Bounded-error Approach Research Articles

A bounded-error approach to actuator fault diagnosis and remaining useful life prognosis of Takagi-Sugeno fuzzy systems

The paper presents an actuator fault diagnosis and prognosis scheme for Takagi-Sugeno fuzzy system. It overcomes the drawbacks of the approaches presented in the relevant literature by taking into consideration the problem of the robustness. The proposed approach consists of an actuator fault estimator which provides knowledge about faults with their uncertainty intervals. Thus, the fault detection mechanism relies on an acceptable threshold imposed on these intervals. Once the fault is detected, the remaining useful life of an actuator is predicted what is expressed in the so-called time-to-failure. Similarly as in the case of fault estimation, the remaining useful life is provided as an uncertainty interval. It should be notated that previously reported approaches to Takagi-Sugeno systems cannot either provide the uncertainty of fault estimates for remaining useful life. To tackle the development of the above schemes the theory of quadratic boundedness and feasible parameter set-based estimation are employed. The final part of the paper portrays a case study which clearly exhibits the performance of the proposed approach.

Robust fault detection and isolation scheme using fuzzy wavelet network with a hybrid design algorithm

This paper presents a new robust fault detection and isolation scheme using fuzzy wavelet network based on the bounded error approach. An ecient hybrid design algorithm, which consists of the orthogonal least square and the arti cial bee colony algorithms, is proposed to design fuzzy wavelet network for modeling normal and faulty behaviors of the system. The proposed model provides an alternative description of the behavior of the system with high accuracy, but it su ers from model uncertainty because of model-reality mismatch in practical applications. To overcome this diculty, the bounded error approach inspired from robust identi cation theory is applied to estimate the model uncertainty which de nes a con dence interval of the model output and derives adaptive threshold for residual evaluation. Also, online fault isolation process is performed using fuzzy wavelet network models of the faulty system and analyzing the relation between a bank of residuals. Performance and eciency of the proposed scheme is evaluated by simulating the nonlinear two-tank liquid level control system. Finally, some performance indexes are de ned, and then the Monte-Carlo analysis is carried out to evaluate the reliability and robustness of the proposed scheme.

A recursive technique for tracking the feasible parameter set in bounded error estimation

SummaryIn this paper, a new recursive algorithm is proposed for tracking parameter changes of a time‐varying linear system. Since a bounded error approach is adopted for both modeling the measurement noise and the parameter change process, the problem addressed amounts to the design of a procedure for updating an estimate of the feasible parameter set. The approximating regions considered are in the form of outbounding orthotopes. The novelty of the approach lies in the use of a selection technique which keeps track only of a special subset of the constraints defining the feasible set. These inequalities represent the binding constraints of suitable linear programs of limited size. The devised algorithm is tested on several numerical examples, showing remarkable performance both in computational burden, which is comparable to that of classical recursive estimation algorithms like recursive least squares (RLS) and quality of the set estimate as compared to alternative techniques available in the literature.

A bounded-error approach to simultaneous state and actuator fault estimation for a class of nonlinear systems

This paper proposes an approach for the joint state and fault estimation for a class of uncertain nonlinear systems with simultaneous unknown input and actuator faults. This is achieved by designing an unknown input observer combined with a set-membership estimation in the presence of disturbances and measurement noise. The observer is designed using quadratic boundedness approach that is used to overbound the estimation error. Sufficient conditions for the existence and stability of the proposed state and actuator fault estimator are expressed in the form of linear matrix inequalities (LMIs). Simulation results for a quadruple-tank system show the effectiveness of the proposed approach.

Slide Window Bounded-Error Time-Varying Systems Identification

This technical note presents a new identification method for discrete linear systems with time-varying parameters based on bounded-error approach. It is assumed a bounded additive error on measurements and a bound on parameter variation. Each time instant, the identification method uses a slide window along historical data and an explicit expression to provide an outer bound of the set of model parameters that is consistent with measurements, model structure and bounds on error and variations considered. Furthermore, the center estimation of the obtained outer solution set is a suitable nominal estimation of the parameters. This center is the optimal solution of a least squares problem that penalizes the prediction error of the model and the parameter variations. The explicit expression that provides the outer bound of the parameters and the optimal property of the center estimation are the main contributions of the technical note. In order to clarify the proposed method, an application example and a comparison with a previous recursive bounded-error method are included.

