Optimal design of multi-parametric nonlinear systems using a parametric continuation based Genetic Algorithm approach

Abstract

In this paper, a procedure for the optimal design of multi-parametric nonlinear systems is presented which makes use of a parametric continuation strategy based on simple shooting method. Shooting method is used to determine the periodic solutions of the nonlinear system and multi-parametric continuation is then employed to trace the change in the system dynamics as the design parameters are varied. The information on the variation of system dynamics with the value of the parameter vector is then used to find out the exact parameter values for which the system attains the required response. This involves a multiparametric optimisation procedure which is accomplished by the coupling of parameter continuation with different search algorithms. Genetic Algorithm as well as Gradient Search methods are coupled with parametric continuation to develop an optimisation scheme. Furthermore, in the coupling of continuation and Genetic Algorithm, a "norm-minimising" strategy is developed and made use of minimising the use of continuation. The optimisation procedure developed is applied to the Duffing oscillator for the minimisation of the system acceleration with nonlinear stiffness and damping coefficient as the parameters and the results are reported. It is also briefly indicated how the pro-B. Balaram ( ) · posed method can be successfully used to tune nonlinear vibration absorbers.

A multi-parametric recursive continuation method for nonlinear dynamical systems

“…Since then, multi-parametric optimization was coupled with continuation, Kernevez et al [53] used a descent optimization algorithm coupled with a continuation method to perform the optimization of nonlinear systems. Later, Balaram et al [54] combined the method of Kernevez et al with a genetic algorithm in order to provide a global algorithm of optimization by continuation. They used this method to minimize the acceleration of a Duffing oscillator and to tune nonlinear vibration absorbers.…”

The new method of flatness pattern recognition based on GA–RBF–ARX and comparative research

“…GA is a highly efficient, parallel, global search method [17][18][19], and it imitates the biologic and evolutionary mechanisms and draws on Darwin's theory of evolution and Mendel's genetics [20]. Many traditional search methods are single-point search, but GA is used to deal with more than one individual in the group at the same time, which reflects the performance of global search and avoids falling into the local optimum in the search process.…”

Two New Conjugate Gradient Methods for Unconstrained Optimization

“…e conjugate gradient method (CGM for short) plays an important role in obtaining the numerical solution of the optimal control problem for nonlinear dynamic systems and other mathematical models [1,2]. In this paper, we study the nonlinear CGM for the following unconstrained optimization problem:…”