Comprehensive Satisfactory Design Method for Product Designs

2001 ◽  
Author(s):  
Eiji Adachi
Keyword(s):  
Decision Making ◽  
Design Method ◽  
Simultaneous Equations ◽  
Objective Functions ◽  
Identification Methods ◽  
Multi Objective ◽  
Sensitivity Coefficients ◽  
Design Variables ◽  
Computer Aided ◽  
Market Needs

Abstract Actual product designs aim to fulfill all product requirements of market needs and wants, which are technical or non-technical, logical or illogical, objective or subjective, and quantitative or qualitative. The actual product designs are objective-aiming designs and can be supposed to be multi-objective satisfactory designs with heterogeneous objective functions and dimensional design variables. To realize computer-aided product designs which can obtain rational and satisfactory solutions, we classify the objective functions and contrive methods to deal with non-theoretical, non-technical, subjective, or illogical objective functions as well. This paper shows all of our methods, including an expression of heterogeneous objective functions which consists of objective and evaluated values, a satisfactory design method by simultaneous equations which searches solutions sequentially, identification methods of non-theoretical or non-technical objective functions and sensitivity coefficients for the simultaneous equations, a decision-making method of promising solutions to fulfill product requirements, and also numerical applications of these methods to actual product designs.

Multi-Objective Design Problem of Tire Wear and Visualization of Its Pareto Solutions2

2006 ◽  
Vol 34 (3) ◽  
pp. 170-194 ◽  
Author(s):  
M. Koishi ◽  
Z. Shida
Keyword(s):  
Inverse Problems ◽  
Conceptual Design ◽  
Dimensional Space ◽  
Design Stage ◽  
Objective Functions ◽  
Pareto Solutions ◽  
Design Problems ◽  
Multi Objective ◽  
Design Engineers ◽  
Design Variables

Abstract Since tires carry out many functions and many of them have tradeoffs, it is important to find the combination of design variables that satisfy well-balanced performance in conceptual design stage. To find a good design of tires is to solve the multi-objective design problems, i.e., inverse problems. However, due to the lack of suitable solution techniques, such problems are converted into a single-objective optimization problem before being solved. Therefore, it is difficult to find the Pareto solutions of multi-objective design problems of tires. Recently, multi-objective evolutionary algorithms have become popular in many fields to find the Pareto solutions. In this paper, we propose a design procedure to solve multi-objective design problems as the comprehensive solver of inverse problems. At first, a multi-objective genetic algorithm (MOGA) is employed to find the Pareto solutions of tire performance, which are in multi-dimensional space of objective functions. Response surface method is also used to evaluate objective functions in the optimization process and can reduce CPU time dramatically. In addition, a self-organizing map (SOM) proposed by Kohonen is used to map Pareto solutions from high-dimensional objective space onto two-dimensional space. Using SOM, design engineers see easily the Pareto solutions of tire performance and can find suitable design plans. The SOM can be considered as an inverse function that defines the relation between Pareto solutions and design variables. To demonstrate the procedure, tire tread design is conducted. The objective of design is to improve uneven wear and wear life for both the front tire and the rear tire of a passenger car. Wear performance is evaluated by finite element analysis (FEA). Response surface is obtained by the design of experiments and FEA. Using both MOGA and SOM, we obtain a map of Pareto solutions. We can find suitable design plans that satisfy well-balanced performance on the map called “multi-performance map.” It helps tire design engineers to make their decision in conceptual design stage.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

Multi-Objective Design Optimization of a Mixed-Flow Pump

2009 ◽  
Author(s):  
Yumiko Takayama ◽  
Hiroyoshi Watanabe
Keyword(s):  
Performance Characteristic ◽  
Performance Characteristics ◽  
Inverse Design ◽  
Surface Model ◽  
Objective Functions ◽  
Mixed Flow ◽  
Multi Objective ◽  
Design Variables ◽  
Flow Head ◽  
Flow Pump

