Geometric constraint subsets and subgraphs in the analysis of assemblies and mechanisms

Geometric Reasoning ability is central to many applications in CAD/CAM/CAPP environments. An increasing demand exists for Geometric Reasoning systems which evaluate the feasibility of virtual scenes specified by geometric relations. Thus, the Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF) problem consists of a basic scenario containing geometric entities, whose context is used to propose constraining relations among still undefined entities. If the constraint specification is consistent, the answer of the problem is one of finitely or infinitely many solution scenarios satisfying the prescribed constraints. Otherwise, a diagnostic of inconsistency is expected. The three main approaches used for this problem are numerical, procedural or operational and mathematical. Numerical and procedural approaches answer only part of the problem, and are not complete in the sense that a failure to provide an answer does not preclude the existence of one. The mathematical approach previously presented by the authors describes the problem using a set of polynomial equations. The common roots to this set of polynomials characterizes the solution space for such a problem. That work presents the use of Groebner basis techniques for verifying the consistency of the constraints. It also integrates subgroups of the Special Euclidean Group of Displacements SE(3) in the problem formulation to exploit the structure implied by geometric relations. Although theoretically sound, these techniques require large amounts of computing resources. This work proposes Divide-and-Conquer techniques applied to local GCS/SF subproblems to identify strongly constrained clusters of geometric entities. The identification and preprocessing of these clusters generally reduces the effort required in solving the overall problem. Cluster identification can be related to identifying short cycles in the Spatial Constraint graph for the GCS/SF problem. Their preprocessing uses the aforementioned Algebraic Geometry and Group theoretical techniques on the local GCS/SF problems that correspond to these cycles. Besides improving the efficiency of the solution approach, the Divide-and-Conquer techniques capture the physical essence of the problem. This is illustrated by applying the discussed techniques to the analysis of the degrees of freedom of mechanisms.MSC: 68U07La habilidad del Razonamiento Geométrico es central a muchas aplicaciones de CAD/CAM/CAPP (Computer Aided Design, Manufacturing and Process Planning). Existe una demanda creciente de sistemas de Razonamiento Geométrico que evalúen la factibilidad de escenas virtuales, especificados por relaciones geométricas. Por lo tanto, el problema de Satisfacción de Restricciones Geométricas o de Factibilidad de Escena (GCS/SF) consta de un escenario básico conteniendo entidades geométricas, cuyo contexto es usado para proponer relaciones de restricción entre entidades aún indefinidas. Si la especificación de las restricciones es consistente, la respuesta al problema es uno del finito o infinito número de escenarios solución que satisfacen las restricciones propuestas. De otra forma, un diagnóstico de inconsistencia es esperado. Las tres principales estrategias usadas para este problema son: numérica, procedimental y matemática. Las soluciones numérica y procedimental resuelven solo parte del problema, y no son completas en el sentido de que una ausencia de respuesta no significa la ausencia de ella. La aproximación matemática previamente presentada por los autores describe el problema usando una serie de ecuaciones polinómicas. Las raíces comunes a este conjunto de polinomios caracterizan el espacio solución para el problema. Ese trabajo presenta el uso de técnicas con Bases de Groebner para verificar la consistencia de las restricciones. Ella también integra los subgrupos del grupo especial Euclídeo de desplazamientos SE(3) en la formulación del problema para explotar la estructura implicada por las relaciones geométricas. Aunque teóricamente sólidas, estas técnicas requieren grandes cantidades de recursos computacionales. Este trabajo propone técnicas de Dividir y Conquistar aplicadas a subproblemas GCS/SF locales para identificar conjuntos de entidades geométricas fuertemente restringidas entre sí. La identificación y pre-procesamiento de dichos conjuntos locales, generalmente reduce el esfuerzo requerido para resolver el problema completo. La identificación de dichos sub-problemas locales está relacionada con la identificación de ciclos cortos en el grafo de Restricciones Geométricas del problema GCS/SF. Su preprocesamiento usa las ya mencionadas técnicas de Geometría Algebraica y Grupos en los problemas locales que corresponden a dichos ciclos. Además de mejorar la eficiencia de la solución, las técnicas de Dividir y Conquistar capturan la esencia física del problema. Esto es ilustrado por medio de su aplicación al análisis de grados de libertad de mecanismos.MSC: 68U0

