Dynamic Balancing of Four-Bar Linkages: A Convex Optimization Framework for Efficiently Obtaining Globally Optimal Counterweights

2004 ◽  
Author(s):  
Bram Demeulenaere ◽  
Jan Swevers ◽  
Joris De Schutter
Keyword(s):  
Optimization Problem ◽  
Added Mass ◽  
Global Optimum ◽  
Great Efficiency ◽  
Dynamic Balancing ◽  
Optimization Framework ◽  
Design Charts ◽  
The Cost ◽  
Driving Torque ◽  
Shaking Moment

This paper focusses on reducing the dynamic reactions (shaking force, shaking moment and driving torque) of plane, crank-rocker four-bars through counterweight addition. Determining the mass parameters of the counterweights constitutes an optimization problem, which is classically considered to be nonlinear and hence difficult to solve. A first contribution of this paper is the proof that this optimization problem can be reformulated as a convex program, that is, a nonlinear optimization problem that still has a unique (and hence guaranteed global) optimum, which can be found with great efficiency. Because of the unique features of this formulation, it becomes possible to investigate (and by the guarantee of obtaining a global optimum, in fact prove) the ultimate limits of dynamic balancing, in a reasonable amount of time. When applied to a particular example, this results in design charts, which clearly illustrate (i) the tradeoff between minimizing the different dynamic reactions, and (ii) the fact that adding counterweights is effective, but at the cost of a significant amount of added mass. These design charts constitute a second contribution of the present work.

scholarly journals Ultimate Limits for Counterweight Balancing of Crank-Rocker Four-Bar Linkages

2006 ◽  
Vol 128 (6) ◽  
pp. 1272-1284 ◽  
Author(s):  
Bram Demeulenaere ◽  
Erwin Aertbeliën ◽  
Myriam Verschuure ◽  
Jan Swevers ◽  
Joris De Schutter
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Design Procedure ◽  
Global Optimum ◽  
Convex Program ◽  
Local Optimum ◽  
Local Optima ◽  
Nonlinear Optimization Problem ◽  
Driving Torque ◽  
Shaking Moment

This paper focuses on reducing the dynamic reactions (shaking force, shaking moment, and driving torque) of planar crank-rocker four-bars through counterweight addition. Determining the counterweight mass parameters constitutes a nonlinear optimization problem, which suffers from local optima. This paper, however, proves that it can be reformulated as a convex program, that is, a nonlinear optimization problem of which any local optimum is also globally optimal. Because of this unique property, it is possible to investigate (and by virtue of the guaranteed global optimum, in fact prove) the ultimate limits of counterweight balancing. In a first example a design procedure is presented that is based on graphically representing the ultimate limits in design charts. A second example illustrates the versatility and power of the convex optimization framework by reformulating an earlier counterweight balancing method as a convex program and providing improved numerical results for it.

Ultimate and Practical Limits for Counterweight Balancing of Six-Bar Linkages

2006 ◽  
Author(s):  
Bram Demeulenaere ◽  
Jan Swevers ◽  
Joris De Schutter
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Global Optimum ◽  
Great Efficiency ◽  
Convex Programs ◽  
Local Optima ◽  
Trade Off ◽  
Convex Constraint ◽  
Main Challenge ◽  
Dynamic Forces

The designer’s main challenge when counterweight balancing a linkage is to determine the counterweights that realize an optimal trade-off between the dynamic forces of interest. This problem is often formulated as an optimization problem that is generally nonlinear and therefore suffers from local optima. It has been shown earlier, however, that, through a proper parametrization of the counterweights, a convex program can be obtained. Convex programs are nonlinear optimization problems of which the global optimum is guaranteed to be found with great efficiency. The present paper extends this previous work in two respects: (i) the methodology is generalized from four-bar to planar N-bar (rigid) linkages and (ii) it is shown that requiring the counterweights to be realizable in practice can be cast as a convex constraint. Numerical results for a Watt six-bar linkage suggest much more balancing potential for six-bar linkages than for four-bar linkages.

Counterweight Balancing for Reducing Machine Frame Vibration: A Convex Optimization Framework

2006 ◽  
Author(s):  
Myriam Verschuure ◽  
Bram Demeulenaere ◽  
Jan Swevers ◽  
Joris De Schutter
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Global Optimum ◽  
Convex Optimization Problem ◽  
Optimization Framework ◽  
Convex Optimization Problems ◽  
Drive Speed ◽  
Maximal Reduction

