Functional sets with typed symbols: Framework and mixed Polynotopes for hybrid nonlinear reachability and filtering

Verification and synthesis of Cyber-Physical Systems (CPS) are challenging and still raise numerous issues so far. In this paper, an original framework with mixed sets defined as function images of symbol type domains is first proposed. Syntax and semantics are explicitly distinguished. Then, both continuous (interval) and discrete (signed, boolean) symbol types are used to model dependencies through linear and polynomial functions, so leading to mixed zonotopic and polynotopic sets. Polynotopes extend sparse polynomial zonotopes with typed symbols. Polynotopes can both propagate a mixed encoding of intervals and describe the behavior of logic gates. A functional completeness result is given, as well as an inclusion method for elementary nonlinear and switching functions. A Polynotopic Kalman Filter (PKF) is then proposed as a hybrid nonlinear extension of Zonotopic Kalman Filters (ZKF). Bridges with a stochastic uncertainty paradigm are outlined. Finally, several discrete, continuous and hybrid numerical examples including comparisons illustrate the effectiveness of the theoretical results.Comment: 21 pages, 8 figure

FD-ZKF: A Zonotopic Kalman Filter optimizing fault detection rather than state estimation

Enhancing the sensitivity to faults with respect to disturbances, rather than optimizing the precision of the state estimation using Kalman Filters (KF) is the subject of this paper. The stochastic paradigm (KF) is based on minimizing the trace of the state estimation error covariance. In the context of the bounded-error paradigm using Zonotopic Kalman Filters (ZKF), this is analog to minimize the covariation trace. From this analogy and keeping a similar observer-based structure as in ZKF, a criterion jointly inspired by set-membership approaches and approximate decoupling techniques coming from parity-space residual generation is proposed. Its on-line maximization provides an optimal time-varying observer gain leading to the so-called FD-ZKF filter that allows enhancing the fault detection properties. The characterization of minimum detectable fault magnitude is done based on a sensitivity analysis. The effect of the uncertainty is addressed using a set-membership approach and a zonotopic representation reducing set operations to simple matrix calculations. A case study based on a quadruple-tank system is used both to illustrate and compare the effectiveness of the results obtained from the FD-ZKF approach compared to a pure ZKF approachPostprint (author's final draft

Méthodes d'aide à la décision pour la détection et la localisation de défauts dans les entraînements électriques

LE DIAGNOSTIC DES ENTRAINEMENTS ELECTRIQUES PERMET D'ENVISAGER UNE AMELIORATION DE LA DISPONIBILITE ET DE LA POLITIQUE DE MAINTENANCE DANS LES SYSTEMES DE PRODUCTION. L'OBJECTIF DE LA THESE EST DE DETECTER ET DE LOCALISER EN LIGNE DES DEFAUTS SURVENANT DANS UN ENTRAINEMENT ELECTRIQUE. UNE ANALYSE CAUSALE SERT TOUT D'ABORD A DECOMPOSER SYSTEMATIQUEMENT UN MODELE GLOBAL EN MODELES LOCAUX, INDEPENDAMMENT DE LA NATURE DU MODELE. UN PREMIER JEU DE RESIDUS (INDICATEURS DE DEFAUT) EST AINSI OBTENU. DES METHODES CLASSIQUES DE GENERATION DE RESIDUS, FONDEES SUR DES MODELES NUMERIQUES, SONT EGALEMENT UTILISEES : OBSERVATEURS, EQUATIONS DE PARITE. DANS CE CADRE, DES TECHNIQUES DE DECOUPLAGE PARFAIT ET APPROXIMATIF SONT APPLIQUEES. UNE ETUDE DE SENSIBILITE DES RESIDUS EST MENEE. CERTAINES DE CES METHODES SONT APPLIQUEES A UNE MACHINE A COURANT CONTINU ET D'AUTRES LE SONT A UNE MACHINE ASYNCHRONE. DES OBSERVATEURS ADAPTATIFS REALISANT DES TESTS DE MODELES SONT UTILISES POUR LE DIAGNOSTIC D'UNE MACHINE ASYNCHRONE. L'ETAPE DE DECISION (CLASSIFICATION) REPOSE SUR UN ENSEMBLE DE CRITERES LIES AUX RESIDUS. LA DECISION INDIQUE QUELLES CLASSES DE DEFAUTS SONT LES PLUS COHERENTES AVEC LES OBSERVATIONS DISPONIBLES. LES SENSIBILITES DES RESIDUS PEUVENT SERVIR A SELECTIONNER LES PLUS PERTINENTS (AU SENS D'UN CRITERE DE PERFORMANCE) SOIT PAR L'APPLICATION DE REGLES ELEMENTAIRES, SOIT PAR UNE OPTIMISATION (ALGORITHME GENETIQUE). LES ORDRES DE GRANDEUR RELATIFS DES RESIDUS FOURNISSENT EGALEMENT UNE INFORMATION PLUS RICHE QUE CELLE D'UNE TABLE DE SIGNATURE BOOLEENNE ET PERMETTENT D'AMELIORER AINSI LES PERFORMANCES DE LA LOCALISATION.non disponibl

