【作者】 张丽丽；

【导师】 邱启荣；

【作者基本信息】 华北电力大学(北京) ， 应用数学， 2017， 硕士

【摘要】 在最优化理论与算法中,最小二乘问题作为重要的分支广泛应用于物理、统计与经济等研究领域。而且,在生活中的许多实际问题都是最小二乘问题,因此对于最小二乘问题的算法与应用进行研究是非常有意义的。随着最小二乘问题应用的愈加广泛,对于其算法的研究也就显得尤为重要,近年来出现了很多基于最小二乘的新算法。本文上半部分研究的是最小二乘问题的算法,主要对线性最小二乘和非线性最小二乘问题的算法进行研究,根据约束条件和目标函数的结构特点,进行归类分析,为新算法的提出准备理论依据,也使下一步的研究方向更加明确。论文的后半部分是最小二乘问题的应用研究,本文针对接地网腐蚀诊断这一典型的非线性最小二乘模型,设计了使用最小二乘算法进行局部调优的粒子群算法。本文首先在基本模型的基础上建立了删除冗余的接地网模型,并给出了相应的删除冗余算法,极大程度的提高了计算效率。然后对简化模型运用本文给出的算法进行诊断。最后对所给算法进行仿真模拟,结果显示应用本文给出的算法能够简化模型并进行诊断,从而说明了算法的可行性。更多还原

【Abstract】 In the optimization theory and algorithm,least squares problems are widely used as important branches of physics,statistics and economic research.Moreover,many practical problems in life are least squares problems,so the study of least squares algorithm and application is very meaningful.With the rapid development and extensive application of the least squares problem,the research of the algorithm becomes more and more important.In recent years,a lot of new algorithms based on least squares have appeared.In the first part of this paper,the algorithm of least squares problem is studied.The algorithms of linear least squares and nonlinear least squares are studied.According to the structural characteristics of objective function and constraint condition,the classification analysis is carried out.To prepare the theoretical basis,but also to make the direction of the next step more clearly.In the second part of the paper,the least squares problem is studied.In this paper,a local least squares PSO algorithm is designed to solve the problem of the typical nonlinear least squares model.Based on the basic model,the paper deletes the redundant ground network model and designs the corresponding deletion redundancy algorithm,which greatly improves the computing efficiency.Then,the simplified model is diagnosed by using the algorithm given in this paper.Finally,the simulation results show that the proposed algorithm can simplify the model and make the diagnosis,and the feasibility of the algorithm is proved.更多还原