A Novel Approach for Ellipsoidal Outer-Approximation of the Intersection Region of Ellipses in the Plane

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses are found in an efficient manner. To do so, the intersection points of the ellipses that fall on the boundary of the intersection region are determined, and a set of points is generated on the elliptic arcs connecting every two neighbouring intersection points. By finding the tangent lines to the ellipses at the extended set of points, a set of half-planes is obtained, whose intersection forms a polygon. To find the polygon more efficiently, the points are given an order and the intersection of the half-planes corresponding to every two neighbouring points is calculated. If the polygon is convex and bounded, these calculated points together with the initially obtained intersection points will form its vertices. If the polygon is non-convex or unbounded, we can detect this situation and then generate additional discrete points only on the elliptical arc segment causing the issue, and restart the algorithm to obtain a bounded and convex polygon. Finally, the smallest area ellipse that contains the vertices of the polygon is obtained by solving a convex optimization problem. Through numerical experiments, it is illustrated that the proposed technique returns a tighter outer-approximation of the intersection of multiple ellipses, compared to conventional techniques, with only slightly higher computational cost

Range-Point Migration-Based Image Expansion Method Exploiting Fully Polarimetric Data for UWB Short-Range Radar

Ultrawideband radar with high-range resolution is a promising technology for use in short-range 3-D imaging applications, in which optical cameras are not applicable. One of the most efficient 3-D imaging methods is the range-point migration (RPM) method, which has a definite advantage for the synthetic aperture radar approach in terms of computational burden, high accuracy, and high spatial resolution. However, if an insufficient aperture size or angle is provided, these kinds of methods cannot reconstruct the whole target structure due to the absence of reflection signals from large part of target surface. To expand the 3-D image obtained by RPM, this paper proposes an image expansion method by incorporating the RPM feature and fully polarimetric data-based machine learning approach. Following ellipsoid-based scattering analysis and learning with a neural network, this method expresses the target image as an aggregation of parts of ellipsoids, which significantly expands the original image by the RPM method without sacrificing the reconstruction accuracy. The results of numerical simulation based on 3-D finite-difference time-domain analysis verify the effectiveness of our proposed method, in terms of image-expansion criteria

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive manufacturing requires highly-accurate multiscale and multiphysics analyses. Only high performance computing tools are able to handle such complexity in time frames compatible with time-to-market. However, efficiency, without loss of accuracy, has rarely held the centre stage in the numerical community. Here, in contrast, the framework is designed to adequately exploit the resources of high-end distributed-memory machines. It is grounded on three building blocks: (1) Hierarchical adaptive mesh refinement with octree-based meshes; (2) a parallel strategy to model the growth of the geometry; (3) state-of-the-art parallel iterative linear solvers. Computational experiments consider the heat transfer analysis at the part scale of the printing process by powder-bed technologies. After verification against a 3D benchmark, a strong-scaling analysis assesses performance and identifies major sources of parallel overhead. A third numerical example examines the efficiency and robustness of (2) in a curved 3D shape. Unprecedented parallelism and scalability were achieved in this work. Hence, this framework contributes to take on higher complexity and/or accuracy, not only of part-scale simulations of metal or polymer additive manufacturing, but also in welding, sedimentation, atherosclerosis, or any other physical problem where the physical domain of interest grows in time

A probabilistic interpretation of set-membership filtering: application to polynomial systems through polytopic bounding

Set-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic setting by employing sets of probability measures. Inference in set-membership estimation is thus carried out by computing expectations with respect to the updated set of probability measures P as in the probabilistic case. In particular, it is shown that inference can be performed by solving a particular semi-infinite linear programming problem, which is a special case of the truncated moment problem in which only the zero-th order moment is known (i.e., the support). By writing the dual of the above semi-infinite linear programming problem, it is shown that, if the nonlinearities in the measurement and process equations are polynomial and if the bounding sets for initial state, process and measurement noises are described by polynomial inequalities, then an approximation of this semi-infinite linear programming problem can efficiently be obtained by using the theory of sum-of-squares polynomial optimization. We then derive a smart greedy procedure to compute a polytopic outer-approximation of the true membership-set, by computing the minimum-volume polytope that outer-bounds the set that includes all the means computed with respect to P

UK Rules For Unfired Pressure Vessels

The present code PD 5500, formerly BS 5500 [1] evolved partly from the well-known BS 1500 [2] in the 1950's and BS 1515 [3] first published in 1965; the latter permitted higher level allowable stresses and more advanced rules. In 1969, following a report from the Committee of Enquiry into the Pressure Vessel Industry, the British Standards Institution brought all the pressure vessel interests together under one general committee in order to rationalise the activity. This became PVE/ and presides over a large committee structure. There are a series of functional sub-committees who deal with specific aspects and a large number of technical committees as well as many additional sub committees and working groups. Most of these meet regularly. The technical committee PVE/1, Pressure Vessels, has overall responsibility for BS 5500. The functional committee PVE/1/15 Design Methods has an overall responsibility relating to 'Design' with particular reference to the design section of BS 5500 (Section 3). The first edition of BS 5500 was issued in 1976. The actual issue was delayed for some time because, in the early 1970's, there was an attempt in Europe to produce an international pressure vessel standard. A draft of the international standard appeared as ISO DIS 2694 [4] in 1973 but it was not generally accepted and the attempt was abandoned in the mid 70's. It was decided to use some of the material from 2694 within BS 5500 so that although the Standard was long delayed it benefited to some extent from the international efforts. Initially, committee PVE/l set out the concept of a "master" pressure vessel standard which could readily be applied to any vessel in either ferrous or non-ferrous materials and for highly specialised application with the minimum of supplementary requirements. The layout of BS 5500 is consistent with this concept and although the Standard has perhaps not fulfilled this high ideal, it has certainly been employed widely in many industries including non pressure vessel type applications. When issued it had a number of distinctive features compared with other pressure codes viz; weld joint factors were removed, the present three categories of construction were introduced, there was a new novel external pressure section, it has a loose leaf format and an annual updating was introduced. Further editions of BS 5500 have been issued every three years since 1982

