918 resultados para Dynamic Control Systems


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El objetivo del presente proyecto es identificar y definir la problemática del ruido neutrónico en el tratamiento y procesamiento de los canales de medida y tratamiento del flujo neutrónico interno y externo en los sistemas de control y protección de los reactores nucleares tipo PWR (que trabajan con agua a presión) que dan lugar a actuaciones indeseadas de los sistemas de vigilancia y control no relacionadas con situaciones reales del proceso como cambios significativos en los parámetros de temperatura y por lo tanto de potencia del reactor que reducen la disponibilidad de operación de la central y provocan transitorios no justificados por dichas actuaciones. Finalmente, se proponen algunas soluciones. Abstract The aim of this project is to identify and define the problem of neutron noise in PWR nuclear power plants, its influence on the treatment and processing of the measurement channels and external neutron flux treatment, its contributions to the control and protection systems that result in undesired actions of monitoring and control systems that are not related to the actual process conditions. These actions reduce the availability of plant operation and unjustified transient causes. Finally, some possible solutions are proposed

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Aircraft Operators Companies (AOCs) are always willing to keep the cost of a flight as low as possible. These costs could be modelled using a function of the fuel consumption, time of flight and fixed cost (over flight cost, maintenance, etc.). These are strongly dependant on the atmospheric conditions, the presence of winds and the aircraft performance. For this reason, much research effort is being put in the development of numerical and graphical techniques for defining the optimal trajectory. This paper presents a different approach to accommodate AOCs preferences, adding value to their activities, through the development of a tool, called aircraft trajectory simulator. This tool is able to simulate the actual flight of an aircraft with the constraints imposed. The simulator is based on a point mass model of the aircraft. The aim of this paper is to evaluate 3DoF aircraft model errors with BADA data through real data from Flight Data Recorder FDR. Therefore, to validate the proposed simulation tool a comparative analysis of the state variables vector is made between an actual flight and the same flight using the simulator. Finally, an example of a cruise phase is presented, where a conventional levelled flight is compared with a continuous climb flight. The comparison results show the potential benefits of following user-preferred routes for commercial flights.

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The use of barometric altimetry is to some extent a limiting factor on safety, predictability and efficiency of aircraft operations, and reduces the potential of the trajectory based operations capabilities. However, geometric altimetry could be used to improve all of these aspects. Nowadays aircraft altitude is estimated by applying the International Standard Atmosphere which differs from real altitude. At different temperatures for an assigned barometric altitude, aerodynamic forces are different and this has a direct relationship with time, fuel consumption and range of the flight. The study explores the feasibility of using sensors providing geometric reference altitude, in particular, to supply capabilities for the optimization of vertical profiles and also, their impact on the vertical Air Traffic Management separation assurance processes. One of the aims of the thesis is to assess if geometric altitude fulfils the aeronautical requirements through existing sensors. Also the thesis will elaborate on the advantages of geometric altitude over the barometric altitude in terms of efficiency for vertical navigation. The evidence that geometric altitude is the best choice to improve the efficiency in vertical profile and aircraft capacity by reducing vertical uncertainties will also be shown. In this paper, an atmospheric study is presented, as well as the impact of temperature deviation from International Standard Atmosphere model is analyzed in order to obtain relationship between geometric and barometric altitude. Furthermore, an aircraft model to study aircraft vertical profile is provided to analyse trajectories based on geometric altitudes.

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Energy Efficiency is one of the goals of the Smart Building initiatives. This paper presents an Open Energy Management System which consists of an ontology-based multi-technology platform and a wireless transducer network using 6LoWPAN communication technology. The system allows the integration of several building automation protocols and eases the development of different kind of services to make use of them. The system has been implemented and tested in the Energy Efficiency Research Facility at CeDInt-UPM.

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In this paper the effect of different aircraft automated descent guidance strategies on fuel burn and the temporal predictability of the executed trajectory is investigated. The paper aims to provide an understanding of how airborne automation can be permitted by Air Traffic Control to remain in control of the descent in the presence of disturbances while providing sufficient predictability. Simulations have been performed investigating different guidance strategies. While each strategy has its advantages and disadvantages, results indicate that improved temporal predictability comes at the cost of additional fuel burn and loss of predictability in other dimensions of the trajectory.

