面向多模式多元未知分布的协方差过程监控

doi:10.3969/j.issn.1004-132X.2023.22.009

摘要/Abstract

摘要： 针对工业过程数据的多模式、高维性和非正态性等挑战，设计了一种考虑模式过渡约束的基于协方差检验的多模式在线监测方法。首先利用交叉验证的线性收缩估计方法对待监测数据的协方差矩阵进行估计，然后基于估计的协方差矩阵计算稀疏主特征值检验统计量，进而基于稀疏主特征值检验统计量设计具有滑动窗口的指数加权移动平均（EWMA）控制图——MSPEWMA控制图，结合模式过渡约束得到最终的检验统计量。通过Monte Carlo模拟研究了MSPEWMA控制图在不同条件（变量维度、漂移大小、可控样本大小、过渡约束参数和观测数据分布）下的性能，结果表明，与基于协方差检验的其他控制图相比，新提出的控制图在大漂移和非正态条件下具有更好的监测效果。最后利用风力发电机组真实SCADA数据证明了所提方法的有效性。

关键词: 高维度, 多模式, 分布未知, 协方差估计, 多元指数加权移动平均

Abstract: Aiming at the challenges of multi-mode, high dimension and nonnormality of industrial process data, a multi-mode online monitoring method was designed herein based on covariance tests considering time constraints. Firstly, the covariance matrix of the data to be detected was estimated using a cross-validated linear shrinkage estimation method. Secondly, the sparse principal eigenvalue test statistic was calculated based on the estimated covariance matrix. Subsequently, an EWMA（exponentially weighted moving-average） control chart with sliding window was designed based on the sparse principal eigenvalue test statistic: the MSPEWMA control chart, and the final test statistic was obtained by combining the mode transition constraints. Through Monte Carlo simulation, the performance of the MSPEWMA control chart under different conditions(variable dimension, drift size, control sample size, transition constraint parameters, and observation data distribution) was investigated. The results show that the newly proposed control chart has better monitoring results under large drift and non-normal conditions compared with other control charts based on covariance tests. Finally, the effectiveness of the method was demonstrated using real SCADA data of wind turbines.

Key words: high dimension, multi-mode, unknown distribution, covariance estimation, multivariate exponentially weighted moving-average

中图分类号:

TP277

赵宇, 李艳婷, 吴振宇, 周笛, 胡洁. 面向多模式多元未知分布的协方差过程监控[J]. 中国机械工程, 2023, 34(22): 2721-2736，2757.

ZHAO Yu, LI Yanting, WU Zhenyu, ZHOU Di, HU Jie. Covariance Process Monitoring Scheme for Multi-mode Multivariate Unknown Distributions[J]. China Mechanical Engineering, 2023, 34(22): 2721-2736，2757.

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