A Competitive-Cooperative Game Method for Multi-Objective Optimization Design of a Horizontal Axis Wind Turbine Blade

Abstract

This paper presents a multi-objective optimization model of a wind turbine blade based on blade's parameterized finite element model, where annual energy production and blade mass are the objective functions, and aerodynamic and structural parameters are the design variables. In this study, the maximum axial thrust, strain, displacement, and first-order natural frequency of blade are selected as constraints. A novel competitive-cooperative game method is proposed to obtain the optimal preference solution. In this method, a new exploration method of player's strategy space named 'correlation analysis under fuzzy k-means clustering' is proposed, and the payoff functions are constructed according to competitive and cooperative behaviors. Two optimization schemes with preference objectives are obtained and all goals showed clear improvements over the initial solutions, and this method reveals the relationship between blade shape and desired performance. More deeply, dynamic sensitivities of various design variables to objective functions are obtained for different blade shapes. INDEX TERMS Competitive-cooperative game, parameterized finite element model of wind turbine blade, aerodynamic and structural design, dynamic sensitivity.

Using Genetic Algorithms and Core Values of Cooperative Games to Solve Fuzzy Multiobjective Optimization Problems

“…Alternatively, the approach by Lee [34] treated the two objective functions as a non-cooperative game with two players and tried to obtain the Nash equilibrium. Meng and Xie [35] formulated a competitive-cooperative game method to obtain the optimal preference solutions. A three-objective optimization problem was studied by Li et al [36] in which a three-players game was formulated.…”

Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems

“…Zhang et al [32] considered the subgame perfect Nash equilibrium to be the solutions of the models, and Yu et al [31] incorporated the genetic algorithm to obtain the solutions without converting the three-objective optimization problem into a single-objective optimization problem. Meng and Xie [33] considered a bi-objective optimization problem in which a competitive-cooperative game method was proposed to obtain the optimal preference solutions.…”