Towards Uniformly Distributed Compliance in Compliant Mechanisms: A Multi-Objective Approach

2006 ◽  
Author(s):  
Stephen L. Canfield ◽  
Daniel L. Chlarson ◽  
Alexander Shibakov ◽  
Patrick V. Hull
Keyword(s):  
Finite Element ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Optimality Criteria ◽  
Optimal Designs ◽  
Limiting Factors ◽  
Objective Functions ◽  
Multi Objective ◽  
Simple Addition ◽  
Current Formulation

Researchers in the field of optimal synthesis of compliant mechanisms have been working to develop tools that yield distributed compliant devices to perform specific tasks. However, it has been demonstrated in the literature that much of this work has resulted in mechanisms that localize compliance rather than distribute it as desired. In fact, Yin and Ananthasuresh (2003) [1] demonstrate that based on the current formulation of optimality criteria and analysis via the finite element (FE) technique, a lumped compliant device will always exist as the minimizing solution to the objective function. The addition of constraints on allowable strain simply moves the solution back from this objective. Therefore, modification to the standard optimality criteria needs to take place. Yin and Ananthasuresh [1] proposed and compared several approaches that include distributivity-based measures within the optimality criteria, and demonstrated the effectiveness of this approach. In this paper, the authors propose to build on this problem. In a similar manner, a general approach to the topology synthesis problem will be suggested to yield mechanisms in which the compliance is distributed throughout the device. This work will be based on the idea of including compliance distribution directly within the objective functions, while addressing some of the potential limiting factors in past approaches. The technique will be generalized to allow simple addition of criteria in the future, and to deliver optimal designs through to manufacture. This work will first revisit and propose several quantitative definitions for distributed compliant devices. Then, a multi-objective formulation based on a non-dominating sort and Pareto set method will be incorporated that will provide information on the nature of the problem and compatibility of employed objective functions.

Appropriate Objective Functions for Quantifying Iris Mechanical Properties Using Inverse Finite Element Modeling

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Anup D. Pant ◽  
Syril K. Dorairaj ◽  
Rouzbeh Amini
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Objective Function ◽  
Inverse Modeling ◽  
Measurement Errors ◽  
Ex Vivo ◽  
Treatment Strategies ◽  
Objective Functions ◽  
Estimation Of Parameters

Quantifying the mechanical properties of the iris is important, as it provides insight into the pathophysiology of glaucoma. Recent ex vivo studies have shown that the mechanical properties of the iris are different in glaucomatous eyes as compared to normal ones. Notwithstanding the importance of the ex vivo studies, such measurements are severely limited for diagnosis and preclude development of treatment strategies. With the advent of detailed imaging modalities, it is possible to determine the in vivo mechanical properties using inverse finite element (FE) modeling. An inverse modeling approach requires an appropriate objective function for reliable estimation of parameters. In the case of the iris, numerous measurements such as iris chord length (CL) and iris concavity (CV) are made routinely in clinical practice. In this study, we have evaluated five different objective functions chosen based on the iris biometrics (in the presence and absence of clinical measurement errors) to determine the appropriate criterion for inverse modeling. Our results showed that in the absence of experimental measurement error, a combination of iris CL and CV can be used as the objective function. However, with the addition of measurement errors, the objective functions that employ a large number of local displacement values provide more reliable outcomes.

Pareto Artificial Life Algorithm for Multi-Objective Optimization

2011 ◽  
Vol 4 (2) ◽  
pp. 43-60
Author(s):  
Jin-Dae Song ◽  
Bo-Suk Yang
Keyword(s):  
Objective Function ◽  
Artificial Life ◽  
Pareto Set ◽  
Function Optimization ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Function ◽  
Artificial Life Algorithm ◽  
Single Objective

Most engineering optimization uses multiple objective functions rather than single objective function. To realize an artificial life algorithm based multi-objective optimization, this paper proposes a Pareto artificial life algorithm that is capable of searching Pareto set for multi-objective function solutions. The Pareto set of optimum solutions is found by applying two objective functions for the optimum design of the defined journal bearing. By comparing with the optimum solutions of a single objective function, it is confirmed that the single function optimization result is one of the specific cases of Pareto set of optimum solutions.

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.

Pareto Artificial Life Algorithm for Multi-Objective Optimization

2013 ◽  
pp. 100-115
Author(s):  
Jin-Dae Song ◽  
Bo-Suk Yang
Keyword(s):  
Objective Function ◽  
Artificial Life ◽  
Pareto Set ◽  
Function Optimization ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Function ◽  
Artificial Life Algorithm ◽  
Single Objective

Most engineering optimization uses multiple objective functions rather than single objective function. To realize an artificial life algorithm based multi-objective optimization, this paper proposes a Pareto artificial life algorithm that is capable of searching Pareto set for multi-objective function solutions. The Pareto set of optimum solutions is found by applying two objective functions for the optimum design of the defined journal bearing. By comparing with the optimum solutions of a single objective function, it is confirmed that the single function optimization result is one of the specific cases of Pareto set of optimum solutions.