Numerical analysis of the melt-pool in additive manufacturing processes

En els processos de fabricació additiva (AM), la forma de la melt-pool està relacionada amb la formació de defectes que afecta el comportament mecànic final. En aquest sentit, és essencial entendre la influència de diferents paràmetres del procés, com ara la velocitat d’escaneig o la potència del làser, sobre la melt-pool. Per aquest motiu, s'ha desenvolupat una eina numèrica per predir amb precisió la mida de la melt-pool. El model s’ha implementat dins d’un software HPC d’elements finits que pot resoldre simulacions termo-mecàniques acoplades. El model de font de calor de doble elipsoïde de Goldak s'ha utilitzat per reproduir la distribució de la densitat de potència dins de la melt-pool. A més, per resoldre el canvi de fase a la interfície de la melt-pool, s’ha considerat la calor latent alliberada durant la transformació. Per resoldre el problema no lineal resultant, s'ha implementat el mètode Newton-Raphson. El model s'ha verificat i validat amb èxit en comparació amb l'evidència experimental disponible. Abans, cal calibrar els paràmetres del doble elipsoïde amb els resultats experimentals. Així, l’absorció de l’energia és el paràmetre més sensible per a les mides finals de la melt-pool.En los procesos de fabricación aditiva (AM) la forma de la melt-pool está relacionada con la formación de defectos que afectan el comportamiento mecánico final. En este sentido, es fundamental comprender la influencia de diferentes parámetros del proceso, como la velocidad o la potencia del láser, en la melt-pool. Por esta razón, se ha desarrollado una herramienta numérica para predecir con precisión el tamaño de la melt-pool. El modelo se ha implementado dentro de un solver HPC de elementos finitos que puede resolver simulaciones termo-mecánicas acopladas. El modelo de fuente de calor de doble elipsoide de Goldak se ha utilizado para reproducir la distribución de densidad de potencia dentro de la melt-pool. Además, para resolver el cambio de fase en la interfaz de la melt-pool, se ha considerado el calor latente liberado durante la transformación. Para resolver el problema no lineal resultante, se ha implementado el método de Newton-Raphson. El modelo se ha verificado y validado con éxito frente a la evidencia experimental disponible. De antemano, los parámetros del doble elipsoide se deben calibrar con los resultados experimentales. Así, se ha determinado que la absortividad de energía es el parámetro más sensible para el tamaño final de la melt-pool.In Additive manufacturing (AM) processes the melt-pool shape is related with the defect formation that affects the final mechanical behaviour. In this regard, it is essential to understand the influence of different process parameters, such as the scanning speed or the laser power, on the molten pool. For this reason, a numerical tool to accurately predict the melt pool size has been developed. The model has been implemented within an in-house HPC finite element solver that can solve coupled thermo-mechanical AM simulations. The Goldak's double ellipsoidal heat source model has been used to reproduce the power density distribution within the melt pool. Furthermore, to solve the phase-change at the melt-pool interface, the latent heat released during the transformation has been considered. To solve the resulting nonlinear problem, the Newton-Raphson method has been implemented. The model has been successfully verified and validated against the available experimental evidence. Beforehand, the double ellipsoidal parameters need to be calibrated to match the experimental results. Thus, the energy absorptivity is found to be the most sensitive parameter for the predicted melt pool sizes

A New Multiple Hypothesis Tracker Using Validation Gate with Motion Direction Constraint.

In multi-target tracking scenarios with dense and heterogeneous clutter, there is a substantial increase in the false measurements that originated from the clutter within the validation gate, and consequently, the number of measurement-to-track association hypothesis grows rapidly in traditional multiple hypothesis tracker (MHT), leading to a sharp decrease in data association accuracy and tracking performance. A new multiple hypothesis tracker using validation gate with motion direction constraint (MHT-MDC) is proposed to solve these problems. In the MHT-MDC, a motion direction constraint (MDC) gate is designed by considering the prior target maneuvering information, which effectively reduces the volume of validation gate and, thus, diminishes the number of false measurements in the gate when the innovation covariance is large. Subsequently, the clutter density in the MDC gate is adaptively estimated by the conditional mean estimator of clutter density (CMECD), based on which the score functions in the MDC gate can be calculated. The MHT-MDC is compared with the MHT algorithm in simulations, and the experimental results demonstrate its superior tracking performance for weakly maneuvering targets in high clutter density scenarios