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Highlights • We propose a new deep learning method to conduct structural diagnosis of multiple bearing faults. • This method improves diagnosis accuracy and numerical stability by introducing fault structural information. • We find some inner structures among multiple fault types in view of output kernel. Abstract In recent years, machine learning techniques have been proved a promising tool for bearing fault diagnosis. However, in the traditional machine learning-based diagnosis methods, the fault features tend to be relatively simple and couldn’t work well for different fault type once a specific feature extraction method is determined. Meanwhile, although deep learning techniques can adaptively extract more representative features from bearing fault data, they are generally computationally expensive with slow convergence speed. Even if some deep learning algorithms like Multi-Layer Extreme Learning Machine (ML-ELM) can get fast training speed by means of non-tuned training strategy, they are inevitably of randomness to some extents. To solve this problem, a new deep learning method called deep output kernel learning is proposed in this paper to conduct collaborative diagnosis of multiple bearing fault types. The initial motivation is using the structural domain information among multiple bearing fault types to improve the diagnosis model’s generalization ability and robustness. By adopting ML-ELM as baseline algorithm, this paper firstly utilizes autoencoder to adaptively extract deep features, and then uses them to construct an objective function with output kernel regularizer. Finally, after solving this optimization problem, an output kernel matrix is obtained, and with this matrix, the final diagnosis model is built by fusing the multiple outputs of fault classifier. Experimental results on CWRU and IMS bearing data sets show that, compared to one state-of-the-art signal analysis method and eight typical machine learning-based diagnosis methods including four shallow learning algorithms and four deep learning algorithms, the proposed method can effectively improve the accuracy of bearing fault diagnosis in an acceptable time. Moreover, the results from the Kruskal-Wallis Test also indicate the proposed method has good numerical stability. [ABSTRACT FROM AUTHOR]

• We propose a new deep auto-encoder method with fusing discriminant information. • We presents a gradient descent method to optimize the new model. • This method can improve features' representative ability with no fine-tuning operation. • This method can improve model's numerical stability on insufficient amount of training data. • We find a symmetric structure among multiple fault conditions in form of relatedness matrix. In recent years, deep learning techniques have been proved a promising tool for bearing fault diagnosis. However, to extract deep features with better representative ability, how to introduce discriminant information about different fault types into the deep learning model is still challenging. Moreover, as deep learning techniques heavily rely on mass of measuring data, relatively small amounts of data may cause over-fitting and reduce model stability as well. To solve such problems, a new deep auto-encoder method with fusing discriminant information about multiple fault types is proposed for bearing fault diagnosis. First, a new loss function is designed by introducing structural discriminant information. Specifically, to improve the feature's representative ability, a new discriminant regularizer is designed in the loss function by using maximum correlation entropy. And to represent the structural information among multiple fault types, a relation matrix for fault types is introduced, then a new regularizer with a symmetric constraint on this matrix is constructed. Second, a gradient descent method is provided to optimise this loss function, and the optimal deep features, as well as fault relatedness, are learned simultaneously. Experimental results on CWRU and IMS bearing data sets show that, compared to several state-of-the-art diagnosis methods, the proposed method can effectively improve the diagnostic accuracy with acceptable time efficiency. And the results on the Kruskal–Wallis Test indicate the proposed method has better numerical stability. [ABSTRACT FROM AUTHOR]