Multi-Objective Optimization of Piezoelectric Microactuator Using Genetic Algorithms

2008 ◽  
Author(s):  
H. Esteki ◽  
A. Hasannia
Keyword(s):  
Genetic Algorithms ◽  
Strain Energy ◽  
Compliant Mechanism ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Cross Sectional ◽  
Flexure Hinges ◽  
Design Variables ◽  
Cross Sectional Size ◽  
Real Coded Genetic Algorithms

In flex-tensional piezoactuators, due to the low displacement of piezostacks, a compliant mechanism is used to amplify displacement of piezostack. In this paper, optimization of a compliant mechanism with corner-filleted flexure hinges is carried out using real-coded genetic algorithms (GAs) to avoid trapping in local optimums. The objective functions are displacement amplification and stiffness of mechanism and design variables are cross-sectional size and material used. The constraints which are applied on mechanism are based on piezostack dimensions and manufacturing limits. Displacement amplification and stiffness are calculated using strain energy and Castigliano’s displacement theorem.

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.

Study on the Optimal Design of the Members of Contaniner Building with Building Materials I: Side Board Optimization

2013 ◽  
Vol 859 ◽  
pp. 270-273 ◽  
Author(s):  
Xiao Xiong Zha ◽  
Yang Zuo ◽  
Shi Yun Chen
Keyword(s):  
Software Package ◽  
Design Theory ◽  
Optimization Design ◽  
Building Materials ◽  
Steel Structure ◽  
Building Construction ◽  
Cross Sectional ◽  
Design Variables ◽  
Cross Sectional Dimension ◽  
Cross Sectional Size

Container, as a light steel structure, being increasingly used in building construction, containers used in construction has many advantages and applications. However, the current study mostly from the view of the architecture, as for the mechanical properties of the container building has not mentioned, that brings obstacles of the application and development of the container building. Based on the software package of HyperWorks and optimization design theory, the cross-sectional size of container building is taken as design variables, and then selected objective function and constraint functions. Finally, calculated by software, get the optimal cross-sectional dimension.

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.

Design of C-Frames Using Real-Coded Genetic Optimization Algorithms and NURBS

1999 ◽  
Author(s):  
Ashraf O. Nassef ◽  
Hesham A. Hegazi ◽  
Sayed M. Metwalli
Keyword(s):  
Genetic Algorithms ◽  
Cross Section ◽  
Cross Sections ◽  
Design Parameters ◽  
Binary Representation ◽  
Cross Sectional ◽  
Search Spaces ◽  
The Cross ◽  
Sectional Shape ◽  
Real Coded Genetic Algorithms

Abstract C-frames constitute a large portion of machine tools that are currently used in industry. Examples of these frames include drilling machines, presses, punching and stamping machines, clamps, hooks, etc. The design parameters of these frames include the dimensions of their cross-sections, which should be chosen to withstand the applied loads and minimize the element’s overall weight. Traditionally, the cross-section of C-frame belonged to a set of primitive shapes, which included I, T, trapezoidal and rectangular sections. This paper introduces a new methodology for designing the frame’s cross-section. The cross-sectional shape is represented using non-uniform rational B-Spline (NURBS) in order to give it a form of shape flexibility. A special form of genetic algorithms known as real-coded genetic algorithms is used to conduct the search for the design objectives. Real-coded genetic algorithms are known to outperform the simple binary representation genetic algorithms when dealing with continuous search spaces. The results showed that the optimal shape was a semi I/T-section with the material bulk related to the applied load.

Multi-objective Optimization of a Flexible Rotor in Magnetic Bearings With Critical Speeds and Control Current Constraints

1997 ◽  
Vol 119 (1) ◽  
pp. 186-195 ◽  
Author(s):  
Ting Nung Shiau ◽  
Chun Pao Kuo ◽  
Jiunn Rong Hwang
Keyword(s):  
Expansion Method ◽  
Magnetic Bearings ◽  
Multi Objective Optimization ◽  
Flexible Rotor ◽  
Weighting Method ◽  
Cross Sectional ◽  
Critical Speeds ◽  
Multi Objective ◽  
Design Variables ◽  
Single Objective

This paper presents the single objective optimization and the multi-objective optimization for a flexible rotor system with magnetic bearings. The weight of rotor shaft and the transmitted forces at the magnetic bearings are minimized either individually or simultaneously under the constraints on the critical speeds and the control currents of magnetic bearings. The design variables are the cross-sectional area of the shaft, the bias currents of magnetic bearings, and the positions of the disk and the magnetic bearings. The dynamic characteristics are analyzed using the generalized polynomial expansion method and the sensitivity analysis is also studied. For single objective optimization, the method of feasible directions (MFD) is applied. For multi-objective optimization, the weighting method (WM), the goal programming method (GPM), and the fuzzy method (FM) are employed. It is found that the system design can be significantly affected by the choices of the bias currents of magnetic bearings, the position of the disk with unbalance, and the magnetic bearings. The results also show that a better compromised design can always be obtained for multi-objective optimization.

