Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations

García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment model

Current Mode with RMS Voltage and Offset Control Loops for a Single-Phase Aircraft Inverter Suitable for Parallel and 3-Phase Operation Modes

Rms voltage regulation may be an attractive possibility for controlling power inverters. Combined with a Hall Effect sensor for current control, it keeps its parallel operation capability while increasing its noise immunity, which may lead to a reduction of the Total Harmonic Distortion (THD). Besides, as voltage regulation is designed in DC, a simple PI regulator can provide accurate voltage tracking. Nevertheless, this approach does not lack drawbacks. Its narrow voltage bandwidth makes transients last longer and it increases the voltage THD when feeding non-linear loads, such as rectifying stages. On the other hand, the implementation can fall into offset voltage error. Furthermore, the information of the output voltage phase is hidden for the control as well, making the synchronization of a 3-phase setup not trivial. This paper explains the concept, design and implementation of the whole control scheme, in an on board inverter able to run in parallel and within a 3-phase setup. Special attention is paid to solve the problems foreseen at implementation level: a third analog loop accounts for the offset level is added and a digital algorithm guarantees 3-phase voltage synchronization.

A Semi-Lagrangian Particle Level Set Finite Element Method for Interface Problems

We present a quasi-monotone semi-Lagrangian particle level set (QMSL-PLS) method for moving interfaces. The QMSL method is a blend of first order monotone and second order semi-Lagrangian methods. The QMSL-PLS method is easy to implement, efficient, and well adapted for unstructured, either simplicial or hexahedral, meshes. We prove that it is unconditionally stable in the maximum discrete norm, � · �h,∞, and the error analysis shows that when the level set solution u(t) is in the Sobolev space Wr+1,∞(D), r ≥ 0, the convergence in the maximum norm is of the form (KT/Δt)min(1,Δt � v �h,∞ /h)((1 − α)hp + hq), p = min(2, r + 1), and q = min(3, r + 1),where v is a velocity. This means that at high CFL numbers, that is, when Δt > h, the error is O( (1−α)hp+hq) Δt ), whereas at CFL numbers less than 1, the error is O((1 − α)hp−1 + hq−1)). We have tested our method with satisfactory results in benchmark problems such as the Zalesak’s slotted disk, the single vortex flow, and the rising bubble.

Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

Experimental and statistical investigation of canonical problems in sloshing

En hidrodinámica, el fenómeno de Sloshing se puede definir como el movimiento de la superficie libre de un fluido dentro de un contenedor sometido a fuerzas y perturbaciones externas. El fluido en cuestión experimenta violentos movimientos con importantes deformaciones de su superficie libre. La dinámica del fluido puede llegar a generar cargas hidrodinámicas considerables las cuales pueden afectar la integridad estructural y/o comprometer la estabilidad del vehículo que transporta dicho contenedor. El fenómeno de Sloshing ha sido extensivamente investigado matemática, numérica y experimentalmente, siendo el enfoque experimental el más usado debido a la complejidad del problema, para el cual los modelos matemáticos y de simulación son aun incapaces de predecir con suficiente rapidez y precisión las cargas debidas a dicho fenómeno. El flujo generado por el Sloshing usualmente se caracteriza por la presencia de un fluido multifase (gas-liquido) y turbulencia. Reducir al máximo posible la complejidad del fenómeno de Sloshing sin perder la esencia del problema es el principal reto de esta tesis doctoral, donde un trabajo experimental enfocado en casos canónicos de Sloshing es presentado y documentado con el objetivo de aumentar la comprensión de dicho fenómeno y por tanto intentar proveer información valiosa para validaciones de códigos numéricos. El fenómeno de Sloshing juega un papel importante en la industria del transporte marítimo de gas licuado (LNG). El mercado de LNG en los últimos años ha reportado un crecimiento hasta tres veces mayor al de los mercados de petróleo y gas convencionales. Ingenieros en laboratorios de investigación e ingenieros adscritos a la industria del LNG trabajan continuamente buscando soluciones económicas y seguras para contener, transferir y transportar grandes volúmenes de LNG. Los buques transportadores de LNG (LNGC) han pasado de ser unos pocos buques con capacidad de 75000 m3 hace unos treinta años, a una amplia flota con una capacidad de 140000 m3 actualmente. En creciente número, hoy día se construyen buques con capacidades que oscilan entre 175000 m3 y 250000 m3. Recientemente un nuevo concepto de buque LNG ha salido al mercado y se le conoce como FLNG. Un FLNG es un buque de gran valor añadido que solventa los problemas de extracción, licuefacción y almacenamiento del LNG, ya que cuenta con equipos de extracción y licuefacción a bordo, eliminando por tanto las tareas de transvase de las estaciones de licuefacción en tierra hacia los buques LNGC. EL LNG por tanto puede ser transferido directamente desde el FLNG hacia los buques LNGC en mar abierto. Niveles de llenado intermedios en combinación con oleaje durante las operaciones de trasvase inducen movimientos en los buques que generan por tanto el fenómeno de Sloshing dentro de los tanques de los FLNG y los LNGC. El trabajo de esta tesis doctoral lidia con algunos de los problemas del Sloshing desde un punto de vista experimental y estadístico, para ello una serie de tareas, descritas a continuación, se han llevado a cabo : 1. Un dispositivo experimental de Sloshing ha sido configurado. Dicho dispositivo ha permitido ensayar secciones rectangulares de tanques LNGC a escala con movimientos angulares de un grado de libertad. El dispositivo experimental ha sido instrumentado para realizar mediciones de movimiento, presiones, vibraciones y temperatura, así como la grabación de imágenes y videos. 2. Los impactos de olas generadas dentro de una sección rectangular de un LNGC sujeto a movimientos regulares forzados han sido estudiados mediante la caracterización del fenómeno desde un punto de vista estadístico enfocado en la repetitividad y la ergodicidad del problema. 3. El estudio de los impactos provocados por movimientos regulares ha sido extendido a un escenario más realístico mediante el uso de movimientos irregulares forzados. 4. El acoplamiento del Sloshing generado por el fluido en movimiento dentro del tanque LNGC y la disipación de la energía mecánica de un sistema no forzado de un grado de libertad (movimiento angular) sujeto a una excitación externa ha sido investigado. 5. En la última sección de esta tesis doctoral, la interacción entre el Sloshing generado dentro en una sección rectangular de un tanque LNGC sujeto a una excitación regular y un cuerpo elástico solidario al tanque ha sido estudiado. Dicho estudio corresponde a un problema de interacción fluido-estructura. Abstract In hydrodynamics, we refer to sloshing as the motion of liquids in containers subjected to external forces with large free-surface deformations. The liquid motion dynamics can generate loads which may affect the structural integrity of the container and the stability of the vehicle that carries such container. The prediction of these dynamic loads is a major challenge for engineers around the world working on the design of both the container and the vehicle. The sloshing phenomenon has been extensively investigated mathematically, numerically and experimentally. The latter has been the most fruitful so far, due to the complexity of the problem, for which the numerical and mathematical models are still incapable of accurately predicting the sloshing loads. The sloshing flows are usually characterised by the presence of multiphase interaction and turbulence. Reducing as much as possible the complexity of the sloshing problem without losing its essence is the main challenge of this phd thesis, where experimental work on selected canonical cases are presented and documented in order to better understand the phenomenon and to serve, in some cases, as an useful information for numerical validations. Liquid sloshing plays a key roll in the liquified natural gas (LNG) maritime transportation. The LNG market growth is more than three times the rated growth of the oil and traditional gas markets. Engineers working in research laboratories and companies are continuously looking for efficient and safe ways for containing, transferring and transporting the liquified gas. LNG carrying vessels (LNGC) have evolved from a few 75000 m3 vessels thirty years ago to a huge fleet of ships with a capacity of 140000 m3 nowadays and increasing number of 175000 m3 and 250000 m3 units. The concept of FLNG (Floating Liquified Natural Gas) has appeared recently. A FLNG unit is a high value-added vessel which can solve the problems of production, treatment, liquefaction and storage of the LNG because the vessel is equipped with a extraction and liquefaction facility. The LNG is transferred from the FLNG to the LNGC in open sea. The combination of partial fillings and wave induced motions may generate sloshing flows inside both the LNGC and the FLNG tanks. This work has dealt with sloshing problems from a experimental and statistical point of view. A series of tasks have been carried out: 1. A sloshing rig has been set up. It allows for testing tanks with one degree of freedom angular motion. The rig has been instrumented to measure motions, pressure and conduct video and image recording. 2. Regular motion impacts inside a rectangular section LNGC tank model have been studied, with forced motion tests, in order to characterise the phenomenon from a statistical point of view by assessing the repeatability and practical ergodicity of the problem. 3. The regular motion analysis has been extended to an irregular motion framework in order to reproduce more realistic scenarios. 4. The coupled motion of a single degree of freedom angular motion system excited by an external moment and affected by the fluid moment and the mechanical energy dissipation induced by sloshing inside the tank has been investigated. 5. The last task of the thesis has been to conduct an experimental investigation focused on the strong interaction between a sloshing flow in a rectangular section of a LNGC tank subjected to regular excitation and an elastic body clamped to the tank. It is thus a fluid structure interaction problem.

Multiple Robots, Single Operator: Considerations About Information And Commanding

Multiple robot, single operator scenarios suppose a challenge in terms of human factors. Two relevant issues are keeping the situational awareness and managing the workload of operators. In order to address these problems, this work analyses the management of information and commands in multi-robot missions. About the information, this paper proposes a selection based on mission and operator states. Regarding the commands, this work reflects about the levels of automation and the methods of commanding.