Equilibrium analysis of multibody dynamic systems using genetic algorithm in comparison with constrained and unconstrained optimization techniques

In this paper, an optimization procedure for path generation synthesis of the slider-crank mechanism will be presented. The proposed approach is based on a hybrid strategy, mixing local and global optimization techniques. Regarding the local optimization scheme, based on the null gradient condition, a novel methodology to solve the resulting non-linear equations is developed. The solving procedure consists of decoupling two subsystems of equations which can be solved separately and following an iterative process. In relation to the global technique, a multi-start method based on a genetic algorithm is implemented. The fitness function incorporated in the genetic algorithm will take as arguments the set of dimensional parameters of the slider-crank mechanism. Several illustrative examples will prove the validity of the proposed optimization methodology, in some cases achieving an even better result compared to mechanisms with a higher number of dimensional parameters, such as the four-bar mechanism or the Watt’s mechanism.

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Modeling and Solution Techniques Used for Hydro Generation Scheduling

Water ◽

10.3390/w11071392 ◽

2019 ◽

Vol 11 (7) ◽

pp. 1392 ◽

Cited By ~ 4

Author(s):

Iram Parvez ◽

JianJian Shen ◽

Mehran Khan ◽

Chuntian Cheng

Keyword(s):

Genetic Algorithm ◽

Dynamic Programming ◽

Stochastic Programming ◽

Short Interval ◽

Optimization Techniques ◽

Mixed Integer ◽

Fuzzy Logics ◽

Spinning Reserve ◽

Lagrange Relaxation ◽

Generation Scheduling

The hydro generation scheduling problem has a unit commitment sub-problem which deals with start-up/shut-down costs related hydropower units. Hydro power is the only renewable energy source for many countries, so there is a need to find better methods which give optimal hydro scheduling. In this paper, the different optimization techniques like lagrange relaxation, augmented lagrange relaxation, mixed integer programming methods, heuristic methods like genetic algorithm, fuzzy logics, nonlinear approach, stochastic programming and dynamic programming techniques are discussed. The lagrange relaxation approach deals with constraints of pumped storage hydro plants and gives efficient results. Dynamic programming handles simple constraints and it is easily adaptable but its major drawback is curse of dimensionality. However, the mixed integer nonlinear programming, mixed integer linear programming, sequential lagrange and non-linear approach deals with network constraints and head sensitive cascaded hydropower plants. The stochastic programming, fuzzy logics and simulated annealing is helpful in satisfying the ramping rate, spinning reserve and power balance constraints. Genetic algorithm has the ability to obtain the results in a short interval. Fuzzy logic never needs a mathematical formulation but it is very complex. Future work is also suggested.

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Direct Differentiation Methods for the Design Sensitivity of Multibody Dynamic Systems

Volume 3: 22nd Design Automation Conference ◽

10.1115/96-detc/dac-1087 ◽

1996 ◽

Author(s):

Radu Serban ◽

Jeffrey S. Freeman

Keyword(s):

Sensitivity Analysis ◽

Dynamic Systems ◽

Design Sensitivity ◽

Differential Algebraic Equations ◽

Mechanism Analysis ◽

Algebraic Equations ◽

First Order ◽

Direct Differentiation ◽

Multibody Dynamic ◽

Standard Techniques

Abstract Methods for formulating the first-order design sensitivity of multibody systems by direct differentiation are presented. These types of systems, when formulated by Euler-Lagrange techniques, are representable using differential-algebraic equations (DAE). The sensitivity analysis methods presented also result in systems of DAE’s which can be solved using standard techniques. Problems with previous direct differentiation sensitivity analysis derivations are highlighted, since they do not result in valid systems of DAE’s. This is shown using the simple pendulum example, which can be analyzed in both ODE and DAE form. Finally, a slider-crank example is used to show application of the method to mechanism analysis.

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Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

10.1115/detc2021-68777 ◽

2021 ◽

Author(s):

Adwait Verulkar ◽

Corina Sandu ◽

Daniel Dopico ◽

Adrian Sandu

Keyword(s):

Sensitivity Analysis ◽

Dynamic Systems ◽

Multibody Systems ◽

Friction Model ◽

Design Parameters ◽

Adjoint Sensitivity ◽

Joint Friction ◽

Multibody Dynamic ◽

Model Dynamics ◽

Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

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Optimization of the Parameters of RISE Feedback Controller Using Genetic Algorithm

Mathematical Problems in Engineering ◽

10.1155/2016/3863147 ◽

2016 ◽

Vol 2016 ◽

pp. 1-9

Author(s):

Fayiz Abu Khadra ◽

Jaber Abu Qudeiri ◽

Mohammed Alkahtani

Keyword(s):

Genetic Algorithm ◽

Numerical Simulations ◽

Control Algorithm ◽

Chaotic Systems ◽

Optimization Technique ◽

Optimization Techniques ◽

Algorithm Optimization ◽

External Disturbances ◽

Van Der Pol ◽

Control Methodology

A control methodology based on a nonlinear control algorithm and optimization technique is presented in this paper. A controller called “the robust integral of the sign of the error” (in short, RISE) is applied to control chaotic systems. The optimum RISE controller parameters are obtained via genetic algorithm optimization techniques. RISE control methodology is implemented on two chaotic systems, namely, the Duffing-Holms and Van der Pol systems. Numerical simulations showed the good performance of the optimized RISE controller in tracking task and its ability to ensure robustness with respect to bounded external disturbances.

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Numerical Integration of Multibody Dynamic Systems Involving Nonholonomic Equality Constraints

10.21203/rs.3.rs-339568/v1 ◽

2021 ◽

Author(s):

Sotirios Natsiavas ◽

Panagiotis Passas ◽

Elias Paraskevopoulos

Keyword(s):

Dynamic Systems ◽

Equations Of Motion ◽

Time Integration ◽

Nonholonomic Constraints ◽

Coupled System ◽

Weak Form ◽

Integration Scheme ◽

Motion Constraints ◽

Multibody Dynamic ◽

Time Integration Scheme

Abstract This work considers a class of multibody dynamic systems involving bilateral nonholonomic constraints. An appropriate set of equations of motion is employed first. This set is derived by application of Newton’s second law and appears as a coupled system of strongly nonlinear second order ordinary differential equations in both the generalized coordinates and the Lagrange multipliers associated to the motion constraints. Next, these equations are manipulated properly and converted to a weak form. Furthermore, the position, velocity and momentum type quantities are subsequently treated as independent. This yields a three-field set of equations of motion, which is then used as a basis for performing a suitable temporal discretization, leading to a complete time integration scheme. In order to test and validate its accuracy and numerical efficiency, this scheme is applied next to challenging mechanical examples, exhibiting rich dynamics. In all cases, the emphasis is put on highlighting the advantages of the new method by direct comparison with existing analytical solutions as well as with results of current state of the art numerical methods. Finally, a comparison is also performed with results available for a benchmark problem.

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