Detection,isolation and identification of multiple actuator and sensor faults in nonlinear dynamic systems: Application to a waste water treatment process

The goal in many fault detection and isolation schemes is to increase the isolation and identification speed. This paper, presents a new approach of a nonlinear model based adaptive observer method, for detection, isolation and identification of actuator and sensor faults. Firstly, we will design a new method for the actuator fault problem where, after the fault detection and before the fault isolation, we will try to estimate the output of the instrument. The method is based on the formation of nonlinear observer banks where each bank isolates each actuator fault. Secondly, for the sensor problem we will reformulate the system by introducing a new state variable, so that an augmented system can be constructed to treat sensor faults as actuator faults. A method based on the design of an adaptive observers’ bank will be used for the fault treatment. These approaches use the system model and the outputs of the adaptive observers to generate residues. Residuals are defined in such way to isolate the faulty instrument after detecting the fault occurrence. The advantages of these methods are that we can treat not only single actuator and sensor faults but also multiple faults, more over the isolation time has been decreased. In this study, we consider that only abrupt faults in the system can occur. The validity of the methods will be tested firstly in simulation by using a nonlinear model of waste water treatment process with and without measurement noise and secondly with the same nonlinear model but by using this time real data.     

Fault diagnosis for a class of nonlinear uncertain hybrid systems

This paper presents a fault diagnosis architecture for a class of hybrid systems with nonlinear uncertain time-driven dynamics, measurement noise, and autonomous and controlled mode transitions. The proposed approach features a hybrid estimator based on a modified hybrid automaton framework. The fault detection scheme employs a filtering approach that attenuates the effect of the measurement noise and allows tighter mode-dependent thresholds for the detection of both discrete and parametric faults while guaranteeing no false alarms due to modeling uncertainty and mode mismatches. Both the hybrid estimator and the fault detection scheme are linked with an autonomous guard events identification (AGEI) scheme that handles the effects of mode mismatches due to autonomous mode transitions and allows effective mode estimation. Finally, the fault isolation scheme anticipates which fault events may have occurred and dynamically employs the appropriate isolation estimators for isolating the fault by calculating suitable thresholds and estimating the parametric fault magnitude through adaptive approximation methods. Simulation results from a five-tank hybrid system illustrate the effectiveness of the proposed approach.     

Data-driven recursive least squares methods for non-affined nonlinear discrete-time systems

Aiming at identifying nonlinear systems, one of the most challenging problems in system identification, a class of data-driven recursive least squares algorithms are presented in this work. First, a full form dynamic linearization based linear data model for nonlinear systems is derived. Consequently, a full form dynamic linearization-based data-driven recursive least squares identification method for estimating the unknown parameter of the obtained linear data model is proposed along with convergence analysis and prediction of the outputs subject to stochastic noises. Furthermore, a partial form dynamic linearization-based data-driven recursive least squares identification algorithm is also developed as a special case of the full form dynamic linearization based algorithm. The proposed two identification algorithms for the nonlinear nonaffine discrete-time systems are flexible in applications without relying on any explicit mechanism model information of the systems. Additionally, the number of the parameters in the obtained linear data model can be tuned flexibly to reduce computation complexity. The validity of the two identification algorithms is verified by rigorous theoretical analysis and simulation studies.     

On-line model-based fault detection and isolation for PEM fuel cell stack systems

Efficient and reliable operation of Polymer Electrolyte Membrane (PEM) fuel cells are key requirements for their successful commercialization and application. The use of diagnostic techniques enables the achievement of these requirements. This paper focuses on model-based fault detection and isolation (FDI) for PEM fuel cell stack systems. The work consists in designing and selecting a subset of consistency relations such that a set of predefined faults can be detected and isolated. Despite a nonlinear model of the PEM fuel cell stack system will be used, consistency relations that are easily implemented by a variable back substitution method will be selected. The paper also shows the significance of structural models to solve diagnosis issues in complex systems.     

Dynamic output feedback fault tolerant controller design for discrete-time switched systems with actuator fault

This paper investigates the problem of dynamic output feedback fault tolerant controller design for discrete-time switched systems with actuator fault. By using reduced-order observer method and switched Lyapunov function technique, a fault estimation algorithm is achieved for the discrete-time switched system with actuator fault. Then based on the obtained online fault estimation information, a switched dynamic output feedback fault tolerant controller is employed to compensate for the effect of faults by stabilizing the closed-loop systems. Finally, an example is proposed to illustrate the obtained results.     

