Limnimeter and rain gauge FDI in sewer networks using an interval parity equations based detection approach and an enhanced isolation scheme

In this paper, a methodology for limnimeter and rain-gauge fault detection and isolation (FDI) in sewer networks is presented. The proposed model based FDI approach uses interval parity equations for fault detection in order to enhance robustness against modelling errors and noise. They both are assumed unknown but bounded, following the so-called interval (or set-membership) approach. On the other hand, fault isolation relies on an algorithm that reasons using several fault signature matrices that store additional information to the typical binary one used in standard FDI approaches. More precisely, the considered fault signature matrices contain information about residual fault sign/sensitivity and time/order of activation. The paper also proposes an identification procedure to obtain the interval models used in fault detection that delivers the nominal model plus parameter uncertainty is proposed. To exemplify the proposed FDI methodology, a case study based on the Barcelona sewer network is used.     

Fault detection and isolation of the three-tank system using the modal interval analysis

Analytical redundancy is a widely used technique for fault detection. It consists of comparing the behaviour of a real system with a reference obtained by simulation of its model. The main problem is that there are always imprecisions and uncertainties which are not represented in the model so the behaviour of the real system and the behaviour of the model are not exactly the same. One way to represent these uncertainties in the model is using interval models. The results of the simulation of these types of models may be represented by envelopes. This paper proposes an approach to generate envelopes based on interval techniques of the modal interval analysis. As an example, this approach is used to detect and isolate faults in a physical system formed by three interconnected tanks.     

Combining FDI and AI approaches within causal-model-based diagnosis.

This paper presents a model-based diagnostic method designed in the context of process supervision. It has been inspired by both artificial intelligence and control theory. AI contributes tools for qualitative modeling, including causal modeling, whose aim is to split a complex process into elementary submodels. Control theory, within the framework of fault detection and isolation (FDI), provides numerical models for generating and testing residuals, and for taking into account inaccuracies in the model, unknown disturbances and noise. Consistency-based reasoning provides a logical foundation for diagnostic reasoning and clarifies fundamental assumptions, such as single fault and exoneration. The diagnostic method presented in the paper benefits from the advantages of all these approaches. Causal modeling enables the method to focus on sufficient relations for fault isolation, which avoids combinatorial explosion. Moreover, it allows the model to be modified easily without changing any aspect of the diagnostic algorithm. The numerical submodels that are used to detect inconsistency benefit from the precise quantitative analysis of the FDI approach. The FDI models are studied in order to link this method with DX component-oriented reasoning. The recursive on-line use of this algorithm is explained and the concept of local exoneration is introduced.     

Fault detection and isolation for a wind turbine benchmark using a mixed Bayesian/Set-membership approach

This paper addresses the problem of fault detection and isolation of wind turbines using a mixed Bayesian/Set-membership approach. Modeling errors are assumed to be unknown but bounded, following the set-membership approach. On the other hand, measurement noise is also assumed to be bounded, but following a statistical distribution inside the bounds. To avoid false alarms, the fault detection problem is formulated in a set-membership context. Regarding fault isolation, a new fault isolation scheme that is inspired on the Bayesian fault isolation framework is developed. Faults are isolated by matching the fault detection test results, enhanced by a complementary consistency index that measures the certainty of not being in a fault situation, with the structural information about the faults stored in the theoretical fault signature matrix. The main difference with respect to the classical Bayesian approach is that only models of fault-free behavior are used. Finally, the proposed FDI method is assessed against the wind turbine FDI benchmark proposed in the literature, where a set of realistic fault scenarios in wind turbines are proposed.     