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The aim of this work was twofold: on the one hand, to describe a comparative study of two intelligent control techniques-fuzzy and intelligent proportional-integral (PI) control, and on the other, to try to provide an answer to an as yet unsolved topic in the automotive sector-stop-and-go control in urban environments at very low speeds. Commercial vehicles exhibit nonlinear behavior and therefore constitute an excellent platform on which to check the controllers. This paper describes the design, tuning, and evaluation of the controllers performing actions on the longitudinal control of a car-the throttle and brake pedals-to accomplish stop-and-go manoeuvres. They are tested in two steps. First, a simulation model is used to design and tune the controllers, and second, these controllers are implemented in the commercial vehicle-which has automatic driving capabilities-to check their behavior. A stop-and-go manoeuvre is implemented with the two control techniques using two cooperating vehicles.

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Today's motivation for autonomous systems research stems out of the fact that networked environments have reached a level of complexity and heterogeneity that make their control and management by solely human administrators more and more difficult. The optimisation of performance metrics for the air traffic management system, like in other networked system, has become more complex with increasing number of flights, capacity constraints, environmental factors and safety regulations. It is anticipated that a new structure of planning layers and the introduction of higher levels of automation will reduce complexity and will optimise the performance metrics of the air traffic management system. This paper discusses the complexity of optimising air traffic management performance metrics and proposes a way forward based on higher levels of automation.

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The purpose of this document is to create a modest integration guide for embedding a Linux Operating System on ZedBoard development platform, based on Xilinx’s Zynq-7000 All Programmable System on Chip which contains a dual core ARM Cortex-A9 and a 7 Series FPGA Artix-7. The integration process has been structured in four chapters according to the logic generation of the different parts that compose the embedded system. With the intention of automating the generation process of a complete Linux distribution specific for ZedBoard platform, BuildRoot development platform it is used. Once the embedding process finished, it was decided to add to the system the required functionalities for adding support for IEEE1588 Standard for Precision Clock Synchronization Protocol for Networked Measurement and Control Systems, through a user space Linux program which implements the protocol. That PTP user space implementation program has been cross-compiled, executed on target and tested for evaluating the functionalities added. RESUMEN El propósito de este documento es crear una modesta guía de integración de un sistema operativo Linux para la plataforma de desarrollo ZedBoard, basada en un System on Chip del fabricante Xilinx llamado Zynq-7000. Este System on Chip está compuesto por un procesador de doble núcleo ARM Cortex-A9 y una FPGA de la Serie 7 equiparable a una Artix-7. El proceso de integración se ha estructurado en cuatro grandes capítulos que se rigen según el orden lógico de generación de las distintas partes por las que el sistema empotrado está compuesto. Con el ánimo de automatizar el proceso de creación de una distribución de Linux específica para la plataforma ZedBoard, se ha utilizado la plataforma de desarrollo BuildRoot. Una vez terminado el proceso de integración del sistema empotrado, se procedió a dar dotar al sistema de las funcionalidades necesarias para dar soporte al estándar de sincronización de relojes en redes de área local, PTP IEEE1588, a través de una implementación del mismo en un programa de lado de usuario el cual ha sido compilado, ejecutado y testeado para evaluar el correcto funcionamiento de las funcionalidades añadidas.

