Industrial processes usually exhibit great nonlinearity generated from the effects of complex mechanisms, system integrations and multiple working conditions. Although a variety of dictionary learning algorithms have been proposed in recent years for industrial process fault diagnosis, most of them only model the process data via a linear combination of a few dictionary atoms, which cannot effectively characterize the nonlinear relationships among variables and may lead to limited diagnosis performance. Recent improvements in multilayer neural networks, especially the autoencoders, offer opportunities to tackle the nonlinear problem. However, the overall limited availability of fault samples poses great challenges in achieving satisfactory performance. To address the mentioned issues simultaneously, the present study proposes an Autoencoder Embedded Dictionary Learning approach (AEDL) for nonlinear industrial process fault diagnosis. First, an autoencoder is employed to learn a nonlinear mapping that maps the linearly inseparable industrial process data to a high-dimensional space, where a desired dictionary is learned according to the basic dictionary learning algorithm. Next, two supervised graphs, leveraging the priors of industrial process data, are introduced into the learning process to make the proposed approach robust to training samples. After obtaining the dictionary, the coding coefficients of the process data over the dictionary can be used for fault diagnosis via a simple classifier. As revealed from the encouraging experimental results on the Tennessee Eastman process, the developed approach outperforms several dictionary learning approaches and some other nonlinear fault diagnosis methods.

工业过程通常表现出很大的非线性，这是由复杂机制，系统集成和多种工作条件的影响所产生的。尽管近年来已经提出了各种用于工业过程故障诊断的字典学习算法，但是它们中的大多数仅通过几个字典原子的线性组合对过程数据进行建模，这无法有效地表征变量之间的非线性关系，并可能导致诊断性能有限。多层神经网络，特别是自动编码器的最新改进，为解决非线性问题提供了机会。然而，故障样品的总体有限可用性对实现令人满意的性能提出了巨大的挑战。为了同时解决上述问题，本研究提出了一种用于非线性工业过程故障诊断的自动编码器嵌入式字典学习方法（AEDL）。首先，采用自动编码器学习非线性映射，该映射将线性不可分割的工业过程数据映射到高维空间，在该空间中根据基本字典学习算法学习所需的字典。接下来，利用工业过程数据的先验性，将两个监督图引入学习过程中，以使所提出的方法对训练样本具有鲁棒性。在获得字典之后，可以通过简单的分类器将字典上的过程数据的编码系数用于故障诊断。从田纳西州伊士曼过程的令人鼓舞的实验结果中可以看出，