基于慢特征分析与最小二乘支持向量回归集成的草酸钴合成过程粒度预报

doi:10.11949/0438-1157.20231394

摘要/Abstract

摘要：

草酸钴合成过程是钴湿法冶炼的关键单元操作，其粒度分布是重要的质量指标，然而难以在线实时测量。同时，草酸钴合成过程通常存在非线性、多约束和慢时变特征。因此，提出一种集成慢特征分析（slow feature analysis，SFA）与最小二乘支持向量回归（least square support vector regression，LSSVR）的草酸钴粒度预报模型对草酸钴合成过程质量指标实现在线测量。在该方法中，首先，SFA方法可以有效地捕获过程的慢特征向量，解决慢时变问题；然后，利用LSSVR方法建立慢特征与粒度之间的非线性关系模型，进而实现质量指标在线预报。最后，应用非线性的数值案例以及草酸钴合成过程数据，验证该方法的有效性。实验结果显示：相较于单一的径向基函数神经网络（radial basis function neural network，RBFNN）、LSSVR预测模型以及SFA与NN相结合的预报模型，所提方法在数值案例中的预测精度分别提升了13.31%、2.26%、1.72%；在草酸钴合成过程中的预测精度分别提升了13.27%、9.96%、8.92%。

关键词: 草酸钴合成过程, 软测量, 慢特征分析, 最小二乘支持向量回归, 化学过程, 预测, 神经网络

Abstract:

Cobalt oxalate synthesis process is a key unit operation of cobalt hydrometallurgy, and its particle size distribution is an important quality index. However, it is difficult to measure online in real-time. At the same time, the synthesis process of cobalt oxalate usually has the characteristics of nonlinearity, multiple constraints and slow time variation. In this paper, a cobalt oxalate particle size prediction model integrating slow feature analysis and least square support vector regression was proposed to achieve online measurement of particle size cobalt oxalate synthesis process. In this method, first, the SFA method can effectively capture the slow feature vector of the process and solve the slow time-varying problem. Then, the LSSVR method is used to establish a nonlinear relationship model between slow features and particle size, and then realize the online prediction of quality indicators. Finally, a nonlinear numerical case and data on the synthesis process of cobalt oxalate are used to verify the effectiveness of the proposed method. The experimental results show that compared with the single radial basis function neural network (RBFNN), LSSVR prediction model and the combined prediction model of SFA and NN, the prediction accuracy of the proposed method in numerical cases is improved by 13.31%, 2.26% and 1.72% respectively. The prediction accuracy of cobalt oxalate synthesis is improved by 13.27%, 9.96% and 8.92%, respectively.

Key words: cobalt oxalate synthesis process, soft sensor, slow feature analysis, least squares support vector regression, chemical processes, prediction, neural networks

中图分类号:

TH89

张晗, 张淑宁, 刘珂, 邓冠龙. 基于慢特征分析与最小二乘支持向量回归集成的草酸钴合成过程粒度预报[J]. 化工学报, 2024, 75(6): 2313-2321.

Han ZHANG, Shuning ZHANG, Ke LIU, Guanlong DENG. Particle size prediction of cobalt oxalate synthesis process based on slow feature analysis and least squares support vector regression[J]. CIESC Journal, 2024, 75(6): 2313-2321.

图/表 12

图1 草酸钴合成工艺图

Fig.1 Diagram of cobalt oxalate synthesis process

表1 不同变量对应的参数值

Table 1 Parameter values for different variables

变量	数值
$C o C l 2$ 的浓度/(mol·m^-3)	1089.6~1111.6
$N H 4 2 C 2 O 4$ 的浓度/(mol·m^-3)	1676.6~1710.4
$C o C l 2$ 的初始体积/m³	1.40
温度/K	325
K_b	1.3621×10⁴
K_g	1.5840×10⁴
k_b/(s^-1·μm^-3)	6.21×10³¹
k_g/(s^-1·μm)	2.70×10¹⁴

