稀疏化鲁棒最小二乘支持向量机与多目标遗传优化

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，针对标准LS-SVR 的目标函数没有正则化项、鲁棒性差的问题，将IGGIII 权函数引入稀疏化后的S-LS-SVR 模型，进行鲁棒性改进，得到鲁棒性较强的R-S-LS-SVR 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(NSGA-II)优化R-S-LS-SVR 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。工业试验及比较分析验证了所提方法的有效性和先进性。

关键词 鲁棒LS-SVR；稀疏建模；NSGA-II；多目标评价指标；硅含量

Soft-sensor Modeling of Silicon Content in Hot Metal Based on Sparse Robust LS-SVR and Multi-objective Optimization

ABSTRACT To solve the problem that the parameters of silicon content ([Si]) of hot mental is difficult to be detected directly and obtained by manual analysis, which brings large time delay, a method of sparse and robust least squares support vector regression (R-S-LS-SVR) is proposed to establish the dynamic modeling of [Si] with the help of multi-objective genetic optimization of model parameters. 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, the maximal independent set of sample data in feature space mapping set is extracted to realize the sparse of training sample set and reduce the computational complexity of modeling; Next, in view of the problem that the standardLS-SVR has no regularization term, a method to improve the modeling robustness is proposed by introducing IGGIII weightingfunction into the obtained S-LS-SVR model; Last, the multi-objective evaluation index that synthesizes the modeling residue and the estimated trend is presented to compensate for the deficiency of the single RMSE index. Based on it, an on-line soft sensor model of the hot metal [Si] with the optimal parameters is obtained by using the multi-objective genetic algorithm (NSGA-II) with the non-dominated sort and elitist strategy. Industrial verification and analysis show that the the effectiveness and superiority of the proposed method.

高炉炼铁是钢铁生产中的重要单元，其作用就是将固态的铁矿石通过复杂高温、高压等物理化学变化和多相多场耦合效应，在焦炭、煤气等作用下还原成液态的铁水。如图1 所示，一个典型的高炉炼铁系统主要由高炉本体、上料系统、送风系统、高炉烟气净化系统、渣铁处理系统和喷吹燃料系统等组成[1]。由于炼铁高炉内部在高温、高压的条件下进行着复杂的气-固、气-液、固-固、固-液等多相转换，众多变量和参数之间错综复杂、相互耦合，被公认为是最复杂的逆流反应器。一直以来，高炉炼铁过程的建模、控制与优化是维持高炉稳定顺行、高产、优质、低耗的重要手段[1]。目前，由于测量手段的限制，反映铁水质量和高炉热状态的关键指标——硅含量([Si])的测量一般仍采用人工定期抽样化验的方式进行，由于人工检测的滞后性和不精确性，使得基于[Si]质量参数的高炉炉况判断和高炉操作异常困难。因此，实现优质、低耗的高炉运行优化与控制就必须实现铁水[Si]质量参数的在线估计或软测量。

高炉炼铁过程的上述复杂动态特性，使得用于铁水[Si]在线估计的机理模型不易建立。对于难以机理建模的复杂工业过程，数据驱动的智能建模和统计建模受到了越来越广泛的关注[2]。王义康等提出了基于混沌时间序列的铁水[Si]支持向量回归模型(SVR)，在±0.1 误差内的命中率大88%，有较好的模型预测能力[3]；Henrik Saxen建立了可实现周期性铁水[Si]预测的离散时间序列模型，将模型的线性部分与非线性部分分别