多维未知输入时滞下工业软测量随机增量建模方法

刘鑫; 刘小庆; 代伟

doi:10.12263/DZXB.20250927

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多维未知输入时滞下工业软测量随机增量建模方法

学术论文 | 更新时间：2026-04-24

- 多维未知输入时滞下工业软测量随机增量建模方法
- A Stochastic Incremental Network for Industrial Soft Sensing with Unknown Multidimensional Input Time-Delays
- 电子学报 2025年53卷第12期页码：4630-4639
- 作者机构：
  
  中国矿业大学信息与控制工程学院，江苏徐州 221116
- 作者简介：
  
  [ "刘鑫男，1990年7月出生于江苏省盐城市.现为中国矿业大学信息与控制工程学院副教授、博士生导师.主要研究方向为系统辨识、数据驱动的工业建模和软测量.E-mail: 15B904027@hit.edu.cn" ]
  [ "刘小庆男，2001年3月出生于河南省商丘市.现为中国矿业大学信息与控制工程学院硕士研究生.主要研究方向为系统辨识、数据驱动的工业软测量建模.E-mail: xiaoqing_cumt@163.com" ]
  [ "代伟男，1984年3月出生于河南省安阳市.现为中国矿业大学信息与控制工程学院教授、博士生导师.主要研究方向为复杂工业过程建模、运行优化与控制.E-mail: weidai@cumt.edu.cn" ]
- 基金信息：
  
  国家自然科学基金(62573417);江苏省自然科学基金(BK20252089);中国博士后科学基金(2023M743776;2024T171003)
- DOI：10.12263/DZXB.20250927
  中图分类号： TP27;
- 收稿：2025-11-14，
  
  录用：2025-12-10，
  
  纸质出版：2025-12-25
- 稿件说明：
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刘鑫, 刘小庆, 代伟. 多维未知输入时滞下工业软测量随机增量建模方法[J]. 电子学报, 2025, 53(12): 4630-4639.

LIU Xin, LIU Xiao-qing, DAI Wei. A Stochastic Incremental Network for Industrial Soft Sensing with Unknown Multidimensional Input Time-Delays[J]. Acta Electronica Sinica, 2025, 53(12): 4630-4639.
刘鑫, 刘小庆, 代伟. 多维未知输入时滞下工业软测量随机增量建模方法[J]. 电子学报, 2025, 53(12): 4630-4639. DOI：10.12263/DZXB.20250927

LIU Xin, LIU Xiao-qing, DAI Wei. A Stochastic Incremental Network for Industrial Soft Sensing with Unknown Multidimensional Input Time-Delays[J]. Acta Electronica Sinica, 2025, 53(12): 4630-4639. DOI：10.12263/DZXB.20250927

摘要

未知时滞是工业软测量建模过程中常见的难题，若忽略时滞变量的解析（尤其是多维未知时滞变量）可直接降低模型的可靠性及准确性，进而导致建模任务失败.基于此，本文在随机配置网络（Stochastic Configuration Network，SCN）的基础上，综合考虑多维未知输入时滞和网络模型参数的迭代优化求解问题，提出了一种多维未知输入时滞下工业软测量随机增量建模方法.首先，利用随机配置网络作为基础模型映射输入输出数据间的非线性关系，揭示传统最小二乘估计对时滞变量的敏感性，进而利用期望最大化（Expectation-Maximization，EM）方法搭建未知时滞和网络模型参数的概率求解框架，将多维未知时滞参数概率辨识问题公式化；其次，构建未知时滞变量的解空间，通过计算时滞变量的后验概率密度函数，量化时滞变量在解空间的概率分布；最后，通过迭代优化求解策略给出未知时滞和网络模型参数的联合求解公式，避免独立估计导致的误差累积，得到期望的软测量模型.在模型验证过程中，本文通过数值仿真和一个典型的磨矿过程的工业应用，证明了提出的软测量模型的有效性和可靠性.

Abstract

Unknown time-delays pose a common challenge in industrial soft sensor modeling. Neglecting the identification of unknown time-delay variables

particularly for multidimensional unknown time-delay variables

can undermine model reliability and accuracy

leading to modeling failure. Accordingly

this paper proposes a stochastic incremental modeling method for industrial soft sensing with multidimensional unknown input time-delays

which is developed based on stochastic configuration network (SCN) to jointly solve the iterative optimization problem of multidimensional unknown input time-delays and network model parameters. Initially

the stochastic configuration network is utilized as a basic model to map the nonlinear relationships between input and output data

thereby revealing the sensitivity of conventional least-squares estimation to time-delay variables. Subsequently

the expectation-maximization (EM) algorithm is employed to establish a probabilistic framework

which formulates the probabilistic identification problem of the multidimensional unknown time-delay parameters. Furthermore

a solution space for the unknown time-delay variables is constructed

and the probability distribution of the unknown time-delay variables within solution space is quantified by calculating the posterior probability density function. Finally

an iterative optimization strategy is adopted to derive a joint estimation formula for the parameters of both the unknown time-delay and the network model

thereby avoiding the error accumulation caused by separate estimations and obtaining the desired soft sensor model. For model validation

the effectiveness and reliability of the proposed soft sensor model are validated through a numerical simulation and an industrial application involving a typical grinding process.

关键词

Keywords

references

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