Due to the interference of strong noise, feature extraction faces the challenge of limited information, which is not conducive to motor equipment fault diagnosis. This paper proposes a fault diagnosis method based on the empirical wavelet transform (EWT) and an improved ConvNeXt network. The modal components were extracted from the signals of different sensors using empirical wavelet transform, noise was removed, and then the signals were reconstructed. Secondly, the short-time Fourier transform (STFT) was used to convert the one-dimensional signal after noise reduction and reconstruction into a two-dimensional time-frequency spectrum image that enhanced signal features. Single-channel images generated by a single sensor were fused to form multi-channel images, thereby boosting the feature extraction capability of the ConvNeXt network. Additionally, the Ghost convolution module and the efficient local attention mechanism (ELA) were introduced into the ConvNeXt-T (ConvNeXt-Tiny) network, further enhancing the network’s performance. Experimental validation was conducted on application examples of various fault diagnostic devices, and comparisons were made with existing mainstream deep learning methods such as SE-InceptionV3, CBAM-ResNet, and CNN-LSTM etc. Experimental results confirmed under different noise environments and variable operating conditions, the proposed method achieved better diagnostic accuracy and enhanced generalization performance.

Soft sensor technology has been widely applied in key areas of industrial process monitoring. To address challenges such as strong nonlinearity, complex temporal dependencies, and dynamic system behavior commonly encountered in industrial soft sensor data modeling, we propose a hybrid dynamic modeling method that integrates gated recurrent unit (GRU) with temporal convolutional network-Transformer (TCN-Transformer) architecture. TCN-Transformer module is employed to extract multi-scale temporal patterns and capture long-range dependencies among auxiliary variables, while GRU network processes the historical information of target variables through its gated memory mechanism. The complementary feature representations from both components are summed before being passed into a fully connected layer for prediction. To validate the effectiveness of GRU-TCN-Transformer framework, comprehensive case studies were conducted on two typical industrial processes: the prediction of butane (C₄) concentration in a debutanizer column and the estimation of hydrogen sulfide (H₂S) and sulfur dioxide (SO₂) concentrations in a sulfur recovery unit (SRU). Experimental results demonstrate that the proposed hybrid dynamic modeling method significantly outperforms traditional dynamic modeling methods—convolutional neural network (CNN), long short-term memory (LSTM), and TCN—across multiple evaluation metrics. Specifically, for C₄ concentration estimation, the proposed method reduced root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) by 55.0%, 51.0% and 50.1%, respectively, and improved R² by 2.3% compared to the best-performing TCN-Transformer model. For H₂S estimation, it achieved reductions of 30%, 30.61% and 29.23% in RMSE, MAE, and MAPE, respectively, while increasing R² by 11.09% over the best LSTM-TCN-Transformer model. For SO₂ estimation, the proposed model reduced RMSE, MAE, and MAPE by 7.91%, 9.09% and 9.64%, respectively, with a 0.87% increase in R². These comparative results further confirm the improvements in prediction accuracy, indicating that the proposed model is capable of meeting the stringent requirements of industrial applications.

For short-term wind power forecasting, an interval A2-C1 type-2 (IT2) Takagi-Sugeno-Kang (TSK) fuzzy logic system (FLS) method (“A” means antecedent and “C” consequent) based on an extended Kalman filter (EKF) optimization algorithm is proposed. Compared with the type-1 (T1) FLS model, the IT2 TSK FLS method can simultaneously model both intra- and inter-individual uncertainty and further optimize the antecedent and consequent parameters using the EKF to improve forecasting performance further. The proposed IT2 A2-C1 FLS method is applied to Mackey-Glass chaotic time series and wind power forecasting instances in a certain region, under the same conditions. It is also compared with the T1 TSK FLS and IT2 TSK FLS methods with back propagation (BP) and particle swarm optimization (PSO) algorithms, as well as IT2 A2-C0 TSK FLS methods with EKF. The experimental results confirm that the proposed IT2 A2-C1 FLS method is superior to the other FLS methods regarding performance, which demonstrates its effectiveness and application potential.

For photovoltaic power prediction, a kind of sparse representation modeling method using feature extraction techniques is proposed. Firstly, all these factors affecting the photovoltaic power output are regarded as the input data of the model. Next, the dictionary learning techniques using the K-mean singular value decomposition (K-SVD) algorithm and the orthogonal matching pursuit (OMP) algorithm are used to obtain the corresponding sparse encoding based on all the input data, i. e. the initial dictionary. Then, to build the global prediction model, the sparse coding vectors are used as the input of the model of the kernel extreme learning machine (KELM). Finally, to verify the effectiveness of the combined K-SVD-OMP and KELM method, the proposed method is applied to a instance of the photovoltaic power prediction. Compared with KELM, SVM and ELM under the same conditions, experimental results show that different combined sparse representation methods achieve better prediction results, among which the combined K-SVD-OMP and KELM method shows better prediction results and modeling accuracy.

