改进鲸鱼优化算法的空间直线度误差评定

Spatial Straightness Error Evaluation with Improved Whale Optimization Algorithm

空间直线度误差评定计算问题本质上属于非线性优化问题,采用传统的数学计算方法很难对其进行求解,且求解精度不高,而智能优化算法在求解该类问题具有较大的优势。因此,本文提出将改进鲸鱼优化算法应用于空间直线度误差评定,该方法满足最小区域条件。首先建立了空间直线度评定的最小区域法数学模型,得出空间直线度目标函数;其次阐述了基本鲸鱼优化算法的原理,并针对其不足,对鲸鱼优化算法的3方面进行改进,采用拉丁超立方体抽样方法初始化种群,增强了种群多样性,将非线性收敛因子取代基本鲸鱼优化算法中的线性收敛因子,并将非线性惯性权重引入鲸鱼优化算法中。通过仿真测试,该算法在收敛速度、精度和稳定性都得到了有效提高,最后,通过两个空间直线度误差评定实例进行验证,结果表明,改进的鲸鱼优化算法在评定精度上要比两端点连线法、鲸鱼优化算法、遗传算法和粒子群算法等算法都更具优势。

The spatial straightness error evaluation calculation problem is essentially a nonlinear optimization one,which is difficult to solve with the traditional mathematical calculation methods;its solution accuracy is not high.The intelligent optimization algorithm has great advantages in solving such problems.Therefore,we propose to apply the improved whale optimization algorithm to the spatial straightness error evaluation.Our method satisfies the minimum area condition.First,the mathematical model of the minimum area method for spatial straightness error evaluation is established,thus obtaining the objective function of spatial straightness.Secondly,the principles of the basic whale optimization algorithm are explained.Its shortcomings are addressed;three aspects of whale optimization algorithm are improved.The population using the Latin hypercube sampling are initialized;the population diversity is enhanced.The nonlinear convergence factor is replaced with the linear convergence factor in the basic whale optimization algorithm.The nonlinear inertia weight is introduced into the whale optimization algorithm.The simulation results show that the algorithm has been effectively improved in convergence speed,accuracy and stability.It is also verified by two examples of spatial straightness error evaluation.The results show that the improved whale optimization algorithm has more advantages in evaluation accuracy than the two-point connection method,the whale optimization algorithm,the genetic algorithm and the particle swarm optimization algorithm.