Olivier Adrot

Parameter uncertainty computation in static linear models

Static linear models characterized by bounded uncertainties on both the equation error and the parameters are studied. The additive equation error is assumed to belong to an interval while the parameters fluctuate inside a time-invariant bounded domain. An algorithm is proposed for evaluating different bounded domains. The algorithm can be extended to cope with the determination of the central value of the domain containing the parameters. Contrary to most of traditional estimators, the resulting estimator takes into account the distribution of the uncertainties of a model.

Brief paper: Parity relations for linear uncertain dynamic systems

A new approach for the design of parity relations for linear dynamic systems with additive and multiplicative uncertainties is presented. Instead of cancelling uncertainties following the example of the so-called robust approaches, uncertain parity relations take uncertainties into account as bounded variables. The method is based on the analysis of zonotopes representing the uncertainties. It leads both to Boolean detection results and to an indicator representing the distance to the opposite decision.

Fault detection based on interval analysis

Abstract This paper deals with a fault detection method taking into account model uncertainties described by bounded variables. A parity space approach is proposed, where the parity matrix depends on uncertain parameters. Since residuals represent a set of feasible behaviors, they therefore define a normal operation domain. In order to simplify its evaluation, residuals are linearized in bounded variables. This procedure generates an approximation, which can be enhanced by estimating bounds of uncertain parameters. Temporal dependencies between residuals are then taken into account in order to increase the precision of consistency tests.

Diagnosis of an uncertain static system

Deals with an original fault detection and isolation method, allowing us to take the structure and the range of model uncertainties into account. We focus on static and structured uncertain models, where each parameter uncertainty is described by a bounded variable. In order to de-couple residuals from unknown physical variables, a parity space approach is proposed, where the parity matrix depends on uncertain parameters. Because of this membership approach, called the bounding approach, residuals represent a set of feasible behaviours and define therefore the normal operating domain of the studied physical system. To simplify its evaluation and work on a simple domain such as a parallelotope, residuals are linearised in the bounded variables and a reduction procedure is applied to decrease their complexity. Once the constraints defining this domain are determined, consistency tests for fault detection and isolation are built.

Fault detection based on uncertain models with bounded parameters and bounded parameter variations

This paper deals with a fault detection method taking into account model uncertainties described by bounded variables. A parity space approach is used for generating testable redundancy relations in which each uncertain parameter is defined by an interval containing all its feasible values. Consistency tests consist in evaluating these set-membership relations and lead to convex sets containing the feasible free-fault behaviours of the supervised system. The objective is to improve fault detection performance by taking into account constraints on variations of uncertain parameters, which do not randomly vary.

Residual generation for uncertain models

The generation of redundancy equations using a parity space technique is a very effective method for fault detection and identification (FDI) in LTI models. However, for physical systems, the assumption of models with invariant parameters is too difficult to be accepted, it is then advisable to propose a method taking into account time parameter fluctuations. In this paper, a technique for parity vector generation in linear models affected by bounded uncertainties, is proposed. In order to eliminate unknown variables, the projection matrix depends on uncertainties. A systematic method for matrix projection computation is developed, leading to an exact expression of the parity vector. Since uncertainties are bounded, residues move in a bounded domain representing the normal operating of the studied system.

Estimation of Bounded Model Uncertainties

The aim is to identify the parameter values of a given input-output model such that estimated model outputs are consistent with measured outputs of the system to be modeled. Parameter estimation based on a set-membership approach is a non-probabilistic method for characterizing the uncertainty with which each model parameter is known. In this case, the sought model is consistent with data if the estimated output domain contains measured system outputs at each instant. Dynamic linear Multi-Inputs Multi-Outputs (MIMO) models are considered in this paper. Every equation error is bounded while model parameters fluctuate inside a time-invariant domain represented by a zonotope. The proposed method helps to find the characteristics of this domain (center, shape, size) by taking into account the couplings between bounded variables of output equations in order to increase model accuracy.

FAULT DETECTION BASED ON SET-MEMBERSHIP INVERSION

This paper deals with a set-membership method for fault detection. Based on interval analysis, the proposed approach focuses on the design of consistency tests for dynamical systems with additive and multiplicative parameter uncertainties. Instead of canceling uncertainties following the example of the so-called robust approaches, uncertain analytical redundancy relations take uncertainties into account as bounded variables. The use of a set-membership inversion method allows non-linear analytical redundancy relations to be directly processed without requiring any linearization.

Parameter Uncertainties Characterisation for Linear Models.

Abstract: Parameter estimation mainly consists in characterising a parameter set consistent with measurements, the model and the equation error description. The problem to be solved is that of finding the set of admissible parameter values corresponding to an admissible error. The uncertainties must be treated by a global analysis of the problem: both the equation error and the parameter set are considered unknown. Then, a solution is given as a domain of time-variant parameters and a bounded set of the error. This procedure consists in explaining the measurements performed at all time by optimising a precision criterion based on the poly tope theory.

Multi-fault detection of systems with bounded uncertainties

Fault detection in linear static models with uncertain parameters is studied. Using a parity space technique, a method based on the bounding approach is proposed. Several types of structured faults may affect a physical system and in this context, two cases are distinguished: i) the structured fault is a prior identified as a region in the parameter space, by considering the physical knowledge on the studied system. The corresponding procedure is called supervised; ii) the second case corresponds to a fault which has an unknown structure. The corresponding procedure is called unsupervised fault. In this article, a strategy consists first in characterizing various fault structures and then in establishing a fault detection and identification (FDI) procedure by using interval analysis.