Soft-sensing of Pr/Nd component content under different single illumination conditions

doi:10.11949/j.issn.0438-1157.20180819

Abstract

Abstract:

It is known that due to the change of light condition on rare earth extraction industry, makes soft-sensing model for rare earth element content based on the color characteristics of the rare earth solution have larger error. First, the Grey Edge algorithm with parameter optimization is used to correct the image of rare earth solution under different illumination conditions to the standard illumination. Then, the first moment of H, S and I components in the HSI color space of the Pr/Nd solution image is used as a model. The weighted least squares support vector machine (WLSSVM) is used to model the component content. Finally, the simulation experiments of rare earth solution images under different illumination conditions are carried out. The simulation results show that the images of rare earth solutions under different illumination conditions can meet the high-accuracy and rapid requirements of element component content detection in rare earth extraction process.

Key words: extraction process, component content, color correction, parameter optimization, WLSSVM

摘要：

针对镨/钕稀土萃取工业生产现场光照条件变化导致具有颜色特征的镨/钕组分含量难以准确检测的问题，提出了一种基于单光照条件变化的组分含量软测量方法。首先，采用参数优化的Grey Edge算法，将不同光照条件下的稀土溶液图像校正到标准光照下；然后，以镨/钕溶液图像HSI颜色空间中的H、S、I分量一阶矩为模型的输入变量，利用加权最小二乘支持向量机（WLSSVM）建立组分含量软测量模型；最后采用工业数据对所提方法进行仿真实验，结果表明所提方法在不同光照条件下均能满足稀土萃取过程组分含量检测的准确度和快速性要求。

关键词: 萃取过程, 组分含量, 颜色校正, 参数优化, 加权最小二乘支持向量机

CLC Number:

TP 273

Jianyong ZHU, Xuqian ZHANG, Hui YANG, Rongxiu LU. Soft-sensing of Pr/Nd component content under different single illumination conditions[J]. CIESC Journal, 2019, 70(2): 780-788.

朱建勇, 张旭乾, 杨辉, 陆荣秀. 单光照条件变化的镨/钕元素组分含量软测量[J]. 化工学报, 2019, 70(2): 780-788.

Figures/Tables 17

Table 1 Illumination estimation algorithm under framework of Grey Edge

算法	标识	公式	假设
Max RGB	$e 0, ∞, 0$	$∫ \| f x \| ∞ d x 1 ∞ = k e$	颜色通道的最大响应是由场景中白色表面引起
Grey world	$e 0,1, 0$	$∫ f x d x = k x$	场景中所有物理表面的平均反射是无色差的
Shades of Grey	$e 0, p, 0$	$∫ \| f x \| p d x 1 p = k e$	场景中所有物理表面的平均反射是无色差的
1st order Grey Edge	$e 1, p, σ$	$∫ \| f x σ x \| p d x 1 p = k e$	场景中所有物理表面的平均反射的差分是无色差的
2nd order Grey Edge	$e 2, p, σ$	$∫ \| f x x σ x \| p d x 1 p = k e$	场景中所有物理表面的平均反射的差分是无色差的

Table 1 Illumination estimation algorithm under framework of Grey Edge

算法	标识	公式	假设
Max RGB	$e 0, ∞, 0$	$∫ \| f x \| ∞ d x 1 ∞ = k e$	颜色通道的最大响应是由场景中白色表面引起
Grey world	$e 0,1, 0$	$∫ f x d x = k x$	场景中所有物理表面的平均反射是无色差的
Shades of Grey	$e 0, p, 0$	$∫ \| f x \| p d x 1 p = k e$	场景中所有物理表面的平均反射是无色差的
1st order Grey Edge	$e 1, p, σ$	$∫ \| f x σ x \| p d x 1 p = k e$	场景中所有物理表面的平均反射的差分是无色差的
2nd order Grey Edge	$e 2, p, σ$	$∫ \| f x x σ x \| p d x 1 p = k e$	场景中所有物理表面的平均反射的差分是无色差的

