Automatic constraint-based synthesis of non-uniform rational B-spline surfaces

In this dissertation a technique for the synthesis of sculptured surface models subject to several constraints based on design and manufacturability requirements is presented. A design environment is specified as a collection of polyhedral models which represent components in the vicinity of the surface to be designed, or regions which the surface should avoid. Non-uniform rational B-splines (NURBS) are used for surface representation, and the control point locations are the design variables. For some problems the NURBS surface knots and/or weights are included as additional design variables. The primary functional constraint is a proximity metric which induces the surface to avoid a tolerance envelope around each component. Other functional constraints include: an area/arc-length constraint to counteract the expansion effect of the proximity constraint, orthogonality and parametric flow constraints (to maintain consistent surface topology and improve machinability of the surface), and local constraints on surface derivatives to exploit part symmetry. In addition, constraints based on surface curvatures may be incorporated to enhance machinability and induce the synthesis of developable surfaces;The surface synthesis problem is formulated as an optimization problem. Traditional optimization techniques such as quasi-Newton, Nelder-Mead simplex and conjugate gradient, yield only locally good surface models. Consequently, simulated annealing (SA), a global optimization technique is implemented. SA successfully synthesizes several highly multimodal surface models where the traditional optimization methods failed. Results indicate that this technique has potential applications as a conceptual design tool supporting concurrent product and process development methods

Synthesis of Spatially and Intrinsically Constrained Curves Using Simulated Annealing

A general technique is presented for automatic generation of B-spline curves in a spatially constrained environment, subject to specified intrinsic shape properties. Spatial constraints are characterized by a distance metric relating points on the curve to polyhedral models of obstacles which the curve should avoid. The shape of the curve is governed by constraints based on intrinsic curve properties such as parametric variation and curvature. To simultaneously address the independent goals of global obstacle avoidance and local control of intrinsic shape properties, curve synthesis is formulated as a combinatorial optimization problem and solved via simulated annealing. Several example applications are presented which demonstrate the robustness of the technique. The synthesis of both uniform and nonuniform B-spline curves is also demonstrated. An extension of the technique to general sculptured surface model synthesis is briefly described, and a preliminary example of simple surface synthesis presented

Hybrid Intelligent Optimization Methods for Engineering Problems

The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and quantification studies, we improved new mutation strategies and operators to provide beneficial diversity within the population. We called this new approach as multi-frequency vibrational GA or PSO. They were applied to different aeronautical engineering problems in order to study the efficiency of these new approaches. These implementations were: applications to selected benchmark test functions, inverse design of two-dimensional (2D) airfoil in subsonic flow, optimization of 2D airfoil in transonic flow, path planning problems of autonomous unmanned aerial vehicle (UAV) over a 3D terrain environment, 3D radar cross section minimization problem for a 3D air vehicle, and active flow control over a 2D airfoil. As demonstrated by these test cases, we observed that new algorithms outperform the current popular algorithms. The principal role of this multi-frequency approach was to determine which individuals or particles should be mutated, when they should be mutated, and which ones should be merged into the population. The new mutation operators, when combined with a mutation strategy and an artificial intelligent method, such as, neural networks or fuzzy logic process, they provided local and global diversities during the reproduction phases of the generations. Additionally, the new approach also introduced random and controlled diversity. Due to still being population-based techniques, these methods were as robust as the plain GA or PSO algorithms. Based on the results obtained, it was concluded that the variants of the present multi-frequency vibrational GA and PSO were efficient algorithms, since they successfully avoided all local optima within relatively short optimization cycles

Magnetic suspension turbine flow meter

Measurement of liquid flow in certain area such as industrial plant is in critical. Inaccurate measurement can cause serious result. Most of the liquid flow are using Bernoulli principle‘s but in turbine flow meter the flow rate is determine differently by using kinetic energy. Turbine flow meter is one of flow rate transducer that widely used in metallurgical, petroleum, chemical and other industrial and agricultural areas, as shown in Figure 1.1. It is present as high precision of flow meter and when fluid flow troughs it the impeller that faces the fluid will rotate due to flow force exist. The rotation speed is directly proportional to the speed of fluid. During the process, the working states of impeller and bearing are very complicated due the interactive effects from the fluid axial thrust, impeller rotating, and static and dynamic components. In current turbine flow meter design, the common material use for meter bulk body is 1Cr18Ni9Ti, while for the blade 2Gr13 are used. Axis and bearing are made from stainless steel or carbide alloy. The space between the axis and bearing determines it minimum flow rate and life span, and also determines its measurement range (1:10~1:15 - maximum flow rate to minimum flow rate). Since the turbine has movable parts it can produce friction between the axis and ring during the operation. This will cause accuracy of the measurement decrease and can damage the impeller blade. In this research, the friction can be reduced by adopting the principle of magnetic suspension. Rotating shaft will levitate in the magnetic field due to the forces. Friction coefficient reduced because of rotating shaft rotates without abrasion and mechanical contact in space

