of the performance index. It is shown that the existing performance indices are not appropriate choices in the sense that they do not satisfy some expected intuitive properties. To resolve this, an alternative performance index is defined after converting the FDI problem to a standard control problem. This performance index is shown to satisfy the expected properties.     

On the disturbed fault detection and isolation problem

In this paper we study the fault detection and isolation problem in presence of disturbances. In the case of observer-based residual generation, the problem amounts to finding two gain matrices such that two problems are simultaneously solved. These problems are insensitivity of the residuals to disturbances and the existence of some special structure for the transfer from faults to residuals. We prove in this paper that this joint problem can be solved if and only if the usual (undisturbed) fault detection and isolation problem can be solved for a system with a reduced number of outputs.     

A frequency domain approach to fault detection in sampled-data systems

This paper deals with fault detection problems in sampled-data (SD) systems. A tool is first introduced for the analysis of intersample behavior of SD systems in the frequency domain from the viewpoint of fault detection and isolation. Based on it, a direct design approach of fault detection systems for SD systems is proposed, and further the problem of full decoupling from unknown disturbances is studied.     

一种基于最优未知输入观测器的故障诊断方法

针对含有未知输入干扰和噪音的不确定动态系统,使用全阶未知输入观测器(Unknown input observer, UIO)来消除干扰项,实现状态估计, 结合Kalman滤波器算法来求解状态反馈矩阵,以使得输出残差信号的协方差最小,从而增强系统对噪声的鲁棒性,实现了 一种基于最优未知输入观测器的残差产生器.采用极大似然比(Generalized likelihood ratio, GLR)的方法对残差信号进行评估,通过设定的阈值来提高诊断率. 最后以风力发电机组传动系统出现加性传感器故障和乘性传感器故障为例, 进行了残差信号的仿真,仿真结果说明了该方法的有效性.     

Dynamic threshold generators for robust fault detection in linear systems with parameter uncertainty

The problem of developing robust thresholds for fault detection is addressed. An inequality for the solution of a linear system with uncertain parameters is provided and is shown to be a valuable tool for developing dynamic threshold generators for fault detection. Such threshold generators are desirable for achieving robustness against model uncertainty in combination with sensitivity to small faults.The usefulness of the inequality is illustrated by developing an algorithm for detection of sensor faults in a turbofan engine. The proposed algorithm consists of a state observer with integral action. A dynamic threshold generator is derived under the assumption of parametric uncertainty in the process model. Successful simulations with measurement data show that the algorithm is capable of detecting faults without generating false alarms.     

Subspace decomposition approach of fault deviations and its application to fault reconstruction

In the present work, a new subspace decomposition approach of fault deviations is developed in the context of principal component analysis (PCA) based monitoring system for fault diagnosis via reconstruction. The fault effects are decomposed in different monitoring subspaces, principal subspace (PCS) and residual subspace (RS), and the significant fault deviations that are responsible for the concerned alarming monitoring statistic are calculated. This is achieved by designing a two-step feature decomposition procedure in each monitoring subspace. In the first step, the relative fault deviations are sorted by comparing the fault variations with the normal variations. All possible fault deviations that may contribute to the out-of-control monitoring statistics are collected. In the second step, PCA is performed on the chosen fault information where the largest fault deviation directions are decomposed in order. By the two-step decomposition, in each monitoring subspace, two different parts are separated for the purpose of fault reconstruction. One is composed of the concerned fault deviations that contribute to alarming monitoring statistics which are thus significant to remove the out-of-control signals. The other is composed of general variations that are deemed to follow normal rules and thus insignificant to remove alarming monitoring statistics. Theoretical support is framed and the related statistical characteristics are analyzed. Its feasibility and performance are illustrated with data from the three-tank system and the Tennessee Eastman (TE) benchmark process.     

时滞依赖H_/H∞观测器的线性系统故障检测

本文研究了线性连续时滞系统的鲁棒故障检测问题.利用H_/H∞故障检测方法,设计了故障检测观测器,并给出了时滞依赖的故障检测观测器设计条件.本文直接给出刻画有限频故障检测性能的线性矩阵不等式条件,避免因引入加权函数而产生的不准确性.最后,仿真算例表明时滞依赖的有限频故障检测观测器可以取得比已有结果更好的故障检测性能.     

Fault detection and diagnosis in synchronous motors using hidden Markov model-based semi-nonparametric approach

Early detection and diagnosis of faults in industrial machines would reduce the maintenance cost and also increase the overall equipment effectiveness by increasing the availability of the machinery systems. In this paper, a semi-nonparametric approach based on hidden Markov model is introduced for fault detection and diagnosis in synchronous motors. In this approach, after training the hidden Markov model classifiers (parametric stage), two matrices named probabilistic transition frequency profile and average probabilistic emission are computed based on the hidden Markov models for each signature (nonparametric stage) using probabilistic inference. These matrices are later used in forming a similarity scoring function, which is the basis of the classification in this approach. Moreover, a preprocessing method, named squeezing and stretching is proposed which rectifies the difficulty of dealing with various operating speeds in the classification process. Finally, the experimental results are provided and compared. Further investigations are carried out, providing sensitivity analysis on the length of signatures, the number of hidden state values, as well as statistical performance evaluation and comparison with conventional hidden Markov model-based fault diagnosis approach. Results indicate that implementation of the proposed preprocessing, which unifies the signatures from various operating speeds, increases the classification accuracy by nearly 21% and moreover utilization of the proposed semi-nonparametric approach improves the accuracy further by nearly 6%.     

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.