An echo state network (ESN) is a recurrent neural network with low computational complexity. However, a single ESN cannot extract effective features from complex inputs, especially for dealing with low-cost condition signals in machinery fault diagnosis. A novel deep learning model, referred to as the deep fuzzy ESN (DFESN), was proposed to improve the feature extraction capability with less computational burden. In the present method, the output data of the previous ESN reservoir were regarded as abstract feature vectors for the next ESN input. The features were reinforced in each hidden layer by using fuzzy clustering as a tuning step for classification enhancement. In this way, layer-wise fuzzy-tuning was developed to replace traditional overall feedback fine-tuning in deep models. This improved learning efficiency and robustness while overcoming the vanishing gradient problem for deep learning. The superiority of the proposed approach was evaluated by both theoretical analysis and experimental tests. The results showed that the present DFESN features improved classification accuracy and reduced the computational burden. In addition to machinery fault diagnosis, the proposed DFESN also has potential for other deep learning applications.

Health condition is a vital factor affecting printing quality for a 3D printer. In this work, an attitude monitoring approach is proposed to diagnose the fault of the delta 3D printer using support vector machines (SVM). An attitude sensor was mounted on the moving platform of the printer to monitor its 3-axial attitude angle, angular velocity, vibratory acceleration and magnetic field intensity. The attitude data of the working printer were collected under different conditions involving 12 fault types and a normal condition. The collected data were analyzed for diagnosing the health condition. To this end, the combination of binary classification, one-against-one with least-square SVM, was adopted for fault diagnosis modelling by using all channels of attitude monitoring data in the experiment. For comparison, each one channel of the attitude monitoring data was employed for model training and testing. On the other hand, a back propagation neural network (BPNN) was also applied to diagnose fault using the same data. The best fault diagnosis accuracy (94.44%) was obtained when all channels of the attitude monitoring data were used with SVM modelling. The results indicate that the attitude monitoring with SVM is an effective method for the fault diagnosis of delta 3D printers.

Reservoir inflow forecast plays a crucial part in programming, development, operation, and management of water resource systems. To better reveal the complex properties of daily reservoir inflow, a clustered deep fusion (CDF) approach is proposed in this paper. First, variational mode decomposition (VMD) is used to decompose the daily reservoir inflow series into multiple modes, which are clustered into different sets by fuzzy $c$ -means according to the Xie-Beni index in view of attribute domain. In each cluster, a deep autoencoder model (DAE) is developed for deep representations of the attributes in the deep domain. DAE outputs are finally fused at the synthesis domain into the forecasting results using random forest (RF). In this way, the inflow time series may be successively observed in the attribute domain, deep domain, and synthesis domain, which results in a clearer understanding of reservoir inflow trend. The present approach is modeled and evaluated using historical data collected from the Three Gorges Reservoir, China. For comparison, two kinds of learning patterns—deep learning (VMD-DAE-RF and DAE) and shallow learning (feed-forward neural network, least-squares support regression, and RF)—are applied to the same case. The results indicate that the proposed CDF model outperforms all comparison models in terms of mean absolute percentage error (6.174%), root mean-square error ($\mathrm{1,077.428}{\mathrm{m}}^3/\mathrm{s}$ ), and correlation coefficient criteria (0.987). Thus, it is concluded that deep learning in the cluster fusion architecture is more promising.