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Despite its tremendous success, the multivariate statistical analysis technique has deficiencies related to the parameters and thresholds. The diagnosis performance is significantly influenced by detection thresholds, and it is difficult to choose the optimum parameters. 3 In addition, detection thresholds often cannot effectively characterize incipient faults that occurred without any observable changes in a statistical manner.Most recently, artificial intelligence technologies have been successfully used for fault diagnosis in view of the uncertainties and complexities of the system. Neural networks (NNs) and support vector machines (SVMs) have been demonstrated in chemical engineering applications. 17,18 Because it is considered to be a discriminating problem, fault diagnosis can be addressed by pattern recognition. 19 There are various researches to demonstrate the effectiveness of NNs for fault diagnosis. 20,21 Within NNs, back-propagation algorithm is the most widely used training mechanism 22 ; however, the residual is decreased when transforming it back forward layer-by-layer. Due to the limitations of this training mechanism and the computational complexity, it is difficult to optimize the weights when there are more than 3 hidden layers. 23 Support vector machines can achieve excellent classification performance for high-dimensional data 18 and are suitable for discriminating multiple faults in chemical processes. However, conventional artificial intelligence technologies are incredibly fragile in fault diagnosis because of their atomic symbol feature representations; they have not focused on pursuing higher-order correlations and underlying patterns of faults.As statistical analysis technologies and artificial intelligence technologies are all driven by data, they just do data preprocessing and feature representation in different ways. However, faults are defined by shallow architectures in these current technologies. Deep architectures and high-order correlations can be considerably more efficient than shallow architectures in terms of the computational elements and parameters required for representing unknown functions. 24 Therefore, the feature representation in fault diagnosis still remains a challenge. This was a difficult task prior to the important contribution of Hinton and Yann LeCun. 25 They developed deep networks and proposed corresponding fast learning algorithms. 26 Deep learning has become a remarkable topic in image recognition, speech recognition, and video processing and has outperformed state-of-the-art methods due to its strong learning ability. 27,28 The application of deep learning technologies in complex systems with multiple variables, including fault diagnosis, is of particular interest. However, few studies have focused on the deep learning based fault diagnosis to date, 29,30 and most of them focused on the processing of sensory data, which were almost all images and not multivariate fault signals. For fault signals, the details and small changes can be represented by higher-...

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As shallow architecture is inefficient in terms of computational elements, some incipient fault features can be characterized through the composition of many nonlinearities, ie, with deep network. In this paper, a novel approach is developed for multivariate statistical process monitoring based on higher-order correlations. First, the correlations among monitoring variables can be learned by a multilayer learning framework hierarchically: The higher the number of layers to be stacked, the more nonlinear and abstract features can be characterized. Second, 3 monitoring statistics, SRE, M 2 , and C, are presented to monitor whether the process is remaining in control, and they are instructive for the identification of fault types. Moreover, only normal data are used in training phase; this can avoid the unbalance problem of different types of fault data. These capabilities of the proposed approach are illustrated with two industrial benchmarks, Tennessee Eastman process and Metal Etch process. /journal/cem 1 of 18 processes. Therefore, a higher-order cumulants analysis algorithm is developed in Wang et al 9 to use the higher-order statistics for the state monitoring of multivariate processes. But the estimation of a cumulant with a higher order (>4) is not accurate. Besides, some nonlinear statistical analysis approaches, such as kernel PCA 10 and multiscale entropy, 11 were developed. Kernel PCA has been proven powerful as a preprocessing step for classification algorithms 10 ; however, its performance is related to the kernel functions. The multiscale entropy is an enhanced multiscale method to evaluate the regularity of complex time series based on the application of sample entropy; however, the determination of parameters, the number of consecutive data points, and the given tolerance has no theoretical philosophy. 11 In fact, the mixture of linearity and nonlinearity always exists in industrial measurements. The distinction and separation of variable correlations are mentioned in Li et al 12 through a hierarchical modeling strategy. Despite its tremendous success, the current statistical analysis technologies still have difficulty in using higher-order information for the multivariate processes monitoring. The incipient fault, whose details and small changes may reflect in higher-order correlation relationships, has been paid less attention.In view of the uncertainties and complexities of the industrial system, artificial intelligence technologies have been successfully used for process monitoring. The effectiveness of neural networks (NNs) has been demonstrated by various researches for fault diagnosis in chemical engineering applications. 13,14 As the conventional artificial intelligence technologies are shallow architectures, ie, only two levels of data-dependent computational elements, they can be inefficient in terms of computational units. [15][16][17] Hinton and LeCun had developed deep network architectures and proposed corresponding fast learning algorithms to overcome the limitations of traditional NN...