面向多速率难测时滞工业过程的质量指标建模方法

代伟; 包颖; 建中华; 南静; 秦岩

doi:10.16383/j.aas.c260029

面向多速率难测时滞工业过程的质量指标建模方法

doi: 10.16383/j.aas.c260029 cstr: 32138.14.j.aas.c260029

代伟^1,,
包颖^1,,
建中华^1,,
南静^2,,
秦岩^1,

1.
中国矿业大学信息与控制工程学院徐州 221116
2.
重庆大学自动化学院重庆 400044

基金项目: 国家自然科学基金(62373361, U24A20272), 江苏省杰出青年基金(BK20240102), 江苏省研究生科研与实践创新计划(SJCX25_1395), 中国矿业大学研究生创新计划(2025WLJCRCZL116)资助

详细信息

作者简介:
代伟：中国矿业大学信息与控制工程学院教授.主要研究方向为复杂工业过程建模、运行优化与控制.本文通信作者. E-mail: weidai@cumt.edu.cn

包颖：中国矿业大学信息与控制工程学院硕士研究生. 主要研究方向为复杂工业过程多速率数据建模. E-mail: baoying@cumt.edu.cn

建中华：中国矿业大学信息与控制工程学院博士研究生. 2023年获中国矿业大学硕士学位. 主要从事工业数据分析、数据驱动的过程监测和软测量建模. E-mail: jzh@cumt.edu.cn

南静：中国矿业大学信息与控制工程学院助理研究员. 主要从事复杂流程工业过程建模、增量学习和神经网络轻量化等方面研究. E-mail: jingn@cumt.edu.cn

秦岩：重庆大学自动化学院教授. 主要从事工业过程预测性维护、迁移学习和增量学习等方面研究. E-mail: yan.qin@cqu.edu.cn

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出版历程
- 收稿日期: 2026-01-13
- 录用日期: 2026-06-04
- 网络出版日期: 2026-07-10

A Quality Indices Modeling Method for Multirate Industrial Processes With Difficult-to-Measure Time Delay

DAI Wei^1
,,
BAO Ying^1
,,
JIAN Zhong-Hua^1
,,
NAN Jing^2
,,
QIN Yan^1
,

1.
School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China
2.
Sc-hool of Automation, Chongqing University, Chongqing 400044, China

Funds: Supported by National Natural Science Foundation of China (62373361, U24A20272),Distinguished Young Scholars of Jiangsu Province (BK20240102), Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJCX25_1395), and Graduate Innovation Program of China University of Mining and Technology (2025WLJCRCZL116)

More Information

Author Bio:
DAI Wei　Professor at the School of Information and Control Engineering, China University of Mining and Technology. His research interests include modeling, operational optimization, and control of complex industrial processes.Corresponding author of this paper

BAO Ying　Master candidate at the School of Information and Control Engineering, China University of Mining and Technology. Her research primarily focuses on multi-rate data modeling for complex industrial processes

JIAN Zhong-Hua　Ph.D. candidate at the School of Information and Control Engineering, China University of Mining and Technology. He received his master degree from China University of Mining and Technology in 2023. His research interests include process data analysis, data-driven process monitoring, and soft sensor modeling

NAN Jing　Assistant Researcher at the School of Information and Control Engineering, China University of Mining and Technology. His research primarily focuses on complex industrial process modeling, incremental learning, and neural network lightweighting

QIN Yan　Professor at the School of Automation, Chongqing University. His research primarily focuses on predictive maintenance for industrial process, transfer learning and incremental learning

摘要

摘要: 实际工业数据因检测方式不同, 过程变量与质量指标往往采样速率各异, 受低采样率数据影响, 可有效利用的样本稀缺, 传统建模精度难以提升. 此外, 因过程响应特性及传感器部署分布差异使各过程变量相对最终产品质量指标存在不同程度时滞, 但实际现场无法进行阶跃测试使得过程时滞难以测量, 进一步增加了建模难度. 为此, 本文提出一种面向多速率难测时滞工业过程的质量指标建模方法, 该方法首先设计基于核Copula熵的数据依赖结构时滞估计方法, 通过核Copula熵定量分析过程数据依赖结构关联强度, 将时滞参数估计问题转化为寻找最大依赖结构关联度问题, 引入专家经验约束依赖结构寻优过程, 保证时滞参数符合工业现场情况并修正数据时序对应关系. 进一步, 提出一种多速率采样数据时空约束网络模型, 该模型通过融合数据的时序特性与空间关联性, 构建时序因果的邻近样本质量指标的时空距离相似度约束矩阵, 据此充分挖掘无质量指标标签样本信息辅助模型构建, 提升软测量建模精度, 并且证明了网络模型的收敛性. 最后, 基于数值仿真和实际磨矿数据工业实验验证了所提方法的可行性和有效性
- 工业过程 /
- 多速率采样数据 /
- 时滞估计 /
- 软测量建模
Abstract: In actual industrial processes, variations in detection methods often result in differing sampling rates between process variables and quality indices. Such multirate data characteristics lead to a scarcity of usable samples with quality index labels, posing significant challenges for traditional modeling approaches in achieving high accuracy. Furthermore, process variables frequently exhibit varying degrees of time delay relative to quality indices due to diverse process response characteristics and sensor distributions. The impracticality of conducting step tests under field conditions further complicates the accurate measurement of these delays. To address these issues, this paper proposes a quality index modeling method for multirate industrial processes with difficult-to-measure time delays. First, a data dependency structure time-delay estimation approach based on kernel copula entropy is developed. By quantitatively assessing the strength of dependency structures, this approach transforms time-delay estimation into an optimization problem of finding the maximum dependency structure. This optimization is further constrained by expert knowledge to ensure industrial plausibility and facilitate temporal data alignment. Subsequently, a Multirate Sampled-data Spatiotemporal Constrained Network is designed. By fusing the temporal characteristics and spatial correlations of causally related samples, this network constructs a constraint matrix to effectively utilize abundant samples without quality index labels for model construction. The convergence of the proposed method is theoretically demonstrated. Finally, comprehensive numerical simulations and industrial case studies on grinding process data validate the feasibility and superiority of the proposed method.
- Industrial processes /
- multirate sampled data /
- time-delay estimation /
- soft sensor modeling