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Los sistemas técnicos son cada vez más complejos, incorporan funciones más avanzadas, están más integrados con otros sistemas y trabajan en entornos menos controlados. Todo esto supone unas condiciones más exigentes y con mayor incertidumbre para los sistemas de control, a los que además se demanda un comportamiento más autónomo y fiable. La adaptabilidad de manera autónoma es un reto para tecnologías de control actualmente. El proyecto de investigación ASys propone abordarlo trasladando la responsabilidad de la capacidad de adaptación del sistema de los ingenieros en tiempo de diseño al propio sistema en operación. Esta tesis pretende avanzar en la formulación y materialización técnica de los principios de ASys de cognición y auto-consciencia basadas en modelos y autogestión de los sistemas en tiempo de operación para una autonomía robusta. Para ello el trabajo se ha centrado en la capacidad de auto-conciencia, inspirada en los sistemas biológicos, y se ha explorado la posibilidad de integrarla en la arquitectura de los sistemas de control. Además de la auto-consciencia, se han explorado otros temas relevantes: modelado funcional, modelado de software, tecnología de los patrones, tecnología de componentes, tolerancia a fallos. Se ha analizado el estado de la técnica en los ámbitos pertinentes para las cuestiones de la auto-consciencia y la adaptabilidad en sistemas técnicos: arquitecturas cognitivas, control tolerante a fallos, y arquitecturas software dinámicas y computación autonómica. El marco teórico de ASys existente de sistemas autónomos cognitivos ha sido adaptado para servir de base para este análisis de autoconsciencia y adaptación y para dar sustento conceptual al posterior desarrollo de la solución. La tesis propone una solución general de diseño para la construcción de sistemas autónomos auto-conscientes. La idea central es la integración de un meta-controlador en la arquitectura de control del sistema autónomo, capaz de percibir la estado funcional del sistema de control y, si es necesario, reconfigurarlo en tiempo de operación. Esta solución de metacontrol se ha formalizado en cuatro patrones de diseño: i) el Patrón Metacontrol, que define la integración de un subsistema de metacontrol, responsable de controlar al propio sistema de control a través de la interfaz proporcionada por su plataforma de componentes, ii) el patrón Bucle de Control Epistémico, que define un bucle de control cognitivo basado en el modelos y que se puede aplicar al diseño del metacontrol, iii) el patrón de Reflexión basada en Modelo Profundo propone una solución para construir el modelo ejecutable utilizado por el meta-controlador mediante una transformación de modelo a modelo a partir del modelo de ingeniería del sistema, y, finalmente, iv) el Patrón Metacontrol Funcional, que estructura el meta-controlador en dos bucles, uno para el control de la configuración de los componentes del sistema de control, y otro sobre éste, controlando las funciones que realiza dicha configuración de componentes; de esta manera las consideraciones funcionales y estructurales se desacoplan. La Arquitectura OM y el metamodelo TOMASys son las piezas centrales del marco arquitectónico desarrollado para materializar la solución compuesta de los patrones anteriores. El metamodelo TOMASys ha sido desarrollado para la representación de la estructura y su relación con los requisitos funcionales de cualquier sistema autónomo. La Arquitectura OM es un patrón de referencia para la construcción de una metacontrolador integrando los patrones de diseño propuestos. Este meta-controlador se puede integrar en la arquitectura de cualquier sistema control basado en componentes. El elemento clave de su funcionamiento es un modelo TOMASys del sistema decontrol, que el meta-controlador usa para monitorizarlo y calcular las acciones de reconfiguración necesarias para adaptarlo a las circunstancias en cada momento. Un proceso de ingeniería, complementado con otros recursos, ha sido elaborado para guiar la aplicación del marco arquitectónico OM. Dicho Proceso de Ingeniería OM define la metodología a seguir para construir el subsistema de metacontrol para un sistema autónomo a partir del modelo funcional del mismo. La librería OMJava proporciona una implementación del meta-controlador OM que se puede integrar en el control de cualquier sistema autónomo, independientemente del dominio de la aplicación o de su tecnología de implementación. Para concluir, la solución completa ha sido validada con el desarrollo de un robot móvil autónomo que incorpora un meta-controlador con la Arquitectura OM. Las propiedades de auto-consciencia y adaptación proporcionadas por el meta-controlador han sido validadas en diferentes escenarios de operación del robot, en los que el sistema era capaz de sobreponerse a fallos en el sistema de control mediante reconfiguraciones orquestadas por el metacontrolador. ABSTRACT Technical systems are becoming more complex, they incorporate more advanced functionalities, they are more integrated with other systems and they are deployed in less controlled environments. All this supposes a more demanding and uncertain scenario for control systems, which are also required to be more autonomous and dependable. Autonomous adaptivity is a current challenge for extant control technologies. The ASys research project proposes to address it by moving the responsibility for adaptivity from the engineers at design time to the system at run-time. This thesis has intended to advance in the formulation and technical reification of ASys principles of model-based self-cognition and having systems self-handle at runtime for robust autonomy. For that it has focused on the biologically inspired capability of self-awareness, and explored the possibilities to embed it into the very architecture of control systems. Besides self-awareness, other themes related to the envisioned solution have been explored: functional modeling, software modeling, patterns technology, components technology, fault tolerance. The state of the art in fields relevant for the issues of self-awareness and adaptivity has been analysed: cognitive architectures, fault-tolerant control, and software architectural reflection and autonomic computing. The extant and evolving ASys Theoretical Framework for cognitive autonomous systems has been adapted to provide a basement for this selfhood-centred analysis and to conceptually support the subsequent development of our solution. The thesis proposes a general design solution for building self-aware autonomous systems. Its central idea is the integration of a metacontroller in the control architecture of the autonomous system, capable of perceiving the functional state of the control system and reconfiguring it if necessary at run-time. This metacontrol solution has been formalised into four design patterns: i) the Metacontrol Pattern, which defines the integration of a metacontrol subsystem, controlling the domain control system through an interface provided by its implementation component platform, ii) the Epistemic Control Loop pattern, which defines a modelbased cognitive control loop that can be applied to the design of such a metacontroller, iii) the Deep Model Reflection pattern proposes a solution to produce the online executable model used by the metacontroller by model-to-model transformation from the engineering model, and, finally, iv) the Functional Metacontrol pattern, which proposes to structure the metacontroller in two loops, one for controlling the configuration of components of the controller, and another one on top of the former, controlling the functions being realised by that configuration; this way the functional and structural concerns become decoupled. The OM Architecture and the TOMASys metamodel are the core pieces of the architectural framework developed to reify this patterned solution. The TOMASys metamodel has been developed for representing the structure and its relation to the functional requirements of any autonomous system. The OM architecture is a blueprint for building a metacontroller according to the patterns. This metacontroller can be integrated on top of any component-based control architecture. At the core of its operation lies a TOMASys model of the control system. An engineering process and accompanying assets have been constructed to complete and exploit the architectural framework. The OM Engineering Process defines the process to follow to develop the metacontrol subsystem from the functional model of the controller of the autonomous system. The OMJava library provides a domain and application-independent implementation of an OM Metacontroller than can be used in the implementation phase of OMEP. Finally, the complete solution has been validated in the development of an autonomous mobile robot that incorporates an OM metacontroller. The functional selfawareness and adaptivity properties achieved thanks to the metacontrol system have been validated in different scenarios. In these scenarios the robot was able to overcome failures in the control system thanks to reconfigurations performed by the metacontroller.

