Robust zonotopic set-membership approach for model-based prognosis: application on linear parameter-varying systems

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksA robust set-membership Prognostics and Health Management (PHM) methodology is presented in this paper. The key advantages of the set-membership approach for states and parameters estimation are enhanced by employing zonotopes that are less conservative and computationally complex than other sets. The optimal tuning of the proposed observer is formulated using the Linear Matrix Inequality (LMI) approach. Moreover, the Joint Estimation of States and Parameters (JESP) leads to a non-linear representation of a monitored system that is transformed into a Linear Parameter-Varying (LPV) system by means of the non-linear embedding approach. The considered case study is based on a slowly degraded DC-DC converter. The aim of the proposed PHM approach is to forecast the Remaining Useful Life (RUL) on a system level. Additionally, the proposed RUL forecasting approach is independent of previous knowledge of the degradation behaviors being only dependent on the estimated zonotopic parameters. Finally, the obtained results demonstrate the efficiency of the proposed approach.Peer ReviewedPostprint (published version

Robust zonotopic prognostics approaches for LPV systems based on set-membership and extended Kalman filter

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThis paper proposes robust model-based prognostics approaches based on zonotopic Joint Estimation of States and Parameters (JESP) for Linear Parameter-Varying (LPV) systems. Zonotopes are employed due to their simple computations with a reduced number of vertices. Thus, Zonotopic Set-Membership (ZSM) and Zonotopic Extended Kalman Filter (ZEKF) approaches are investigated for the JESP which plays a crucial role in the proposed Prognostics and Health Management (PHM) approach. The zonotopic estimators are optimally-tuned using a specially formulated Linear Matrix Inequality (LMI) framework to guarantee a high estimation accuracy and less conservative results. Furthermore, a Recursive ZSM (RZSM) approach is derived from a conventional Recursive Least Squares (RLS) filter for the sake of Remaining Useful Life (RUL) forecasting of exponentially-decayed parameters. Additionally, a polynomial RUL forecasting approach has been also proposed based on the ZEKF approach. Finally, a degraded DC-DC converter is modelled as an LPV system and examined with the proposed approaches, and the obtained results show their efficiency.Peer ReviewedPostprint (published version

Diagnostic et Surveillance des Systèmes Complexes

The growing demand for fault tolerance in more and more complex automatic control systems, can only be reached using efficient fault detection and isolation algorithms and the accommodation/reconfiguration concepts. This research presents a contribution to the analysis of fault tolerant estimation (control) with respect to sensor (actuator) failures in LTI systems. The first section describes the control and estimation problem taking into account fault tolerance and supervision problem. The second one is concerned with the Design of Fault Tolerant Sensor (Actuator) networks such that the observability (controllability) of the variables, which are necessary for a required function, remains satisfied in the presence of sensor (actuator) failures. Individual observability (controllability) indexes are used to build Minimal and Redundant Sensor (Actuator) Subsets considering estimation (control) properties. These subsets are organized into an oriented graph that contains all the possible accommodation/reconfiguration paths. Structural and probabilistic criteria are proposed in order to evaluate the system fault tolerance. We propose algorithms which build the graph and allows to compute the two measures associated with each node. A ship boiler and a hydraulic process are used to illustrate the analysis and the proposed algorithms.L'augmentation continue de la complexité des processus automatisés crée une demande croissante vis à vis de leur tolérance aux fautes. Celle-ci peut être obtenue en utilisant des algorithmes de détection et de localisation de défaillances et des algorithmes d'accommodation/reconfiguration de la commande, du système ou de ses objectifs. Ce mémoire propose une contribution à l’analyse de la tolérance aux fautes de la fonction d’estimation (de la fonction de commande), en cas de défaillances de capteurs (d'actionneurs), pour les systèmes linéaires.La première partie présente les concepts généraux de commande et d’estimation de systèmes linéaires en vue de la tolérance aux fautes et de la supervision de processus.La deuxième est consacrée à la conception de schémas d’instrumentation (d’action) en vue de la tolérance aux fautes. Les indices d'observabilité (de commandabilité) individuels sont utilisés pour construire les sous-ensembles de capteurs (d'actionneurs) redondants et minimaux pour lesquels le système est observable (commandable). Ces sous ensembles sont organisés selon un graphe orienté contenant tous les chemins d'accommodation/ reconfiguration. Pour évaluer la tolérance aux fautes du système, on définit deux critères respectivement structurel et probabiliste. On propose des algorithmes qui permettent de construire le graphe et de calculer les deux critères associés à chaque nœud. Ces algorithmes ont été appliqués au placement de capteurs d’un système thermique et à la sélection d’actionneurs d’un système hydraulique

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