Fault identification in nonlinear hybrid systems

The problem of fault identification in hybrid systems is investigated. It is assumed that the hybrid systems under consideration consist of a finite automaton, the set of nonlinear differential equations, and so-called mode activator that coordinates the action of these two parts. To solve the fault identification problem, sliding mode observers are used. The suggested approach for constructing sliding mode observers is based on the reduced order model of the original system. This allows to reduce complexity of sliding mode observers and relax the limitations imposed on the original system. Examples illustrate details of the solution.     

Bond graph model-based system mode identification and mode-dependent fault thresholds for hybrid systems

Hybrid system models exploit the modelling abstraction that fast state transitions take place instantaneously so that they encompass discrete events and the continuous time behaviour for the while of a system mode. If a system is in a certain mode, e.g. two rigid bodies stick together, then residuals of analytical redundancy relations (ARRs) within certain small bounds indicate that the system is healthy. An unobserved mode change, however, invalidates the current model for the dynamic behaviour. As a result, ARR residuals may exceed current thresholds indicating faults in system components that have not happened. The paper shows that ARR residuals derived from a bond graph cannot only serve as fault indicators but may also be used for bond graph model-based system mode identification. ARR residuals are numerically computed in an off-line simulation by coupling a bond graph of the faulty system to a non-faulty system bond graph through residual sinks. In real-time simulation, the faulty system model is to be replaced by measurements from the real system. As parameter values are uncertain, it is important to determine adaptive ARR thresholds that, given uncertain parameters, allow to decide whether the dynamic behaviour in a current system mode is the one of the healthy system so that false alarms or overlooking of true faults can be avoided. The paper shows how incremental bond graphs can be used to determine adaptive mode-dependent ARR thresholds for switched linear time-invariant systems with uncertain parameters in order to support robust fault detection. Bond graph-based hybrid system mode identification as well as the determination of adaptive fault thresholds is illustrated by application to a power electronic system easy to survey. Some simulation results have been analytically validated.     

Robust state estimation and fault diagnosis for uncertain hybrid systems

Robust state estimation and fault diagnosis are challenging problems in the research into hybrid systems. In this paper a novel robust hybrid observer is proposed for a class of hybrid systems with unknown inputs and faults. Model uncertainties, disturbances and faults are represented as structured unknown inputs. The robust hybrid observer consists of a mode observer for mode identification and a continuous observer for continuous state estimation and mode transition detection. It is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded. Robustness to model uncertainties and disturbances can be guaranteed for the hybrid observer by disturbance decoupling. Furthermore, the detectability and mode identifiability conditions are rigorously analyzed. On the basis of the robust hybrid observer, a robust fault detection and isolation scheme is presented also in the paper. Simulations of a hybrid four-tank system show the proposed approach is effective.     

Adjustable dimension descriptor observer based fault estimation for switched nonlinear systems with partially unknown nonlinear dynamics

This paper focuses on the fault estimation problem for switched systems with partially unknown nonlinear dynamics, actuator and sensor faults, simultaneously. The fault estimation observers are constructed, in which the observer dimension is not fixed and can be selected in a certain range. Both the disturbance decoupling and disturbance attenuation are considered, where the unknown nonlinear dynamics can be decoupled and the effect of modeling error and measurement disturbance is attenuated. Based on the average dwell time and the piecewise Lyapunov function, the observer parameter matrices can be calculated by solving LMIs and matrix equations. Finally, two examples are listed to verify the proposed fault estimation approach.     

Hybrid modeling based double-granularity fault detection and diagnosis for quadrotor helicopter

Fault detection and diagnosis (FDD) is an effective technology to assure the safety and reliability of quadrotor helicopters. However, there are still some unsolved problems in the existing FDD methods, such as the trade-offs between the accuracy and complexity of system models used for FDD, and the rarely explored structure faults in quadrotor helicopters. In this paper, a double-granularity FDD method is proposed based on the hybrid modeling of a quadrotor helicopter which has been developed in authors’ previous work. The hybrid model consists of a prior model and a set of non-parametric models. The coarse-granularity-level FDD is built on the prior model which can isolate the faulty channel(s); while the fine-granularity-level FDD is built on the nonparametric models which can isolate the faulty components in the faulty channel. In both coarse and fine granularity FDD procedures, principal component analysis (PCA) is adopted for online fault detection. Using such a double-granularity scheme, the proposed FDD method has inherent ability in detecting and diagnosing structure faults or failures in quadrotor helicopters. Experimental results conducted on a 3-DOF hover platform can demonstrate the feasibility and effectiveness of the proposed hybrid modeling technique and the hybrid model based FDD method.     