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In the last years, there has been a continued growth in the number of offshore operations for handling large equipment and objects, with emphasis on installation and maintenance of devices for exploiting marine renewable energy like generators for harnessing wind, waves and currents energy. Considering the behaviour of these devices during manoeuvrings, and due to their size and by the interaction with the surrounding fluid, the effect of inertial forces and torques is very important, which requires a specific modelling. This paper especially discusses the masses and moments of inertia modelling problem, with the aim to use it in the simulation of the complex manoeuvres of these devices and in the automatic control systems designed for their offshore operations. Given the importance and complexity of the added mass modelling, a method for its early design identification, developed by the R&D Group on Marine Renewable Energy Technologies of the UPM (GITERM) and its use on special cases like emersion manoeuvres of devices from underwater to the surface will be presented.

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Wireless teleoperation of field robots for maintenance, inspection and rescue missions is often performed in environments with low wireless connectivity, caused by signal losses from the environment and distance from the wireless transmitters. Various studies from the literature have addressed these problems with time-delay robust control systems and multi-hop wireless relay networks. However, such approaches do not solve the issue of how to present wireless data to the operator to avoid losing control of the robot. Despite the fact that teleoperation for maintenance often already involves haptic devices, no studies look at the possibility of using this existing feedback to aid operators in navigating within areas of variable wireless connectivity. We propose a method to incorporate haptic information into the velocity control of an omnidirectional robot to augment the operators perception of wireless signal strength in the remote environment. In this paper we introduce a mapping between wireless signal strength from multiple receivers to the force feedback of a 6 Degree of Freedom haptic master and evaluate the proposed approach using experimental data and randomly generated wireless maps