Capture and Maintenance of Constraints in Engineering Design

The thesis investigates two domains, initially the kite domain and then part of a more demanding Rolls-Royce domain (jet engine design). Four main types of refinement rules that use the associated application conditions and domain ontology to support the maintenance of constraints are proposed. The refinement rules have been implemented in ConEditor and the extended system is known as ConEditor+. With the help of ConEditor+, the thesis demonstrates that an explicit representation of application conditions together with the corresponding constraints and the domain ontology can be used to detect inconsistencies, redundancy, subsumption and fusion, reduce the number of spurious inconsistencies and prevent the identification of inappropriate refinements of redundancy, subsumption and fusion between pairs of constraints.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Geometric Over-Constraints Detection: A Survey

Currently, geometric over-constraints detection is of major interest in several diferent felds. In terms of product development process (PDP), many approaches exist to compare and detect geometric over-constraints, to decompose geometric systems, to solve geometric constraints systems. However, most approaches do not take into account the key characteristics of a geometric system, such as types of geometries, diferent levels at which a system can be decomposed e.g numerical or structural. For these reasons, geometric over-constraints detection still faces challenges to fully satisfy real needs of engineers. The aim of this paper is to review the state-of-the-art of works involving with geometric over-constraints detection and to identify pos sible research directions. Firstly, the paper highlights the user requirements for over-constraints detection when modeling geometric constraints systems in PDP and proposes a set of criteria to analyze the available methods classifed into four categories: level of detecting over-constraints, system decomposition, system modeling and results generation. Secondly, it introduces and analyzes the available methods by grouping them based on the introduced criteria. Finally, it discusses pos sible directions and future challenges

On the detection of over-constrained subparts of configurations when deforming free-form curves

Today, designers use CAD modelers to define and modify NURBS surfaces involved in the design of complex shapes like car bodies or turbine blades. The generated shapes often result from the use of variational modeling techniques where user-specified constraints define the shapes. However, for free-form curve/surfaces, if too much constraints are added to subparts of a configuration, the system will not be solvable even if it is globally well-/under-constrained. When this happens, it is useful to identify locally unsatisfiable subparts of configurations and provide the user feedback for adjustment. Currently, in the domain of geometric constraint solving, techniques are mainly developed for Euler geometries rather than parametric entities like free-form curves/surfaces. In this paper, we apply the Dulmage-Mendelsohn decomposition method to isolate structural over-constrained subparts of configurations. Since structural over-constraints do not necessarily mean unsatisfiable, a Jacobian matrix analysis approach is taken to further detect the inconsistent constraints. Indeed, these numerical methods can be generalized to detect overconstraints on free-form curves. We illustrate our approach on different examples where results show that Gauss elimination, though restricted to linear cases, is more relevant in our context than Dulmage-Mendelsohn decomposition

Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling

This paper aims at providing an in-depth overview of designing interpretable fuzzy inference models from data within a unified framework. The objective of complex system modelling is to develop reliable and understandable models for human being to get insights into complex real-world systems whose first-principle models are unknown. Because system behaviour can be described naturally as a series of linguistic rules, data-driven fuzzy modelling becomes an attractive and widely used paradigm for this purpose. However, fuzzy models constructed from data by adaptive learning algorithms usually suffer from the loss of model interpretability. Model accuracy and interpretability are two conflicting objectives, so interpretation preservation during adaptation in data-driven fuzzy system modelling is a challenging task, which has received much attention in fuzzy system modelling community. In order to clearly discriminate the different roles of fuzzy sets, input variables, and other components in achieving an interpretable fuzzy model, a taxonomy of fuzzy model interpretability is first proposed in terms of low-level interpretability and high-level interpretability in this paper. The low-level interpretability of fuzzy models refers to fuzzy model interpretability achieved by optimizing the membership functions in terms of semantic criteria on fuzzy set level, while the high-level interpretability refers to fuzzy model interpretability obtained by dealing with the coverage, completeness, and consistency of the rules in terms of the criteria on fuzzy rule level. Some criteria for low-level interpretability and high-level interpretability are identified, respectively. Different data-driven fuzzy modelling techniques in the literature focusing on the interpretability issues are reviewed and discussed from the perspective of low-level interpretability and high-level interpretability. Furthermore, some open problems about interpretable fuzzy models are identified and some potential new research directions on fuzzy model interpretability are also suggested. Crown Copyright © 2008

