Distributed Methods for Estimation and Fault Diagnosis: the case of Large-scale Networked Systems

2011/2012L’obiettivo di questa tesi è il monitoraggio di sistemi complessi a larga-scala. L’importanza di questo argomento è dovuto alla rinnovata enfasi data alle problematiche riguardanti la sicurezza e l’affidabilità dei sistemi, diventate requisiti fondamentali nella progettazione. Infatti, la crescente complessità dei moderni sistemi, dove le relazioni fra i diversi componenti, con il mondo esterno e con il fattore umano sono sempre più importanti, implica una crescente attenzione ai rischi e ai costi dovuti ai guasti e lo sviluppo di approcci nuovi per il controllo e il monitoraggio. Mentre nel contesto centralizzato i problemi di stima e di diagnostica di guasto sono stati ampiamente studiati, lo sviluppo di metodologie specifiche per sistemi distribuiti, larga scala o “networked”, come i Cyber-Physical Systems e i Systems-of-Systems, è cominciato negli ultimi anni. Il sistema fisico è rappresentato come l’interconnessione di sottosistemi ottenuti attraverso una decomposizione del sistema complesso dove le sovrapposizioni sono consentite. L’approccio si basa sul modello dinamico non-lineare dei sottosistemi e sull’approssimazione adattativa delle non note interconnessioni fra i sottosistemi. La novità è la proposta di un’architettura unica che tenga conto dei molteplici aspetti che costituiscono i sistemi moderni, integrando il sistema fisico, il livello sensoriale e il sistema di diagnostica e considerando le relazioni fra questi ambienti e le reti di comunicazione. In particolare, vengono proposte delle soluzioni ai problemi che emergono dall’utilizzo di reti di comunicazione e dal considerare sistemi distribuiti e networked. Il processo di misura è effettuato da un insieme di reti di sensori, disaccoppiando il livello fisico da quello diagnostico e aumentando in questo modo la scalabilità e l’affidabilità del sistema diagnostico complessivo. Un nuovo metodo di stima distribuita per reti di sensori è utilizzato per filtrare le misure minimizzando sia la media sia la varianza dell’errore di stima attraverso la soluzione di un problema di ottimizzazione di Pareto. Un metodo per la re-sincronizzazione delle misure è proposto per gestire sistemi multi-rate e misure asincrone e per compensare l’effetto dei ritardi nella rete di comunicazione fra sensori e diagnostici. Poiché uno dei problemi più importanti quando si considerano sistemi distribuiti e reti di comunicazione è per l’appunto il verificarsi di ritardi di trasmissione e perdite di pacchetti, si propone una strategia di compensazione dei ritardi , basata sull’uso di Time Stamps e buffer e sull’introduzione di una matrice di consenso tempo-variante, che permette di gestire il problema dei ritardi nella rete di comunicazione fra diagnostici. Gli schemi distribuiti per la detection e l’isolation dei guasti sono sviluppati, garantendo la convergenza degli stimatori e derivando le condizioni sufficienti per la detectability e l’isolability. La matrice tempo-variante proposta permette di migliorare queste proprietà definendo delle soglie meno conservative. Alcuni risultati sperimentali provano l’efficacia del metodo proposto. Infine, le architetture distribuite per la detection e l’isolation, sviluppate nel caso tempo-discreto, sono estese al caso tempo continuo e nello scenario in cui lo stato non è completamente misurabile, sia a tempo continuo che a tempo discreto.This thesis deals with the problem of the monitoring of modern complex systems. The motivation is the renewed emphasis given to monitoring and fault-tolerant systems. In fact, nowadays reliability is a key requirement in the design of technical systems. While fault diagnosis architectures and estimation methods have been extensively studied for centralized systems, the interest towards distributed, networked, large-scale and complex systems, such as Cyber-Physical Systems and Systems-of-Systems, has grown in the recent years. The increased complexity in modern systems implies the need for novel tools, able to consider all the different aspects and levels constituting these systems. The system being monitored is modeled as the interconnection of several subsystems and a divide et impera approach allowing overlapping decomposition is used. The local diagnostic decision is made on the basis of the knowledge of the local subsystem dynamic model and of an adaptive approximation of the uncertain interconnection with neighboring subsystems. The goal is to integrate all the aspects of the monitoring process in a comprehensive architecture, taking into account the physical environment, the sensor layer, the diagnosers level and the communication networks. In particular, specifically designed methods are developed in order to take into account the issues emerging when dealing with communication networks and distributed systems. The introduction of the sensor layer, composed by a set of sensor networks, allows the decoupling of the physical and the sensing/computation topologies, bringing some advantages, such as scalability and reliability of the diagnosis architecture. We design the measurements acquisition task by proposing a distributed estimation method for sensor networks, able to filter measurements so that both the variance and the mean of the estimation error are minimized by means of a Pareto optimization problem. Moreover, we consider multi-rate systems and non synchronized measurements, having in mind realistic applications. A re-synchronization method is proposed in order to manage the case of multi-rate systems and to compensate delays in the communication network between sensors and diagnosers. Since one of the problems when dealing with distributed, large-scale or networked systems and therefore with a communication network, is inevitably the presence of stochastic delays and packet dropouts, we propose therefore a distributed delay compensation strategy in the communication network between diagnosers, based on the use of Time Stamps and buffers and the definition of a time-varying consensus matrix. The goal of the novel time-varying matrix is twofold: it allows to manage communication delays, packet dropouts and interrupted links and to optimize detectability and isolability skills by defining less conservative thresholds. The distributed fault detection and isolation schemes are studied and analytical results regarding fault detectability, isolability and estimator convergence are derived. Simulation results show the effectiveness of the proposed architecture. For the sake of completeness, the monitoring architecture is studied and adapted to different frameworks: the fault detection and isolation methodology is extended for continuous-time systems and the case where the state is only partially measurable is considered for discrete-time and continuous-time systems.XXV Ciclo198