表1 不同变量对应的参数值

Table 1 Parameter values for different variables

变量	数值
$C o C l 2$ 的浓度/(mol·m^-3)	1089.6~1111.6
$N H 4 2 C 2 O 4$ 的浓度/(mol·m^-3)	1676.6~1710.4
$C o C l 2$ 的初始体积/m³	1.40
温度/K	325
K_b	1.3621×10⁴
K_g	1.5840×10⁴
k_b/(s^-1·μm^-3)	6.21×10³¹
k_g/(s^-1·μm)	2.70×10¹⁴

图2 过程参数对平均粒径的影响

Fig.2 Effect of process parameters on average particle size

图3 SFA-LSSVR软测量模型的整体框架

Fig.3 The overall framework of the SFA-LSSVR soft sensor model

图4 PSO-LSSVR模型结构

Fig.4 Structure of the PSO-LSSVR model

图5 输入函数与输出函数

Fig.5 Input and output functions

图6 累计贡献率

Fig.6 Cumulative contribution rate

图7 经SFA提取后的两个特征

Fig.7 Two features extracted by SFA

表2 数值案例中不同方法的回归结果

Table 2 Regression results of different methods in numerical cases

方法	R²	RMSE
RBFNN	0.8579	1.2170
LSSVR	0.9685	0.4469
SFA-RBFNN	0.9739	0.4567
SFA-LSSVR	0.9911	0.2384

图8 SFA-LSSVR和SFA-RBFNN回归预测的结果比较

Fig.8 Comparison of SFA-LSSVR and SFA-RBFNN regression predictions

图9 两种方法回归预测结果的比较

Fig.9 Comparison of the results of the two methods of regression prediction

表3 草酸钴合成过程中不同方法的回归结果

Table 3 Regression results of different methods in the synthesis of cobalt oxalate