Robust fault diagnosis based on adaptive estimation and set-membership computations

International audienceThe proposed fault diagnosis scheme relies on a residual generation based on an adaptive observer covering linear time varying (LTV), linear parameter varying (LPV), and state-affine non-linear systems, all with bounded uncertainties. A residual evaluation is then performed by set-membership computations based on zonotopes (polytopes defined as the image of a hypercube by a linear application). The main advantage of the approach is its rigorous computation of the propagation of pre-specified modelling uncertainty bounds. Within the assumed uncertainty bounds, fault detection is guaranteed to be free of false alarm, while not being too much conservative, as illustrated on the model of a satellite

METHODES D'AIDE A LA DECISION POUR LA DETECTION ET LA LOCALISATION DE DEFAUTS DANS LES ENTRAINEMENTS ELECTRIQUES

GRENOBLE1-BU Sciences (384212103) / SudocSudocFranceF

Fault diagnosis based on the enclosure of parameters estimated with an adaptive observer

International audienceThe proposed fault diagnosis approach associates an adaptive observer for residual generation with set-membership computations based on zonotopes for residual evaluation. The main advantage of this approach is its rigorous propagation of pre-specified modeling uncertainty bounds to the computed residuals. Within the assumed modeling uncertainty bounds, fault detection is guaranteed to be free of false alarm, while the efforts made with set-membership computation minimize the conservativeness of fault detection decisions. The novelty compared to earlier works mainly resides in a guaranteed robustness to bounded parameter variations and in a method for dealing with occasional lack of input excitation

Set-membership state estimation of autonomous surface vehicles with a partially decoupled extended observer

This work presents a set-membership state estimator for autonomous surface vehicles, based on an augmented state including lumped disturbances. The position and orientation are assumed to be measured subject to bounded noises. A novel dynamical decomposition decouples the estimation problem into two simpler subproblems, for the rotational and positional dynamics. Then, under physically motivated assumptions about the vessel maximum velocities and acceleration rates, the estimator computes sets enclosing the positions, velocities, and lumped generalised disturbances gathering several kinds of modelling uncertainties. The sets are described by zonotopes. A set-based estimation of the lumped generalised disturbances paves the way toward an enhanced motion control scheme, where low-level controllers could compensate them, depending on the estimation accuracy. Several simulations with a well-known test-bed craft compare the performance of the proposed algorithm with a previous one from the literature under realistic environmental conditions

On Using Distorted Sensors for Set-Based Multi-Scale Actuator Fault Diagnosis

International audienceThe off-line fault detection, isolation and identification of multiplicative actuator faults using sensors providing measurements affected by unknown nonlinear distortions and bounded noises are addressed. The only assumption about the unknown functions modeling the sensor distortions is their monotonicity. Bounded disturbances are also considered as unknown inputs of the system time-varying dynamics. Polytopic faulty parameter sets resulting from the search of robust output pairs and from zonotope computations are the basis for a decision scheme which makes use of multi-scale temporal windows. A numerical example modeling part of a distillation column illustrates the off-line diagnosis of three multiplicative actuator faults from a single low-cost noisy sensor with unknown nonlinear distortion and constant bias

Combining FDI and AI Approaches within Causal-Model-based Diagnosis

International audienceThis 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 sub-models. Control Theory, within the framework of Fault Detection and Isolation, 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 sub-models 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 introduce