Bounding the Heat Trace of a Calabi-Yau Manifold

The SCHOK bound states that the number of marginal deformations of certain two-dimensional conformal field theories is bounded linearly from above by the number of relevant operators. In conformal field theories defined via sigma models into Calabi-Yau manifolds, relevant operators can be estimated, in the point-particle approximation, by the low-lying spectrum of the scalar Laplacian on the manifold. In the strict large volume limit, the standard asymptotic expansion of Weyl and Minakshisundaram-Pleijel diverges with the higher-order curvature invariants. We propose that it would be sufficient to find an a priori uniform bound on the trace of the heat kernel for large but finite volume. As a first step in this direction, we then study the heat trace asymptotics, as well as the actual spectrum of the scalar Laplacian, in the vicinity of a conifold singularity. The eigenfunctions can be written in terms of confluent Heun functions, the analysis of which gives evidence that regions of large curvature will not prevent the existence of a bound of this type. This is also in line with general mathematical expectations about spectral continuity for manifolds with conical singularities. A sharper version of our results could, in combination with the SCHOK bound, provide a basis for a global restriction on the dimension of the moduli space of Calabi-Yau manifolds.Comment: 32 pages, 3 figure

Neurofuzzy controller based full vehicle nonlinear active suspension systems

To design a robust controller for active suspension systems is very important for guaranteeing the riding comfort for passengers and road handling quality for a vehicle. In this thesis, the mathematical model of full vehicle nonlinear active suspension systems with hydraulic actuators is derived to take into account all the motions of the vehicle and the nonlinearity behaviours of the active suspension system and hydraulic actuators. Four robust control types are designed and the comparisons among the robustness of those controllers against different disturbance types are investigated to select the best controller among them. The MATLAB SIMULINK toolboxes are used to simulate the proposed controllers with the controlled model and to display the responses of the controlled model under different types of disturbance. The results show that the neurofuzzy controller is more effective and robust than the other controller types. The implementation of the neurofuzzy controller using FPGA boards has been investigated in this work. The Xilinx ISE program is employed to synthesis the VHDL codes that describe the operation of the neurofuzzy controller and to generate the configuration file used to program the FPGA. The ModelSim program is used to simulate the operation of the VHDL codes and to obtain the expected output data of the FPGA boards. To confirm that FPGA the board used as the neurofuzzy controller system operated as expected, a MATLAB script file is used to compare the set of data obtained from the ModelSim program and the set of data obtained from the MATLAB SIMULINK model. The results show that the FPGA board is effective to be used as a neurofuzzy controller for full vehicle nonlinear active suspension systems. The active suspension system has a great performance for vibration isolation. However the main drawback of the active suspension is that it is high energy consumptive. Therefore, to use this suspension system in the proposed model, this drawback should be solved. Electromagnetic actuators are used to convert the vibration energy that arises from the rough road to useful electrical energy to reduce the energy consumption by the active suspension systems. The results show that the electromagnetic devices act as a power generator, i.e. the vibration energy excited by the rough road surface has been converted to a useful electrical energy supply for the actuators. Furthermore, when the nonlinear damper models are replaced by the electromagnetic actuators, riding comfort and the road handling quality are improved. As a result, two targets have been achieved by using hydraulic actuators with electromagnetic suspension systems: increasing fuel economy and improving the vehicle performance

Multi-Criteria Model for the Selection of Construction Materials: An Approach Based on Fuzzy Logic

The process of construction and exploitation of a building passes through the preparation phase, the construction phase and the exploitation phase. Each of these phases involves the selection of criteria and decision making, with the aim of selecting the optimal construction materials for the building. The paper presents a new model for selecting construction materials that is based on fuzzy logic. In order to simulate the expert process of assessing the construction and exploitation of a building during which construction materials are selected, a modular fuzzy logic system was designed with a unique base of knowledge to assist in decision making on the priorities of the construction material. The model consists of four modules that are hierarchically organized on two levels. The size of the output from the model is the measure of a material’s priority. Each of the materials observed (straw, wood, brick and concrete-steel) is assigned a certain value for the criterion function, on the basis of which the user of the system chooses the material for construction. In addition to the structure of the model, the paper presents its testing. Testing was carried out on the case study of selecting materials for the construction of five residential buildings