Fig.1 The 36th series solution under different light conditions

Fig.4 Angle error of different algorithms under TL84

Fig.5 HSI value of uncorrected and corrected image under CWF

Fig.6 HSI value of uncorrected and corrected image under F

Table 2 Correction results under CWF illumination

算法参数	Median	Max	RMS
（0，∞，0）	7.3978	13.5225	7.366
（0，1，0）	5.3077	7.4289	5.3087
（0，6，0）	6.8189	9.4978	6.9954
（1，4，1）	4.7142	9.7849	5.3127
（2，4，1）	2.5971	6.6029	3.4595
本文方法	2.1123	5.7033	3.1383

Table 3 Correction results under TL84 illumination

算法参数	Median	Max	RMS
（0，∞，0）	2.0204	5.2705	2.2363
（0，1，0）	1.9071	2.3626	1.7108
（0，6，0）	2.2160	2.8259	1.9592
（1，3，2）	0.7482	2.1210	1.0725
（2，4，1）	2.6410	4.8058	2.9805
本文方法	0.4064	1.6542	0.5303

Table 4 Correction results under F illumination

算法参数	Median	Max	RMS
（0，∞，0）	11.1272	26.3815	11.8822
（0，1，0）	5.0768	6.5793	5.2294
（0，6，0）	6.5328	8.6094	6.7600
（1，4，1）	2.9674	7.7753	3.6093
（2，4，1）	7.2759	14.8727	7.8799
本文方法	1.8630	5.6311	2.6122

Fig.2 Angle error of different algorithms under CWF

Fig.3 Angle error by different algorithms under F

Table 5 Some parameters optimized by GA

级数	CWF	F	TL84
1	(2,10,3)	(1,4,1)	(0,1,7)
20	(1,9,3)	(1,3,1)	(0,12,7)
40	(2,4,1)	(1,12,1)	(1,2,6)
60	(2,4,1)	(2,4,2)	(2,9,3)
80	(2,1,2)	(0,1,7)	(2,8,6)
98	(2,4,1)	(2,14,3)	(2,3,3)

Fig.7 HSI value of uncorrected and corrected image under TL84

Fig.8 Output result of component content soft-sensing model

Fig.9 Relative error of component content soft-sensing model

Table 6 Parameters of soft-sensing model

建模方法	γ	σ	w_h	w_s	w_i
文献[7]	47.3666	0.6251	—	—	—
LSSVM方法	47.3666	0.6251	—	—	—
LSSVM方法	165.7639	0.7224	—	—	—
本文方法	451.7836	0.5606	0.6755	0.2219	0.1026

Table 7 Comparison of model performance

方法	MEANRE	MAXRE	RMSE
文献[6]	4.3829	23.8627	8.1483
文献[7]	4.6204	25.0991	8.0426
WLSSVM	3.8204	21.13	7.086
CC-文献[6]	2.5032	14.8014	4.8747
CC-文献[7]	2.2765	9.4445	3.3919
CC-LSSVM	1.2974	5.2151	1.9129
CC-WLSSVM	1.2667	3.7082	1.7062

a_kj	——第k个染色体第j位
a_lj	——第l个染色体第j位
F_i	——个体i的适应度值
G_max	——最大进化次数
g	——当前迭代次数
H	——HSI颜色空间的色彩
I	——HSI颜色空间的强度
k	——光照校正系数
k_r,k_g,k_b	——RGB三通道光照校正系数
N	——种群个体数目
S	——HSI颜色空间的饱和度
γ	——惩罚系数
ρ_t	——第t个样本的真实值
$ρ ? t$	——第t个样本的模型预测值
σ	——核函数宽度

a_kj	——第k个染色体第j位
a_lj	——第l个染色体第j位
F_i	——个体i的适应度值
G_max	——最大进化次数
g	——当前迭代次数
H	——HSI颜色空间的色彩
I	——HSI颜色空间的强度
k	——光照校正系数
k_r,k_g,k_b	——RGB三通道光照校正系数
N	——种群个体数目
S	——HSI颜色空间的饱和度
γ	——惩罚系数
ρ_t	——第t个样本的真实值
$ρ ? t$	——第t个样本的模型预测值
σ	——核函数宽度

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