Fault diagnosis is essentially a kind of pattern recognition. The measured signal samples usually distribute on nonlinear low-dimensional manifolds embedded in the high-dimensional signal space, so how to implement feature extraction, dimensionality reduction and improve recognition performance is a crucial task. In this paper a novel machinery fault diagnosis approach based on a statistical locally linear embedding (S-LLE) algorithm which is an extension of LLE by exploiting the fault class label information is proposed. The fault diagnosis approach first extracts the intrinsic manifold features from the high-dimensional feature vectors which are obtained from vibration signals that feature extraction by time-domain, frequency-domain and empirical mode decomposition (EMD), and then translates the complex mode space into a salient low-dimensional feature space by the manifold learning algorithm S-LLE, which outperforms other feature reduction methods such as PCA, LDA and LLE. Finally in the feature reduction space pattern classification and fault diagnosis by classifier are carried out easily and rapidly. Rolling bearing fault signals are used to validate the proposed fault diagnosis approach. The results indicate that the proposed approach obviously improves the classification performance of fault pattern recognition and outperforms the other traditional approaches.

Existing gearbox fault diagnosis methods are prone to noise interference and cannot extract comprehensive fault signals, leading to misdiagnosis or missed diagnosis. This paper proposes a method for gearbox fault diagnosis based on adaptive variational mode decomposition–stationary wavelet transform (AVMD-SWT) and ensemble refined composite multiscale fluctuation dispersion entropy (ERCMFDE). Initially, the kurtosis coefficient and autocorrelation coefficient are presented, and the Intrinsic Mode Functions are denoised through the application of AVMD-SWT. Secondly, the coarse-grained processing method of composite multiscale fluctuation dispersion entropy is extended to encompass three additional approaches: first-order central moment, second-order central moment, and third-order central moment. This enables the comprehensive extraction of feature information from the time series, thereby facilitating the formation of an initial hybrid feature set. Subsequently, recursive feature elimination (RFE) is employed for feature selection. Ultimately, the outcomes of the faults diagnoses are derived through the utilization of a Support Vector Machine with a Sparrow Search Algorithm (SSA-SVM), with the actual faults data collection and analysis conducted on an experimental platform for gearbox fault diagnosis. The experiments demonstrate that the method can accurately identify gearbox faults and achieve a high diagnostic accuracy of 98.78%.

Vibration monitoring and analysis are important methods in wind turbine gearbox fault diagnosis, and determining how to extract fault characteristics from the vibration signal is of primary importance. This paper presents a fault diagnosis approach based on modified hierarchical fluctuation dispersion entropy of tan-sigmoid mapping (MHFDE_TANSIG) and northern goshawk optimization–support vector machine (NGO–SVM) for wind turbine gearboxes. The tan-sigmoid (TANSIG) mapping function replaces the normal cumulative distribution function (NCDF) of the hierarchical fluctuation dispersion entropy (HFDE) method. Additionally, the hierarchical decomposition of the HFDE method is improved, resulting in the proposed MHFDE_TANSIG method. The vibration signals of wind turbine gearboxes are analyzed using the MHFDE_TANSIG method to extract fault features. The constructed fault feature set is used to intelligently recognize and classify the fault type of the gearboxes with the NGO–SVM classifier. The fault diagnosis methods based on MHFDE_TANSIG and NGO–SVM are applied to the experimental data analysis of gearboxes with different operating conditions. The results show that the fault diagnosis model proposed in this paper has the best performance with an average accuracy rate of 97.25%.

The fault diagnosis of a gearbox is crucial to ensure its safe operation. Entropy has become a common tool for measuring the complexity of time series. However, entropy bias may occur when the data are not long enough or the scale becomes larger. This paper proposes a gearbox fault diagnosis method based on Refined Time-Shifted Multiscale Reverse Dispersion Entropy (RTSMRDE), t-distributed Stochastic Neighbour Embedding (t-SNE), and the Sparrow Search Algorithm Support Vector Machine (SSA-SVM). First, the proposed RTSMRDE was used to calculate the multiscale fault features. By incorporating the refined time-shift method into Multiscale Reverse Dispersion Entropy (MRDE), errors that arose during the processing of complex time series could be effectively reduced. Second, the t-SNE algorithm was utilized to extract sensitive features from the multiscale, high-dimensional fault features. Finally, the low-dimensional feature matrix was input into SSA-SVM for fault diagnosis. Two gearbox experiments showed that the diagnostic model proposed in this paper had an accuracy rate of 100%, and the proposed model performed better than other methods in terms of diagnostic performance.

Icing is a popular research area in wind energy, and the icing problem of the supercooled droplet–ice crystal mixed-phase condition is one of the new challenges. A numerical method for analyzing the icing characteristics of wind turbine airfoil under mixed-phase conditions is presented. The control equations for the dynamics of supercooled droplets and ice crystals are formulated using the Lagrangian method. Equations for the conservation of mass and energy during the icing process involving supercooled droplets and ice crystals are constructed. The impact of erosion phenomena on the mixed-phase icing process is examined, and methodologies for solving the control equations are introduced. The numerical method is utilized for modeling mixed-phase icing under a range of conditions. The results of these simulations are then compared with data obtained from icing wind tunnel tests to assess the validity of the method. The influence of various mixed-phase conditions on ice shapes is studied. It is found that higher icing temperatures correspond to a larger icing range and amount. The increase in supercooled droplet content, ice crystal content, and ice crystal diameter all contribute to enhanced ice accretion. However, the effects of ice crystal content and diameter are relatively minor.

The diagnosis of faults in wind turbine gearboxes based on signal processing represents a significant area of research within the field of wind power generation. This paper presents an intelligent fault diagnosis method based on ensemble-refined composite multiscale fluctuation-based reverse dispersion entropy (ERCMFRDE) for a wind turbine gearbox vibration signal that is nonstationary and nonlinear and for noise problems. Firstly, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and stationary wavelet transform (SWT) are adopted for signal decomposition, noise reduction, and restructuring of gearbox signals. Secondly, we extend the single coarse-graining processing method of refined composite multiscale fluctuation-based reverse dispersion entropy (RCMFRDE) to the multiorder moment coarse-grained processing method, extracting mixed fault feature sets for denoised signals. Finally, the diagnostic results are obtained based on the least squares support vector machine (LSSVM). The dataset collected during the gearbox fault simulation on the experimental platform is employed as the research object, and the experiments are conducted using the method proposed in this paper. The experimental results demonstrate that the proposed method is an effective and reliable approach for accurately diagnosing gearbox faults, exhibiting high diagnostic accuracy and a robust performance.