Discretizing Continuous Problems for Faster Global Convergence

2003 ◽  
Author(s):  
Madara Ogot ◽  
Sherif Aly
Keyword(s):  
Global Optimization ◽  
Mechanical Design ◽  
Test Problems ◽  
Additional Parameter ◽  
Continuous Variables ◽  
Discrete State ◽  
Continuous Space ◽  
Design Variables ◽  
Asme Journal ◽  
Efficient Exploration

Global optimization of mechanical design problems using heuristic methods such as Simulated annealing (SA) and genetic algorithms (GAs) have been able to find global or near-global minima where prior methods have failed. The use of these nongradient based methods allow the broad efficient exploration of multimodal design spaces that could be continuous, discrete or mixed. From a survey of articles in the ASME Journal of Mechanical Design over the last 10 years, we have observed that researchers will typically run these algorithms in continuous mode for problems that contain continuous design variables. What we suggest in this paper is that computational efficiencies can be significantly increased by discretizing all continuous variables, perform a global optimization on the discretized design space, and then conduct a local search in the continuous space from the global minimum discrete state. The level of discretization will depend on the complexity of the problem, and becomes an additional parameter that needs to be tuned. The rational behind this assertion is presented, along with results from four test problems.

Cluster Analysis for the Cognitive Selection of Nonlinear Programming Algorithms

1990 ◽  
Author(s):  
Jin-xian Ma ◽  
Shi-huai Xie ◽  
Yong Chen
Keyword(s):  
Cluster Analysis ◽  
Nonlinear Programming ◽  
Expert System ◽  
Mechanical Design ◽  
Test Problems ◽  
Comparative Performance ◽  
Nonlinear Programming Algorithms ◽  
Cognitive Selection ◽  
Programming Algorithms ◽  
Selection Of

Abstract In recent years, cluster analysis has played an increasingly important role in statistical pattern recognition. Hoeltzel and Chieng have shown an example on cognitive selection of nonlinear programming algorithms in a mechanical design expert system. In this paper, an improved dynamic clustering of 3000 samples came from a comparative performance evaluation of six typical nonlinear programming softwares with randomly generated test problems has been made. Explanations resulting from the cluster analysis have been used to build rules to form the knowledge base of an optimization expert system.

Optimal Tolerancing: The Link Between Design and Manufacturing Productivity

1994 ◽  
Author(s):  
Mark Iannuzzi ◽  
Eric Sandgren
Keyword(s):  
Optimal Allocation ◽  
Mechanical Design ◽  
Computational Design ◽  
Optimization Method ◽  
Design Tool ◽  
Superior Performance ◽  
Test Problems ◽  
Tolerance Range ◽  
Manufacturing Productivity ◽  
Combined Algorithm

Abstract A computational design tool is presented which permits the optimal allocation of tolerances for mechanical and electrical components and assemblies. The basic approach involves the coupling of a nontraditional optimization method with a Monte Carlo based tolerance analysis. The objective is to determine the tolerance range value to assign to each nominal dimension which minimizes the production cost of the component or assembly while simultaneously meeting all critical dimensional and functional constraints imposed upon the design. A discretization of possible tolerance range values is performed and a global search is conducted by a genetic algorithm. Both the fine and course grain performance of the combined algorithm is demonstrated on a series of test problems ranging from a simple assembly of blocks to several real mechanical design problems. Solutions generated on problems taken from the literature indicate superior performance to existing techniques. Extensions which would allow for a complete optimal dimensional management environment are examined.

The new CM-Series TEMs: integration of a five-axis motorized, fully computer-controlled goniometer

1993 ◽  
Vol 51 ◽  
pp. 258-259
Author(s):  
Marc J.C. de Jong ◽  
P. Emile S.J. Asselbergs ◽  
Max T. Otten
Keyword(s):  
Mechanical Design ◽  
Computer Control ◽  
Objective Lens ◽  
Access Port ◽  
Vibration Stability ◽  
Transmission Electron ◽  
Computer Controlled ◽  
High Degree ◽  
Five Axis ◽  
Five Axes

A new step forward in Transmission Electron Microscopy has been made with the introduction of the CompuStage on the CM-series TEMs: CM120, CM200, CM200 FEG and CM300. This new goniometer has motorization on five axes (X, Y, Z, α, β), all under full computer control by a dedicated microprocessor that is in communication with the main CM processor. Positions on all five axes are read out directly - not via a system counting motor revolutions - thereby providing a high degree of accuracy. The CompuStage enters the octagonal block around the specimen through a single port, allowing the specimen stage to float freely in the vacuum between the objective-lens pole pieces, thereby improving vibration stability and freeing up one access port. Improvements in the mechanical design ensure higher stability with regard to vibration and drift. During stage movement the holder O-ring no longer slides, providing higher drift stability and positioning accuracy as well as better vacuum.

Tire Modeling by Finite Elements

1992 ◽  
Vol 20 (1) ◽  
pp. 33-56 ◽  
Author(s):  
L. O. Faria ◽  
J. T. Oden ◽  
B. Yavari ◽  
W. W. Tworzydlo ◽  
J. M. Bass ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Rolling Contact ◽  
Test Problems ◽  
State Behavior ◽  
Normal Contact ◽  
New Developments ◽  
Applied Torque ◽  
Dimensional Finite Element ◽  
Tire Modeling ◽  
Three Dimensional Finite Element

Abstract Recent advances in the development of a general three-dimensional finite element methodology for modeling large deformation steady state behavior of tire structures is presented. The new developments outlined here include the extension of the material modeling capabilities to include viscoelastic materials and a generalization of the formulation of the rolling contact problem to include special nonlinear constraints. These constraints include normal contact load, applied torque, and constant pressure-volume. Several new test problems and examples of tire analysis are presented.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

Design of a Human Knee Reeducation Mechanism

2019 ◽  
Vol 11 (1) ◽  
pp. 42-53
Author(s):  
Allaoua Brahmia ◽  
Ridha Kelaiaia
Keyword(s):  
Lower Limb ◽  
Mechanical Design ◽  
Kinematic Chain ◽  
Lower Limbs ◽  
Kinematic Structure ◽  
Robotic Device ◽  
Human Knee ◽  
Kinematic Study ◽  
Rehabilitation Exercise ◽  
New Machine

Abstract To establish an exercise in open muscular chain rehabilitation (OMC), it is necessary to choose the type of kinematic chain of the mechanical / biomechanical system that constitutes the lower limbs in interaction with the robotic device. Indeed, it’s accepted in biomechanics that a rehabilitation exercise in OMC of the lower limb is performed with a fixed hip and a free foot. Based on these findings, a kinematic structure of a new machine, named Reeduc-Knee, is proposed, and a mechanical design is carried out. The contribution of this work is not limited to the mechanical design of the Reeduc-Knee system. Indeed, to define the minimum parameterizing defining the configuration of the device relative to an absolute reference, a geometric and kinematic study is presented.

Mechanical Design of a Low Cost Transhumeral Prosthesis

2017 ◽  
Author(s):  
Luis Arturo Gómez Malagón ◽  
João Luiz Vilar Dias
Keyword(s):  
Mechanical Design ◽  
Low Cost
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