Distributed Clustering-based Sensor Fault Diagnosis for HVAC Systems

We design a Sensor Fault Detection and Isolation architecture for an IWSN monitoring an HVAC System, based on a clustering approach

Fault detection and isolation in a networked multi-vehicle unmanned system

Recent years have witnessed a strong interest and intensive research activities in the area of networks of autonomous unmanned vehicles such as spacecraft formation flight, unmanned aerial vehicles, autonomous underwater vehicles, automated highway systems and multiple mobile robots. The envisaged networked architecture can provide surpassing performance capabilities and enhanced reliability; however, it requires extending the traditional theories of control, estimation and Fault Detection and Isolation (FDI). One of the many challenges for these systems is development of autonomous cooperative control which can maintain the group behavior and mission performance in the presence of undesirable events such as failures in the vehicles. In order to achieve this goal, the team should have the capability to detect and isolate vehicles faults and reconfigure the cooperative control algorithms to compensate for them. This dissertation deals with the design and development of fault detection and isolation algorithms for a network of unmanned vehicles. Addressing this problem is the main step towards the design of autonomous fault tolerant cooperative control of network of unmanned systems. We first formulate the FDI problem by considering ideal communication channels among the vehicles and solve this problem corresponding to three different architectures, namely centralized, decentralized, and semi-decentralized. The necessary and sufficient solvability conditions for each architecture are also derived based on geometric FDI approach. The effects of large environmental disturbances are subsequently taken into account in the design of FDI algorithms and robust hybrid FDI schemes for both linear and nonlinear systems are developed. Our proposed robust FDI algorithms are applied to a network of unmanned vehicles as well as Almost-Lighter-Than-Air-Vehicle (ALTAV). The effects of communication channels on fault detection and isolation performance are then investigated. A packet erasure channel model is considered for incorporating stochastic packet dropout of communication channels. Combining vehicle dynamics and communication links yields a discrete-time Markovian Jump System (MJS) mathematical model representation. This motivates development of a geometric FDI framework for both discrete-time and continuous-time Markovian jump systems. Our proposed FDI algorithm is then applied to a formation flight of satellites and a Vertical Take-Off and Landing (VTOL) helicopter problem. Finally, we investigate the problem of fault detection and isolation for time-delay systems as well as linear impulsive systems. The main motivation behind considering these two problems is that our developed geometric framework for Markovian jump systems can readily be applied to other class of systems. Broad classes of time-delay systems, namely, retarded, neutral, distributed and stochastic time-delay systems are investigated in this dissertation and a robust FDI algorithm is developed for each class of these systems. Moreover, it is shown that our proposed FDI algorithms for retarded and stochastic time-delay systems can potentially be applied in an integrated design of FDI/controller for a network of unmanned vehicles. Necessary and sufficient conditions for solvability of the fundamental problem of residual generation for linear impulsive systems are derived to conclude this dissertation

Distributed fault detection and isolation of large-scale nonlinear systems: an adaptive approximation approach