In most cases of high specific speed mixed-flow pump applications, it is necessary to satisfy more than one performance characteristic such as deign point efficiency, shut-off power/head and non-stall characteristic (no positive slope in flow-head curve). However, it is known that these performance characteristics are in relation of trade-offs. As a result, it is difficult to optimize these performance characteristics by conventional way such as trial and error approach by modifying geometrical parameters. This paper presents the results of the multi-objective optimization strategy of mixed-flow pump design by means of three dimensional inverse design approach, Computational Fluid Dynamics (CFD), Design of Experiments (DoE), response surface model (RSM) and Multi Objective Genetic Algorism (MOGA). The parameters to control blade loading distributions and meridional geometries for impeller and diffuser blades in inverse design were chosen as design variables of the optimization process. Pump efficiency, maximum slope in flow-head curve and shut-off power/head were selected as objective functions. Objective functions of pumps, designed by design variables specified in DoE, were evaluated by using CFD. Then, trade-off relations between objective functions were analyzed by using Pareto fronts obtained by MOGA. Some pumps which have specific performance characteristic (non-stall, low shut-off power, high efficiency etc.) designed along the Pareto front were numerically evaluated.

Optimal design of a parallel robotic gripper using enhanced multi-objective ant lion optimizer with a sensitivity analysis approach

2020 ◽  
Vol 40 (5) ◽  
pp. 703-721
Author(s):  
Golak Bihari Mahanta ◽  
Deepak BBVL ◽  
Bibhuti B. Biswal ◽  
Amruta Rout
Keyword(s):  
Sensitivity Analysis ◽  
Distribution Function ◽  
Design Parameters ◽  
Objective Functions ◽  
Content Type ◽  
Multi Objective ◽  
The Past ◽  
Design Variables ◽  
Pick And Place ◽  
Ant Lion

Purpose From the past few decades, parallel grippers are used successfully in the automation industries for performing various pick and place jobs due to their simple design, reliable nature and its economic feasibility. So, the purpose of this paperis to design a suitable gripper with appropriate design parameters for better performance in the robotic production systems. Design/methodology/approach In this paper, an enhanced multi-objective ant lion algorithm is introduced to find the optimal geometric and design variables of a parallel gripper. The considered robotic gripper systems are evaluated by considering three objective functions while satisfying eight constraint equations. The beta distribution function is introduced for generating the initial random number at the initialization phase of the proposed algorithm as a replacement of uniform distribution function. A local search algorithm, namely, achievement scalarizing function with multi-criteria decision-making technique and beta distribution are used to enhance the existing optimizer to evaluate the optimal gripper design problem. In this study, the newly proposed enhanced optimizer to obtain the optimum design condition of the design variables is called enhanced multi-objective ant lion optimizer. Findings This study aims to obtain optimal design parameters of the parallel gripper with the help of the developed algorithms. The acquired results are investigated with the past research paper conducted in that field for comparison. It is observed that the suggested method to get the best gripper arrangement and variables of the parallel gripper mechanism outperform its counterparts. The effects of the design variables are needed to be studied for a better design approach concerning the objective functions, which is achieved by sensitivity analysis. Practical implications The developed gripper is feasible to use in the assembly operation, as well as in other pick and place operations in different industries. Originality/value In this study, the problem to find the optimum design parameter (i.e. geometric parameters such as length of the link and parallel gripper joint angles) is addressed as a multi-objective optimization. The obtained results from the execution of the algorithm are evaluated using the performance indicator algorithm and a sensitivity analysis is introduced to validate the effects of the design variables. The obtained optimal parameters are used to develop a gripper prototype, which will be used for the assembly process.

Kinematic Multi-Objective Optimization of Circular-Toothed Gerotor Pumps by Genetic Algorithm

2017 ◽  
Author(s):  
Andrew J. Robison ◽  
Andrea Vacca
Keyword(s):  
Genetic Algorithm ◽  
Design Method ◽  
Third Party ◽  
Low Flow ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Generation Algorithm ◽  
Multi Objective ◽  
Pareto Curve

A gerotor gear generation algorithm has been developed that evaluates key performance objective functions to be minimized or maximized, and then an optimization algorithm is applied to determine the best design. Because of their popularity, circular-toothed gerotors are the focus of this study, and future work can extend this procedure to other gear forms. Parametric equations defining the circular-toothed gear set have been derived and implemented. Two objective functions were used in this kinematic optimization: maximize the ratio of displacement to pump radius, which is a measure of compactness, and minimize the kinematic flow ripple, which can have a negative effect on system dynamics and could be a major source of noise. Designs were constrained to ensure drivability, so the need for additional synchronization gearing is eliminated. The NSGA-II genetic algorithm was then applied to the gear generation algorithm in modeFRONTIER, a commercial software that integrates multi-objective optimization with third-party engineering software. A clear Pareto front was identified, and a multi-criteria decision-making genetic algorithm was used to select three optimal designs with varying priorities of compactness vs low flow variation. In addition, three pumps used in industry were scaled and evaluated with the gear generation algorithm for comparison. The scaled industry pumps were all close to the Pareto curve, but the optimized designs offer a slight kinematic advantage, which demonstrates the usefulness of the proposed gerotor design method.

