摘要
为了实现对空间直线度误差的精确、快速评定,研究了它的数学模型和逐次二次规划(SQP)算法。根据最小区域定义及数学规划理论,建立了空间直线度评定的非线性规划模型,指出了该模型实质上是多目标优化的问题,并将该优化问题转化成单目标优化问题。由于该非线性规划模型还是凸的、二次的,因此提出了用SQP法来实施。SQP法在评定过程中保留了模型中的非线性信息,对初始参数的要求低,且稳定、可靠、效率高。几个算例的结果均满足凸规划全局最优判别准则,精度达到10-3mm,耗时在0.4 s左右。结果有力地验证了上述结论。
In order to realize accurate and fast evaluation for spatial straightness, its mathematical model and Successive Quadratic Programming（SQP） algorithm were investigated. Based on the condition of minimum zone method, a nonlinear programming model was established for spatial straightness error evaluation. This nonlinear model was further proved to be a multi-target optimization problem in essence, and could be transformed into a single-target optimization problem. A unified and efficient SQP algorithm was proposed to solve the model. As the nonlinear programming model is convex and SQP algorithm can retain such nonlinear information, the algorithm has very loose requirements for initial parameters and shows its stable, reliable and highly efficient in optimization. Several experi- ments of spatial straightness error evaluation were carried out, the results can meet the requirements for convex programming＇s global optimization very well,the precision is 103 mm and consumed time is about 0.4 s, which has proved the above mentioned conclusion.
出处
《光学精密工程》
EI
CAS
CSCD
北大核心
2008年第8期1423-1428,共6页
Optics and Precision Engineering
基金
国家自然科学基金资助项目(No.60677043)
关键词
计量学
空间直线度
误差评定
最小区域
多目标优化
逐次二次规划法
metrology
spatial straightness
tion
Successive Quadratic Progerror evaluation
minimumramming（SQP） algorithmzone
multi-target optimiza