Contributions to the Optimisation of aircraft noise abatement procedures

Tot i que en les últimes dècades la reducció del soroll emès pels avions ha estat substancial, el seu impacte a la població ubicada a prop dels aeroports és un problema que encara persisteix. Contenir el soroll generat per les operacions d'aeronaus, tot assumint al mateix temps la creixent demanda de vols, és un dels principals desafiaments a que s'enfronten les autoritats aeroportuàries, els proveïdors de serveis per a la navegació aèria i els operadors de les aeronaus. A part de millorar l'aerodinàmica o les emissions sonores de les aeronaus, l'impacte acústic de les seves operacions es pot reduir també gràcies a la definició de nous procediments de vol més òptims. Aquests procediments s'anomenen generalment Procediments d'Atenuació de Soroll (PAS) i poden incloure rutes preferencials de vol (a fi d'evitar les zones poblades) i també perfils de vol verticals optimitzats. Els procediments actuals per a la reducció de soroll estan molt lluny de ser els òptims. En general, la seva optimització no és possible a causa de les limitacions d'avui en dia en els mètodes de navegació, els equips d'aviònica i la complexitat present en alguns espais aeris. D'altra banda, molts PAS s'han dissenyat de forma manual per un grup d'experts i amb l'ajuda de diverses iteracions. Tot i això, en els propers anys s'esperen nous sistemes d'aviònica i conceptes de gestió del trànsit aeri que permetin millorar el disseny d'aquests procediments, fent que siguin més flexibles. En els pocs casos on s'optimitzen PAS, se sol utilitzar una mètrica acústica en l'elaboració de les diferents funcions objectiu i per tant, no es tenen en compte les molèsties sonores reals. La molèstia és un concepte subjectiu, complexe i que depèn del context en que s'usa i la seva integració en l'optimització de trajectòries segueix essent un aspecte a estudiar.La present tesi doctoral es basa en el fet que en el futur serà possible definir trajectòries més flexibles i precises. D'aquesta manera es permetrà la definició de procediments de vol òptims des d'un punt de vista de molèsties acústiques. Així doncs, es considera una situació en que aquest tipus de procediments poden ser dissenyats de forma automàtica o semi-automàtica per un sistema expert basat en tècniques d'optimització i de raonament aproximat. Això serviria com una eina de presa de decisions per planificadors de l'espai aeri i dissenyadors de procediments. En aquest treball es desenvolupa una eina completa pel càlcul de PAS òptims. Això inclou un conjunt de models no lineals que tinguin en compte la dinàmica de les aeronaus, les limitacions de la trajectòria i les funcions objectiu. La molèstia del soroll es modela utilitzant tècniques de lògica difusa en funció del nivell màxim de so percebut, l'hora del dia i el tipus de zona a sobrevolar. Llavors, s'identifica i es formula formalment el problema com a un problema de control òptim multi-criteri. Per resoldre'l es proposa un mètode de transcripció directa per tal de transformar-lo en un problema de programació no lineal. A continuació s'avaluen una sèrie de tècniques d'optimització multi-objectiu i entre elles es destaca el mètode d'escalarització, el més utilitzat en la literatura. No obstant això, s'exploren diverses tècniques alternatives que permeten superar certs inconvenients que l'escalarització presenta. En aquest context, es presenten i proven tècniques d'optimització lexicogràfica, jeràrquica, igualitària (o min-max) i per objectius. D'aquest anàlisi es desprenen certes conclusions que permeten aprofitar les millors característiques de cada tècnica i formar finalment una tècnica composta d'optimització multi-objectiu. Aquesta última estratègia s'aplica amb èxit a un escenari real i complex, on s'optimitzen les sortides cap a l'Est de la pista 02 de l'aeroport de Girona. En aquest exemple, dos tipus diferents d'aeronaus volant a diferents períodes del dia són simulats obtenint, conseqüentment, diferents trajectòries òptimes.Aunque en las últimas décadas la reducción del ruido emitido por los aviones ha sido sustancial, su impacto en la población ubicada cerca de los aeropuertos es un problema persistente. Contener este ruido, asumiendo al mismo tiempo la creciente demanda de vuelos, es uno de los principales desafíos a que se enfrentan las autoridades aeroportuarias, los proveedores de servicios para la navegación y los operadores. Aparte de mejorar la aerodinámica o las emisiones sonoras de las aeronaves, su impacto acústico se puede reducir también gracias a la definición de nuevos procedimientos de vuelo optimizados. Éstos, se denominan generalmente Procedimientos de Atenuación de Ruido (PAR) y pueden incluir rutas preferenciales de vuelo (a fin de evitar las zonas pobladas) y también perfiles de vuelo optimizados.Los procedimientos actuales para la reducción de ruido están muy lejos de ser los óptimos. En general, su optimización no es posible debido a las limitaciones de hoy en día en los métodos de navegación, los equipos de aviónica y la complejidad presente en algunos espacios aéreos. Por otra parte, muchos PAR se han diseñado de forma manual por un grupo de expertos y con la ayuda de varias iteraciones. Sin embargo, en los próximos años se esperan nuevos sistemas de aviónica y conceptos de gestión del tráfico aéreo que permitan mejorar el diseño de estos procedimientos, haciendo que sean más flexibles. En los pocos casos donde se optimizan PAR, se suele utilizar una métrica acústica en la elaboración de las diferentes funciones objetivo y por lo tanto, no se tienen en cuenta las molestias sonoras reales. La molestia es un concepto subjetivo, complejo y que depende del contexto en que se usa y su integración en la optimización de trayectorias sigue siendo un aspecto a estudiar. La presente tesis doctoral se basa en el hecho de que en el futuro será posible definir trayectorias más flexibles y precisas. De esta manera se permitirá la definición de procedimientos