Kamel Ben Othman

Choice of conjunctive operator of TSK fuzzy systems and stability domain study

This paper deals with the impact study of the choice of conjunctive operator between input variables of TSK fuzzy models, t-norm, on stability domain estimation. The approach is based on stability conditions issued from vector norms corresponding to a vector-Lyapunov function. In particular, for considered second-order TSK models we show that Zadehs t-norm, logic product min, gives the largest estimation of stability domain.

Multiple observer design for a non-linear Takagi–Sugeno system submitted to unknown inputs and outputs

In this study, the authors focus on the state estimation of a non-linear system described by a Takagi–Sugeno multiple model submitted to unknown inputs and outputs. The proposed approach consists of a mathematical transformation which enables to consider the unknown outputs as unknown inputs that can be eliminated by a designed multiple observer. To evaluate the efficiency of the proposed approach, the convergence conditions of the state estimation error are formulated as linear matrix inequalities. Simulation examples are given to illustrate the proposed methods.

State and Faults Estimation Based on Proportional Integral Sliding Mode Observer for Uncertain Takagi–Sugeno Fuzzy Systems and its Application to a Turbo-Reactor

This paper deals with the problem of state and faults estimation for nonlinear uncertain systems described by Takagi–Sugeno fuzzy structures (called also multiple models). In this work, actuator faults are considered as unknown inputs. The state and faults estimation is made using a structure of sliding mode observer where an integral term is added. This new structure of observer is called proportional integral sliding mode observer. The added integral term permits the unknown input estimation. For the sensor faults estimation, a mathematical transformation is used. The application of this mathematical transformation to the initial system output let to conceive an augmented system where the initial sensor fault appears as an unknown input. The observer convergence conditions are formulated in the form of Linear Matrix Inequalities allowing computing the observer gains. The proposed proportional integral sliding mode observer is applied to a numerical example showing the efficiency of the fault and the state estimation. In order to show the efficiency of the proposed method, it is applied to a turbo-reactor system.

Design of unknown inputs and multiple integral observers for Takagi-Sugeno multiple model

In this paper, a proportional multiple integral observer (PMI) and a proportional integral observer with unknown inputs (PIUI) are proposed in order to estimate the state, the actuator and the sensor faults of nonlinear systems described by a Takagi-Sugeno multiple model. The convergence of the estimation errors between the system and each observer are studied using the Lyapunov theory. Academic examples are provided in order to illustrate the proposed methods. A comparaison between the two observers is made through mobile robot.

On the structure determination of a dynamic PCA model using sensitivity of fault detection

Abstract Abstract This work proposes a dynamic PCA modeling method for dynamical non-linear processes. This method uses fault free data to construct data matrix used to compute the correlation matrix and faulty system data in order to fix the dynamic PCA model parameters (the time-lag and the number of principal components). It is shown that the sensitivity of dynamic PCA-based fault detection depends on the parameters used in the model. This method is tested on a three serial interconnected tanks and subject to fluid circulation faults in its pipes.

Bayesian network and probability boxes to analyze uncertainty in unavailability assessment

In this article the problem of uncertainty in assessing unavailability of Safety Instrumented Systems (SIS) is treated. The characteristic parameters of the SIS including Common Cause Failure (CCF) factors are replaced by probability densities families (p-boxes) allowing in reliability experts to express their uncertainty on the statement of values probabilities. We show how the imprecision is modeled and propagated in a Bayesian Networks which induces uncertainty about the failure probability on demand of the SIS and its Safety Integrity Level (SIL). We will demonstrate how the uncertainty on some characteristic parameters values causes significant variations on the level risk.

Observer design and active fault tolerant control for Takagi-Sugeno systems affected by sensors faults

This paper deals with the problem of active fault tolerant control strategy for nonlinear systems described by Takagi-Sugeno models. The proposed control law uses the estimated fault. The considered systems are affected by sensor faults. A mathematical transformation is used in order to conceive an augmented system in which the sensor faults affecting the initial system appear as unknown inputs. A proportional integral observer with unknown inputs is conceived in order to estimate simultaneously states and sensor faults. The stability of the system with the proposed fault tolerant control strategy is formulated using Lyapunov theory and the observer gains are obtained by solving linear matrices inequalities. To illustrate the proposed method, it is applied to the three columns.

Fuzzy Bayesian network to model safety systems performance

This article, targets the problem of uncertainty in assessing unavailability of systems, using fuzzy Bayesian networks. The elementary probabilities usually considered in Bayesian networks are replaced by fuzzy numbers. It allows experts to express their uncertainty about the basic parameters of systems and to evaluate the impact of the uncertainty on the safety systems performance. We will demonstrate how the uncertainty on some characteristic parameters values causes significant variations on the systems unavailability. In order to highlight the comparison and to show the exactness of the approach, we propose a Monte Carlo sampling approach where we consider triangular probability distribution of common cause failures factors.

An improved principal component analysis scheme for sensor fault detection and isolation : Application to a three tanks system

In this paper a sensor fault detection and isolation procedure based on principal component analysis (PCA) is proposed to monitor a three interconnected tanks system. The PCA model is built to maximize fault detection sensitivity using a new index. The localization procedure is carried out using two methods. The first is based on the variables contribution to the fault index. The second is based on the reconstruction approach.