Mathematical modeling of a steam generator for sensor fault detection

A dynamic model for a nuclear power plant steam generator (vertical, preheated, U-tube recirculation-type) is formulated as a sixth-order nonlinear system. The model integrates nodal mass and energy balances for the primary water, the U-tube metal and the secondary water and steam. The downcomer flow is determined by a static balance of momentum. The mathematical system is solved using transient input data from the Philippsburg 2 (FRG) nuclear power plant. The results of the calculation are compared with actual measured values. The proposed model provides a low-cost tool for the automatic control and simulation of the steam generating process. The “parity-space” algorithm is used to demonstrate the applicability of the mathematical model for sensor fault detection and identification purposes. This technique provides a powerful means of generating temporal analytic redundancy between sensor signals. It demonstrates good detection rates of sensor errors using relatively few steps of scanning time and allows the reconfiguration of faulty signals.     

A low-order active fault-tolerant state space self-tuner for the unknown sampled-data nonlinear singular system using OKID and modified ARMAX model-based system identification

In this paper, we present two control schemes for the unknown sampled-data nonlinear singular system. One is an observer-based digital redesign tracker with the state-feedback gain and the feed-forward gain based on off-line observer/Kalman filter identification (OKID) method. The presented control scheme is able to make the unknown sampled-data nonlinear singular system to well track the desired reference signal. The other is an active fault tolerance state-space self-tuner using the OKID method and modified autoregressive moving average with exogenous inputs (ARMAX) model-based system identification for unknown sampled-data nonlinear singular system with input faults. First, one can apply the off-line OKID method to determine the appropriate (low-) order of the unknown system order and good initial parameters of the modified ARMAX model to improve the convergent speed of recursive extended-least-squares (RELS) method. Then, based on modified ARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown sampled-data nonlinear singular system with immeasurable system state. Moreover, in order to overcome the interference of input fault, one can use a fault-tolerant control scheme for unknown sampled-data nonlinear singular system by modifying the conventional self-tuner control (STC). The presented method can effectively cope with partially abrupt and/or gradual system input faults. Finally, some illustrative examples including a real circuit system are given to demonstrate the effectiveness of the presented design methodologies.     

Supervisory fault-tolerant regulation for nonlinear systems

This paper focuses on the fault-tolerant output regulation problem for nonlinear systems with faults generated by exogenous systems that belong to a certain pre-specified set of models. The novelty is to design a fault-tolerant control (FTC) scheme for the overall system process where different faults may occur respectively at different time instants of the process, which is called the successional faulty case. The proposed FTC framework relies on a simple supervisory switching among a family of pre-computed candidate controllers. The output regulation goal is maintained in such a successional faulty case. A DC motor example illustrates the efficiency of the proposed method.     

Design of observers for nonlinear systems with H ∞ performance analysis

This paper investigates the problem of observer design for nonlinear systems. By using differential mean value theorem, which allows transforming a nonlinear error dynamics into a linear parameter varying system, and based on Lyapunov stability theory, an approach of observer design for a class of nonlinear systems with time‐delay is proposed. The sufficient conditions, which guarantee the estimation error to asymptotically converge to zero, are given. Furthermore, an adaptive observer design for a class of nonlinear system with unknown parameter is considered. A method of H _∞ adaptive observer design is presented for this class of nonlinear systems; the sufficient conditions that guarantee the convergence of estimation error and the computing method for observer gain matrix are given. Finally, an example is given to show the effectiveness of our proposed approaches. Copyright © 2013 John Wiley & Sons, Ltd.     

Multi-class support vector machine optimized by inter-cluster distance and self-adaptive deferential evolution

Support vector machine (SVM) is a popular tool for machine learning task. It has been successfully applied in many fields, but the parameter optimization for SVM is an ongoing research issue. In this paper, to tune the parameters of SVM, one form of inter-cluster distance in the feature space is calculated for all the SVM classifiers of multi-class problems. Inter-cluster distance in the feature space shows the degree the classes are separated. A larger inter-cluster distance value implies a pair of more separated classes. For each classifier, the optimal kernel parameter which results in the largest inter-cluster distance is found. Then, a new continuous search interval of kernel parameter which covers the optimal kernel parameter of each class pair is determined. Self-adaptive differential evolution algorithm is used to search the optimal parameter combination in the continuous intervals of kernel parameter and penalty parameter. At last, the proposed method is applied to several real word datasets as well as fault diagnosis for rolling element bearings. The results show that it is both effective and computationally efficient for parameter optimization of multi-class SVM.     