方法	R²	RMSE
RBFNN	0.8496	0.0877
LSSVR	0.8827	0.0736
SFA-RBFNN	0.8931	0.0710
SFA-LSSVR	0.9823	0.0479

参考文献 30

1	Chu F, Zhao X, Yao Y, et al. Transfer learning for batch process optimal control using LV-PTM and adaptive control strategy[J]. Journal of Process Control, 2019, 81: 197-208.
2	Zhang S N, Deng G L, Wang F L. Active learning strategy for online prediction of particle size distribution in cobalt oxalate synthesis process[J]. IEEE Access, 1809, 7: 40810-40821.
3	Yan W W, Tang D, Lin Y J. A data-driven soft sensor modeling method based on deep learning and its application[J]. IEEE Transactions on Industrial Electronics, 2017, 64(5): 4237-4245.
4	Zhang S N, Chu F, Deng G L, et al. Soft sensor model development for cobalt oxalate synthesis process based on adaptive Gaussian mixture regression[J]. IEEE Access, 2019, 7: 118749-118763.
5	Yuan X F, Ge Z Q, Song Z H. Locally weighted kernel principal component regression model for soft sensing of nonlinear time-variant processes[J]. Industrial & Engineering Chemistry Research, 2014, 53(35): 13736-13749.
6	Yuan X F, Wang Y L, Yang C H, et al. Probabilistic density-based regression model for soft sensing of nonlinear industrial processes[J]. Journal of Process Control, 2017, 57: 15-25.
7	Ren J C, Liu D, Wan Y. Modeling and application of Czochralski silicon single crystal growth process using hybrid model of data-driven and mechanism-based methodologies[J]. Journal of Process Control, 2021, 104: 74-85.
8	Kalmár C, Turányi T, Zsély I G, et al. The importance of chemical mechanisms in sonochemical modelling[J]. Ultrasonics Sonochemistry, 2022, 83: 105925.
9	Chang S C, Chen X, Zhao C H. Flexible clockwork recurrent neural network for multirate industrial soft sensor[J]. Journal of Process Control, 2022, 119: 86-100.
10	张雷. 基于数据驱动的复杂工业过程软测量方法研究与应用[D]. 长沙: 湖南大学, 2019.
	Zhang L. Research and application of data-driven soft sensor method for complex industrial processes[D]. Changsha: Hunan University, 2019.
11	Yao L, Ge Z Q. Refining data-driven soft sensor modeling framework with variable time reconstruction[J]. Journal of Process Control, 2020, 87: 91-107.
12	Feng L J, Zhao C H, Huang B. Adversarial smoothing tri-regression for robust semi-supervised industrial soft sensor[J]. Journal of Process Control, 2021, 108: 86-97.
13	Griesing-Scheiwe F, Shardt Y A W, Perez-Zuniga G, et al. Soft sensor design for variable time delay and variable sampling time[J]. Journal of Process Control, 2020, 92: 310-318.
14	田业. 面向复杂流程工业的数据驱动软测量建模研究及应用[D]. 北京: 北京化工大学, 2023.
	Tian Y. Research and application of data-driven soft sensor modeling for complex process industry[D]. Beijing: Beijing University of Chemical Technology, 2023.
15	Jade A M, Srikanth B, Jayaraman V K, et al. Feature extraction and denoising using kernel PCA[J]. Chemical Engineering Science, 2003, 58(19): 4441-4448.
16	Chiplunkar R, Huang B. Output relevant slow feature extraction using partial least squares[J]. Chemometrics and Intelligent Laboratory Systems, 2019, 191: 148-157.
17	Zamprogna E, Barolo M, Seborg D E. Optimal selection of soft sensor inputs for batch distillation columns using principal component analysis[J]. Journal of Process Control, 2005, 15(1): 39-52.
18	Geladi P, Kowalski B R. Partial least-squares regression: a tutorial[J]. Analytica Chimica Acta, 1986, 185: 1-17.
19	Liu X Q, Li K, McAfee M, et al. Improved nonlinear PCA for process monitoring using support vector data description[J]. Journal of Process Control, 2011, 21(9): 1306-1317.
20	Che Y P, Zhao Z G, Wang Z G, et al. Iterative learning model predictive control for multivariable nonlinear batch processes based on dynamic fuzzy PLS model[J]. Journal of Process Control, 2022, 119: 1-12.
21	Chitralekha S B, Shah S L. Application of support vector regression for developing soft sensors for nonlinear processes[J]. The Canadian Journal of Chemical Engineering, 2010, 88(5): 696-709.
22	Alaei H K, Salahshoor K. The design of new soft sensors based on PCA and a neural network for parameters estimation of a petroleum reservoir[J]. Petroleum Science and Technology, 2012, 30(22): 2294-2305.
23	Mei C L, Yang M, Shu D X, et al. Soft sensor based on Gaussian process regression and its application in erythromycin fermentation process[J]. Chemical Industry and Chemical Engineering Quarterly, 2016, 22(2): 127-135.
24	Zhang S N, Wang F L, He D K, et al. Batch-to-batch control of particle size distribution in cobalt oxalate synthesis process based on hybrid model[J]. Powder Technology, 2012, 224: 253-259.
25	Jia R D, Mao Z Z, He D K, et al. Hierarchical batch-to-batch optimization of cobalt oxalate synthesis process based on data-driven model[J]. Chemical Engineering Research and Design, 2019, 144: 185-197.
26	Meng Y M, Yu S S, Zhang J L, et al. Hybrid modeling based on mechanistic and data-driven approaches for cane sugar crystallization[J]. Journal of Food Engineering, 2019, 257: 44-55.
27	Grondin-Perez B, Benne M, Damour C, et al. On-line estimation of mother liquor purity during the final stage of a cane sugar crystallization plant using neural network model[J]. International Sugar Journal, 2009, 111(1332): 751-756.
28	Wiskott L, Sejnowski T J. Slow feature analysis: unsupervised learning of invariances[J]. Neural Computation, 2002, 14(4): 715-770.
29	Zhang M, Zhou L, Jie J, et al. Soft sensor development based on quality-relevant slow feature analysis and Bayesian regression with application to propylene polymerization[J]. Journal of Sensors, 2021, 2021: 9985747.
30	Corrigan J, Zhang J. Developing accurate data-driven soft-sensors through integrating dynamic kernel slow feature analysis with neural networks[J]. Journal of Process Control, 2021, 106: 208-220.