de vuelo óptimos desde un punto de vista de molestias acústicas. Se considera una situación en que este tipo de procedimientos pueden ser diseñados de forma automática o semi-automática por un sistema experto basado en técnicas de optimización y de razonamiento aproximado. Esto serviría como una herramienta de toma de decisiones para planificadores del espacio aéreo y diseñadores de procedimientos.En este trabajo se desarrolla una herramienta completa para el cálculo de PAR óptimos. Esto incluye un conjunto de modelos no lineales que tengan en cuenta la dinámica de las aeronaves, las limitaciones de la trayectoria y las funciones objetivo. La molestia del ruido se modela utilizando técnicas de lógica difusa en función del nivel máximo de sonido percibido, la hora del día y el tipo de zona a sobrevolar. Entonces, se identifica y se formula formalmente el problema como un problema de control óptimo multi-criterio. Para resolverlo se propone un método de transcripción directa para transformarlo en un problema de programación no lineal. A continuación se evalúan una serie de técnicas de optimización multi-objetivo y entre ellas se destaca el método de escalarización, el más utilizado en la literatura. Sin embargo, se exploran diversas técnicas alternativas que permiten superar ciertos inconvenientes que la escalarización presenta. En este contexto, se presentan y prueban técnicas de optimización lexicográfica, jerárquica, igualitaria (o min-max) y por objetivos. De este análisis se desprenden ciertas conclusiones que permiten aprovechar las mejores características de cada técnica y formar finalmente una técnica compuesta de optimización multi-objetivo. Esta última estrategia se aplica con éxito en un escenario real y complejo, donde se optimizan las salidas hacia el Este de la pista 02 del aeropuerto de Girona. En este ejemplo, dos tipos diferentes de aeronaves volando a diferentes periodos del día son simulados obteniendo, consecuentemente, diferentes trayectorias óptimas.Despite the substantial reduction of the emitted aircraft noise in the last decades, the noise impact on communities located near airports is a problem that still lingers. Containing the sound generated by aircraft operations, while meeting the increasing demand for aircraft transportation, is one of the major challenges that airport authorities, air traffic service providers and aircraft operators may deal with. Aircraft noise can be reduced by improving the aerodynamics of the aircraft, the engine noise emissions but also in designing new optimised flight procedures. These procedures, are generally called Noise Abatement Procedures (NAP) and may include preferential routings (in order to avoid populated areas) and also schedule optimised vertical flight path profiles. Present noise abatement procedures are far from being optimal in regards to minimising noise nuisances. In general, their optimisation is not possible due to the limitations of navigation methods, current avionic equipments and the complexity present at some terminal airspaces. Moreover, NAP are often designed manually by a group of experts and several iterations are needed. However, in the forthcoming years, new avionic systems and new Air Traffic Management concepts are expected to significantly improve the design of flight procedures. This will make them more flexible, and therefore will allow them to be more environmental friendly. Furthermore, in the few cases where NAP are optimised, an acoustical metric is usually used when building up the different optimisation functions. Therefore, the actual noise annoyance is not taken into account in the optimisation process. The annoyance is a subjective, complex and context-dependent concept. Even if sophisticated noise annoyance models are already available today, their integration into an trajectory optimisation framework is still something to be further explored. This dissertation is mainly focused on the fact that those precise and more flexible trajectories will enable the definition of optimal flight procedures regarding the noise annoyance impact, especially in the arrival and departure phases of flights. In addition, one can conceive a situation where these kinds of procedures can be designed automatically or semi-automatically by an expert system, based on optimisation techniques and approximate reasoning. This would serve as a decision making tool for airspace planners and procedure designers.A complete framework for computing optimal NAP is developed in this work. This includes a set of nonlinear models which take into account aircraft dynamics, trajectory constraints and objective functions. The noise annoyance is modelled by using fuzzy logic techniques in function of the perceived maximum sound level, the hour of the day and the type of over-flown zone. The problem tackled, formally identified and formulated as a multi-criteria optimal control problem, uses a direct transcription method to transform it into a Non Linear Programming problem. Then, an assessment of different multi-objective optimisation techniques is presented. Among these techniques, scalarisation methods are identified as the most widely used methodologies in the present day literature. Yet, in this dissertation several alternative techniques are explored in order to overcome some known drawbacks of this technique. In this context, lexicographic, hierarchical, egalitarian (or min-max) and goal optimisation strategies are presented and tested. From this analysis some conclusions arise allowing us to take advantage of the best features of each optimisation technique aimed at building a final compound multi-objective optimisation strategy. Finally, this strategy is applied successfully to a complex and real scenario, where the East departures of runway 02 at the airport of Girona (Catalonia, Spain) are optimised. Two aircraft types are simulated at different periods of the day obtaining different optimal trajectories.Postprint (published version

