In this paper, a novel structured collaborative sparse dictionary learning approach is proposed to improve the monitoring performance of discriminative dictionary learning for multimode processes. The mode discriminability and data reconstruction are first balanced by decomposing the dictionary coefficients into between- and within-class parts and introducing a within-class self-expression regularization term. A weight vector of between-class coefficients is subsequently exploited for accurate mode identification of data that falls into the overlapping regions between different class distributions. Moreover, in order to pinpoint the fault variables, a scalable fault isolation method is developed which imposes a constraint of statistical control limit and introduces the /-structured sparsity regularization terms. The mode identification capability of the proposed method is proved theoretically by Theorems 1 and 2, and a lower-bound magnitude is provided by Theorem 3 for fault isolation. Finally, extensive experiments conducted in the numerical and industrial process demonstrate that our proposed method outperforms some state-of-the-art methods.

中文翻译：

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用于监控多模式过程的结构化协作稀疏字典学习

本文提出了一种新颖的结构化协作稀疏字典学习方法，以提高多模式过程判别字典学习的监控性能。首先通过将字典系数分解为类间和类内部分并引入类内自表达正则化项来平衡模式判别性和数据重构。随后利用类间系数的权重向量来准确识别落入不同类分布之间重叠区域的数据。此外，为了查明故障变量，开发了一种可扩展的故障隔离方法，该方法施加统计控制极限的约束并引入/结构稀疏正则化项。定理1和定理2从理论上证明了该方法的模式识别能力，定理3给出了故障隔离的下界幅度。最后，在数值和工业过程中进行的大量实验表明，我们提出的方法优于一些最先进的方法。