Multi-Objective Optimization of Compliant Mechanisms Including Failure Theories

2007 ◽  
Author(s):  
Stephen L. Canfield ◽  
Daniel L. Chlarson ◽  
Alexander Shibakov ◽  
Joseph D. Richardson ◽  
Anupam Saxena
Keyword(s):  
Multiobjective Optimization ◽  
Compliant Mechanisms ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Design Problems ◽  
Design Objective ◽  
Multi Objective ◽  
Failure Theory ◽  
Measuring Efficiency ◽  
Failure Theories

This paper will present a version of failure theory suitable for designing optimal compliant mechanisms. The resulting theory will be incorporated as design objective functions within a multi-objective optimizing engine with the purpose of producing optimal and robust compliant mechanisms suitable for manufacture. Combining these failure-based objective functions with the classical ones measuring efficiency in performing a task, in the context of diversity promoting multiobjective optimization (see [1]) will demonstrate the tool’s ability to produce optimal compliant mechanisms that are failure-proof as well as provide insights into the complexity of particular design problems.

INFLUENCE OF OBJECTIVE FUNCTIONS IN STRUCTURAL DAMAGE IDENTIFICATION USING REFINED AND SIMPLE MODELS

2009 ◽  
Vol 09 (04) ◽  
pp. 607-625 ◽  
Author(s):  
RICARDO PERERA ◽  
SHENG-EN FANG
Keyword(s):  
Dynamic Response ◽  
Objective Function ◽  
Structural Damage ◽  
Damage Identification ◽  
Computational Cost ◽  
Computational Time ◽  
Fe Model ◽  
Beam Model ◽  
Objective Functions ◽  
Multi Objective

The most usual approach for solving damage identification problems is the use of the finite element (FE) model updating method. To apply the method, a minimization of an objective function measuring the fit between measured and model predicted data is performed. Then, the success of the procedure depends strongly on the accuracy of the FE model and the choice of a suitable objective function. Although detailed FE models provide an accurate means for calculating the dynamic response of the structure, their size and complexity involve a large number of parameters to be updated and a high computational cost. In order to shorten the computational time, more simplified and practical models able to model the global dynamic response of the structure accurately would be desirable. Furthermore, working with several objective functions instead of only one would increase the robustness and performance of the procedure. In this paper, a multi-objective simple beam model is proposed and compared with a more refined model based on plane elements. Furthermore, in the multi-objective framework, different combinations of objective functions are studied. The reliability and effectiveness of the proposed model has been evaluated in a damage detection problem of a reinforced concrete frame experimentally tested under different levels of damage.

scholarly journals DETERMINATION OF SUBJECTS’ SIGNIFICANCE RATE AND OPTIMAL INFORMATION CONTROL IN SOCIAL NETWORKS

2021 ◽  
Vol 3 ◽  
pp. 254-272
Author(s):  
Sharif Guseynov ◽  
Aleksandrs Berežnojs ◽  
Jekaterina Aleksejeva
Keyword(s):  
Social Networks ◽  
Optimal Control ◽  
Objective Function ◽  
Limiting Factors ◽  
Information Control ◽  
Dynamic Parameters ◽  
Objective Functions ◽  
Governing Body ◽  
Optimal Information

This paper examines social networks, where each agent is characterized by some dynamic parameters, the dynamics of which is resulting from the influence of other agents having their own objective functions and limiting factors, as well as from control/governing body with its own objective function. In this paper, referring to the type of social networks described above, the following two interrelated problems are investigated: the problem of determining the degree of information influence on social networks; the problem of finding optimal control in social networks.  

scholarly journals Searching for an optimized single-objective function matching multiple objectives with automatic calibration of hydrological models

2016 ◽  
Author(s):  
Fuqiang Tian ◽  
Yu Sun ◽  
Hongchang Hu ◽  
Hongyi Li
Keyword(s):  
Objective Function ◽  
Power Function ◽  
Automatic Calibration ◽  
Efficiency Coefficient ◽  
Hydrological Models ◽  
Objective Functions ◽  
Multi Objective ◽  
Hydrological Variable ◽  
Flow Part ◽  
Single Objective