动力系统实测数据的非线性混沌模型重构

动力系统实测非线性混沌数据的模型重构技术是相空间重构的重要内容。在判定了实测数据的非线性混沌特征,计算了实测数据的分维数,Lyapunov指数,并对其进行了本征值分解和噪声去除及确定其模型阶数以后,提出了一个动力系统实测数据的非线性混沌模型,给出了相应的模型参数辨识方法,并用其确立的混沌模型进行了预测工作,计算结果表明:模型参数辨识方法能迅速地将参数估计值带到多峰目标函数的全局最少值附近,然后再采用优化理论能较准确地求出模型的参数,用得到的混沌模型对系统进行预测工作其预测效果良好,且混沌时序不可能作长期预测。     

A novel feedback controller design with robust fault isolation ability

This paper proposes a novel feedback controller design scheme which can achieve fault isolation based on the control signal or its embedded signal, i.e., with the self-fault-isolation ability. First of all, according to the well-known Youla parameterization, a controller structure consisting of state and residual joint feedback is developed. Then, the residual feedback gain and observer gain are designed to make the cooperative structured residual feedback signal have fault isolation ability. Some free design parameters in the two gains are further utilized for robust self-fault-isolation. Moreover, the state feedback gain is designed, in the framework of switched system, to realize the self-fault-diagnosis and isolation, based on the control signal directly. The proposed control structure also has the advantage of cooperative fault tolerance. Finally, the simulation of HVAC (Heating, Ventilation and Air Conditioning) system, composed of four rooms in one story building scenario, is carried out to demonstrate the effectiveness and superiority of the proposed feedback controller design approach.     

Gradient-based iterative identification for MISO Wiener nonlinear systems: Application to a glutamate fermentation process

This paper deals with modeling and parameter identification of multiple-input single-output Wiener nonlinear systems. The basic idea is to construct a multiple-input single-output Wiener nonlinear model and to derive the gradient-based iterative algorithm for the proposed model. The proposed method has been applied to identify the parameters of a glutamate fermentation process. The results of real data simulation show that this method is effective.     

Gain-scheduled fault detection on stochastic nonlinear systems with partially known transition jump rates

In this paper, the problem of continuous gain-scheduled fault detection (FD) is studied for a class of stochastic nonlinear systems which possesses partially known jump rates. Initially, by using gradient linearization approach, the nonlinear stochastic system is described by a series of linear jump models at some selected working points. Subsequently, observer-based residual generator is constructed for each jump linear system. Then, a new observer-design method is proposed for each re-constructed system to design H_∞ observers that minimize the influences of the disturbances, and to formulate a new performance index that increase the sensitivity to faults. Finally, continuous gain-scheduled approach is employed to design continuous FD observers on the whole nonlinear stochastic system. Simulation example is given to show the effectiveness and potential of the developed techniques.     

Fuzzy temporal fault tree analysis of dynamic systems

Fault tree analysis (FTA) is a powerful technique that is widely used for evaluating system safety and reliability. It can be used to assess the effects of combinations of failures on system behaviour but is unable to capture sequence dependent dynamic behaviour. A number of extensions to fault trees have been proposed to overcome this limitation. Pandora, one such extension, introduces temporal gates and temporal laws to allow dynamic analysis of temporal fault trees (TFTs). It can be easily integrated in model-based design and analysis techniques. The quantitative evaluation of failure probability in Pandora TFTs is performed using exact probabilistic data about component failures. However, exact data can often be difficult to obtain. In this paper, we propose a method that combines expert elicitation and fuzzy set theory with Pandora TFTs to enable dynamic analysis of complex systems with limited or absent exact quantitative data. This gives Pandora the ability to perform quantitative analysis under uncertainty, which increases further its potential utility in the emerging field of model-based design and dependability analysis. The method has been demonstrated by applying it to a fault tolerant fuel distribution system of a ship, and the results are compared with the results obtained by other existing techniques.