[1]	黎宏陶, 王振雷, 王昕. 基于即时学习的改进条件高斯回归软测量[J]. 化工学报, 2024, 75(6): 2299-2312.
[2]	陈思睿, 毕景良, 王雷, 李元媛, 陆规. 气液两相流流型特征无监督提取的卷积自编码器：机理及应用[J]. 化工学报, 2024, 75(3): 847-857.
[3]	张领先, 刘斌, 邓琳, 任宇航. 基于改进TSO优化Xception的PEMFC故障诊断[J]. 化工学报, 2024, 75(3): 945-955.
[4]	董益斌, 熊敬超, 王敬宇, 汪守康, 王亚飞, 黄群星. 融合激光雷达料位测算的锅炉燃烧优化模型预测控制[J]. 化工学报, 2024, 75(3): 924-935.
[5]	蒙西, 王岩, 孙子健, 乔俊飞. 基于注意力模块化神经网络的城市固废焚烧过程氮氧化物排放预测[J]. 化工学报, 2024, 75(2): 593-603.
[6]	肖拥君, 时兆翀, 万仁, 宋璠, 彭昌军, 刘洪来. 反向传播神经网络用于预测离子液体的自扩散系数[J]. 化工学报, 2024, 75(2): 429-438.
[7]	王林, 江荣鼎, 张春晓, 李修真, 谈莹莹. 含R1234yf混合工质汽液相平衡的混合规则评估与预测研究[J]. 化工学报, 2024, 75(2): 475-483.
[8]	刘起超, 张世博, 周云龙, 李昱庆, 陈聪, 冉议文. 起伏振动水平管气液两相流型及转变机理[J]. 化工学报, 2024, 75(2): 493-504.
[9]	尹刚, 钱中友, 曹文琦, 全鹏程, 许亨权, 颜非亚, 王民, 向禹, 向冬梅, 卢剑, 左玉海, 何文, 卢润廷. 基于Adaboost-PSO-SVM的铝电解槽健康状态诊断方法研究[J]. 化工学报, 2024, 75(1): 354-365.
[10]	温凯杰, 郭力, 夏诏杰, 陈建华. 一种耦合CFD与深度学习的气固快速模拟方法[J]. 化工学报, 2023, 74(9): 3775-3785.
[11]	尹刚, 李伊惠, 何飞, 曹文琦, 王民, 颜非亚, 向禹, 卢剑, 罗斌, 卢润廷. 基于KPCA和SVM的铝电解槽漏槽事故预警方法[J]. 化工学报, 2023, 74(8): 3419-3428.
[12]	诸程瑛, 王振雷. 基于改进深度强化学习的乙烯裂解炉操作优化[J]. 化工学报, 2023, 74(8): 3429-3437.
[13]	闫琳琦, 王振雷. 基于STA-BiLSTM-LightGBM组合模型的多步预测软测量建模[J]. 化工学报, 2023, 74(8): 3407-3418.
[14]	徐野, 黄文君, 米俊芃, 申川川, 金建祥. 多源信息融合的离心式压缩机喘振诊断方法[J]. 化工学报, 2023, 74(7): 2979-2987.
[15]	郭雨莹, 敬加强, 黄婉妮, 张平, 孙杰, 朱宇, 冯君炫, 陆洪江. 稠油管道水润滑减阻及压降预测模型修正[J]. 化工学报, 2023, 74(7): 2898-2907.