Fuzzy Sets, Fuzzy Logic and Their Applications 2020

The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity

Fuzzy Controllers

Trying to meet the requirements in the field, present book treats different fuzzy control architectures both in terms of the theoretical design and in terms of comparative validation studies in various applications, numerically simulated or experimentally developed. Through the subject matter and through the inter and multidisciplinary content, this book is addressed mainly to the researchers, doctoral students and students interested in developing new applications of intelligent control, but also to the people who want to become familiar with the control concepts based on fuzzy techniques. Bibliographic resources used to perform the work includes books and articles of present interest in the field, published in prestigious journals and publishing houses, and websites dedicated to various applications of fuzzy control. Its structure and the presented studies include the book in the category of those who make a direct connection between theoretical developments and practical applications, thereby constituting a real support for the specialists in artificial intelligence, modelling and control fields

Intelligent Control Strategies for an Autonomous Underwater Vehicle

The dynamic characteristics of autonomous underwater vehicles (AUVs) present a control problem that classical methods cannot often accommodate easily. Fundamentally, AUV dynamics are highly non-linear, and the relative similarity between the linear and angular velocities about each degree of freedom means that control schemes employed within other flight vehicles are not always applicable. In such instances, intelligent control strategies offer a more sophisticated approach to the design of the control algorithm. Neurofuzzy control is one such technique, which fuses the beneficial properties of neural networks and fuzzy logic in a hybrid control architecture. Such an approach is highly suited to development of an autopilot for an AUV. Specifically, the adaptive network-based fuzzy inference system (ANFIS) is discussed in Chapter 4 as an effective new approach for neurally tuning course-changing fuzzy autopilots. However, the limitation of this technique is that it cannot be used for developing multivariable fuzzy structures. Consequently, the co-active ANFIS (CANFIS) architecture is developed and employed as a novel multi variable AUV autopilot within Chapter 5, whereby simultaneous control of the AUV yaw and roll channels is achieved. Moreover, this structure is flexible in that it is extended in Chapter 6 to perform on-line control of the AUV leading to a novel autopilot design that can accommodate changing vehicle pay loads and environmental disturbances. Whilst the typical ANFIS and CANFIS structures prove effective for AUV control system design, the well known properties of radial basis function networks (RBFN) offer a more flexible controller architecture. Chapter 7 presents a new approach to fuzzy modelling and employs both ANFIS and CANFIS structures with non-linear consequent functions of composite Gaussian form. This merger of CANFIS and a RBFN lends itself naturally to tuning with an extended form of the hybrid learning rule, and provides a very effective approach to intelligent controller development.The Sea Systems and Platform Integration Sector, Defence Evaluation and Research Agency, Winfrit

Robot Manipulators

Robot manipulators are developing more in the direction of industrial robots than of human workers. Recently, the applications of robot manipulators are spreading their focus, for example Da Vinci as a medical robot, ASIMO as a humanoid robot and so on. There are many research topics within the field of robot manipulators, e.g. motion planning, cooperation with a human, and fusion with external sensors like vision, haptic and force, etc. Moreover, these include both technical problems in the industry and theoretical problems in the academic fields. This book is a collection of papers presenting the latest research issues from around the world