An Optimal Study of a Gripper Compliant Mechanism Based on Fuzzy-Taguchi Method

2013 ◽  
Vol 418 ◽  
pp. 141-144 ◽  
Author(s):  
Thanh Phong Dao ◽  
Shyh Chour Huang
Keyword(s):  
Taguchi Method ◽  
Optimization Problem ◽  
Virtual Work ◽  
Compliant Mechanism ◽  
Vertical Force ◽  
Horizontal Force ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Rigid Body Model ◽  
Energy Store

In this paper, a gripper mechanism with two flexible elements for grasping the objects was investigated. In general, to achieve the good the flexibility and the life strength, the flexible hinges often offer the highest elastic energy store while the lowest stress concentration is also required simultaneously. Therefore, to handle this multi-objective optimization problem, this study used the fuzzy logic based Taguchi method. The two input parameters, namely a vertical force and a horizontal force that primarily influence the displacement and the stress. These were controlled with regard to two-objective functions as the torque of torsional spring and the stress. In addition, formulating two-objective functions was based on the procedure of a pseudo-rigid-body model (PRBM) and the principle of virtual work. The results found that a vertical force of 0.5 lb and a horizontal force of 0.4 lb are favorable parameters for a suggested gripper. Using ANOVA, the results also revealed that a vertical force is the most significant parameter with highest F value of 1.188.

An Instant Center Approach Toward the Conceptual Design of Compliant Mechanisms

2005 ◽  
Vol 128 (3) ◽  
pp. 542-550 ◽  
Author(s):  
Charles J. Kim ◽  
Sridhar Kota ◽  
Yong-Mo Moon
Keyword(s):  
Conceptual Design ◽  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometry Optimization ◽  
Building Blocks ◽  
Cross Sectional ◽  
Rigid Body Model ◽  
Cross Sectional Size

As with conventional mechanisms, the conceptual design of compliant mechanisms is a blend of art and science. It is generally performed using one of two methods: topology optimization or the pseudo-rigid-body model. In this paper, we present a new conceptual design methodology which utilizes a building block approach for compliant mechanisms performing displacement amplification/attenuation. This approach provides an interactive, intuitive, and systematic methodology for generating initial compliant mechanism designs. The instant center is used as a tool to construct the building blocks. The compliant four-bar building block and the compliant dyad building block are presented as base mechanisms for the conceptual design. It is found that it is always possible to obtain a solution for the geometric advantage problem with an appropriate combination of these building blocks. In a building block synthesis, a problem is first evaluated to determine if any known building blocks can satisfy the design specifications. If there are none, the problem is decomposed to a number of sub-problems which may be solved with the building blocks. In this paper, the problem is decomposed by selecting a point in the design space where the output of the first building block coincides with the second building block. Two quantities are presented as tools to aid in the determination of the mechanism's geometry – (i) an index relating the geometric advantage of individual building blocks to the target geometric advantage and (ii) the error in the geometric advantage predicted by instant centers compared to the calculated value from FEA. These quantities guide the user in the selection of the location of nodes of the mechanism. Determination of specific cross-sectional size is reserved for subsequent optimization. An example problem is provided to demonstrate the methodology's capacity to obtain good initial designs in a straightforward manner. A size and geometry optimization is performed to demonstrate the viability of the design.

scholarly journals Multiobjective Optimization of a Flexible Rotor in Magnetic Bearings With Critical Speeds and Control Current Constraints

1994 ◽  
Author(s):  
Ting Nung Shiau ◽  
Chun Pao Kuo ◽  
Jiunn Rong Hwang
Keyword(s):  
Expansion Method ◽  
Magnetic Bearings ◽  
Multi Objective Optimization ◽  
Flexible Rotor ◽  
Weighting Method ◽  
Cross Sectional ◽  
Critical Speeds ◽  
Multi Objective ◽  
Design Variables ◽  
Single Objective

This paper presents the single objective optimization and the multi-objective optimization for a flexible rotor system with magnetic bearings. The weight of rotor shaft and the transmitted forces at the magnetic bearings are minimized either individually or simultaneously under the constraints on the critical speeds and the control currents of magnetic bearings. The design variables are the cross-sectional area of the shaft, the bias currents of magnetic bearings, and the positions of the disk and the magnetic bearings. The dynamic characteristics are analyzed using the generalized polynomial expansion method and the sensitivity analysis is also studied. For single objective optimization, the method of feasible directions (MFD) is applied. For multi-objective optimization, the methods including the weighting method (WM), goal programming method (GPM), and the fuzzy method (FM) are employed. It is found that the system design can be significantly affected by the choices of the bias currents of magnetic bearings, the position of the disk with unbalance and the magnetic bearings. The results also show that a better compromized design can always be obtained for multi-objective optimization.

Multi-Objective Optimization of Pin-Fin Heatsinks

2009 ◽  
Author(s):  
Keisuke Horiuchi ◽  
Atsuo Nishihara ◽  
Kazuyuki Sugimura
Keyword(s):  
Pressure Drop ◽  
Thermal Resistance ◽  
Approximation Model ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Multi Objective ◽  
Pin Fin ◽  
Design Variables ◽  
Kriging Approximation

The multi-objective optimization of pin-fin heatsinks using a Kriging approximation model is presented based on systematic experimental results. Thermal resistance and pressure drop are the objective functions in this study. Pareto solutions to the objective functions are illustrated. We derived the design rules for the diameter, height, and pitches for the uniform staggered arrays of pin-fin heatsinks by correlating the objective functions with design variables. We also analyzed the contribution of all design variables to the thermal resistance as well as the pressure drop. We found that both the thermal resistance and the pressure drop are the most sensitive to the ratio of transverse pitch to pin-fin diameter.

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