Optimization for Decision Making II

In the current context of the electronic governance of society, both administrations and citizens are demanding the greater participation of all the actors involved in the decision-making process relative to the governance of society. This book presents collective works published in the recent Special Issue (SI) entitled “Optimization for Decision Making II”. These works give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and the application of optimization techniques to support decisions are particularly complex and a wide range of optimization techniques and methodologies are used to minimize risks, improve quality in making decisions or, in general, to solve problems. In addition, a sensitivity or robustness analysis should be done to validate/analyze the influence of uncertainty regarding decision-making. This book brings together a collection of inter-/multi-disciplinary works applied to the optimization of decision making in a coherent manner

Methods of modelling the mental representation of individuals derived from descriptions in text

SIGLEAvailable from British Library Document Supply Centre- DSC:D95935 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Massivel y parallel declarative computational models

Current computer archictectures are parallel, with an increasing number of processors. Parallel programming is an error-prone task and declarative models such as those based on constraints relieve the programmer from some of its difficult aspects, because they abstract control away. In this work we study and develop techniques for declarative computational models based on constraints using GPI, aiming at large scale parallel execution. The main contributions of this work are: A GPI implementation of a scalable dynamic load balancing scheme based on work stealing, suitable for tree shaped computations and effective for systems with thousands of threads. A parallel constraint solver, MaCS, implemented to take advantage of the GPI programming model. Experimental evaluation shows very good scalability results on systems with hundreds of cores. A GPI parallel version of the Adaptive Search algorithm, including different variants. The study on different problems advances the understanding of scalability issues known to exist with large numbers of cores; ### SUMÁRIO: Actualmente as arquitecturas de computadores são paralelas, com um crescente número de processadores. A programação paralela é uma tarefa propensa a erros e modelos declarativos baseados em restrições aliviam o programador de aspectos difíceis dado que abstraem o controlo. Neste trabalho estudamos e desenvolvemos técnicas para modelos de computação declarativos baseados em restrições usando o GPI, uma ferramenta e modelo de programação recente. O Objectivo é a execução paralela em larga escala. As contribuições deste trabalho são as seguintes: a implementação de um esquema dinâmico para balanceamento da computação baseado no GPI. O esquema é adequado para computações em árvores e efectiva em sistemas compostos por milhares de unidades de computação. Uma abordagem à resolução paralela de restrições denominadas de MaCS, que tira partido do modelo de programação do GPI. A Avaliação experimental revelou boa escalabilidade num sistema com centenas de processadores. Uma versão paralela do algoritmo Adaptive Search baseada no GPI, que inclui diferentes variantes. O estudo de diversos problemas aumenta a compreensão de aspectos relacionados com a escalabilidade e presentes na execução deste tipo de algoritmos num grande número de processadores

Constraint-Enabled Design Information Representation for Mechanical Products Over the Internet

Global economy has made manufacturing industry become more distributed than ever before. Product design requires more involvement from various technical disciplines at different locations. In such a geographically and temporally distributed environment, efficient and effective collaboration on design is vital to maintain product quality and organizational competency. Interoperability of design information is one of major barriers for collaborative design. Current standard CAD data formats do not support design collaboration effectively in terms of design information and knowledge capturing, exchange, and integration within the design cycle. Multidisciplinary design constraints cannot be represented and transferred among different groups, and design information cannot be integrated efficiently within a distributed environment. Uncertainty of specification cannot be modeled at early design stages, while constraints for optimization are not embedded in design data. In this work, a design information model, Universal Linkage model, is developed to represent design related information for mechanical products in a distributed form. It incorporates geometric and non-geometric constraints with traditional geometry and topology elements, thus allows more design knowledge sharing in collaborative design. Segments of design data are linked and integrated into a complete product model, thus support lean design information capturing, storage, and query. The model is represented by Directed Hyper Graph and Product Markup Language to preserve extensibility and openness. Incorporating robustness consideration, an Interval Geometric Modeling scheme is presented, in which numerical parameters are represented by interval values. This scheme is able to capture uncertainty and inexactness of design and reduces the chances of conflict in constraint imposition. It provides a unified constraint representation for the process of conceptual design, detailed design, and design optimization. Corresponding interval constraint solving methods are studied