Robustness Against Large Variations in Multi-Objective Optimization Problems

2013 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis
Keyword(s):  
Optimization Problems ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Design Environment ◽  
Multi Objective ◽  
Uncertainty Sources ◽  
Design Variables ◽  
Robustness Index ◽  
Environment Parameters

In the presence of multiple optimal solutions in multi-modal optimization problems and in multi-objective optimization problems, the designer may be interested in the robustness of those solutions to make a decision. Here, the robustness is related to the sensitivity of the performance functions to uncertainties. The uncertainty sources include the uncertainties in the design variables, in the design environment parameters, in the model of objective functions and in the designer’s preference. There exist many robustness indices in the literature that deal with small variations in the design variables and design environment parameters, but few robustness indices consider large variations. In this paper, a new robustness index is introduced to deal with large variations in the design environment parameters. The proposed index is bounded between zero and one, and measures the probability of a solution to be optimal with respect to the values of the design environment parameters. The larger the robustness index, the more robust the solution with regard to large variations in the design environment parameters. Finally, two illustrative examples are given to highlight the contributions of this paper.

Multi-Objective Robust Optimization of Deep Groove Ball Bearings Considering Manufacturing Tolerances Based on Fatigue and Wear Considerations

2021 ◽  
pp. 1-43
Author(s):  
Md Saif Ahmad ◽  
Rajiv Tiwari ◽  
Twinkle Mandawat
Keyword(s):  
Objective Function ◽  
Ball Bearings ◽  
Rolling Element Bearings ◽  
Objective Functions ◽  
Dynamic Capacity ◽  
Multi Objective ◽  
Design Variables ◽  
Deep Groove ◽  
Rolling Element ◽  
Manufacturing Tolerances

Abstract In designing any machine element, we need to optimize the design to attain its maximum utilization. Herein deep groove ball bearings has been chosen for optimization. Optimization has been done in such a way that the design is robust so that manufacturing tolerances can be considered in the design. Robust design ensures that changes in design variables due to manufacturing tolerances have minimum effect on the objective function, i.e. its performance. Robustness is achieved by maximizing the mean value of the objective function and minimizing its deviation. For rolling element bearings, its life is one of the most crucial considerations. The rolling bearing rating life depends on dynamic capacity, lubrication conditions, contamination, mounting, lubrication, manufacturing accuracy, material quality, etc. and thus the dynamic capacity and elasto-hydrodynamic minimum film thickness has been taken as objective functions for the current problem. Rolling element bearings have standard boundary dimensions, which include the outer diameter, inner diameter and bearing width for the case of deep groove ball bearings. So the performance can be improved by changing internal dimensions, which are the bearing pitch diameter, ball diameter, the inner and outer raceway groove curvature coefficients and, the number of rolling elements. These five internal geometrical parameters are taken as design variables, moreover five design constraint factors are also included. Thirty-six constraint equations are considered, which are mainly based on geometrical and strength considerations. In the present work, the objective functions are optimized individually (i.e., the single-objective optimization) and then simultaneously (i.e., the multi-objective optimization). NSGA-II (non-dominated sorting genetic algorithm) has been used as the optimization tool. Pareto optimal fronts are obtained for one of the bearings. Out of many points on the Pareto-front, only the knee solutions have been presented in the tables. This work shows that geometrically feasible bearings can be designed by optimizing multiple objective functions simultaneously and also incorporating the variations in dimensions, which occur due to manufacturing tolerance.

Multi-objective design optimization of power-cycling hydrodynamic mechanical transmissions

2018 ◽  
Vol 233 (4) ◽  
pp. 1392-1410 ◽  
Author(s):  
Xiaojun Liu ◽  
Dongye Sun ◽  
Datong Qin ◽  
Junlong Liu
Keyword(s):  
Numerical Simulation ◽  
Design Methodology ◽  
Speed Ratio ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multi Objective ◽  
Design Variables ◽  
Power Cycling ◽  
Automatic Transmissions ◽  
Mechanical Transmissions

