基于k-近邻互信息的发酵过程高斯过程回归建模

doi:10.11949/0438-1157.20190606

摘要/Abstract

摘要：

发酵过程中基质浓度往往无法在线测量，采用高斯过程回归（GPR）建立基质浓度的估计模型，实现了其软测量。不同于传统软测量方法对基质浓度的估计，该方法不仅可以得到估计值，还能够得到其估计方差。考虑到发酵过程中各变量之间的非线性、相关性，为了提高模型的预测性能，在模型建立之前首先用k-近邻互信息（k-MI）辅助变量选择方法对模型的输入变量进行选择。从青霉素发酵过程的应用结果来看，采用kMI-GPR方法取得了较好的估计效果。

关键词: 发酵过程, 高斯过程回归, k-近邻互信息, 软测量

Abstract:

The concentration of the substrate during fermentation is often not measured online. In this paper, Gaussian process regression (GPR) is used to establish an estimation model of substrate concentration, and its soft measurement is realized. Different from traditional regression models, the GPR model can not only predict the quality value, but also provide the estimation variance. In order to improve the prediction performance of the model in the nonlinear fermentation process with correlated variables, the input variables of the model are selected by the k-nearest neighbor mutual information (k-MI) method before the model development. The application results of penicillin fermentation process show the ideal prediction performance based on the kMI-GPR model.

Key words: fermentation process, Gaussian process regression, k-nearest neighbor mutual information, soft sensor

中图分类号:

TP 273

赵荣荣, 赵忠盖, 刘飞. 基于k-近邻互信息的发酵过程高斯过程回归建模[J]. 化工学报, 2019, 70(12): 4741-4748.

Rongrong ZHAO, Zhonggai ZHAO, Fei LIU. Gaussian process regression modeling of fermentation process based on k-nearest neighbor mutual information[J]. CIESC Journal, 2019, 70(12): 4741-4748.

图/表 9

图1 青霉素发酵装置

Fig.1 Penicillin fermentation apparatus

图2 候选辅助变量与主导变量之间的互信息

Fig.2 Mutual informations between candidate secondary variables and primary variable

图3 基质浓度软测量建模流程

Fig.3 Flow chart of substrate concentration soft-sensing modeling

图4 kMI-GPR模型预测结果

Fig.4 Prediction results by kMI-GPR

图5 PLS-GPR模型预测结果

Fig.5 Prediction results by PLS-GPR

图6 kMI-SVM模型预测结果

Fig.6 Prediction results by kMI-SVM

图7 三种模型预测误差

Fig.7 Prediction errors of three diffferent models

图8 三种模型预测输出（有噪声）

Fig.8 Prediction values of three diffferent models(with noise)

表1 三种模型预测误差评价

Table 1 Prediction errors evaluation of three different models

Model	No noise			With noise
Model	$σ A R E$	$σ R M S E$	$σ M A X E$	$σ A R E$	$σ R M S E$	$σ M A X E$
kMI-GPR	0.5264	0.1410	0.8149	4.5148	0.2746	1.5371
kMI-SVM	11.2389	0.3768	1.2968	5.8723	0.5409	2.7882
PLS-GPR	3.9837	0.5892	3.0999	1.0641	2.5734	14.0338

表1 三种模型预测误差评价

Table 1 Prediction errors evaluation of three different models

Model	No noise			With noise
Model	$σ A R E$	$σ R M S E$	$σ M A X E$	$σ A R E$	$σ R M S E$	$σ M A X E$
kMI-GPR	0.5264	0.1410	0.8149	4.5148	0.2746	1.5371
kMI-SVM	11.2389	0.3768	1.2968	5.8723	0.5409	2.7882
PLS-GPR	3.9837	0.5892	3.0999	1.0641	2.5734	14.0338

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