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图 1 多速率采样过程数据示意图

Fig. 1 Diagram of multirate sampling process data

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图 2 多速率采样数据时序对应关系示意图

Fig. 2 Diagram of multirate sampling data timing correspondence

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图 3 多速率难测时滞工业过程的质量指标建模方法流程图

Fig. 3 Schematic diagram of quality indices modeling methods for multirate industrial processes with difficult-to-measure time delay

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图 4 磨矿过程工艺流程图

Fig. 4 Schematic diagram of grinding process

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图 5 不同采样间隔下时滞参数估计方法结果对比

Fig. 5 Performance comparison of time-delay estimation methods for multiple sampling rates

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图 6 不同采样间隔下软测量建模方法结果对比

Fig. 6 Performance comparison of soft sensor modeling methods for multiple sampling rates

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图 7 磨矿数据最优参数组合寻优过程

Fig. 7 Optimization process for the optimal parameter combination in grinding data

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图 8 磨矿数据软测量建模方法拟合效果对比

Fig. 8 Fitting performance comparison of soft sensor modeling methods for grinding data

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图 9 磨矿数据超参数敏感性分析实验结果

Fig. 9 Hyperparameter sensitivity analysis on grinding data

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表 1 所提方法与对比方法的参数设置

Table 1 Parameter settings of the proposed and compared methods

类别	符号	参数说明	取值或搜索范围
通用设置	$ N_h $	隐藏层节点数	10
	$ Ratio $	训练/验证/测试比例	5:2:3
	$ T_{max} $	随机参数尝试次数	10
MSTN	$ \alpha $	时空融合因子	$ \{0.7,\; \dots,\; 1.0\}_{\Delta=0.1}^\dagger $
(本文方法)	$ \sigma_s $	空间核宽度	$ \{2^k \mid k \in [-3,\; 3]\}^\dagger $
	$ \sigma_t $	时间核宽度	$ \{2^k \mid k \in [-3,\; 3]\}^\dagger $
	$ R $	时空约束系数	$ \{2^k \mid k \in [-3,\; 10]\}^\dagger $
GLSCN	$ C $	$ L_2 $正则化系数	$ 10^{-6} $
	$ R_g $	流形正则化系数	500
	$ U $	一致性正则化系数	0.001
HSAN	$ lr $	学习率	0.001
	$ Epoch $	训练循环次数	50
	$ Batch $	训练批大小	5
	$ h_{lstm} $	LSTM隐藏层维度	10
KPLSR	$ \sigma_{ker} $	高斯核带宽	中位数法
	$ PCs $	主成分数	4
$ ^\dagger $详细最优值见表2及第4.3节.

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表 2 不同采样间隔下最优参数组合

Table 2 Optimal parameter combinations for multiple sampling rates

间隔	R	$ {\boldsymbol{\alpha}} $	$ {\boldsymbol{\sigma_s}} $	$ {\boldsymbol{\sigma_t}} $
10	1024	0.7	1	4
20	1024	0.9	0.125	2
30	1024	0.8	0.5	0.125
40	1024	0.9	0.125	0.25
50	512	0.8	0.125	4

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表 3 磨矿数据时滞估计结果对比

Table 3 Comparison of time-delay estimation results for grinding data

	$ x_1 $	$ x_2 $	$ x_3 $	$ x_4 $	耗时(s)
实际情况	10	19	65	5	—
KCE	13	19	70	5	686.32
CE	13	12	70	12	437.57
MIC	10	12	69	11	1349.09
GRA	14	13	60	6	418.06
PCC	11	22	66	11	431.47
DTW	8	14	62	15	3422.11
“-”表示该项为专家经验基准值, 故不存在算法计算耗时.

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表 4 磨矿数据软测量建模方法性能与计算耗时对比

Table 4 Performance and computation time comparison of soft sensor models for grinding data

	RMSE	MAE	OV	训练时间(s)	测试时间(s)
MSTN	4.2546$ \pm $0.6891	3.2662$ \pm $0.3388	3.7779	4.6342	0.0020
GLSCN	4.3844$ \pm $0.5384	3.2897$ \pm $0.2866	3.8390	69.0924	0.0022
Compact IELM	4.4222$ \pm $0.5996	3.3955$ \pm $0.3605	3.8564	0.0132	0.0021
HSAN	4.3975$ \pm $0.5416	3.4495$ \pm $0.4888	3.4314	5.2418	0.3085
KPLSR	5.6425$ \pm $0.0000	4.2282$ \pm $0.0000	5.6425	0.0467	0.0012

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表 5 磨矿数据消融实验

Table 5 Ablation study results for grinding data

评价指标	MSTN	KCE+MSTN	KCE+IRWNN
RMSE	4.4034$ \pm $0.5371	4.2546$ \pm $0.6891	4.3400$ \pm $0.7244
OV	3.8400	3.7779	3.7880

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