Abstract. In the calibration of hydrological models, evaluation criteria are explicitly and quantitatively defined as single- or multi-objective functions when utilizing automatic calibration approaches. In most previous studies, there is a general opinion that no single-objective function can represent all of the important characteristics of even one specific kind of hydrological variable (e.g., streamflow). Thus hydrologists must turn to multi-objective calibration. In this study, we demonstrated that an optimized single-objective function can compromise multi-response modes (i.e., multi-objective functions) of the hydrograph, which is defined as summation of a power function of the absolute error between observed and simulated streamflow with the exponent of power function optimized for specific watersheds. The new objective function was applied to 196 model parameter estimation experiment (MOPEX) watersheds across the eastern United States using the semi-distributed Xinanjiang hydrological model. The optimized exponent value for each watershed was obtained by targeting four popular objective functions focusing on peak flows, low flows, water balance, and flashiness, respectively. The results showed that the optimized single-objective function can achieve a better hydrograph simulation compared to the traditional single-objective function Nash-Sutcliffe efficiency coefficient for most watersheds, and balance high flow part and low flow part of the hydrograph without substantial differences compared to multi-objective calibration. The proposed optimal single-objective function can be practically adopted in the hydrological modeling if the optimal exponent value could be determined a priori according to hydrological/climatic/landscape characteristics in a specific watershed. This is, however, left for future study.

An Optimality Criteria Approach for the Topology Synthesis of Compliant Mechanisms

1998 ◽  
Author(s):  
A. Saxena ◽  
G. K. Ananthasuresh
Keyword(s):  
Energy Density ◽  
Mathematical Programming ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Optimality Criteria ◽  
Optimality Criteria Method ◽  
New Energy ◽  
Method Of Solution ◽  
Design Parameterization ◽  
The Continuum

Abstract The physical insight used in formulating a multi-criteria optimization problem for the synthesis of compliant mechanisms, is quickly lost if mathematical programming techniques (SLP, SQP etc.) are used to determine the optimal solution. As opposed to the previous works that relied upon mathematical programming search techniques to find the optimum solution, in this paper we present an alternative method of solution called the optimality criteria method. Optimality criteria methods have proven to be effective in structural optimization problems with a large number of variables, and very few constraints as is the case in the topology synthesis of compliant mechanisms. The important new results of this paper include: (i) the derivation of a physically insightful optimal property of compliant mechanisms which states that the ratio of the mutual potential energy density and the strain energy density is uniform throughout the continuum (ii) the development of the optimality criteria method of solution in the form of a simple update formula for the design variables by using the above property (iii) design parameterization using the frame finite-element based ground-structure that appropriately accounts for the requisite bending behavior in the continuum, and (iv) numerical implementation of previously reported density based design parameterization using bilinear plane-stress elements. In addition, a new energy based multi-criteria objective function is presented to maximize the useful output energy (which is equivalent to maximizing the mechanical advantage) while meeting the kinematic requirements. Several examples are included to demonstrate the validity of the optimal property, the optimality-criteria method of solution, and the improvements made possible by the new energy based objective function.

scholarly journals Finite Element Based Overall Optimization of Switched Reluctance Motor Using Multi-Objective Genetic Algorithm (NSGA-II)

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 576
Author(s):  
Mohamed El-Nemr ◽  
Mohamed Afifi ◽  
Hegazy Rezk ◽  
Mohamed Ibrahim
Keyword(s):  
Genetic Algorithm ◽  
Finite Element ◽  
Optimal Design ◽  
Switched Reluctance Motor ◽  
Design Parameters ◽  
Objective Functions ◽  
Nsga Ii ◽  
Switched Reluctance ◽  
Multi Objective ◽  
Reluctance Motor

The design of switched reluctance motor (SRM) is considered a complex problem to be solved using conventional design techniques. This is due to the large number of design parameters that should be considered during the design process. Therefore, optimization techniques are necessary to obtain an optimal design of SRM. This paper presents an optimal design methodology for SRM using the non-dominated sorting genetic algorithm (NSGA-II) optimization technique. Several dimensions of SRM are considered in the proposed design procedure including stator diameter, bore diameter, axial length, pole arcs and pole lengths, back iron length, shaft diameter as well as the air gap length. The multi-objective design scheme includes three objective functions to be achieved, that is, maximum average torque, maximum efficiency and minimum iron weight of the machine. Meanwhile, finite element analysis (FEA) is used during the optimization process to calculate the values of the objective functions. In this paper, two designs for SRMs with 8/6 and 6/4 configurations are presented. Simulation results show that the obtained SRM design parameters allow better average torque and efficiency with lower iron weight. Eventually, the integration of NSGA-II and FEA provides an effective approach to obtain the optimal design of SRM.

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