For short-term PV power prediction, based on interval type-2 Takagi-Sugeno-Kang fuzzy logic systems (IT2 TSK FLS), combined with improved grey wolf optimizer (IGWO) algorithm, an IGWO-IT2 TSK FLS method was proposed. Compared with the type-1 TSK fuzzy logic system method, interval type-2 fuzzy sets could simultaneously model both intra-personal uncertainty and inter-personal uncertainty based on the training of the existing error back propagation (BP) algorithm, and the IGWO algorithm was used for training the model premise and consequent parameters to further improve the predictive performance of the model. By improving the gray wolf optimization algorithm, the early convergence judgment mechanism, nonlinear cosine adjustment strategy, and Levy flight strategy were introduced to improve the convergence speed of the algorithm and avoid the problem of falling into local optimum. The interval type-2 TSK FLS method based on the IGWO algorithm was applied to the real-world photovoltaic power time series forecasting instance. Under the same conditions, it was also compared with different IT2 TSK FLS methods, such as type Ⅰ TSK FLS method, BP algorithm, genetic algorithm, differential evolution, particle swarm optimization, biogeography optimization, gray wolf optimization, etc. Experimental results showed that the proposed method based on IGWO algorithm outperformed other methods in performance, showing its effectiveness and application potential.

A hybrid forecasting model was proposed to improve the accuracy of short-term photovoltaic (PV) power generation forecasting, which combined the clustering of trained self-organizing map(SOM) network and optimized kernel extreme learning machine(KELM) method. First, a pure SOM was employed to complete the initial partitions of the training data set. Then clustering was executed on the trained SOM network by fuzzy C-means(FCM). Meanwhile, the davies-bouldin index(DBI) was hired to determine the optimal size of clusters. Finally, in each data partition, the regional KELM model was built with the KELM optimized by differential evolution, or the regional linear regression(MR) model was built with the multiple MR using the least square method to complete the coefficient evaluation. In addition, varying local multiple regression model was also proposed based on SOM. The proposed model based on SOM-FCM and KELM was employed to one-hour-ahead PV power forecasting instances of three different solar power plants provided by the GEFCom2014. Compared with other control models, the mean absolute error (MAE) of plant 1 was reduced by 61.41%, that of plant 2 by 60.19%, and that of plant 3 by 58.92%. The root means square errors (RMSE) of plant 1 was reduced by 52.06%, that of plant 2 by 54.56%, and that of plant 3 by 51.43% on average. The forecasting accuracy was significantly improved with the proposed model.

The inherent intermittency and uncertainty of photovoltaic (PV) power generation impede the development of grid-connected PV systems. Accurately forecasting PV output power is an effective way to address this problem. A hybrid forecasting model that combines the clustering of a trained self-organizing map (SOM) network and an optimized kernel extreme learning machine (KELM) method to improve the accuracy of short-term PV power generation forecasting are proposed. First, pure SOM is employed to complete the initial partitions of the training dataset; then the fuzzy c-means (FCM) algorithm is used to cluster the trained SOM network and the Davies-Bouldin index (DBI) is utilized to determine the optimal size of clusters, simultaneously. Finally, in each data partition, the clusters are combined with the KELM method optimized by differential evolution algorithm to establish a regional KELM model or combined with multiple linear regression (MR) using least squares to complete coefficient evaluation to establish a regional MR model. The proposed models are applied to one-hour-ahead PV power forecasting instances in three different solar power plants provided by GEFCom2014. Compared with other single global models, the root mean square errors (RMSEs) of the proposed regional KELM model are reduced by 52.06% in plant 1, 54.56% in plant 2, and 51.43% in plant 3 on average. Such results demonstrate that the forecasting accuracy has been significantly improved using the proposed models. In addition, the comparisons between the proposed and existing state-of-the-art forecasting methods presented have demonstrated the superiority of the proposed methods. The forecasts of different methods in different seasons revealed the strong robustness of the proposed method. In four seasons, the MAEs and RMSEs of the proposed SF-KELM are generally the smallest. Moreover, the R² value exceeds 0.9, which is the closest to 1.