A Study on Optimum Design Using Fuzzy Numbers As Design Variables

1995 ◽  
Author(s):  
Masao Arakawa ◽  
Hiroshi Yamakawa
Keyword(s):  
Fuzzy Sets ◽  
Optimum Design ◽  
Fuzzy Numbers ◽  
Fuzzy Optimization ◽  
Design Parameters ◽  
Numerical Examples ◽  
Design Variables ◽  
Conventional Methods

Abstract In this study, we summerize the method of fuzzy optimization using fuzzy numbers as design variables. In order to detect flaw in fuzzy calculation, we use LR-fuzzy numbers, which is known as its simplicity in calculation. We also use simple fuzzy numbers’ operations, which was proposed in the previous papers. The proposed method has unique characteristics that we can obtain fuzzy sets in design variables (results of the design) directly from single numerical optimizing process. Which takes a large number of numerical optimizing processes when we try to obtain similar results in the conventional methods. In the numerical examples, we compare the proposed method with several other methods taking imprecision in design parameters into account, and demonstrate the effectiveness of the proposed method.

Optimum Design of Anti-Siphon Device used to Prevent Cerebrospinal Fluid from Overdraining

2003 ◽  
Vol 17 (08n09) ◽  
pp. 1374-1380
Author(s):  
Jong Yun Jang ◽  
Chong Sun Lee ◽  
Chang Min Suh
Keyword(s):  
Cerebrospinal Fluid ◽  
Numerical Simulations ◽  
Optimum Design ◽  
Upright Position ◽  
Design Parameters ◽  
Design Variables

The present study investigated design parameters of an anti-siphon device used with shunt valves to treat patients with hydrocephalus. Structural analyses were performed to understand roles of design variables and optimize performance of the diaphragm-type anti-siphon device (hereafter referred to as the ASD). Experiments were performed on the lab-made product and showed good agreements with the numerical simulations. Using the simulations, we were able to design a more physiological ASD which gave equal opening pressures in both supine and upright postures. Tissue encapsulization phenomenon was also simulated and the results indicated underdrainage of CSF in the upright position of the patient.

scholarly journals A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers

2010 ◽  
Vol 2010 ◽  
pp. 1-25 ◽  
Author(s):  
Debashree Guha ◽  
Debjani Chakraborty
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Theoretical Development ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Intuitionistic Fuzzy

The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers. Firstly the existing distance measures for intuitionistic fuzzy sets are analyzed and compared with the help of some examples. Then the new distance measure for intuitionistic fuzzy numbers is proposed based on interval difference. Also in particular the type of distance measure for triangle intuitionistic fuzzy numbers is described. The metric properties of the proposed measure are also studied. Some numerical examples are considered for applying the proposed measure and finally the result is compared with the existing ones.

scholarly journals A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 441 ◽  
Author(s):  
Minxia Luo ◽  
Jingjing Liang
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.

Robust Design Using Fuzzy Numbers: Consideration of Correlation of Design Variables in Fuzzy Operation

2000 ◽  
Author(s):  
Masao Arakawa ◽  
Hiroshi Yamakawa ◽  
Hiroshi Ishikawa
Keyword(s):  
Lower Bound ◽  
Robust Design ◽  
Fuzzy Numbers ◽  
Human Errors ◽  
Numerical Examples ◽  
The Real ◽  
The Past ◽  
Design Variables ◽  
Modeling Errors

Abstract These days robust design has become more and more important to raise reliability in the products under many kinds of imprecision, including human errors, modeling errors and so on. In the past, robust design only tries to obtain the robust design variables that have less sensitivity with quasi-optimum solutions. Recently, many researchers try to design not only of design variable’s value but also to its deviations. Which means that robust design tries to have wider range of design variables and still keeps robustness in the design. For the simplicity of calculation, most of them assume independence of design variables, thus, the ranges are determined by their upper and lower bound. However, in the real design almost every design variables are not independent with the influence of constraints. In this study, we will newly propose the method that can determine the relationships of design variables, something like correlation of design variables. We will show the effectiveness of the method by some numerical examples.

