A Multi-correlated Time-delay Estimation Method in the Blast Furnace Ironmaking Process Based on Time-series Correlation Matrix
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摘要: 高炉冶炼过程由炉料传输反应时间和冶炼单元在空间和时间分布上的差异带来的变量时延影响了数据的准确性和真实因果关系, 因此有效地估计过程变量间的时延信息, 并在时序上配准数据, 是后续过程建模、优化控制与性能评估的核心. 考虑到变量间时延的多重关联性, 提出了一种基于时序关联矩阵的时延参数估计方法. 首先, 根据过程变量的时延参数在时空上重构对应的时序关联矩阵, 并引入灰色关联分析量化时序矩阵的多重关联相关性; 接着, 考虑到穷举所有时序关联矩阵的时间复杂度, 提出了一种双尺度协同搜索策略的动态多群粒子群算法用于快速寻找最优的时延参数, 提出的粒子群算法能兼顾全局探索能力和局部探测能力并跳出局部最优解; 最后, 基于一个数值仿真和某钢铁厂2# 高炉的工业实验验证了所提时延参数估计方法的可行性和有效性, 且通过所提方法在时序上重构的数据能有效提高后续硅含量软测量模型性能.Abstract: Variable time-delay is brought by transportation and reaction time of materials and the different distributions of smelting units in spatial and temporal, which affects the accuracy and the actual causal relationship of collected data. Therefore, the estimation of variable time-delay information and the reconstruction of data in time series effectively are the key points of subsequent process modeling, optimal control, and performance evaluation. Considering the multiple correlations characteristic of variable time-delay, an estimation method based on a time-series correlation matrix is proposed. First, the time-series correlation matrix is reconstructed in time and space according to the time-delay parameters, where grey correlation analysis is used to quantify the multi-correlated correlation. Then, considering the number of time-series correlation matrices and the time complexity of the exhaustive method, a dynamic multi-swarm particle swarm optimization based on a double-scale collaborative search strategy is proposed to search for the optimal time-delay parameters. The proposed optimization algorithm can consider both global exploration and local exploitation ability and escape local optimal solutions. Finally, the feasibility and effectiveness of the proposed time-delay estimation method are verified by a numerical simulation and an industrial experiment of 2# blast furnace in a steel plant. In addition, a significant improvement can be observed in the performance of the soft-sensor model of silicon content with the reconstruction of data in time series.
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图 1 高炉三维仿真模拟图
Fig. 1 Three-dimensional simulation diagram of the blast furnace cast field
图 2 高炉炼铁过程中变时滞问题描述
Fig. 2 Illustration of variable time-delay problem in the blast furnace ironmaking process
图 3 基于DMS-PSO-CS算法的时延参数估计框架
Fig. 3 Time-delay parameter estimation framework based on DMS-PSO-CS algorithm
图 4 基于DMS-PSO-CS算法时延估计的铁水硅含量预测结果
Fig. 4 The prediction details of silicon content in molten iron with time-delay estimation based on DMS-PSO-CS algorithm
图 5 基于PSO算法时延估计的铁水硅含量预测结果
Fig. 5 The prediction details of silicon content in molten iron with time-delay estimation based on PSO algorithm
图 6 基于MIC算法时延估计的铁水硅含量预测结果
Fig. 6 The prediction details of silicon content in molten iron with time-delay estimation based on MIC algorithm
图 7 基于PCC算法时延估计的铁水硅含量预测结果
Fig. 7 The prediction details of silicon content in molten iron with time-delay estimation based on PCC algorithm
图 8 无时延估计的铁水硅含量预测结果
Fig. 8 The prediction details of silicon content in molten iron without time-delay estimation
表 1 数值仿真中基于不同方法估计的过程变量时延值
Table 1 The estimated variable time-delay values based on different methods in numerical simulation
变量 PCC MIC PSO DMS-PSO-CS $ \tau ' $ $ {x_1} $ 1 1 1 1 1 $ {x_2} $ 0 2 2 2 2 $ {x_3} $ 2 0 3 3 3 $ {x_4} $ 1 3 3 4 4 
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表 2 基于不同方法估计的过程变量时延参数
Table 2 The estimated process variable time-delayvalues based on different methods
变量 (单位) PCC MIC PSO DMS-PSO-CS 富氧率(wt%) 1 5 5 5 透气性指数$(\rm m^{3}/min \cdot kPa)$ 1 1 1 2 一氧化碳(wt%) 1 2 1 1 二氧化碳(wt%) 1 1 1 1 标准风速(m/s) 6 6 2 1 富氧流量$(\rm m^{3}/s)$ 1 3 6 1 冷风流量$(\rm m^{3}/min)$ 6 2 2 2 鼓风动能(J/s) 1 2 2 3 炉腹煤气量 (t) 6 1 2 2 炉腹煤气指数 6 2 2 2 顶压 (kPa) 1 3 1 4 富氧压力(kPa) 2 3 6 6 冷风压力 (kPa) 1 1 6 2 全压差(kPa) 1 2 2 2 热风压力(kPa) 1 1 5 2 实际风速 (m/s) 1 3 2 2 冷风温度 (°C) 1 6 1 1 热风温度 (°C) 1 6 2 2 顶温(°C) 1 5 1 2 顶温下降管 (°C) 1 1 2 6 阻力系数 1 1 2 1 鼓风湿度 ($ \rm g/m^{3} $) 3 6 1 1 本小时实际喷煤量(t/h) 2 1 1 3 上小时实际喷煤量 (t/h) 1 1 5 5 铁水温度 (°C) 1 1 1 1
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表 3 基于不同建模策略下的铁水硅含量软测量模型性能
Table 3 Soft-sensor model performance of silicon content in molten iron based on different modeling strategies
序号 建模策略 TrRMSE TrMAE TsRMSE TsMAE 训练时间 (s) 1 SDAE + DM-PSO-CS 0.0715 0.0530 0.0723 0.0542 12.2 $ \times $ 60 + 8 2 SDAE + PSO 0.0748 0.0565 0.0759 0.0574 12.4 $ \times $ 60 + 10 3 SDAE + MIC 0.0752 0.0562 0.0765 0.0575 12.3 $ \times $ 60 + 12 4 SDAE + PCC 0.0763 0.0561 0.0776 0.0573 12.2 $ \times $ 60 + 10 5 SVR + DM-PSO-CS 0.0775 0.0572 0.0792 0.0588 7 6 RVFLN + DM-PSO-CS 0.0769 0.0573 0.0782 0.0585 3 7 SDAE + 无时延估计 0.0826 0.0605 0.0840 0.0613 12.3 $ \times $ 60 + 9
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