This paper focusses on reducing, through counterweight addition, the vibration of an elastically mounted, rigid machine frame that supports a linkage. In order to determine the counterweights that yield a maximal reduction in frame vibration, a non-linear optimization problem is formulated with the frame kinetic energy as objective function and such that a convex optimization problem is obtained. Convex optimization problems are nonlinear optimization problems that have a unique (global) optimum, which can be found with great efficiency. The proposed methodology is successfully applied to improve the results of the benchmark four-bar problem, first considered by Kochev and Gurdev. For this example, the balancing is shown to be very robust for drive speed variations and to benefit only marginally from using a coupler counterweight.

scholarly journals Braille Block Detection via Multi-Objective Optimization from an Egocentric Viewpoint

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2775
Author(s):  
Tsubasa Takano ◽  
Takumi Nakane ◽  
Takuya Akashi ◽  
Chao Zhang
Keyword(s):  
Optimization Problem ◽  
Line Pair ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Optimization Framework ◽  
Visually Impaired People ◽  
Comprehensive Comparison ◽  
Basic Characteristics ◽  
Support Devices

In this paper, we propose a method to detect Braille blocks from an egocentric viewpoint, which is a key part of many walking support devices for visually impaired people. Our main contribution is to cast this task as a multi-objective optimization problem and exploits both the geometric and the appearance features for detection. Specifically, two objective functions were designed under an evolutionary optimization framework with a line pair modeled as an individual (i.e., solution). Both of the objectives follow the basic characteristics of the Braille blocks, which aim to clarify the boundaries and estimate the likelihood of the Braille block surface. Our proposed method was assessed by an originally collected and annotated dataset under real scenarios. Both quantitative and qualitative experimental results show that the proposed method can detect Braille blocks under various environments. We also provide a comprehensive comparison of the detection performance with respect to different multi-objective optimization algorithms.

scholarly journals An Optimization Method for the Configuration of Inter Array Cables for Floating Offshore Wind Farm

2017 ◽  
Author(s):  
Yann Poirette ◽  
Martin Guiton ◽  
Guillaume Huwart ◽  
Delphine Sinoquet ◽  
Jean Marc Leroy
Keyword(s):  
Wind Farm ◽  
Optimization Problem ◽  
Initial Point ◽  
Trust Region ◽  
Optimization Method ◽  
Global Optimum ◽  
Offshore Wind ◽  
Finite Element Software ◽  
Constrained Problems ◽  
Floating Offshore Wind Turbines

IFP Energies nouvelles (IFPEN) is involved for many years in various projects for the development of floating offshore wind turbines. The commercial deployment of such technologies is planned for 2020. The present paper proposes a methodology for the numerical optimization of the inter array cable configuration. To illustrate the potential of such an optimization, results are presented for a case study with a specific floating foundation concept [1]. The optimization study performed aims to define the least expensive configuration satisfying mechanical constraints under extreme environmental conditions. The parameters to be optimized are the total length, the armoring, the stiffener geometry and the buoyancy modules. The insulated electrical conductors and overall sheath are not concerned by this optimization. The simulations are carried out using DeepLines™, a Finite Element software dedicated to simulate offshore floating structures in their marine environment. The optimization problem is solved using an IFPEN in-house tool, which integrates a state of the art derivative-free trust region optimization method extended to nonlinear constrained problems. The latter functionality is essential for this type of optimization problem where nonlinear constraints are introduced such as maximum tension, no compression, maximum curvature and elongation, and the aero-hydrodynamic simulation solver does not provide any gradient information. The optimization tool is able to find various local feasible extrema thanks to a multi-start approach, which leads to several solutions of the cable configuration. The sensitivity to the choice of the initial point is demonstrated, illustrating the complexity of the feasible domain and the resulting difficulty in finding the global optimum configuration.

Adaptive Complex Method for Efficient Design Optimization

2007 ◽  
Author(s):  
Marcus Pettersson ◽  
Johan O¨lvander
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Global Optimum ◽  
Direct Search ◽  
Complex Method ◽  
Efficient Design ◽  
Direct Search Methods ◽  
Simulation Based ◽  
Set Of Points ◽  
Quasi Newton

Box’s Complex method for direct search has shown promise when applied to simulation based optimization. In direct search methods, like Box’s Complex method, the search starts with a set of points, where each point is a solution to the optimization problem. In the Complex method the number of points must be at least one plus the number of variables. However, in order to avoid premature termination and increase the likelihood of finding the global optimum more points are often used at the expense of the required number of evaluations. The idea in this paper is to gradually remove points during the optimization in order to achieve an adaptive Complex method for more efficient design optimization. The proposed method shows encouraging results when compared to the Complex method with fix number of points and a quasi-Newton method.