Set-theoretic methods in robust detection and isolation of sensor faults

This paper proposes a sensorfault detection and isolation (FDI) approach based on interval observers and invariant sets. In fault detection (FD), both interval observer-based and invariant set-based mechanisms are used to provide real-time fault alarms. In fault isolation (FI), the proposed approach also uses these two different mechanisms. The former, based on interval observers, aims to isolate faults during the transient-state operation induced by faults. If the former does not succeed, the latter, based on both interval observers and invariant sets, is started to guarantee FI after the system enters into steady state. Besides, a collection of invariant set-based FDI conditions are established by using all available system-operating information provided by all interval observers. In order to reduce computational complexity, a method to remove all available but redundant/unnecessary system-operating information is incorporated into this approach. If the considered faults satisfy the proposed FDI conditions, it can be guaranteed that they are detectable and isolable after their occurrences. This paper concludes with a case study based on a subsystem of a wind turbine benchmark, which can illustrate the effectiveness of this FDI technique.     

Fault diagnosis based on identified discrete-event models

Fault diagnosis of Discrete-Event Systems consists of detecting and isolating the occurrence of faults within a bounded number of event occurrences. Recently, a new model for discrete-event system identification with the aim of fault detection, called Deterministic Automaton with Outputs and Conditional Transitions (DAOCT), has been proposed in the literature. The model is computed from observed fault-free paths, and represents the fault-free system behavior. In order to obtain compact models, loops are introduced in the model, which implies that sequences that are not observed can be generated leading to an exceeding language. This exceeding language is associated with possible non-detectable faults, and must be reduced in order to use the model for fault detection. After detecting the fault occurrence, its isolation is carried out by analyzing residuals. In this paper, we present a fault diagnosis scheme based on the DAOCT model. We show that the proposed fault diagnosis scheme is more efficient than other approaches proposed in the literature, in the sense that the exceeding language can be drastically reduced, reducing the number of non-detectable fault occurrences, and, in some cases, reducing also the delay for fault diagnosis. A practical example, consisting of a plant simulated by using a 3D simulation software controlled by a Programmable Logic Controller, is used to illustrate the results of the paper.     

Fault diagnosis with multivariate statistical models part I: using steady state fault signatures

Multivariate statistical approaches to fault detection based on historical operating data have been found to be useful with processes having a large number of measured variables and when causal models are unavailable. For fault isolation or diagnosis they have been less powerful because of the non-causal nature of the data on which they are based. To improve the fault isolation with these methods, additional data on past faults have been used to supplement the models. A critical review of this fault isolation literature is given, and an improved approach capable of handling both simple and complex faults is presented. This approach extracts fault signatures that are vectors of movement of the fault in both the model space and the residual space. The directions of these vectors are then compared to the corresponding vector directions of known faults in the fault library. Isolation is then based on a joint plot of the angles between the vectors of the current fault and those of the known faults. Although the fault signatures are based on steady-state information, the methodology assumes that time varying disturbances due to common-cause sources are always present, and it is applied to dynamic data as soon as a fault is detected. The method is demonstrated using a simulated CSTR system with feedback control, and is shown to be effective in isolating both simple and complex faults.     

Rainfall–runoff multi-modelling for sensor fault diagnosis

In view of the limitations of flood and pollution prevention in urban sewage networks, the control of hydraulic equipment now calls for more reliable measurements provided by different sensors. The sensor fault detection and isolation described here requires the availability of a rainfall–runoff relationship in order to apply analytical redundancy-based diagnostic procedures. However, because this relationship is conspicuously non-linear and time varying, the latter relationship is identified by using a multi-model approach. The proposed modelling approach has been successfully tested on a watershed located in an urban area of Nancy, in eastern France, using actual rainfall and runoff data taken from the sewerage control centre database. The model obtained is then used to increase the degree of information redundancy in order to implement a sensor fault diagnostic procedure. Since no statistical hypothesis on measurement uncertainties can be made, interval arithmetic is used to derive residual tolerance.     

