Wind power interval prediction (WPIP) plays an increasingly important role in evaluations of the uncertainty of wind power and becomes necessary for managing and planning power systems. However, the intermittent and fluctuating characteristics of wind power mean that high-quality prediction intervals (PIs) production is a challenging problem. In this article, we propose a novel hybrid model for the WPIP based on the gated recurrent unit (GRU) neural networks and variational mode decomposition (VMD). In the hybrid model, VMD is employed to decompose complex wind power data into simplified modes. Basic GRU prediction models, comprising a GRU input layer, multiple fully connected layers, and a rank-ordered terminal layer, are then trained for each mode to produce PIs, which are combined to obtain final PIs. In addition, an adaptive optimization method based on constructed intervals (CIs) is proposed to build high-quality training labels for supervised learning with the hybrid model. Several numerical experiments were implemented to validate the effectiveness of the proposed method. The results indicate that the proposed method performs better than the traditional interval prediction models with much higher quality PIs, and it requires less training time.

It confronts great difficulty to apply the traditional rolling bearing fault diagnosis methods to adaptively extract features conducive to fault diagnosis under complex operating conditions, and obtaining numerous fault data under real operating conditions is difficult and costly. To address this problem, a fault diagnosis method based on two-dimensional time-frequency images and data augmentation is proposed. To begin with, the original one-dimensional time series signal is converted into two-dimensional time-frequency images by continuous wavelet transform to obtain the input data suitable for two-dimensional convolutional neural network (CNN). Secondly, data augmentation technique is employed to expand labeled fault data. Finally, the generated and original fault data are served as training samples to train the fault diagnosis model based on CNNs. Experimental studies are conducted on standard and real-world datasets to validate the proposed method and demonstrate its superiority over the traditional methods in detecting bearing faults.