引用本文:陈添艺,潘东辉,陈新,张海峰.基于稀疏规范变量差异度分析的化工过程微小故障检测[J].控制理论与应用,2026,43(4):755~764.[点击复制]
CHEN Tian-yi,PAN Dong-hui,CHEN Xin,ZHANG Hai-feng.Incipient fault detection for chemical processes based on sparse canonical variable dissimilarity analysis[J].Control Theory & Applications,2026,43(4):755~764.[点击复制]
基于稀疏规范变量差异度分析的化工过程微小故障检测
Incipient fault detection for chemical processes based on sparse canonical variable dissimilarity analysis
摘要点击 156  全文点击 25  投稿时间：2024-01-24  修订日期：2025-10-11
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DOI编号  10.7641/CTA.2024.40066
  2026,43(4):755-764
中文关键词  规范变量差异度分析  微小故障  故障检测  稀疏表征  核密度估计
英文关键词  canonical variate dissimilarity analysis  incipient fault  fault detection  sparse representation  kernel density estimation
基金项目  国家自然科学基金项目(12271002), 安徽省自然科学基金项目(2208085QF205), 安徽省高等学校自然科学基金项目(2022AH050097)资助.
作者单位E-mail
陈添艺 安徽大学 物质科学与信息技术研究院 Q22301163@stu.ahu.edu.cn 
潘东辉* 安徽大学 数学科学学院, 计算智能与信号处理教育部重点实验室 dhpan@ahu.edu.cn 
陈新 安徽大学 数学科学学院, 计算智能与信号处理教育部重点实验室  
张海峰 安徽大学 数学科学学院, 计算智能与信号处理教育部重点实验室  
中文摘要
      微小故障由于其故障征兆不明显, 且在高维数据下可能出现变量共线性的情况, 导致协方差矩阵病态而难 以求逆, 甚至不可逆, 因此传统的多元统计分析方法难以在故障发生早期对其进行检测. 针对上述问题, 本文提出了 基于稀疏规范变量差异度分析(SCVDA)的微小故障检测方法. 首先, 构造改进惩罚矩阵分解算法(IPMD)对Hankel 矩阵执行矩阵分解, 获得稀疏规范变量, 其增强了变量间潜在关系的直观理解, 并有助于发现故障变量. 其次, 利用 正常阶段规范变量的协方差和伪逆分别对状态向量和残差向量进行变量赋权, 进而使用稀疏表征后的规范变量, 来 构造基于条件期望的早期微小故障检测指标. 此外, 采用核密度估计确定非高斯分布数据下统计指标的控制限. 最 后, 通过田纳西伊斯曼(TE)化工过程和连续搅拌反应釜(CSTR)的案例研究结果表明, 所提方法在TE过程中相比SCVA, CVDA在检测率上分别取得了29.0%, 16.6%的提升, 在CSTR过程微小故障检测中, 相比上述算法分别提前142, 96个样本预警到故障.
英文摘要
      Incipient faults often manifest as the subtle nature of their fault symptoms, and the presence of potential variable collinearity in high-dimensional data can lead to ill-conditioned or even non-invertible covariance matrices. This makes it difficult for traditional multivariate statistical analysis methods to detect faults at an early stage. To address this issue, this paper proposes a method for detecting small faults based on sparse canonical variate difference analysis (SCVDA). Firstly, an improved penalized matrix decomposition (IPMD) algorithm is constructed to perform matrix decomposition on the Hankel matrix to obtain sparse canonical variates. This enhances the intuitive understanding of potential relationships between variables and helps identify fault variables. Secondly, the covariance and pseudoinverse of the canonical variates in the normal phase are used to weight the state vectors and residual vectors, respectively. Sparse canonical variates are then used to construct an incipient fault detection index based on conditional expectation. Additionally, the kernel density estimation is employed to determine control limits for statistical indicators under non-Gaussian distributions. Finally, the case studies on the Tennessee Eastman (TE) process and continuous stirred tank reactor (CSTR) process demonstrate that, compared to SCVA and CVDA, the proposed method achieves 29.0% and 16.6% improvements in detection rates in the TE process, and advances the detection of incipient faults by 142 and 96 samples in the CSTR process, respectively .