Wind speed prediction with spatio-temporal correlation is among the most challenging tasks in wind speed prediction. In this paper, the problem of predicting wind speed for multiple sites simultaneously is investigated by using spatio-temporal correlation. This paper proposes a model for wind speed prediction with spatio-temporal correlation, i.e., the predictive deep convolutional neural network (PDCNN). The model is a unified framework, integrating convolutional neural networks (CNNs) and a multi-layer perceptron (MLP). Firstly, the spatial features are extracted by CNNs located at the bottom of the model. Then, the temporal dependencies among these extracted spatial features are captured by the MLP. In this way, the spatial and temporal correlations are captured by PDCNN intrinsically. Finally, PDCNN generates the predicted wind speed by using the learnt spatio-temporal correlations. In addition, three error indices are defined to evaluate the prediction accuracy of the model on the wind turbine array. Experiment results on real-world data show that PDCNN can capture the spatio-temporal correlation effectively, and it outperforms the conventional machine learning models, including multi-layer perceptron, support vector regressor, decision tree, etc.Energies 2018, 11, 705 2 of 18 for exploitation. With the enrichment of spatio-temporal data of wind farms, wind prediction with both temporal correlation and spatial correlation, i.e., spatio-temporal correlation, has come to the research forefront.Existing work on wind speed prediction with spatio-temporal correlation can be roughly classified into three categories:(1) Physical methods, such as numerical weather prediction (NWP)-an accurate technique over longer horizons (from several hours to several days) [10]-formulate the problem of wind speed prediction as a set of high-dimensional, non-linear, differential algebraic equations, according to meteorology and computational fluid dynamics theories. Though physical methods have a good theory base, there are still many factors that limit their application [11], including the demand for considerable computational resources, relatively coarse spatial and temporal resolutions, high dependency for full and accurate information of the environment, etc.(2) Statistical methods find statistical regularities or patterns in massive historical data by establishing the mapping relationship between the predicted wind speed and explanatory variables [12]. These methods include the time-series analysis method [13], the Kriging interpolation method [14], the augmented Kriging interpolation method [15], clustering analysis [16], Von Mises distribution [17], etc. (3) Artificial intelligence (AI) methods, inspired by bionics and natural laws, intend to represent the complex nonlinear relationship between the inputs and the outputs. Various methods have been adopted for wind speed prediction, such as artificial neural networks (ANN) [18], support vector regressor (SVR), recurrent neural networks (RNN) [19], etc. However, the majority ...

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We study the occurrence of vibrational resonance as well as the underlying mechanism in excitable systems. The single vibration resonance and vibration bi-resonance are observed when tuning the amplitude and frequency of high-frequency force simultaneously. Furthermore, by virtue of the phase diagram of low-frequency-signal-free FitzHugh-Nagumo model, it is found that each maxima of response measure is located exactly at the transition boundary of phase patterns. Therefore, it is the transition between different phase-locking modes that induces vibrational resonance in the excitable systems. Finally, this mechanism is verified in the Hodgkin-Huxley neural model. Our results provide insights into the transmission of weak signals in nonlinear systems, which are valuable in engineering for potential applications.

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