Subspace identification of continuous time models for process fault detection and isolation

This paper proposes a novel subspace approach towards identification of optimal residual models for process fault detection and isolation (PFDI) in a multivariate continuous-time system. We formulate the problem in terms of the state space model of the continuous-time system. The motivation for such a formulation is that the fault gain matrix, which links the process faults to the state variables of the system under consideration, is always available no matter how the faults vary with time. However, in the discrete-time state space model, the fault gain matrix is only available when the faults follow some known function of time within each sampling interval. To isolate faults, the fault gain matrix is essential. We develop subspace algorithms in the continuous-time domain to directly identify the residual models from sampled noisy data without separate identification of the system matrices. Furthermore, the proposed approach can also be extended towards the identification of the system matrices if they are needed. The newly proposed approach is applied to a simulated four-tank system, where a small leak from any tank is successfully detected and isolated. To make a comparison, we also apply the discrete time residual models to the tank system for detection and isolation of leaks. It is demonstrated that the continuous-time PFDI approach is practical and has better performance than the discrete-time PFDI approach.     

Fault estimation and controller compensation in Lure systems by LPV-embedding

Previous works have considered the use of set invariance theory for fault detection and isolation in nonlinear Lure systems. This paper extends those results and proposes a new actuator fault-tolerant control approach. The fault-tolerant control scheme is designed based on linear parameter-varying (LPV) models of Lure systems. The actuator fault situation is diagnosed by an invariant set-based fault detection and isolation algorithm. Faults are compensated by adapting the controller gain based on estimates of the fault magnitude. Conditions for correct fault detection and isolation, and closed-loop stability are derived. The proposed fault-tolerant control scheme is compared with a linearised model approach and the performance of both, LPV-embedding and linearised, approaches are analysed for scalar and second-order systems. An example of a chaotic Chua circuit is also provided to illustrate the proposed fault-tolerant control scheme in higher-order systems.     

Adaptive fault detection and isolation approach for actuator stuck faults in closed-loop systems

This paper addresses the fault detection and isolation (FDI) problem for linear time-invariant (LTI) systems under feedback control. Considered all the possible actuator stuck faults, the closed-loop systems are modeled via multiple models, i.e., fault-free model and faulty models. A fault detection observer and a bank of fault isolation observers are designed by using adaptive estimation techniques. The explicit fault detectability and isolability conditions are derived for determining the class of faults that are detectable and isolable. An F-18 aircraft model is employed to illustrate the effectiveness of the proposed FDI approach.     

Fault tolerant control using a fuzzy predictive approach

This paper proposes the application of fault-tolerant control (FTC) using fuzzy predictive control. The FTC approach is based on two steps, fault detection and isolation (FDI) and fault accommodation. The fault detection is performed by a model-based approach using fuzzy modeling and fault isolation uses a fuzzy decision making approach. The information obtained on the FDI step is used to select the model to be used in fault accommodation, in a model predictive control (MPC) scheme. The fault accommodation is performed with one fuzzy model for each identified fault. The FTC scheme is used to accommodate the faults of two systems a container gantry crane and three tank benchmark system. The fuzzy FTC scheme proposed in this paper was able to detect, isolate and accommodate correctly the considered faults of both systems.     

Cascade filter structure for sensor/actuator fault detection and isolation of satellite attitude control system

This paper presents a new scheme for fault detection and isolation in a satellite system. The purpose of this paper is to develop detection, isolation and identification algorithms based on a cascade filter for both total and partial faults in a satellite attitude control system (ACS). The cascade filter consists of a decentralized Kalman filter (DKF) and a bank of interacting multiple model (IMM) filters. The cascade filter is utilized for detection and diagnosis of anticipated sensor and actuator faults in a satellite ACS. Other fault detection and isolation (FDI) schemes are compared with the proposed FDI scheme. The FDI procedure using a cascade filter was developed in three stages. In the first stage, two local filters and a master filter detect sensor faults. In the second stage, the FDI scheme checks sensor residuals to isolate sensor faults, and 11 Extended Kalman filters with actuator fault models detect wherever actuator faults occur. In the third stage of the FDI scheme, four filters identify the fault type, which is either a total or partial fault. An important feature of the proposed FDI scheme is that it can decrease fault isolation time and accomplish not only fault detection and isolation but also fault type identification using a scalar penalty in the conditional density function.     

