Particle size prediction of cobalt oxalate synthesis process based on slow feature analysis and least squares support vector regression

doi:10.11949/0438-1157.20231394

Abstract

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

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

CLC Number:

TH89

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.

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.

Figures/Tables 12

Fig.1 Diagram of cobalt oxalate synthesis process

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

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

Fig.2 Effect of process parameters on average particle size

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

Fig.4 Structure of the PSO-LSSVR model

Fig.5 Input and output functions

Fig.6 Cumulative contribution rate

Fig.7 Two features extracted by SFA

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

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

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

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

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