2007/2008The present thesis work introduces some recent and novel results about the problem of fault diagnosis for distributed nonlinear and large scale systems. The problem of automated fault diagnosis and accommodation is motivated by the need to develop more autonomous and intelligent systems that operate reliably in the presence of system faults. In dynamical systems, faults are characterized by critical and unpredictable changes in the system dynamics, thus requiring the design of suitable fault diagnosis schemes. A fault diagnosis scheme that drew considerable attention and provided remarkable results is the so called model based scheme, which is based upon a mathematical model of the healthy behavior of the system that is being monitored. At each time instant, the model is used to compute an estimate of what should be the current behavior of the system, assuming it is not affected by a fault. If the behavior of the system is characterized by the time evolution of its state vector x(t), and the inputs to the system are denoted as u(t), then the most general nonlinear and uncertain discrete time model can be represented by x(t + 1) = f (x(t), u(t)) + η(t) , where the nonlinear function f represents the nominal model of the healthy system, and η(t) is an uncertainty term. A proven way to compute an estimate of the state x(t) is by using a diagnostic observer, so that in healthy conditions the residual between the true and the estimated value is, in practice, close to zero. Should the residual cross at a certain point a suitable threshold ̄ǫ(t), the observed difference between the model estimate and the actual measurements will be explained by the presence of a fault. The model-based scheme outlined so far has showed many interesting properties and advantages over signal-based ones, but anyway poses practical implementation problems when one tries to apply it to actual distributed, large-scale systems. In fact an implicit assumption about the model-based scheme is that the task of measuring all the state and input vectors components, and the task of computing the estimate of x(t) can be done in real-time by some single and powerful computer. But for large enough systems, this assumptions cannot be fulfilled by available measurement, communication and computation hardware. This problem constitutes the motivation of the present work. It will be solved by developing decomposition strategies in order to break down the original centralized diagnosis problem into many distributed diagnosis subproblems, that are tackled by agents called Local Fault Diagnosers that have a limited view about the system, but that are allowed to communicate between neighboring agents. In order to take advantage of the distributed nature of the proposed schemes, the agents are allowed to cooperate on the diagnosis of parts of the system shared by more than one diagnoser, by using consensus techniques. Chapter 2 introduces the problem of model-based fault diagnosis by presenting recent results about the centralized diagnosis of uncertain nonlinear discrete time systems. The development of a distributed fault diagnosis architecture is covered in the key Chapter 3, while Chapters 4 and 5 show how this distributed architecture is implemented for discrete and continuous time nonlinear and uncertain large–scale systems. In every chapter an illustrative example is provided, as well as analytical results that characterize the performances attainable by the proposed architecture. ---------------------------------------------------Questo lavoro di tesi presenta alcuni risultati recenti ed innovativi sulla diagnostica di guasto per sistemi nonlineari distribuiti e su larga scala. Il problema della diagnostica automatica di guasto è motivata dal bisogno di sviluppare sistemi maggiormenti autonomi e robusti, che possano operare in modo affidabile anche in presenza di guasti. Nei sistemi dinamici, i guasti sono caratterizati da variazioni critiche ed imprevedibili della dinamica, e richiedono perciò la progettazione di schemi di diagnostica adeguati. Uno schema che ha riscosso notevole successo è il cosidetto schema basato su modello, che si fonda su un modello matematico del comportamento sano del sistema sotto osservazione. Ad ogni istante, il modello è usato per calcolare una stima di quello che dovrebbe essere il comportamento attuale, supponendo l’assenza di guasti. Se il comportamento del sistema è caratterizzato attraverso l’evoluzione temporale del vettore di stato x(t), ed il vettore degli ingressi è indicato con u(t), allora il modello più generale per un sistema non lineare ed incerto a tempo discreto è x(t + 1) = f (x(t), u(t)) + η(t) , dove la funzione nonlineare f rappresenta la dinamica del sistema sano, mentre η(t) è l’incertezza di modello. Un modo comprovato per calcolare una stima dello stato x(t) fa uso di un osservatore diagnostico, cosicché in condizioni normali il residuo tra il valore vero e quello stimato è, in pratica, quasi nullo. Se dovesse ad un certo punto superare un’opportuna soglia, la differenza osservata tra la stima del modello ed il valore vero misurato sarebbe spiegabile con la presenza di un guasto. Lo schema basato su modello riassunto finora ha mostrato molte proprietà interessanti e vantaggi rispetto quelli basati su segnali, ma pone in ogni caso problemi di tipo pratico quando lo si voglia applicare a sistemi reali distribuiti e su larga scala. Infatti un’ipotesi sottointesa dello schema basato su modello è che il compito di misurare tutte le componenti di x(t) e di u(t), e quello di calcolare la stima di x(t) possa essere portato a termine in tempo reale da un singolo nodo di calcolo. Nel caso di sistemi sufficientemente vasti, però, questa ipotesi non può essere rispettata da alcuna delle risorse di calcolo disponibili in pratica. Questo problema è alla base del presente lavoro di tesi. Verrà risolto sviluppando delle strategie di decomposizione in modo da suddividere il problema di diagnostica centralizzato in molteplici sotto-problemi distribuiti, dati in carico ad agenti detti Diagnostici Locali, che hanno una visione limitata del sistema, ma che possono comunicare con agenti vicini. In modo da sfruttare la natura distribuita dello schema proposto, gli agenti potranno cooperare sulla diagnostica di parti del sistema che siano comuni a più diagnostici, attraverso tecniche di consenso. Il Capitolo 2 introduce il problema della diagnostica basata su modello attraverso dei risultati recenti sulla diagnostica centralizzata di sistemi a tempo discreto con dinamica non lineare ed incerta. Lo sviluppo dell’architettura di diagnostica distribuita è trattato nel fondamentale Capitolo 3, mentre i Capitoli 4 e 5 mostrano come questa architettura distribuita è implementata a tempo discreto e a tempo continuo. In ogni capitolo è presente un esempio didattico, oltre a risultati analitici che caratterizzano le prestazioni ottenibili dall’architettura proposta.XX Ciclo197

