http://hdl.handle.net/10256/26094 2025-05-13T19:19:06Z http://hdl.handle.net/10256/26097 Modal Interval Analysis: New Tools for Numerical Information Sainz, Miguel Ángel; Armengol Llobet, Joaquim; Calm i Puig, Remei; Herrero i Viñas, Pau; Jorba, Lambert; Vehí, Josep This book presents an innovative new approach to interval analysis. Modal Interval Analysis (MIA) is an attempt to go beyond the limitations of classic intervals in terms of their structural, algebraic and logical features. The starting point of MIA is quite simple: It consists in defining a modal interval that attaches a quantifier to a classical interval and in introducing the basic relation of inclusion between modal intervals through the inclusion of the sets of predicates they accept. This modal approach introduces interval extensions of the real continuous functions, identifies equivalences between logical formulas and interval inclusions, and provides the semantic theorems that justify these equivalences, along with guidelines for arriving at these inclusions. Applications of these equivalences in different areas illustrate the obtained results. The book also presents a new interval object: marks, which aspire to be a new form of numerical treatment of errors in measurements and computations 2014-01-01T00:00:00Z http://hdl.handle.net/10256/26096 Chapter 4. FDI Approach Puig, Vicenç; Fuente, María Jesús de la; Armengol Llobet, Joaquim Model-based Fault Detection and Isolation (FDI) of dynamic systems is based on the use of models (analytical redundancy) to check the consistency of observed behaviors. This consistency check is based on computing the difference between the predicted value from the model and the real value measured by the sensors. Then, this difference, known as residual, is compared with a threshold value (zero in the ideal case). When the residual is greater than the threshold, it is considered that there is a fault in the system. Otherwise, it is considered that either the system is working properly or, if it is faulty, the fault cannot be detected. This is denoted as residual evaluation. Due to the presence of noise, disturbances, and model errors, the residuals are never zero, even if there is no fault. Therefore, the detection decision requires testing the residual against thresholds, obtained empirically or by theoretical considerations. Also the desensitizing of the residual from the noise, the disturbances, and the model errors while maximizing fault sensitivity is the goal of the robust design of the detection and diagnosis algorithms. Fault detection is followed by the fault isolation procedure which intends to distinguish a particular fault from others. While a single residual is sufficient to detect faults, a set (or a vector) of residuals is required for fault isolation [13]. If a fault can be distinguished from other faults using a residual set, then it is said that this fault is isolable 2019-06-23T00:00:00Z http://hdl.handle.net/10256/26095 Introducción Armengol Llobet, Joaquim; Fuente, María Jesús de la; Puig, Vicenç Nowadays, physical and software systems, designed and built through engineering processes and software, are everywhere: our home and our office are full of electronic devices, our factories are almost fully automatized, we have cars and trucks full of complex electronic systems, almost every electronic system contains hundreds or thousands of lines of code, our computers run operating systems made up of hundreds of small programs, etc. Hence, it is required that these systems work as expected and as safer as possible. For these tasks, automated diagnosis is mandatory because for most devices, it is almost impossible to obtain necessary experience to build knowledge-based systems before they become obsolete, or there are enough number of variants for the same mechanism that it is not possible to adjust existing solutions. In those cases where a lot of data are available, it would be possible to learn models using data-driven techniques 2019-06-23T00:00:00Z