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EPICS (Experimental Physics and Industrial Control System) lies in a set of software tools and applications which provide a software infrastructure for building distributed data acquisition and control systems. Currently there is an increase in use of such systems in large Physics experiments like ITER, ESS, and FREIA. In these experiments, advanced data acquisition systems using FPGA-based technology like FlexRIO are more frequently been used. The particular case of ITER (International Thermonuclear Experimental Reactor), the instrumentation and control system is supported by CCS (CODAC Core System), based on RHEL (Red Hat Enterprise Linux) operating system, and by the plant design specifications in which every CCS element is defined either hardware, firmware or software. In this degree final project the methodology proposed in Implementation of Intelligent Data Acquisition Systems for Fusion Experiments using EPICS and FlexRIO Technology Sanz et al. [1] is used. The final objective is to provide a document describing the fulfilled process and the source code of the data acquisition system accomplished. The use of the proposed methodology leads to have two diferent stages. The first one consists of the hardware modelling with graphic design tools like LabVIEWFPGA which later will be implemented in the FlexRIO device. In the next stage the design cycle is completed creating an EPICS controller that manages the device using a generic device support layer named NDS (Nominal Device Support). This layer integrates the data acquisition system developed into CCS (Control, data access and communication Core System) as an EPICS interface to the system. The use of FlexRIO technology drives the use of LabVIEW and LabVIEW FPGA respectively. RESUMEN. EPICS (Experimental Physics and Industrial Control System) es un conjunto de herramientas software utilizadas para el desarrollo e implementación de sistemas de adquisición de datos y control distribuidos. Cada vez es más utilizado para entornos de experimentación física a gran escala como ITER, ESS y FREIA entre otros. En estos experimentos se están empezando a utilizar sistemas de adquisición de datos avanzados que usan tecnología basada en FPGA como FlexRIO. En el caso particular de ITER, el sistema de instrumentación y control adoptado se basa en el uso de la herramienta CCS (CODAC Core System) basado en el sistema operativo RHEL (Red Hat) y en las especificaciones del diseño del sistema de planta, en la cual define todos los elementos integrantes del CCS, tanto software como firmware y hardware. En este proyecto utiliza la metodología propuesta para la implementación de sistemas de adquisición de datos inteligente basada en EPICS y FlexRIO. Se desea generar una serie de ejemplos que cubran dicho ciclo de diseño completo y que serían propuestos como casos de uso de dichas tecnologías. Se proporcionará un documento en el que se describa el trabajo realizado así como el código fuente del sistema de adquisición. La metodología adoptada consta de dos etapas diferenciadas. En la primera de ellas se modela el hardware y se sintetiza en el dispositivo FlexRIO utilizando LabVIEW FPGA. Posteriormente se completa el ciclo de diseño creando un controlador EPICS que maneja cada dispositivo creado utilizando una capa software genérica de manejo de dispositivos que se denomina NDS (Nominal Device Support). Esta capa integra la solución en CCS realizando la interfaz con la capa EPICS del sistema. El uso de la tecnología FlexRIO conlleva el uso del lenguaje de programación y descripción hardware LabVIEW y LabVIEW FPGA respectivamente.