Fault diagnosis for uncertain networked systems

Fault diagnosis has been at the forefront of technological developments for several decades. Recent advances in many engineering fields have led to the networked interconnection of various systems. The increased complexity of modern systems leads to a larger number of sources of uncertainty which must be taken into consideration and addressed properly in the design of monitoring and fault diagnosis architectures. This chapter reviews a model-based distributed fault diagnosis approach for uncertain nonlinear large-scale networked systems to specifically address: (a) the presence of measurement noise by devising a filtering scheme for dampening the effect of noise; (b) the modeling of uncertainty by developing an adaptive learning scheme; (c) the uncertainty issues emerging when considering networked systems such as the presence of delays and packet dropouts in the communication networks. The proposed architecture considers in an integrated way the various components of complex distributed systems such as the physical environment, the sensor level, the fault diagnosers, and the communication networks. Finally, some actions taken after the detection of a fault, such as the identification of the fault location and its magnitude or the learning of the fault function, are illustrated

Fault Diagnosis in a Networked Control System under Communication Constraints: A Quadrotor Application

This paper considers the problem of attitude sensor fault diagnosis in a quadrotor helicopter. The proposed approach is composed of two stages. The first one is the modelling of the system attitude dynamics taking into account the induced communication constraints. Then a robust fault detection and evaluation scheme is proposed using a post-filter designed under a particular design objective. This approach is compared with previous results based on the standard Kalman filter and gives better results for sensor fault diagnosis

Perturbation-Tolerant Structural Controllability for Linear Systems

This paper proposes a novel notion named perturbation-tolerant structural controllability (PTSC) to study controllability preservation for a structured linear system under structured perturbations. To be precise, we consider a structured system whose entries can be classified into three categories: fixed zero entries, unknown generic entries whose values are fixed but unknown, and perturbed entries that can take arbitrary complex values. Such a system is PTSC if, for almost all values of the unknown generic entries in the parameter space, the corresponding controllable system realizations can preserve controllability under arbitrary complex-valued perturbations with their zero/nonzero structure prescribed by the perturbed entries. It is proven genericity exists in this notion, that is, depending on the structure of the structured system, for almost all of its controllable realizations, either there exists an addable structured perturbation prescribed by the perturbed entries so that the resulting system is uncontrollable, or there is not such a perturbation. We give a decomposition-based necessary and sufficient condition for a single-input linear system, ensuring PTSC, whose verification has polynomial time complexity; we then present some intuitive graph-theoretic conditions for PTSC. For the multi-input case, we provide some necessary conditions for PTSC. As an application, our results can serve as some feasibility conditions for the conventional structured controllability radius problems from a generic view.Comment: Fix some typos. arXiv admin note: substantial text overlap with arXiv:2103.1190

