Computational Geometry Concepts Research Articles

Convex Hulls and the size and the Size of the Hidden Layer in a MLP Based Classifier

Designing a feedforward neural network has always posed many questions regarding the number of hidden layers and the number of neurons on each hidden layer. While there is no unique and global solution, it is known that the particularities of the problem to solve, especially for classification, offer some guidance about how to solve these questions. One heuristic approach, when only a hidden layer is involved, analyzes how the involved classes are separated from each other using a finite number of hyperplanes, thereby defining the size of the hidden layer on the network. On this article, using computational geometry concepts, an automated and time efficient method is presented and discussed for estimating the quantity of neurons in the hidden layer by computing the number of hyperplanes separating the classes, based on convex hulls and approximation to alpha shapes. Examples on different situations that may arise and the results on using it are illustrated. It can be seen from the results that the proposed method gives very good estimation for the number of hidden neurons.

A Set-Theoretic Reconfiguration Feedback Control Scheme Against Simultaneous Stuck Actuators

This paper presents a fault-tolerant control scheme for constrained discrete-time linear systems against stuck actuators and bounded disturbances. The results proposed here are a significant generalization of a similar algorithm that has been designed only to manage healthy/out-of-service actuator units. A key feature of the proposed scheme consists of taking advantage of polyhedral algebra and computational geometry concepts in order to characterize the reconfiguration logic of the proposed fault-tolerant architecture. This is achieved by describing the plant via a set of a finite number of piecewise affine (PWA) systems capable to cover all the admissible faulty stuck scenarios. It is then proved that one-step sequences of controllable sets can be formally defined within a PWA system paradigm under the key property that each region is a polyhedron.

Computational geometry‐based methodology for identification of potential islanding initiators in high solar PV penetration distribution feeders

Accidental disconnection of a live feeder section is a major concern accompanying large distributed solar photovoltaic (PV) generation integration. High localised penetration can alter power flows leading to anomalous occurrences. Load-inverter power balance during grid-side disturbances, for different load models, may cause unique situations that can trigger the interconnection point protective devices. One such phenomenon, identified as a potential cause of unintentional islanding on radial feeder models (a modified IEEE feeder in simulation and verified on a laboratory-hardware network), has been used in this work. A pre-emptive detection strategy has been implemented to identify such islanding initiators among other power system transients. Computational geometry concepts have been utilised to create an optimisation-derived feature extraction methodology for effective training of a classifier module realised in a Raspberry Pi microcomputer. This module predicts the class labels of test data points transmitted from simulations carried on a personal computer for the feeder model. The proposed pre-emptive islanding detection strategy can trigger an appropriate change in a PV inverter's operating mode before a feeder protective device is tripped by such island initiating anomalies. The online classification accuracy and speed indicate a possible integration of the proposed methodology and strategy with the inverter's control circuitry.

Static Structural and Modal Analysis Using Isogeometric Analysis

Abstract Isogeometric Analysis (IGA) is a new analysis method for unification of Computer Aided Design (CAD) and Computer Aided Engineering (CAE). With the use of NURBS basis functions for both modelling and analysis, the bottleneck of meshing is avoided and a seamless integration is achieved. The CAD and computational geometry concepts in IGA are new to the analysis community. Though, there is a steady growth of literature, details of calculations, explanations and examples are not reported. The content of the paper is complimentary to the existing literature and addresses the gaps. It includes summary of the literature, overview of the methodology, step-by-step calculations and Matlab codes for example problems in static structural and modal analysis in 1-D and 2-D. At appropriate places, comparison with the Finite Element Analysis (FEM) is also included, so that those familiar with FEM can appreciate IGA better.

Fast and reliable gate arrangement pre-design of resin infusion processes

In Resin Infusion (RI) processes, the flow front shape progression is mainly conditioned by the initial arrangement of the injection and vent gate line locations and the permeability of the preform. The main goal of this research is to develop fast (not necessarily physically-based) tools at the pre-design stage that could help designers with a suitable arrangement of injection nozzles and vents. This pre-design should then be validated by full-physics simulation or lab test, but could be considered as a suitable starting point in the designing process. RI simulators could eventually be equipped with this kind of pre-design tools as a means to provide very fast (at the cost of a somewhat reduced accuracy) designs. In the approach here presented the pre-design tools are based entirely on geometrical assumptions. Under these hypotheses, and assuming that the vents will be placed on the boundary of the piece, the distance field from this boundary will provide useful information on the optimal position of injection nozzles. In this work, inspired by the concept of medial axis, we propose a numerical technique that computes numerically approximate distance fields by invoking computational geometry concepts that can be used for the estimation of the gate arrangement in infusion processes. Detailed descriptions of the developed algorithm, together with first proofs of its performance are given.

Improving Computational Efficiency in LCM by Using Computational Geometry and Model Reduction Techniques

LCM simulation is computationally expensive because it needs an accurate solution of flowequations during the mold filling process. When simulating large computing times are not compatiblewith standard optimization techniques (for example for locating optimally the injection nozzles)or with process control that in general requires fast decision-makings. In this work, inspired by theconcept of medial axis, we propose a numerical technique that computes numerically approximatedistance fields by invoking computational geometry concepts that can be used for the optimal locationof injection nozzles in infusion processes. On the other hand we also analyze the possibilities thatmodel order reduction offers to fast and accurate solutions of flow models in mold filling processes.

An objective approach to digital removal of saccular aneurysms: technique and applications

Human studies of haemodynamic factors in the pathogenesis of cerebral aneurysms require knowledge of the pre-aneurysmal vasculature. This paper presents an objective and automated technique to digitally remove an aneurysm and reconstruct the parent artery, based on lumen geometries segmented from angiographic images. Relying on robust computational geometry concepts, notably Voronoi diagrams of the digitised lumen surface, the aneurysm attachment region is first defined objectively using lumen centrelines. Centrelines within this region are replaced by smooth interpolations, which then guide the interpolation of Voronoi points within the attachment region. Combined with Voronoi points from outside the attachment region, the parent artery lumen, without the aneurysm, can be reconstructed. Plausible reconstructions were obtained, automatically, for a set of 10 side-wall or terminal aneurysms, of various sizes and shapes, from the ANEURISK project data set. Application of image-based computational fluid dynamics analysis to a five side-wall aneurysm cases data set revealed an association between the recently proposed gradient oscillatory number (GON) and the site of aneurysm formation in four of five cases; however, elevated GON was also evident at non-aneurysmal sites. A potential application to the automated delineation of aneurysms for morphological characterisations is also suggested. The proposed approach may serve as a broad platform for investigating haemodynamic and morphological factors in aneurysm initiation, rupture and therapy in a way amenable to large-scale clinical studies or routine clinical use. Nevertheless, while the parent artery reconstructions are plausible, it remains to be proven that they are faithful representations of the pre-aneurysmal artery.

The importance of computational geometry for digital cartography

This paper describes the use of computational geometry concepts in the digital cartography. It presents an importance of 2D geometric structures, geometric operations and procedures for automated or semi automated simplification process. This article is focused on automated building simplification procedures, some techniques are illustrated and discussed. Concrete examples with the requirements to the lowest time complexity, emphasis on the smallest area enclosing rectangle, convex hull or self intersection procedures, are given. Presented results illustrate the relationship of digital cartography and computational geometry.