The Fuzzy Reliability Optimum Design of Offshore Jacket Platforms

2002 ◽  
Author(s):  
Gangjun Zhai ◽  
Haigui Kang ◽  
Facong Xu
Keyword(s):  
Optimum Design ◽  
Structural Reliability ◽  
Fuzzy Optimization ◽  
Optimization Method ◽  
Optimum Level ◽  
Design Variables ◽  
Fuzzy Constraint ◽  
Cut Set ◽  
Optimum Model ◽  
Optimum Solution

In consideration of the fuzzy constraint boundary and through analysis of structural reliability, a model of structural fuzzy optimum design is established based on reliability for offshore jacket platforms. According to the characteristics of offshore jacket platforms, the tolerance coefficient of the constraint boundary is determined with the fuzzy optimization method. The optimum level cut set λ*, which is the intersection of the fuzzy constraint set and fuzzy objective set, is determined with the bound search method, and then the fuzzy optimum solution of fuzzy optimization problem is obtained. The center offshore platform SZ36-1 is designed with the fuzzy optimum model based on reliability above; the results are compared with those from deterministic optimum design and fuzzy optimum design. The tendency of design variables and its reasons in the above three methods are analyzed. The results of an example show that the fuzzy optimum design based on reliability is stable and reliable.

Robust Design Using Fuzzy Numbers

1998 ◽  
Author(s):  
Masao Arakawa ◽  
Hiroshi Yamakawa ◽  
Ichiro Hagiwara
Keyword(s):  
Stochastic Optimization ◽  
Normal Distribution ◽  
Robust Design ◽  
Design Methodology ◽  
Fuzzy Numbers ◽  
Fuzzy Optimization ◽  
New Method ◽  
Objective Functions ◽  
The Past ◽  
Design Variables

Abstract In this study, we will propose a new method of robust design, which is formulated by using fuzzy numbers as design variables and parameters. In the past robust design methodology, especially by considering usage of optimization, its basic formulations have been done by stochastic optimization. In those cases, they could not handle the deviation in design variables of both sides of shape or their index for their width, because they were mainly based on normal distribution. In this study, we will compare the formulation of fuzzy optimization and stochastic optimization and clarify the characteristics of the proposed method from differences between formulations. Through those comparisons, we will explain the benefit and suitability of the proposed method to robust design in settings of objective functions, treatments of constraints and benefit of design variables which can treat both sides of index for its deviation.

scholarly journals Design and discrete optimization of hybrid aluminum/composite drive shafts for automotive industry

2021 ◽  
Vol 9 (3B) ◽  
Author(s):  
Bertan Beylergil ◽  
Keyword(s):  
Optimum Design ◽  
Automotive Industry ◽  
Screening Method ◽  
Drive Shaft ◽  
Design Parameters ◽  
Fe Model ◽  
Aluminum Composite ◽  
Design Variables ◽  
Inner Diameter ◽  
Design Requirements

Fiber reinforced composites have been widely used in automotive industry since they offer significant weight reduction, low manufacturing and tooling cost, and better integration of parts compared to metal counterparts. In this study, design optimization of a hybrid aluminum/composite drive shaft subjected to torsion was carried out using ANSYS Workbench with ACP module. The numerical validation of finite element (FE) model was carried out by means of theoretical, experimental, and numerical studies in the literature. The ply material, lay-up orientations, and thickness of aluminum layer were considered as design variables. The geometric parameters in design were the length and inner diameter of the drive shaft. Two important design constraints, the minimum first mode natural frequency and design torque, were considered to satisfy the design requirements of a rear-wheel drive shaft used in automotive industry. The optimum design variables were determined by using screening method. The optimum design parameters (length, inner diameter, ply angle, and material) were presented in tabular form. Compared to nonoptimized scenario, the optimized solution reduced the cost of the hybrid composite drive shaft about 30% without ignoring the design requirements.

Shape Optimization of Hydraulic Structures: an Example of an Optimum Design of a Fish Passage

10.29007/2k64 ◽  
2018 ◽  
Author(s):  
Pat Prodanovic ◽  
Cedric Goeury ◽  
Fabrice Zaoui ◽  
Riadh Ata ◽  
Jacques Fontaine ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shape Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Optimization Problem ◽  
A Priori ◽  
Coupled System ◽  
Fish Passage ◽  
Hydraulic Structures ◽  
Design Variables

This paper presents a practical methodology developed for shape optimization studies of hydraulic structures using environmental numerical modelling codes. The methodology starts by defining the optimization problem and identifying relevant problem constraints. Design variables in shape optimization studies are configuration of structures (such as length or spacing of groins, orientation and layout of breakwaters, etc.) whose optimal orientation is not known a priori. The optimization problem is solved numerically by coupling an optimization algorithm to a numerical model. The coupled system is able to define, test and evaluate a multitude of new shapes, which are internally generated and then simulated using a numerical model. The developed methodology is tested using an example of an optimum design of a fish passage, where the design variables are the length and the position of slots. In this paper an objective function is defined where a target is specified and the numerical optimizer is asked to retrieve the target solution. Such a definition of the objective function is used to validate the developed tool chain. This work uses the numerical model TELEMAC- 2Dfrom the TELEMAC-MASCARET suite of numerical solvers for the solution of shallow water equations, coupled with various numerical optimization algorithms available in the literature.

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