最小二乘支持向量机在U71Mn高锰钢表面粗糙度预测模型中的运用
庄曙东1,2，史柏迪*,1,2，陈天翔1，陈威1
（1.河海大学 机电工程学院，江苏 常州 213022；2.南京航空航天大学 江苏省精密与微细制造技术重点实验室，江苏 南京，213009）
摘要：获取了U71Mn高锰钢在特定主轴转速n、进给量f、铣削深度ap、铣削宽度ae加工条件下的表面粗糙度Ra的原始数据。基于留出法原则将原始数据依次随机分为两组，一组为训练集用于训练U71Mn高锰钢的预测模型；另一组数据为验证集用于验证模型，并且通过机器学习性能评价指标来确定模型的最终预测精确率。通过实际建模对比发现最小二乘支持向量机预测模型其拟合以及预测精度明显高于传统多元线性回归模型。最小二乘支持向量机（LSSVM）通过对原支持向量机算法（SVM）进行了算法改进，在算法中把原求解Lagrange乘子α不等式约束的二次规划（QP）问题，转化为等式约束即求解线性方程组，显著减少了计算机运算的时间复杂度。并且通过寻求结构化风险最小提高了学习机的泛化能力，在观测样本数量较小的情况下，容易实现经验风险和置信范围的最小化，使模型对未知样本有良好的鲁棒性与预测精度。
关键词：U71Mn高锰钢；最小二乘支持向量机；表面粗糙度预测模型
中图分类号：TG84 文献标志码：A doi：10.3969/j.issn.1006-0316.2020.06.003
文章编号：1006－0316 (2020) 06－0017－08
Application of Least Squares Support Vector Machine to Prediction Models of Surface Roughness of U71Mn High Manganese Steel
ZHUANG Shudong1,2，SHI Baidi1,2，CHEN Tianxiang1，CHEN Wei1
( 1.School of Mechanical and Electrical Engineering, Hohai University, Changzhou 213022, China; 2.Jiangsu Key Laboratory of Precision instruments, Nanjing University of Aeronautics and Astronautics，Nanjing 213009, China )
Abstract：The raw data of surface roughness Ra of U71Mn high manganese steel are obtained under the conditions of specific spindle speed n, feed rate f, milling depth ap and milling width ae. Based on the cross validation principle, the raw data are randomly divided into two groups: one is the training set to train the prediction models of U71Mn high manganese steel; the other is the validation set to verify the model, and the final prediction accuracy of the model is defined by the evaluation index of machine learning performance. By comparing the models, the present work finds that the prediction accuracy of least squares support vector machine (LSSVM) is significantly higher than the traditional multiple linear regression model. LSSVM improves algorithm of the original support vector machine (SVM). The quadratic programming (QP), which solves the constraint of Lagrange multiplier α inequality, is transformed into the equation constraint, that is, solving the linear equations, which significantly reduces the time complexity of computer operation. The generalization ability of the learning machine is improved by seeking the minimum structural risk. With small number of observation samples, the empirical risk and confidence range is likely to be minimized, which makes the model have good robustness and prediction accuracy.
Key words：U71Mn high manganese steel；prediction models of surface roughness；least squares support vector machine
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收稿日期：2019－12－11
基金项目：江苏省高校实验室研究会立项资助研究课题（GS2019YB18）；江苏省精密与微细制造技术重点实验室关于机械加工中精密制造的工艺、数学建模的研究课题；中央高校基本科研业务费（2018B44614）；教育部产学合作协同育人项目（20180269005）
作者简介：庄曙东（1970－）男，江苏常州人，博士，高级工程师，硕士生导师，主要研究方向为智能制造。*通信作者：史柏迪（1996－）男，江苏常州人，硕士研究生，主要研究方向为表面粗糙度预测，E-mail：sbdhaha413@outlook.com。
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