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Two simulated annealing optimization schemas for rational bézier curve fitting in the presence of noise

Fitting curves to noisy data points is a difficult problem arising in many scientific and industrial domains. Although polynomial functions are usually applied to this task, there are many shapes that cannot be properly fitted by using this approach. In this paper, we tackle this issue by using rational Bézier curves. This is a very difficult problem that requires computing four different sets of unknowns (data parameters, poles, weights, and the curve degree) strongly related to each other in a highly nonlinear way. This leads to a difficult continuous nonlinear optimization problem. In this paper, we propose two simulated annealing schemas (the all-in-one schema and the sequential schema) to determine the data parameterization and the weights of the poles of the fitting curve. These schemas are combined with least-squares minimization and the Bayesian Information Criterion to calculate the poles and the optimal degree of the best fitting Bézier rational curve, respectively. We apply our methods to a benchmark of three carefully chosen examples of 2D and 3D noisy data points. Our experimental results show that this methodology (particularly, the sequential schema) outperforms previous polynomial-based approaches for our data fitting problem, even in the presence of noise of low-medium intensity.This research has been kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project Ref. #TIN2012-30768, Toho University (Funabashi, Japan), and the University of Cantabria (Santander, Spain)

Improved Modified Chaotic Invasive Weed Optimization Approach to Solve Multi-Target Assignment for Humanoid Robot

The paper presents an improved modified chaotic invasive weed optimization (IMCIWO) approach for solving a multi-target assignment for humanoid robot navigation. MCIWO is improved by utilizing the Bezier curve for smoothing the path and replaces the conventional split lines. In order to efficiently determine subsequent locations of the robot from the present location on the provided terrain, such that the routes to be specifically generated for the robot are relatively small, with the shortest distance from the barriers that have been generated using the IMCIWO approach. The MCIWO approach designed the path based on obstacles and targets position which is further smoothened by the Bezier curve. Simulations are performed which is further validated by real-time experiments in WEBOT and NAO robot respectively. They show good effectiveness with each other with a deviation of under 5%. Ultimately, the superiority of the developed approach is examined with existing techniques for navigation, and findings are substantially improved

Optimized NURBS Curve Based G-Code Part Program for CNC Systems

Indiana University-Purdue University Indianapolis (IUPUI)Computer Numerical Control (CNC) is widely used in many industries that needs high speed machining of the parts with high precision, accuracy and good surface finish. In order to avail this the generation of the CNC part program size will be immensely big and leads to an inefficient process, which increases the delivery time and cost of products. This work presents the automation of high-accuracy CNC tool trajectory planning from CAD to G-code generation through optimal NURBs surface approximation. The proposed optimization method finds the minimum number of NURBS control points for a given admissible theoretical cord error between the desired and manufactured surfaces. The result is a compact part program that is less sensitive to data starvation than circular and spline interpolations with potential better surface finish. The proposed approach is demonstrated with the tool path generation of an involute gear profile and a topologically optimized structure is developed using this approach and then finally it is 3D printed

تمثيل الإطار الخارجي للكلمات العربية بكفاءة من خلال الدمج بين نموذج الكنتور النشط وتحديد ونقاط الزوايا

