工程科学学报，第38卷，第9期：1233-1241,2016年9月 Chinese Journal of Engineering,Vol.38,No.9:1233-1241,September 2016 D0l:10.13374/j.issn2095-9389.2016.09.006:http://journals.ustb.edu.cn 基于稀疏化鲁棒LS-SVR与多目标优化的铁水硅含量 软测量建模 郭东伟2》，周平12)四 1)东北大学流程工业综合自动化国家重点实验室，沈阳1108192)矿治过程自动控制技术国家重点实验室，北京102628 ☒通信作者，E-mail:zhouping(@mail.ncu.cdu.cn 摘要针对高炉炼铁过程的关键工艺指标一铁水硅含量]难以直接在线检测且化验过程滞后的问题，提出一种基于 稀疏化鲁棒最小二乘支持向量机(R-S-LS-SV)与多目标遗传参数优化的铁水[S]动态软测量建模方法.首先，针对标准 最小二乘支持向量机(LS一SVR)的拉格朗日乘子与误差项成正比导致最终解缺少稀疏性的问题，提取样本数据在特征空间映 射集的极大无关组来实现训练样本集的稀疏化，降低建模的计算复杂度：其次，标准最小二乘支持向量机的目标函数鲁棒性 不足的问题将GGⅢ加权函数引入稀疏化后的最小二乘支持向量机模型进行鲁棒性改进，得到鲁棒性较强的稀疏化鲁棒最 小二乘支持向量机模型：最后，针对常规均方根误差评价模型性能的不足，提出从建模误差与估计趋势评价建模性能的多目 标评价指标.在此基础上，利用非支配排序的带有精英策略的多目标遗传算法优化模型参数，从而获得具有最优参数的铁水 S]在线软测量模型.工业实验及比较分析验证了所提方法的有效性和先进性. 关键词炼铁：硅含量；建模：最小二乘法：支持向量机：多目标优化 分类号TP18 Soft-sensor modeling of silicon content in hot metal based on sparse robust LS-SVR and multi-objective optimization GUO Dong-eei,ZHOU Ping) 1)State Key Laboratory of Synthetical Automation for Process Industries,Northeastem University,Shenyang 110819,China 2)State Key Laboratory of Process Automation in Mining Metallurgy,Beijing 102628,China Corresponding author,E-mail:zhouping@mail.neu.edu.cn ABSTRACT To solve the problem that the parameter of silicon content [Si])in hot mental is difficult to be directly detected and obtained by manual analysis with large time delay,a method of sparse and robust least squares support vector regression (R-S-IS- SVR)was proposed to establish a dynamic model of [Si]with the help of the multi-objective genetic optimization of model parame- ters.First,owing to the issue that the Lagrange multiplier of the standard least squares support vector machine (LS-SVR)is directly proportional to the error term and solves the lack of sparsity,the maximal independent set of sample data in the feature space mapping set was extracted to realize the sparse of the training sample set and reduce the computational complexity of modeling.Next,in view of the problem that the standard least squares support vector machine has no regularization term,a method to improve the modeling ro- bustness was proposed by introducing the IGGIlI weighting function into the obtained sparse least squares support vector regression (S-IS-SVR)model.Last,the multi-objective evaluation index that synthesizes the modeling residue and the estimated trend was 收稿日期：2015-11-20 基金项目：国家自然科学基金资助项目(61473064：61290323：61333007)：中央高校基本科研业务费资助项目(N130108001):辽宁省教有厅 科技基金资助项目(120150186)工程科学学报，第 38 卷，第 9 期: 1233--1241，2016 年 9 月 Chinese Journal of Engineering，Vol． 38，No． 9: 1233--1241，September 2016 DOI: 10． 13374 /j． issn2095--9389． 2016． 09． 006; http: / /journals． ustb． edu． cn 基于稀疏化鲁棒 LS--SVＲ 与多目标优化的铁水硅含量 软测量建模 郭东伟1，2) ，周 平1，2)  1) 东北大学流程工业综合自动化国家重点实验室，沈阳 110819 2) 矿冶过程自动控制技术国家重点实验室，北京 102628  通信作者，E-mail: zhouping@ mail． neu． edu． cn 摘 要 针对高炉炼铁过程的关键工艺指标———铁水硅含量［Si］难以直接在线检测且化验过程滞后的问题，提出一种基于 稀疏化鲁棒最小二乘支持向量机( Ｒ--S--LS--SVＲ) 与多目标遗传参数优化的铁水［Si］动态软测量建模方法． 首先，针对标准 最小二乘支持向量机( LS--SVＲ) 的拉格朗日乘子与误差项成正比导致最终解缺少稀疏性的问题，提取样本数据在特征空间映 射集的极大无关组来实现训练样本集的稀疏化，降低建模的计算复杂度; 其次，标准最小二乘支持向量机的目标函数鲁棒性 不足的问题将 IGGIII 加权函数引入稀疏化后的最小二乘支持向量机模型进行鲁棒性改进，得到鲁棒性较强的稀疏化鲁棒最 小二乘支持向量机模型; 最后，针对常规均方根误差评价模型性能的不足，提出从建模误差与估计趋势评价建模性能的多目 标评价指标． 在此基础上，利用非支配排序的带有精英策略的多目标遗传算法优化模型参数，从而获得具有最优参数的铁水 ［Si］在线软测量模型． 工业实验及比较分析验证了所提方法的有效性和先进性． 关键词 炼铁; 硅含量; 建模; 最小二乘法; 支持向量机; 多目标优化 分类号 TP18 Soft-sensor modeling of silicon content in hot metal based on sparse robust LS--SVＲ and multi-objective optimization GUO Dong-wei 1，2) ，ZHOU Ping1，2)  1) State Key Laboratory of Synthetical Automation for Process Industries，Northeastern University，Shenyang 110819，China 2) State Key Laboratory of Process Automation in Mining ＆ Metallurgy，Beijing 102628，China  Corresponding author，E-mail: zhouping@ mail． neu． edu． cn 收稿日期: 2015--11--20 基金项目: 国家自然科学基金资助项目( 61473064; 61290323; 61333007) ; 中央高校基本科研业务费资助项目( N130108001) ; 辽宁省教育厅 科技基金资助项目( L20150186) ABSTＲACT To solve the problem that the parameter of silicon content ( ［Si］) in hot mental is difficult to be directly detected and obtained by manual analysis with large time delay，a method of sparse and robust least squares support vector regression ( Ｒ--S--LS-- SVＲ) was proposed to establish a dynamic model of ［Si］with the help of the multi-objective genetic optimization of model parame￾ters． First，owing to the issue that the Lagrange multiplier of the standard least squares support vector machine ( LS--SVＲ) is directly proportional to the error term and solves the lack of sparsity，the maximal independent set of sample data in the feature space mapping set was extracted to realize the sparse of the training sample set and reduce the computational complexity of modeling． Next，in view of the problem that the standard least squares support vector machine has no regularization term，a method to improve the modeling ro￾bustness was proposed by introducing the IGGIII weighting function into the obtained sparse least squares support vector regression ( S--LS--SVＲ) model． Last，the multi-objective evaluation index that synthesizes the modeling residue and the estimated trend was