融合物理信息的发酵过程时空图卷积网络模型

doi:10.11949/0438-1157.20251217

摘要/Abstract

摘要：

发酵过程具有高度的非线性、动态性和耦合性，近年来数据驱动模型获得大量应用，但其缺少物理可解释性的黑盒问题备受关注；另一方面，现有的数据驱动建模方法多关注变量之间的时间演化特性，往往忽略变量之间的空间关联关系。本研究提出内嵌发酵机理的时空建模方法，将发酵过程的物理信息引入图卷积网络进行数据建模。首先，基于相似度度量分别构建时间和空间动态图，并结合格兰杰因果关系和最大相似度准则对两类图进行稀疏化处理，再将发酵机理等信息以约束形式融入空间稀疏图，增强空间图的可靠性。其次，建立时空关系的顺序编码框架，将空间图和时间图并行化，分别学习变量在时间和空间的全局信息。然后，将发酵过程中目标变量的单调性约束纳入模型的损失函数，以确保模型的预测符合物理可行性。最后，以文献报导的青霉素发酵为例，验证了所提方法的预测效果，空间图的可视化结果表明所提出的模型与工艺知识相一致。

关键词: 物理信息, 时空关系, 图卷积网络, 发酵, 动态建模, 神经网络

Abstract:

The fermentation process is highly nonlinear, dynamic and coupled. In recent years, data-driven models have been widely applied, but the black box problem of their lack of physical interpretability has attracted much attention. On the other hand, the existing data-driven modeling methods mostly focus on the temporal evolution characteristics among variables and often ignore the spatial correlation relationships among them. This study proposes a spatio-temporal modeling method with an embedded fermentation mechanism, introducing the physical information of the fermentation process into a graph convolutional network for data modeling. Firstly, temporal and spatial dynamic graphs are constructed respectively based on similarity measurement, and the two types of graphs are sparsified by combining Granger causality and the maximum similarity criterion. Then, the fermentation mechanism information is integrated into the spatial sparse graph in the form of constraints to enhance the reliability of the spatial graph. Secondly, establish a sequential coding framework for spatio-temporal relationships, parallelize the spatial graph and the temporal graph, and respectively learn the global information of variables in time and space. Then, the monotonicity information of the target variable during the fermentation process is incorporated into the loss function of the model to ensure that the model's prediction conforms to physical feasibility. Finally, taking penicillin fermentation as an example, the prediction effect of the proposed method was verified. The visualization results of the spatial graph indicated that the proposed model was consistent with the process knowledge.

Key words: physical information, spatiotemporal relationship, graph networks, fermentation, dynamic modeling, neural networks

中图分类号:

TP18

丁卓, 刘飞, 王志国. 融合物理信息的发酵过程时空图卷积网络模型[J]. 化工学报, DOI: 10.11949/0438-1157.20251217.

Zhuo DING, Fei LIU, Zhiguo WANG. Physics-informed Spatio-Temporal Graph Convolutional Network for Fermentation Processes[J]. CIESC Journal, DOI: 10.11949/0438-1157.20251217.

图/表 7

图1 PI-STGCN模型结构

Fig.1 PI-STGCN model structure

图2 青霉素发酵工艺流程

Fig.2 Flow sheet of fed-batch penicillin cultivation process

表1 青霉素发酵过程主要变量

Table 1 Main variables of penicillin fermentation process

序号	变量名	序号	变量名
1	曝气率	8	pH
2	搅拌速率	9	反应罐温度
3	底物流加速率	10	反应热
4	底物流加温度	11	冷水流速
5	溶氧	12	底物浓度
6	培养液体积	13	生物量浓度
7	二氧化碳浓度	14	青霉素浓度

表2 对比模型评价指标比较

Table 2 Comparison of evaluation indexes for different models

模型	青霉素浓度			生物量浓度			底物浓度
模型	MSE	MAE	R²	MSE	MAE	R²	MSE	MAE	R²
ours	0.003	0.045	0.987	0.115	0.067	0.997	0.062	0.091	0.991
LSTM	0.006	0.064	0.969	0.139	0.322	0.985	0.144	0.132	0.985
SVR	0.013	0.101	0.922	0.840	0.875	0.892	0.607	0.259	0.923
GCN	0.069	0.066	0.959	0.330	0.462	0.969	0.267	0.184	0.966
IGCN	0.004	0.051	0.976	0.131	0.235	0.989	0.119	0.123	0.986

图3 PI-STGCN与其他模型预测性能的比较

Fig.3 Comparative Analysis of Prediction Performance: PI-STGCN versus Other Models

图4 α对R2均值的影响

Fig.4 Effect of α on Mean R2

图5 融合机理等信息的稀疏空间图

Fig.5 Sparse spatial graph fused with mechanism knowledge

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