Online fault diagnosis using recursive subspace identification: Application to a dam-gallery open channel system

The paper presents an online strategy for sensor and/or actuator fault detection and isolation applied to a dam-gallery. A recursive subspace identification algorithm is used to estimate the dam-gallery model parameters. The main contribution consists in developing a specific identification scheme, insensitive to a certain type of faults. That is, the identified parameters are invariant to the faults. A fault estimation procedure is proposed to detect potential faults. The proposed approach appears to be suitable for open channel systems for which the characteristics are not easily measurable.     

Robust fault isolation for a class of non-linear input?output systems

The design and analysis of fault diagnosis methodologies for non-linear systems has received significant attention recently. This paper presents a robust fault isolation scheme for a class of non-linear systems with unstructured modelling uncertainty and partial state measurement. The proposed fault diagnosis architecture consists of a fault detection and approximation estimator and a bank of isolation estimators. Each isolation estimator corresponds to a particular type of fault in the fault class. A fault isolation decision scheme is presented with guaranteed performance. If at least one component of the output estimation error of a particular fault isolation estimator exceeds the corresponding adaptive threshold at some finite time, then the occurrence of that type of fault can be excluded. Fault isolation is achieved if this is valid for all but one isolation estimator. Based on the class of non-linear systems under consideration, fault isolability conditions are rigorously investigated, characterizing the class of non-linear faults that are isolable by the proposed scheme. Moreover, the non-conservativeness of the fault isolability conditions is illustrated by deriving a subclass of nonlinear systems and faults for which this condition is also necessary for fault isolability. A simulation example of a simple robotic system is used to show the effectiveness of the robust fault isolation methodology.     

Fault Detection under Fuzzy Model Uncertainty

The paper tackles the problem of robust fault detection using Takagi-Sugeno fuzzy models. A model-based strategy is employed to generate residuals in order to make a decision about the state of the process. Unfortunately, such a method is corrupted by model uncertainty due to the fact that in real applications there exists a model-reality mismatch. In order to ensure reliable fault detection the adaptive threshold technique is used to deal with the mentioned problem. The paper focuses also on fuzzy model design procedure. The bounded-error approach is applied to generating the rules for the model using available measurements. The proposed approach is applied to fault detection in the DC laboratory engine.     

Fault detection and isolation in transient states using principal component analysis

This paper proposes the use of principal component analysis (PCA) for process monitoring and fault detection and isolation in processes with several operation modes and long transient states and start-ups. The principal aspects of the PCA approach and the necessary transformations for dealing with this type of processes are presented. In this paper a classical PCA model is used for each steady state of the process and a modification of a batch PCA approach is applied to the transient states of the continuous process. So, in this last case, the PCA model is performed over a three way matrix arranged with the values of the measured variables of several past transitions with a nominal behaviour. This approach presents some problems, such as the unfolding, alignment and imputation. The methods proposed to deal with these problems are explained in detail and compared in order to design a fault detection and isolation method. Two examples are considered to perform the tasks explained. In both cases good results are obtained.     

Neuro-fuzzy networks and their application to fault detection of dynamical systems

The paper tackles the problem of robust fault detection using Takagi–Sugeno neuro-fuzzy (N-F) models. A model-based strategy is employed to generate residuals in order to make a decision about the state of the process. Unfortunately, such an approach is corrupted by model uncertainty due to the fact that in real applications there exists a model–reality mismatch. In order to ensure reliable fault detection, the adaptive threshold technique is used to deal with the problem. The paper focuses also on the N-F model design procedure. The bounded-error approach is applied to generate rules for the model using available data. The proposed algorithms are applied to fault detection in a valve that is a part of the technical installation at the Lublin sugar factory in Poland. Experimental results are presented in the final part of the paper to confirm the effectiveness of the method.