Set-membership identification of an agro-ecosystem from a small data set: The case of ammonia volatilisation in a flooded rice field

Uncertainty analysis is an essential part of systems modelling. Preferably, the uncertainty analysis should start with a parameter estimation step. However, for agro-ecosystems, available data sets are typically small. Therefore, probabilistic parameter estimation techniques are not adequate. Alternatively, a set-membership or bounded-error approach can be used. In this paper, we demonstrate a set-membership approach to estimate the unknown parameters in a biochemical model from a small data set. As a case study, a biochemical model developed to estimate ammonia volatilisation in a flooded rice field was used. A total of 741 feasible parameter-vectors were found from 4000 simulated parameter- vectors. Eigenvalue decomposition of an ellipsoidal outer-bounding set indicated that the model was most sensitive to the growth rate of the rice plants, β. Visual inspection of the feasible parameter vectors showed that the estimates of the nitrogen uptake rate Kwupt are hyperbolically related to the estimates of β.

Bounded-error uncertainty domain description for continuous-time state-space model

A method is introduced to determine the uncertainty domains of the estimated parameters for multi-input multi-output linear time-invariant continuous-time systems. This method uses a continuous-time subspace-based algorithm in order to identify the parameters of the system. This identification method is specific because the estimated state-space realisation is described with the help of a state-space canonical form. Then, a bounded-error approach is considered in order to characterise the uncertainty domains of the coefficients of the state-space matrices. A simulation example is included to demonstrate the efficiency of the developed method.

Identification for passive robust fault detection using zonotope‐based set‐membership approaches

AbstractIn this paper, the problem of identification for passive robust fault detection, when a bounded description of the modelling uncertainty is considered, is addressed. Two set‐membership identification methods are introduced to address this problem: the interval predictor and bounded error approaches. These two identification approaches naturally lead to two robust fault detection tests: the direct and inverse tests, respectively, which are also introduced and discussed. Implementation algorithms make use of a zonotope to approximate the parameter uncertainty set. Moreover, underlying hypothesis of both approaches is discussed and applicability conditions are stated. A case study based on a four‐tank system is used to illustrate the applicability and the properties of the two identification approaches as well as the corresponding fault detection. Copyright © 2011 John Wiley & Sons, Ltd.

Identification and Uncertainty Domain Quantification: Experimental Validation on a ‘Smart’ Wind Turbine

AbstractIn this paper, a recent subspace-based identification approach is used to obtain an experimental model of a smart rotor, which is a wind turbine rotor equipped with a number of additional actuators and sensors to react to turbulence in a more detailed way. To make sure that the eventual controller is robust, it is essential to quantify the model uncertainty. In this paper a novel bounded error approach is tailored towards the characteristics of the smart rotor. It is shown that the suggested approach can provide realistic uncertainty bounds on the estimated model of a prototyped smart rotor.

State Estimation Using Interval Analysis and Belief-Function Theory: Application to Dynamic Vehicle Localization

A new approach to nonlinear state estimation based on belief-function theory and interval analysis is presented. This method uses belief structures composed of a finite number of axis-aligned boxes with associated masses. Such belief structures can represent partial information on model and measurement uncertainties more accurately than can the bounded-error approach alone. Focal sets are propagated in system equations using interval arithmetics and constraint-satisfaction techniques, thus generalizing pure interval analysis. This model was used to locate a land vehicle using a dynamic fusion of Global Positioning System measurements with dead reckoning sensors. The method has been shown to provide more accurate estimates of vehicle position than does the bounded-error method while retaining what is essential: providing guaranteed computations. The performances of our method were also slightly better than those of a particle filter, with comparable running time. These results suggest that our method is a viable alternative to both bounded-error and probabilistic Monte Carlo approaches for vehicle-localization applications.

