Variational mode decomposition is a new signal decomposition method, which can process non-linear and nonstationary signals. It can overcome the problems of mode mixing and compensate for the shortcomings in empirical mode decomposition. Permutation entropy is a method which can detect the randomness and kinetic mutation behavior of a time series. It can be considered for use in fault diagnosis. The complexity of wind power generation systems means that the randomness and kinetic mutation behavior of their vibration signals are displayed at different scales. Multi-scale permutation entropy analysis is therefore needed for such vibration signals. This research investigated a method based on variational mode decomposition and permutation entropy for the fault diagnosis of a wind turbine roller bearing. Variational mode decomposition was adopted to decompose the bearing vibration signal into its constituent components. The components containing key fault information were selected for the extraction of their permutation entropy. This entropy was used as a bearing fault characteristic value. The nearest neighbor algorithm was employed as a classifier to identify faults in a roller bearing. The experimental data showed that the proposed method can be applied to wind turbine roller bearing fault diagnosis.

The vibration signals of hydropower units are nonstationary when serious vortex occurs in the draft tube of the hydraulic turbine. The traditional signal analysis method based on Fourier transform is not suitable for the nonstationary signals. In the face of the nonstationarity of such signals and the limitation of the empirical mode decomposition method, a new nonstationary and nonlinear signal analyzing method based on variational mode decomposition (VMD) is introduced into hydropower unit vibration signals analysis. Firstly, VMD is used to decompose the signal into an ensemble of band-limited intrinsic mode functions components. Then, frequency spectrum analysis of these components is conducted to obtain the characteristic frequencies of the signal caused by the serious vortex of hydraulic turbine. Analysis of real test data shows that this proposed method can effectively suppress mode mixing. It can realize accurate analysis of nonstationary vibration signals. This provides a new way for analyzing hydropower unit vibration signals.

For the unsteady characteristics of a fault vibration signal from a wind turbine rolling bearing, a bearing fault diagnosis method based on adaptive local iterative filtering and approximate entropy is proposed. The adaptive local iterative filtering method is used to decompose original vibration signals into a finite number of stationary components. The components which comprise major fault information are selected for further analysis. The approximate entropy of the selected components is calculated as a fault feature value and input to a fault classifier. The classifier is based on the nearest neighbor algorithm. The vibration signals from a spherical roller bearing on a wind turbine in its normal state, with an outer race fault, an inner race fault and a roller fault are analyzed. The results show that the proposed method can accurately and efficiently identify the fault modes present in the rolling bearings of a wind turbine.

A condition parameter degradation assessment and prediction model was developed to evaluate and forecast hydropower units based on the Shepard surface, intrinsic time-scale decomposition (ITD), a radial basis function (RBF) artificial neural network and grey theory. The model includes the effect of the active power and the working head on the hydropower unit's condition. The condition parameter degradation time series is decomposed into a finite number of proper rotation components and an approximate component using the ITD method. The GM(1,1) model (a first-order one-variable grey model) is then used to predict the approximate component time series. The proper rotation component time series are then predicted separately by building different RBF neural networks. Finally, the original condition parameter degradation time series is found by adding these results. Real condition monitoring data from a pumped storage power station in China is used to verify the method. The results show that this method accurately reflects the condition parameter degradation for the hydropower unit.

A prediction method of characteristic parameter degradation for a hydropower unit is presented based on radial basis function (RBF) interpolation, empirical mode decomposition (EMD), approximate entropy, artificial neural network and grey theory. Considering the effect of active power and working head, the characteristic parameter degradation model of a hydropower unit is built by using RBF interpolation. The EMD method is used to decompose the characteristic parameter degradation time series of the hydropower unit into a number of intrinsic mode function (IMF) components. The approximate entropy of each IMF component is calculated. According to their different properties, the neural network or grey theory is used to predict them, respectively. All the predicted results are added to obtain the final forecasting result of the original characteristic parameter degradation time series. The case study results demonstrate that the proposed method has an extremely high prediction accuracy, and can be applied in the hydropower unit condition prediction effectively.