基于物理信息神经网络的石化污水处理过程智能预测研究

doi:10.11949/0438-1157.20250987

摘要/Abstract

摘要：

石化污水生物处理因进水波动大与调控滞后，出水易不达标。传统数值模拟成本高、泛化弱；纯数据驱动模型又因采样稀疏而难以构建。现有方法均无法满足实时预测与优化控制需求，亟需新策略。针对上述挑战，并弥补PINNs在污水处理领域损失函数设计与算法收敛性方面的研究空白，本研究提出一种融合反应机理与数据驱动的混合建模方法。首先，为构建一个更为精细且平滑的机理框架，本研究以经典生物化学反应模型为基础，通过消融实验系统地引入并量化了操作条件pH的关键影响。在此基础上，创新性地采用循环神经网络嵌入的物理信息神经网络（RNN-PINN）进行求解。该算法将描述生化反应动力学的微分控制方程作为硬约束，融入神经网络的训练过程，实现了对复杂动态系统的高效、高精度求解。研究结果证明，RNN-PINN模型在求解精度（相对误差<1%）上与传统的欧拉法和四阶龙格-库塔法相当，但在鲁棒性、迁移能力及时间外推性能上表现更优，尤其能在多变初始条件下保持稳定预测。此外，本研究从实验与理论双重角度对该算法的收敛性进行了深入分析。这些发现共同验证了RNN-PINN在石化污水生物处理建模中的高精度、强泛化能力与良好收敛性，为解决工业场景中采样数据稀疏的预测难题提供了有效的解决方案。

关键词: 污染, 废水, 生物过程, 数值模拟, 预测

Abstract:

Biological treatment of petrochemical wastewater frequently suffers from effluent quality violations due to significant influent fluctuations and control lags. Existing modeling approaches face critical limitations: traditional numerical simulations are computationally expensive and exhibit poor generalization, while purely data-driven models are difficult to train from sparse sampling data. Consequently, none can adequately meet the demands of real-time prediction and optimal control, necessitating the development of new strategies. To address these challenges and bridge the research gap concerning Physics-Informed Neural Networks (PINNs) in wastewater treatment—specifically in loss function design and algorithm convergence—this study proposes a hybrid modeling method that integrates reaction mechanisms with data-driven approaches. First, to establish a more refined and smooth mechanistic framework, we enhance a classic biochemical reaction model by systematically introducing and quantifying the critical influence of operational pH through ablation experiments. Building on this framework, we innovatively employ a RecurrentNeural Network-embedded PINN (RNN-PINN) for solving the system. The algorithm embeds the differential equations governing biochemical reaction kinetics as hard constraints into the neural network's training process, enabling efficient and high-precision solutions for complex dynamic systems. The results demonstrate that the RNN-PINN achieves solution accuracy (relative error < 1%) comparable to traditional Euler and fourth-order Runge-Kutta methods, but exhibits superior performance in robustness, transferability, and temporal extrapolation, maintaining stable predictions under varying initial conditions. Furthermore, the algorithm's convergence is rigorously analyzed from both experimental and theoretical perspectives. These findings collectively validate the high accuracy, strong generalization capability, and sound convergence of the proposed RNN-PINN for modeling petrochemical wastewater biological treatment, offering an effective solution to the prediction challenge in industrial scenarios with sparse data.

Key words: pollution, wastewater, biological process, numerical simulation, prediction

中图分类号:

TE992.2

索寒生, 韩嘉航, 韩丽君, 宁宇. 基于物理信息神经网络的石化污水处理过程智能预测研究[J]. 化工学报, DOI: 10.11949/0438-1157.20250987.

Hansheng SUO, Jiahang HAN, Lijun HAN, Yu NING. Physics-informed neural networks for intelligent prediction of petrochemical wastewater treatment processes[J]. CIESC Journal, DOI: 10.11949/0438-1157.20250987.

