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A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and is expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity. Etymology The term system comes from the Latin word systēma, in turn from Greek σύστημα systēma: "whole concept made of several parts or members, system", literary "composition". History According to Marshall McLuhan, "System" means "something to look at". You must have a very high visual gradient to have systematization. But in philosophy, prior to Descartes, there was no "system". Plato had no "system". Aristotle had no "system". In the 19th century the French physicist Nicolas Léonard Sadi

Local Vulnerabilities and Global Robustness of Coupled Dynamical Systems on Complex Networks

Melvyn Sandy Tyloo

Coupled dynamical systems are omnipresent in everyday life. In general, interactions between individual elements composing the system are captured by complex networks. The latter greatly impact the way coupled systems are functioning and evolving in time. An important task in such a context, is to identify the most fragile components of a system in a fast and efficient manner. It is also highly desirable to have bounds on the amplitude and duration of perturbations that could potentially drive the system through a transition from one equi- librium to another. A paradigmatic model of coupled dynamical system is that of oscillatory networks. In these systems, a phenomenon known as synchronization where the individual elements start to behave coherently may occur if couplings are strong enough. We propose frameworks to assess vulnerabilities of such synchronous states to external perturbations. We consider transient excursions for both small-signal response and larger perturbations that can potentially drive the system out of its initial basin of attraction. In the first part of this thesis, we investigate the robustness of complex network-coupled oscillators. We consider transient excursions following external perturbations. For ensemble averaged perturbations, quite remarkably we find that robustness of a network is given by a family of network descriptors that we called generalized Kirchhoff indices and which are defined from extensions of the resistance distance to arbitrary powers of the Laplacian matrix of the system. These indices allow an efficient and accurate assessment of the overall vulnera- bility of an oscillatory network and can be used to compare robustness of different networks. Moreover, a network can be made more robust by minimizing its Kirchhoff indices. Then for specific local perturbations, we show that local vulnerabilities are captured by generalized resistance centralities also defined from extensions of the resistance distance. Most fragile nodes are therefore identified as the least central according to resistance centralities. Based on the latter, rankings of the nodes from most to least vulnerable can be established. In summary, we find that both local vulnerabilities and global robustness are accurately evaluated with resistance centralities and Kirchhoff indices. Moreover, the framework that we define is rather general and may be useful to analyze other coupled dynamical systems. In the second part, we focus on the effect of larger perturbations that eventually lead the sys- tem to an escape from its initial basin of attraction. We consider coupled oscillators subjected to noise with various amplitudes and correlation in time. To predict desynchronization and transitions between synchronous states, we propose a simple heuristic criterion based on the distance between the initial stable fixed point and the closest saddle point. Surprisingly, we find numerically that our criterion leads to rather accurate estimates for the survival probability and first escape time. Our criterion is general and may be applied to other dynamical systems.

EPFL2020

Online Stream Mining for Condition Monitoring in Large Infrastructure Systems

Nils Robin Bouchardon

Supervisory Control and Data Acquisition (SCADA) systems are nowadays widely used in modern industry. Their utility has been proven over the past decades to supervise any automated processes. The scope of applications of such a system has been extended from industrial to infrastructure and facility processes. Classic SCADA systems offer tools to help monitoring and analyzing data from this type of systems, but the existing approaches are often limited to Data Warehousing and Reporting. The main problem of these solutions is that they are not designed to work on online mode and can be seen as batch processing on archived data. In this thesis we study how to link machine learning solutions to SCADA systems on large infrastructures. The solution we propose in this work is a complete framework with its architecture providing a ’toolkit’ with different modules to build online solutions on top of a SCADA system.

2015

Local Vulnerabilities and Global Robustness of Coupled Dynamical Systems on Complex Networks

Melvyn Sandy Tyloo

EPFL2020