Industrial data are in general corrupted by noises and outliers. In this context, robustness to the contaminated data is a challenging issue in process monitoring. In this article, a novel method named low-rank joint embedding is proposed for robust process monitoring. By learning a low-rank coefficient matrix, low-rank joint embedding can capture the global structure of the original data and alleviate the negative effect of outliers, making the monitoring results more reliable. Moreover, a manifold regularization is introduced to preserve the local geometric structure of data, which enables the extracted low-dimensional representation of data to be more faithful and informative to enhance the monitoring capability. Based on projection learning, the low-rank joint embedding can learn an explicit projection that transforms the data not involved in the training data into the low-dimensional space, avoiding the out-of-sample problem. Furthermore, a reconstruction-based contribution plots based on the low-rank joint embedding is developed to identify the potential faulty variables. Case studies on the Tennessee Eastman process and a real industrial application demonstrate the effectiveness of the proposed monitoring approach.

中文翻译：

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低秩联合嵌入及其在鲁棒过程监测中的应用

工业数据通常会被噪声和异常值破坏。在这种情况下，对受污染数据的鲁棒性在过程监控中是一个具有挑战性的问题。在本文中，提出了一种名为低秩联合嵌入的新方法来进行鲁棒的过程监控。通过学习低秩系数矩阵，低秩联合嵌入可以捕获原始数据的全局结构并减轻离群值的负面影响，从而使监视结果更加可靠。此外，引入了流形正则化以保留数据的局部几何结构，这使得提取的数据的低维表示更加真实和有用，从而增强了监视能力。基于投影学习，低秩联合嵌入可以学习显式投影，该显式投影将训练数据中不涉及的数据转换为低维空间，从而避免了样本外问题。此外，开发了基于低秩联合嵌入的基于重建的贡献图，以识别潜在的故障变量。关于田纳西州伊士曼过程和实际工业应用的案例研究证明了所提出的监控方法的有效性。