图/表 18

图1 石化行业污水处理流程

Fig.1 Wastewater Treatment Process in the Petrochemical Industry

图2 生物处理反应器示意图

Fig.2 Schematic Diagram of Biochemical Treatment Reactor

图3 微生物比增长速率变化趋势图

Fig.3 Figure of the Specific Growth Rate Trend of Microorganisms

图4 物理信息神经网络架构示意图

Fig.4 Schematic Diagram of Physics-Informed Neural Network Architecture

图5 传统数值算法的消融实验结果

Fig.5 Results of Ablation Experiments for Traditional Numerical Algorithms

表1 污水生物处理反应过程的物理约束

Table 1 Physical Constraints of Biological Wastewater Treatment Reaction Processes

参数/变量	取值范围
溶解氧浓度 $S O$	0.0-10.0mg/L
反应温度 $T 0$	15.0-35.0 $℃$
$p H$	0.0-14.0
菌种浓度 $S$	$≥ 0$ .0mg/L
污染物浓度 $X$	$≥ 0$ .0mg/L

表1 污水生物处理反应过程的物理约束

Table 1 Physical Constraints of Biological Wastewater Treatment Reaction Processes

参数/变量	取值范围
溶解氧浓度 $S O$	0.0-10.0mg/L
反应温度 $T 0$	15.0-35.0 $℃$
$p H$	0.0-14.0
菌种浓度 $S$	$≥ 0$ .0mg/L
污染物浓度 $X$	$≥ 0$ .0mg/L

图6 循环神经网络架构示意图

Fig.6 Schematic Diagram of Recurrent Neural Network Architecture

表2 超参数网格搜索结果

Table 2 Hyperparameter Grid Search Results

超参数名	数值	准确性
隐藏层神经单元个数	100	89.35%
	150	98.21%
	200	99.81%
神经网络层数	1	99.77%
	2	99.81%
	3	99.82%

图7 超参数消融实验结果

Fig.7 Ablation Study Results on Hyperparameters.

图8 损失函数权重敏感性分析结果

Fig.8 Model Training Convergence Process with Data Downsampling and Early Stopping.

图9 数据降采样及基于早停的训练收敛过程

Fig.9 Model Training Convergence Process with Data Downsampling and Early Stopping.

表3 工艺参数取值表

Table 3 Values of Process Parameters

参数	数值
污染物（COD）初始浓度	240.0mg/L
菌种（异养菌）初始浓度	500.0mg/L
反应时间	0.2h
初始温度	25.0 $℃$
初始pH值	7.8
溶解氧（ $S O$ ）浓度	1.0mg/L

表3 工艺参数取值表

Table 3 Values of Process Parameters

参数	数值
污染物（COD）初始浓度	240.0mg/L
菌种（异养菌）初始浓度	500.0mg/L
反应时间	0.2h
初始温度	25.0 $℃$
初始pH值	7.8
溶解氧（ $S O$ ）浓度	1.0mg/L

图10 传统数值算法与RNN-PINN算法模拟结果对比注:Traditional Numerical Algorithms and RNN-PINN Algorithms

Fig.10 Comparison of Simulation Results between

表4 算法结果及性能对比表

Table 4 Comparison of Algorithm Results and Performance

算法

计算效率

（推理时间：秒）

四阶龙格库塔方法

（基准）

Fig.11 Comparison of Simulation Results between注:Traditional Numerical Algorithms and FNN-PINN Algorithms

表5 FNN-PINN算法结果及性能表

Table 5 Table of FNN-PINN Algorithm Results and Performance

名称

计算效率

（推理时间：秒）

表6 各测试场景下模型结果评价指标值

Table 6 Model Evaluation Metrics across Test Scenarios

预测场景	准确性	MSE	$R 2$	推理时间（秒）
平均迁移准确性: 94.87%
短期预测 (0-0.1天)	99.81%	0.96	0.999944	0.0018
中期预测 (0-0.3天)	99.79%	1.26	0.999928	0.0016
长期预测 (0-0.5天)	99.50%	6.91	0.999615	0.0028
不同初值1 (COD=200)	89.95%	779.16	0.965980	0.0032
不同初值2 (COD=280)	92.60%	806.52	0.935560	0.0018
不同初值3(异养菌=400)	87.69%	4837.26	0.273108	0.0018

表6 各测试场景下模型结果评价指标值

Table 6 Model Evaluation Metrics across Test Scenarios

预测场景	准确性	MSE	$R 2$	推理时间（秒）
平均迁移准确性: 94.87%
短期预测 (0-0.1天)	99.81%	0.96	0.999944	0.0018
中期预测 (0-0.3天)	99.79%	1.26	0.999928	0.0016
长期预测 (0-0.5天)	99.50%	6.91	0.999615	0.0028
不同初值1 (COD=200)	89.95%	779.16	0.965980	0.0032
不同初值2 (COD=280)	92.60%	806.52	0.935560	0.0018
不同初值3(异养菌=400)	87.69%	4837.26	0.273108	0.0018

图12 RNN-PINN迁移能力与泛化能力测试

Fig.12 Evaluation of the Transferability and Generalization Capabilities of the RNN-PINN Model

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