The Calculation of Photovoltaic System Generation Access Capacity in Distribution Network Based on Probabilistic Power Flow and the PSO Optimization

2012 ◽  
Vol 529 ◽  
pp. 371-375
Author(s):  
Lu Yao Ma ◽  
Shu Jun Yao ◽  
Yan Wang ◽  
Jing Yang ◽  
Long Hui Liu
Keyword(s):  
Distributed Generation ◽  
Power Flow ◽  
Optimization Problem ◽  
Flow Model ◽  
Expansion Method ◽  
Pso Algorithm ◽  
Photovoltaic System ◽  
System Generation ◽  
Probabilistic Power Flow ◽  
The Cost

With the distributed generation such as photovoltaic power system (PVS) is largely introduced into power grid, some significant problems such as system instability problem increase seriously. In order to make full use of PVS and make sure the voltage exceeding probability is limited within a certain range to ensure the power quality, as well as consider the cost of access device, the suitable PVS access node and capacity is important. Based on this problem, this paper establishes the probabilistic power flow model of PVS by introducing the combined Cumulants and the Gram-Charlier expansion method. Also, to solve the nonlinear combinatorial optimization problem, this paper uses PSO algorithm. Finally to get the suitable PVS access node and capacity, also calculate the solution of voltage exceeding probability.

Optimization of the Robot Calibration Process

1992 ◽  
Author(s):  
G. Zak ◽  
R. G. Fenton ◽  
B. Benhabib
Keyword(s):  
Optimization Problem ◽  
Kinematic Model ◽  
Optimization Procedure ◽  
Calibration Procedure ◽  
Residual Error ◽  
Industrial Robots ◽  
Multiple Objective Optimization ◽  
Robot Calibration ◽  
Calibration Process ◽  
The Cost

Abstract Most industrial robots cannot be off-line programmed to carry out a task accurately, unless their kinematic model is suitably corrected through a calibration procedure. However, proper calibration is an expensive and time-consuming procedure due to the highly accurate measurement equipment required and due to the significant amount of data that must be collected. To improve the efficiency of robot calibration, an optimization procedure is proposed in this paper. The objective of minimizing the cost of the calibration is combined with the objective of minimizing the residual error after calibration in one multiple-objective optimization. Prediction of the residual error for a given calibration process presents the main difficulty for implementing the optimization. It is proposed that the residual error is expressed as a polynomial function. This function is obtained as a result of fitting a response surface to either experimental or simulated sample estimates of the residual error. The optimization problem is then solved by identifying a reduced set of possible solutions, thus greatly simplifying the decision maker’s choice of an effective calibration procedure. An application example of this method is also included.

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

2021 ◽  
Vol 12 (4) ◽  
pp. 98-116
Author(s):  
Noureddine Boukhari ◽  
Fatima Debbat ◽  
Nicolas Monmarché ◽  
Mohamed Slimane
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Local Optima ◽  
Portfolio Optimization Problem

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

scholarly journals Cloud Brokering with Bundles: Multi-objective Optimization of Services Selection

2019 ◽  
Vol 44 (4) ◽  
pp. 407-426
Author(s):  
Jedrzej Musial ◽  
Emmanuel Kieffer ◽  
Mateusz Guzek ◽  
Gregoire Danoy ◽  
Shyam S. Wagle ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Real Data ◽  
Cloud Service ◽  
Optimal Choice ◽  
Cloud Services ◽  
Multi Objective Optimization ◽  
Problem Instances ◽  
The Cost ◽  
Special Case ◽  
Single Objective

Abstract Cloud computing has become one of the major computing paradigms. Not only the number of offered cloud services has grown exponentially but also many different providers compete and propose very similar services. This situation should eventually be beneficial for the customers, but considering that these services slightly differ functionally and non-functionally -wise (e.g., performance, reliability, security), consumers may be confused and unable to make an optimal choice. The emergence of cloud service brokers addresses these issues. A broker gathers information about services from providers and about the needs and requirements of the customers, with the final goal of finding the best match. In this paper, we formalize and study a novel problem that arises in the area of cloud brokering. In its simplest form, brokering is a trivial assignment problem, but in more complex and realistic cases this does not longer hold. The novelty of the presented problem lies in considering services which can be sold in bundles. Bundling is a common business practice, in which a set of services is sold together for the lower price than the sum of services’ prices that are included in it. This work introduces a multi-criteria optimization problem which could help customers to determine the best IT solutions according to several criteria. The Cloud Brokering with Bundles (CBB) models the different IT packages (or bundles) found on the market while minimizing (maximizing) different criteria. A proof of complexity is given for the single-objective case and experiments have been conducted with a special case of two criteria: the first one being the cost and the second is artificially generated. We also designed and developed a benchmark generator, which is based on real data gathered from 19 cloud providers. The problem is solved using an exact optimizer relying on a dichotomic search method. The results show that the dichotomic search can be successfully applied for small instances corresponding to typical cloud-brokering use cases and returns results in terms of seconds. For larger problem instances, solving times are not prohibitive, and solutions could be obtained for large, corporate clients in terms of minutes.

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