Geometric Fault Detection and Isolation of Infinite Dimensional Systems

A broad class of dynamical systems from chemical processes to flexible mechanical structures, heat transfer and compression processes in gas turbine engines are represented by a set of partial differential equations (PDE). These systems are known as infinite dimensional (Inf-D) systems. Most of Inf-D systems, including PDEs and time-delayed systems can be represented by a differential equation in an appropriate Hilbert space. These Hilbert spaces are essentially Inf-D vector spaces, and therefore, they are utilized to represent Inf-D dynamical systems. Inf-D systems have been investigated by invoking two schemes, namely approximate and exact methods. Both approaches extend the control theory of ordinary differential equation (ODE) systems to Inf-D systems, however by utilizing two different methodologies. In the former approach, one needs to first approximate the original Inf-D system by an ODE system (e.g. by using finite element or finite difference methods) and then apply the established control theory of ODEs to the approximated model. On the other hand, in the exact approach, one investigates the Inf-D system without using any approximation. In other words, one first represents the system as an Inf-D system and then investigates it in the corresponding Inf-D Hilbert space by extending and generalizing the available results of finite-dimensional (Fin-D) control theory. It is well-known that one of the challenging issues in control theory is development of algorithms such that the controlled system can maintain the required performance even in presence of faults. In the literature, this property is known as fault tolerant control. The fault detection and isolation (FDI) analysis is the first step in order to achieve this goal. For Inf-D systems, the currently available results on the FDI problem are quite limited and restricted. This thesis is mainly concerned with the FDI problem of the linear Inf-D systems by using both approximate and exact approaches based on the geometric control theory of Fin-D and Inf-D systems. This thesis addresses this problem by developing a geometric FDI framework for Inf-D systems. Moreover, we implement and demonstrate a methodology for applying our results to mathematical models of a heat transfer and a two-component reaction-diffusion processes. In this thesis, we first investigate the development of an FDI scheme for discrete-time multi-dimensional (nD) systems that represent approximate models for Inf-D systems. The basic invariant subspaces including unobservable and unobservability subspaces of one-dimensional (1D) systems are extended to nD models. Sufficient conditions for solvability of the FDI problem are provided, where an LMI-based approach is also derived for the observer design. The capability of our proposed FDI methodology is demonstrated through numerical simulation results to an approximation of a hyperbolic partial differential equation system of a heat exchanger that is represented as a two-dimensional (2D) system. In the second part, an FDI methodology for the Riesz spectral (RS) system is investigated. RS systems represent a large class of parabolic and hyperbolic PDE in Inf-D systems framework. This part is mainly concerned with the equivalence of different types of invariant subspaces as defined for RS systems. Necessary and sufficient conditions for solvability of the FDI problem are developed. Moreover, for a subclass of RS systems, we first provide algorithms (for computing the invariant subspaces) that converge in a finite and known number of steps and then derive the necessary and sufficient conditions for solvability of the FDI problem. Finally, by generalizing the results that are developed for RS systems necessary and sufficient conditions for solvability of the FDI problem in a general Inf-D system are derived. Particularly, we first address invariant subspaces of Fin-D systems from a new point of view by invoking resolvent operators. This approach enables one to extend the previous Fin-D results to Inf-D systems. Particularly, necessary and sufficient conditions for equivalence of various types of conditioned and controlled invariant subspaces of Inf-D systems are obtained. Duality properties of Inf-D systems are then investigated. By introducing unobservability subspaces for Inf-D systems the FDI problem is formally formulated, and necessary and sufficient conditions for solvability of the FDI problem are provided

Impact of Random Deployment on Operation and Data Quality of Sensor Networks

Several applications have been proposed for wireless sensor networks, including habitat monitoring, structural health monitoring, pipeline monitoring, and precision agriculture. Among the desirable features of wireless sensor networks, one is the ease of deployment. Since the nodes are capable of self-organization, they can be placed easily in areas that are otherwise inaccessible to or impractical for other types of sensing systems. In fact, some have proposed the deployment of wireless sensor networks by dropping nodes from a plane, delivering them in an artillery shell, or launching them via a catapult from onboard a ship. There are also reports of actual aerial deployments, for example the one carried out using an unmanned aerial vehicle (UAV) at a Marine Corps combat centre in California -- the nodes were able to establish a time-synchronized, multi-hop communication network for tracking vehicles that passed along a dirt road. While this has a practical relevance for some civil applications (such as rescue operations), a more realistic deployment involves the careful planning and placement of sensors. Even then, nodes may not be placed optimally to ensure that the network is fully connected and high-quality data pertaining to the phenomena being monitored can be extracted from the network. This work aims to address the problem of random deployment through two complementary approaches: The first approach aims to address the problem of random deployment from a communication perspective. It begins by establishing a comprehensive mathematical model to quantify the energy cost of various concerns of a fully operational wireless sensor network. Based on the analytic model, an energy-efficient topology control protocol is developed. The protocol sets eligibility metric to establish and maintain a multi-hop communication path and to ensure that all nodes exhaust their energy in a uniform manner. The second approach focuses on addressing the problem of imperfect sensing from a signal processing perspective. It investigates the impact of deployment errors (calibration, placement, and orientation errors) on the quality of the sensed data and attempts to identify robust and error-agnostic features. If random placement is unavoidable and dense deployment cannot be supported, robust and error-agnostic features enable one to recognize interesting events from erroneous or imperfect data