The power-cycling hydrodynamic mechanical transmissions have the advantages of continuously adjustable speed ratio and high efficiency compared with the traditional automatic transmissions, so they may be a good substitute for the prior art. For off-highway vehicles which frequently work in low speed and confront great resistance, the zero-speed-ratio torque ratio (TR) of the power-cycling hydrodynamic mechanical transmissions represents the power performance of the vehicles. Furthermore, the complexity of the transmissions is an indispensable consideration for industrial designers. The radial and axial dimensions of the power-cycling hydrodynamic mechanical transmissions are determined by the effective diameter of the torque converter’s circuit and the number of transmissions gears, respectively. In order to optimize the zero-speed-ratio TR and the complexity of the power-cycling hydrodynamic mechanical transmissions, a design methodology is proposed. Considering that there is no explicit mathematical relationship between the design variables and the multi-objective functions, the parametric design and numerical simulation for the torque converter are carried out. The intrinsic mapping between the design variables and the multi-objective functions is fitted by the radial basis function neural network. On this basis, the fast and elitist non-dominated sorting genetic algorithm (NSGA-ΙΙ) is used to solve the multi-objective optimization problem. The numerical simulation for one group of solution selected from the Pareto optimal solutions is conducted. The simulation results indicate that the design methodology proposed in this study is effective. The optimal results show that the zero-speed-ratio TR of the power-cycling hydrodynamic mechanical transmissions is heavily influenced by the radial and axial space of such transmissions. The design optimization helps to find the optimal solutions for the power-cycling HMTs, which are superior to the traditional automatic transmissions and match well the prime mover.

scholarly journals MULTI-OBJECTIVE OPTIMIZATION OF REINFORCED CONCRETE FRAMES USING NSGA-II ALGORITHM

2016 ◽  
Vol 8 (4) ◽  
pp. 157-164 ◽  
Author(s):  
Mehdi Babaei ◽  
Masoud Mollayi
Keyword(s):  
Genetic Algorithm ◽  
Reinforced Concrete ◽  
Steel Structures ◽  
American Concrete Institute ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Design Variables ◽  
Pareto Fronts

In recent decades, the use of genetic algorithm (GA) for optimization of structures has been highly attractive in the study of concrete and steel structures aiming at weight optimization. However, it has been challenging for multi-objective optimization to determine the trade-off between objective functions and to obtain the Pareto-front for reinforced concrete (RC) and steel structures. Among different methods introduced for multi-objective optimization based on genetic algorithms, Non-Dominated Sorting Genetic Algorithm II (NSGA II) is one of the most popular algorithms. In this paper, multi-objective optimization of RC moment resisting frame structures considering two objective functions of cost and displacement are introduced and examined. Three design models are optimized using the NSGA-II algorithm. Evaluation of optimal solutions and the algorithm process are discussed in details. Sections of beams and columns are considered as design variables and the specifications of the American Concrete Institute (ACI) are employed as the design constraints. Pareto-fronts for the objective space have been obtained for RC frame models of four, eight and twelve floors. The results indicate smooth Pareto-fronts and prove the speed and accuracy of the method.

Geometric Size Optimization of Annular Step Fin Using Multi-Objective Genetic Algorithm

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Abhijit Deka ◽  
Dilip Datta
Keyword(s):  
Heat Transfer ◽  
Genetic Algorithm ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Pareto Optimal ◽  
Objective Functions ◽  
Cross Sectional ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Design Variables

Although an annular stepped fin can produce better cooling effect in comparison to an annular disk fin, it is yet to be studied in detail. In the present work, one-dimensional heat transfer in a two-stepped rectangular cross-sectional annular fin with constant base temperature and variable thermal conductivity is modeled as a multi-objective optimization problem. Taking cross-sectional half-thicknesses and outer radii of the two fin steps as design variables, an attempt is made to obtain the efficient fin geometry primarily by simultaneously maximizing the heat transfer rate and minimizing the fin volume. For further assessment of the fin performance, three more objective functions are studied, which are minimization of the fin surface area and maximization of the fin efficiency and effectiveness. Evaluating the heat transfer rate through the hybrid spline difference method, the well-known multi-objective genetic algorithm, namely, nondominated sorting genetic algorithm II (NSGA-II), is employed for approximating the Pareto-optimal front containing a set of tradeoff solutions in terms of different combinations of the considered five objective functions. The Pareto-optimal sensitivity is also analyzed for studying the influences of the design variables on the objective functions. As an outcome, it can be concluded that the proposed procedure would give an open choice to designers to lead to a practical stepped fin configuration.

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