基于CauDformer模型的工业浓缩参数预测

doi:10.16182/j.issn1004731x.joss.25-0785

摘要/Abstract

摘要：

为解决中药工业浓缩过程中，传统预测方法难以应对非线性、高维耦合及高度偏态分布等复杂特征，且现有深度学习模型未充分考虑变量间因果关系、忽视频域周期性特征及长程依赖建模能力不足的问题，提出了一种改进型多变量时间序列预测模型CauDformer。基于iTransformer架构，通过引入因果多头自注意力机制(C-MHSA)，利用下三角因果掩码强制约束变量间的依赖方向，引导模型关注物理合理的因果链条；设计频域增强模块，利用实数快速傅里叶变换(RFFT)提取序列的周期性与波动特征，辅助模型捕捉长程依赖；提出自适应时频融合损失机制，在训练过程中动态调整时域重建损失与频域辅助损失的权重，以缓解模型训练早期的拟合不稳定问题。采用Optuna框架进行贝叶斯超参数优化。基于金银花三效浓缩工艺的真实数据，构建了包含12个关键变量的多步预测任务。实验结果表明：CauDformer在10、30及60 min的预测时域下，其平均绝对误差和均方误差均明显优于PatchTST、DLinear、TimeXer等先进模型，验证了该模型在复杂工业过程建模中的高精度与强鲁棒性。

关键词: 时间序列预测, 工业浓缩, 因果注意力, 频域增强, 贝叶斯优化

Abstract:

To solve the problems in the industrial concentration process of traditional Chinese medicine that traditional prediction methods are difficult to deal with complex characteristics such as nonlinearity, high-dimensional coupling, and highly skewed distribution and that existing deep learning models insufficiently consider causal relationships among variables, ignore frequency-domain periodic characteristics, and lack long-range dependency modeling capabilities, an improved multivariate time series prediction model CauDformer was proposed in this paper. Based on the iTransformer architecture, a causal multi-head self-attention mechanism (C-MHSA) was introduced to compulsorily constrain the dependency direction among variables by utilizing a lower triangular causal mask, guiding the model to focus on physically reasonable causal chains; a frequency-domain enhancement module was designed to extract the periodic and fluctuation characteristics of sequences using the real fast Fourier transform (RFFT), assisting the model in capturing long-range dependencies; an adaptive time-frequency fusion loss mechanism was proposed to dynamically adjust the weights of time-domain reconstruction loss and frequency-domain auxiliary loss during the training process, to mitigate the fitting instability in the early stage of model training. The Optuna framework was adopted for Bayesian hyperparameter optimization. Based on the real data of the honeysuckle triple-effect concentration process, a multi-step prediction task including 12 key variables was constructed. The experimental results indicate that under the prediction horizons of 10, 30, and 60 min, the mean absolute error and mean squared error of CauDformer are significantly superior to those of advanced models such as PatchTST, DLinear, and TimeXer, which verifies the high precision and strong robustness of this model in complex industrial process modeling.

Key words: time series prediction, industrial concentration, causal attention, frequency domain enhancement, Bayesian optimization

中图分类号:

TP391.1

徐楷彭,王艳,张欣等 . 基于CauDformer模型的工业浓缩参数预测[J]. 系统仿真学报, 2026, 38(7): 2105-2118.

Xu Kaipeng,Wang Yan,Zhang Xin,et al . Prediction of Industrial Concentration Parameters Based on CauDformer Model[J]. Journal of System Simulation, 2026, 38(7): 2105-2118.

图/表 12

图1

图2

表1

关键变量及其描述

变量名称	具体描述	变量名称	具体描述
$u 1$	蒸汽压力	$u 7$	三效压力
$u 2$	进液流速	$u 8$	三效温度
$u 3$	一效压力	$v 1$	大循环出液温度
$u 4$	一效温度	$v 2$	大循环出液累计
$u 5$	二效压力	$v 3$	大循环出液流速
$u 6$	二效温度	$v 4$	大循环出液密度

表1

图3

图4

图5

表2

图6

图7

表3

图8

表4

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超参数名称	取值范围
学习率	10^-5~10^-3
损失权重起始值	0.1~0.9
损失权重终止值	0.9~0.1
批次大小	16、32、64、128
模型隐藏维度	128、256、512
编码器层数	2、3、4
Dropout率	0.05~0.25

序号	模型	10 min		30 min		60 min
序号	模型	MAE	MSE	MAE	MSE	MAE	MSE
a	TimeXer	0.043 4	0.250 8	0.092 5	1.033 6	0.137 0	1.397 8
b	TiDE	0.059 7	0.422 4	0.096 7	0.830 0	0.139 5	1.327 2
c	PatchTST	0.041 3	0.248 3	0.087 1	0.703 1	0.134 8	1.373 2
d	DLinear	0.273 3	0.508 5	0.359 9	1.028 5	0.625 8	2.253 2
e	iTransformer	0.042 4	0.283 0	0.092 3	0.764 6	0.153 7	1.355 2
f	Ours	0.027 8	0.243 4	0.057 9	0.638 1	0.095 7	1.104 8

变体	因果注意力机制	频域增强模块	自适应时频融合	结果
变体	因果注意力机制	频域增强模块	自适应时频融合	MAE	MSE
Ⅰ	×	×	×	0.153 7	1.355 2
Ⅱ	√	×	×	0.125 2	1.285 7
Ⅲ	√	√	×	0.097 0	1.113 7
Ⅳ	√	√	√	0.095 7	1.104 8
Ⅴ	×	√	√	0.110 9	1.189 8