Graphical curves and surfaces fitting are hot areas of research studies and application, such as artistic applications, analysis applications and encoding purposes. Outline capture of digital word images is important in most of the desktop publishing systems. The shapes of the characters are stored in the computer memory in terms of their outlines, and the outlines are expressed as Bezier curves. Existing methods for Arabic font outline description suffer from low fitting accuracy and efficiency. In our research, we developed a new method for outlining shapes using Bezier curves with minimal set of curve points. A distinguishing characteristic of our method is that it combines the active contour method (snake) with corner detection to achieve an initial set of points that is as close to the shape's boundaries as possible. The method links these points (snake + corner) into a compound Bezier curve, and iteratively improves the fitting of the curve over the actual boundaries of the shape. We implemented and tested our method using MATLAB. Test cases included various levels of shape complexity varying from simple, moderate, and high complexity depending on factors, such as: boundary concavities, number of corners. Results show that our method achieved average 86% of accuracy when measured relative to true shape boundary. When compared to other similar methods (Masood & Sarfraz, 2009; Sarfraz & Khan, 2002; Ferdous A Sohel, Karmakar, Dooley, & Bennamoun, 2010), our method performed comparatively well. Keywords: Bezier curves, shape descriptor, curvature, corner points, control points, Active Contour Model.تعتبر المنحنيات والأسطح الرسومية موضوعاً هاماً في الدراسات البحثية وفي التطبيقات البرمجية مثل التطبيقات الفنية، وتطبيقات تحليل وترميز البيانات. ويعتبر تخطيط الحدود الخارجية للكلمات عملية أساسية في غالبية تطبيقات النشر المكتبي. في هذه التطبيقات تخزن أشكال الأحرف في الذاكرة من حيث خطوطها الخارجية، وتمثل الخطوط الخارجية على هيئة منحنيات Bezier. الطرق المستخدمة حالياً لتحديد الخطوط الخارجية للكلمات العربية تنقصها دقة وكفاءة الملاءمة ما بين الحدود الحقيقية والمنحنى الرسومي الذي تقوم بتشكيله. في هذا البحث قمنا بتطوير طريقة جديدة لتخطيط الحدود الخارجية للكلمات تعتمد على منحنيات Bezier بمجموعة أقل من المنحنيات الجزئية. تتميز طريقتنا بخاصية مميزة وهي الدمج بين آلية لاستشعار الزوايا مع آلية نموذج الكنتور النشط (الأفعى). يتم الدمج بين نقاط الزوايا ونقاط الأفعى لتشكيل مجموعة موحدة من النقاط المبدئية قريبة قدر الإمكان من الحدود الحقيقية للشكل المراد تحديده. يتشكل منحنى Bezier من هذه المجموعة المدمجة، وتتم عملية تدريجية على دورات لملاءمة المنحنى على الحدود الحقيقية للشكل. قام الباحث بتنفيذ وتجربة الطريقة الجديدة باستخدام برنامج MATLAB. وتم اختيار أشكال رسومية كعينات اختبار تتصف بمستويات متباينة من التعقيد تتراوح ما بين بسيط إلى متوسط إلى عالي التعقيد على أساس عوامل مثل تقعرات الحدود، عدد نقاط الزوايا، الفتحات الداخلية، إلخ. وقد أظهرت نتائج الاختبار أن طريقتنا الجديدة حققت دقة في الملائمة تصل نسبتها إلى 86% مقارنة بالحدود الحقيقية للشكل المستهدف. وكذلك فقد كان أداء طريقتنا جيداً بالمقارنة مع طرق أخرى مماثلة

Evalutionary algorithms for ship hull skinning approximation

Traditionally, the design process of a hull involves simulation using clay models. This must be done cautiously, accurately and efficiently in order to sustain the performance of ship. Presently, the current technology of Computer Aided Design, Manufacturing, Engineering and Computational Fluid Dynamic has enabled a 3D design and simulation of a hull be done at a lower cost and within a shorter period of time. Besides that, automated design tools allow the transformation of offset data in designing the hull be done automatically. One of the most common methods in constructing a hull from the offset data is the skinning method. Generally, the skinning method comprised of skinning interpolation and skinning approximation. Skinning interpolation constructs the surface perfectly but improper selection of parameterization methods may cause bumps, wiggles, or uneven surfaces on the generated surface. On the other hand, using the skinning surface approximation would mean that the surface can only be constructed closer to data points. Thus, the error between the generated surface and the data points must be minimized to increase the accuracy. Therefore, this study aims to solve the error minimization problem in order to produce a smoother and fairer surface by proposing Non Uniform Rational B-Spline surface using various evolutionary optimization algorithms, namely, Gravitational Search Algorithm, Particle Swarm Optimization and Genetic Algorithm. The proposed methods involve four procedures: extraction of offset data from line drawing plan; generation of control points; optimization of a surface; and validations of hull surfaces. Validation is done by analyzing the surface curvature and errors between the generated surface and the given data points. The experiments were implemented on both ship hull and free form models. The findings from the experiments are compared with interpolated skinning surface and conventional skinning surface approximation. The results show that the optimized skinning surfaces using the proposed methods yield a smaller error, less control points generation and feasible surfaces while maintaining the shape of the hull