Set membership estimation of fractional models in the frequency domain

The main objective of this paper is to estimate the whole set of feasible parameters of a fractional differentiation model, based on gain and phase frequency data. All parameters, including differentiation orders, are expressed as intervals and then estimated using a bounded error approach. A contraction method named forward-backward propagation is first applied to reduce the initial searching space. Then, a set inversion algorithm named SIVIA is applied on the reduced searching space to obtain the whole set of feasible parameters. One of the interesting points of this study is to show the separate contribution of gain and phase data on the final estimation.

A new hybrid system identification algorithm with automatic tuning

Hybrid system identification is composed of two subproblems: estimate the discrete state or mode for each data point, and estimate the submodel governing the dynamics of the continuous state for each mode. For linear hybrid systems, the paper proposes to tackle these problems in a single step by simultaneously approximating each submodel while associating data points to each of these. The method borrows ideas from bounded-error approaches and Support Vector Regression to extend the algebraic procedure. The algorithm can easily deal with noise by fixing a predefined accuracy threshold. This bound on the error can be different for each mode when the noise level is considered to switch with the system. An extension of the algorithm to automatically tune itself in accordance with the noise level of each mode is also provided. The method can be seen as an an extension of the algebraic approach, but also as an alternative to the bounded error approach when a predefined or preferred model structure is given or when the noise level is unknown. An extension of the method to nonlinear submodels is provided in the companion paper (Lauer and Bloch, 2008).

On fault detection under soft computing model uncertainty

The paper deals with the problems of robust fault detection using soft computing techniques, in particular neural networks (Group Method of Data Handling, GMDH), multi-layer perceptron), and neuro-fuzzy networks (Takagi-Sugeno model). The model based approach to Fault Detection and Isolation (FDI) is considered. The main objective is to show how to employ the bounded-error approach to determine the uncertainty of the neural and fuzzy models. It is shown that, based on soft computing models uncertainty defined as a confidence range for the model output, adaptive thresholds can be defined. Finally, the presented approaches are tested on a servoactuator being an FDI benchmark in the DAMADICS project.

Robust Predictive Control using a GOBF Model for MISO Systems

In this paper we develop a new method for robust predictive control for MISO systems represented on the Generalized Orthonormal Basis Functions. Unknown But Bounded Error approaches are used to update the uncertainty domain of the resultant model coefficients. This method uses a worst case strategy solved by a min-max optimization problem taking into account the constraints relative to parameter uncertainties and to measurement signals.

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.

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.

Constraints propagation techniques on intervals for a guaranteed localization using redundant data

In order to estimate continuously the dynamic location of a car, dead reckoning and absolute sensors are usually merged. The models used for this fusion are non-linear and, therefore, classical tools (such as Bayesian estimation) cannot provide a guaranteed estimation. In some applications, integrity is essential and the ability to guaranty the result is a crucial point. There are bounded-error approaches that are insensitive to non-linearity. In this context, the random errors are only modeled by their maximum bounds. This paper presents a new technique to merge the data of redundant sensors with a guaranteed result based on constraints propagation techniques on real intervals. We have thus developed an approach for the fusion of the two ABS wheel encoders of the rear wheels of a car, a fiber optic gyro and a differential GPS receiver in order to estimate the absolute location of a car. Experimental results show that the precision that one can obtain is acceptable, with a guaranteed result, in comparison with an extended Kalman filter. Moreover, constraints propagation techniques are well adapted to a real-time context.

FAULT DETECTION UNDER FUZZY MODEL UNCERTAINTY

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

A bounded-error approach to piecewise affine system identification

This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.

ROBUST FAULT DETECTION VIA GMDH NEURAL NETWORKS

This paper presents a new parameter and confidence estimation techniques for dynamic Group Method of Data Handling Neural Networks (GMDHNNs). The main objective is to show how to employ the bounded error approach to solve such a challenging task that occurs in many practical situations. In particular, the proposed approach can be easily applied in robust fault detection schemes.