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La obtención de energía a partir de la fusión nuclear por confinamiento magnético del plasma, es uno de los principales objetivos dentro de la comunidad científica dedicada a la energía nuclear. Desde la construcción del primer dispositivo de fusión, hasta la actualidad, se han llevado a cabo multitud de experimentos, que hoy en día, gran parte de ellos dan soporte al proyecto International Thermonuclear Experimental Reactor (ITER). El principal problema al que se enfrenta ITER, se basa en la monitorización y el control del plasma. Gracias a las nuevas tecnologías, los sistemas de instrumentación y control permiten acercarse más a la solución del problema, pero a su vez, es más complicado estandarizar los sistemas de adquisición de datos que se usan, no solo en ITER, sino en otros proyectos de igual complejidad. Desarrollar nuevas implementaciones hardware y software bajo los requisitos de los diagnósticos definidos por los científicos, supone una gran inversión de tiempo, retrasando la ejecución de nuevos experimentos. Por ello, la solución que plantea esta tesis, consiste en la definición de una metodología de diseño que permite implementar sistemas de adquisición de datos inteligentes y su fácil integración en entornos de fusión para la implementación de diagnósticos. Esta metodología requiere del uso de los dispositivos Reconfigurable Input/Output (RIO) y Flexible RIO (FlexRIO), que son sistemas embebidos basados en tecnología Field-Programmable Gate Array (FPGA). Para completar la metodología de diseño, estos dispositivos van a ser soportados por un software basado en EPICS Device Support utilizando la tecnología EPICS software asynDriver. Esta metodología se ha evaluado implementando prototipos para los controladores rápidos de planta de ITER, tanto para casos prácticos de ámbito general como adquisición de datos e imágenes, como para casos concretos como el diagnóstico del fission chamber, implementando pre-procesado en tiempo real. Además de casos prácticos, esta metodología se ha utilizado para implementar casos reales, como el Ion Source Hydrogen Positive (ISHP), desarrollada por el European Spallation Source (ESS Bilbao) y la Universidad del País Vasco. Finalmente, atendiendo a las necesidades que los experimentos en los entornos de fusión requieren, se ha diseñado un mecanismo mediante el cual los sistemas de adquisición de datos, que pueden ser implementados mediante la metodología de diseño propuesta, pueden integrar un reloj hardware capaz de sincronizarse con el protocolo IEEE1588-V2, permitiendo a estos, obtener los TimeStamps de las muestras adquiridas con una exactitud y precisión de decenas de nanosegundos y realizar streaming de datos con TimeStamps. ABSTRACT Fusion energy reaching by means of nuclear fusion plasma confinement is one of the main goals inside nuclear energy scientific community. Since the first fusion device was built, many experiments have been carried out and now, most of them give support to the International Thermonuclear Experimental Reactor (ITER) project. The main difficulty that ITER has to overcome is the plasma monitoring and control. Due to new technologies, the instrumentation and control systems allow an approaching to the solution, but in turn, the standardization of the used data acquisition systems, not only in ITER but also in other similar projects, is more complex. To develop new hardware and software implementations under scientific diagnostics requirements, entail time costs, delaying new experiments execution. Thus, this thesis presents a solution that consists in a design methodology definition, that permits the implementation of intelligent data acquisition systems and their easy integration into fusion environments for diagnostic purposes. This methodology requires the use of Reconfigurable Input/Output (RIO) and Flexible RIO (FlexRIO) devices, based on Field-Programmable Gate Array (FPGA) embedded technology. In order to complete the design methodology, these devices are going to be supported by an EPICS Device Support software, using asynDriver technology. This methodology has been evaluated implementing ITER PXIe fast controllers prototypes, as well as data and image acquisition, so as for concrete solutions like the fission chamber diagnostic use case, using real time preprocessing. Besides of these prototypes solutions, this methodology has been applied for the implementation of real experiments like the Ion Source Hydrogen Positive (ISHP), developed by the European Spallation Source and the Basque country University. Finally, a hardware mechanism has been designed to integrate a hardware clock into RIO/FlexRIO devices, to get synchronization with the IEEE1588-V2 precision time protocol. This implementation permits to data acquisition systems implemented under the defined methodology, to timestamp all data acquired with nanoseconds accuracy, permitting high throughput timestamped data streaming.

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Current worldwide building legislation requirements aim to the design and construction of technical services that reduce energy consumption and improve indoor hygrothermal conditions. The retail sector in Spain, with a lot of outdated technical systems, demands energy conservation measures in order to reduce the increasingly electrical consumption for cooling. Climatic separation with modern air curtains and advanced hygrothermal control systems enables energy savings and can keep suitable indoor air temperature and humidity of stores with intense pedestrian traffic, especially when located in hot humid climates. As stated in the article, the energy savings in commercial buildings with these systems exceeds 30%

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This article investigates experimentally the application of health monitoring techniques to assess the damage on a particular kind of hysteretic (metallic) damper called web plastifying dampers, which are subjected to cyclic loading. In general terms, hysteretic dampers are increasingly used as passive control systems in advanced earthquake-resistant structures. Nonparametric statistical processing of the signals obtained from simple vibration tests of the web plastifying damper is used here to propose an area index damage. This area index damage is compared with an alternative energy-based index of damage proposed in past research that is based on the decomposition of the load?displacement curve experienced by the damper. Index of damage has been proven to accurately predict the level of damage and the proximity to failure of web plastifying damper, but obtaining the load?displacement curve for its direct calculation requires the use of costly instrumentation. For this reason, the aim of this study is to estimate index of damage indirectly from simple vibration tests, calling for much simpler and cheaper instrumentation, through an auxiliary index called area index damage. Web plastifying damper is a particular type of hysteretic damper that uses the out-of-plane plastic deformation of the web of I-section steel segments as a source of energy dissipation. Four I-section steel segments with similar geometry were subjected to the same pattern of cyclic loading, and the damage was evaluated with the index of damage and area index damage indexes at several stages of the loading process. A good correlation was found between area index damage and index of damage. Based on this correlation, simple formulae are proposed to estimate index of damage from the area index damage.