Intrinsic Mode Functions Research Articles

Weak signal detection in chaotic noise background - based on VMD-EEMD and self-attention mechanisms

Abstract In this paper, a method for detection and estimation of weak harmonic signals in chaotic noise background is proposed. Firstly, the observed signal is smoothed by local weighted regression model to reduce the influence of noise. Then, the smoothed signals are decomposed into the intrinsic mode functions by Variational Mode Decomposition and Ensemble Empirical Mode Decomposition (VMD-EEMD). The components are reconstructed in the phase space, and the one-step prediction is carried out by adding a layer of the self-attention mechanism in the Long Short-Term Memory (LSTM). The one-step prediction error is obtained by summing up the prediction results of the components and the weak harmonic signals will be detected from the one-step prediction error. Finally, the periodogram method is used to detect whether the observed signals contain harmonic signals or not. If the observed signals contain harmonic signals, the amplitude and phase are estimated by the least squares method. Simulation experiments show that the method proposed in this paper has good performance. In detection of single harmonic signal, the Mean Absolute Error (MAE) and Mean Square Error (MSE) of the one-step prediction are 0.0212 and 0.00068 respectively; MAE and MSE of the signal estimation are 0.001977 and 0.0007 respectively. In detection of multiple harmonic signals, MAE and MSE of the one-step prediction are 0. 0248 and 0. 0006 respectively; MAE and MSE of the signal estimation are 0. 0035 and 1.681×10−5 respectively. The method proposed in this paper is able to efficiently detect weak harmonic signals from chaotic noise backgrounds and estimate the harmonic signals.

CEEMD-FFT-BiLSTM based model for power line loss prediction

Abstract Line loss rate in transmission lines is an important and inevitable metric to directly affects the economy and efficiency of power supply, which exhibits characteristics of nonlinearity, non-stationary and randomness. To improve the prediction performance of line loss rate, in this paper, a prediction model for line loss based on complete ensemble empirical mode decomposition (CEEMD), fast Fourier transform (FFT), and bidirectional long short-term memory network (BiLSTM) is proposed, denoted as CEEMD-FFT-BiLSTM. The model first performs CEEMD to decompose raw signals into various intrinsic mode functions. FFT then transforms them from the time domain to the frequency domain. BiLSTM is used to learn the long-term dependence, extract features from the frequency domain, and finally achieve a prediction. Experimental results are provided to show that the prediction accuracy of the proposed prediction method is substantially improved, as compared to other methods such as BiLSTM and FFT-BiLSTM. Therefore, the proposed prediction model has a good predictive ability and can effectively improve the prediction accuracy.

A hybrid approach for power quality event identification in power systems: Elasticnet Regression decomposition and optimized probabilistic neural networks

The transformation of traditional grid networks towards smart-grid and microgrid concepts raises many critical issues, and quality in the power supply is one of the prominent ones that needs further research. Developing and applying power quality (PQ) recognition methods with efficient and reliable analysis are essential to the fast-growing issues related to modern smart power distribution systems. In this regard, a hybrid algorithm is proposed for PQ events detection and classification using Elasticnet Regression-based Variational Mode Decomposition (ER-VMD) and Salp Swarm Algorithm optimized Probabilistic Neural Network (SSA-PNN). The Elasticnet Regression (ER) process is suggested to modify the conventional VMD approach instead of the Tikhonov Regularization (TR) method to enhance performance and obtain better band-limited intrinsic mode functions. This idea results in robust and effective reconstruction features and helps to obtain accurate classification using the classifier. In the classification stage, a Salp Swarm Algorithm (SSA) based PNN is used for the PQ event, considering the relevant features obtained from ER-VMD. The system parameters often influence PNN performance, and SSA is used to determine the ideal values to improve the PNN's capacity for more accurate classification. The numerical values of the accuracy percentage, percentage of sensitivity, and percentage of specificity in the case of real-time data are found as 98.58, 100, and 98.46, respectively. The acquired comparison findings demonstrate the effectiveness and robustness of the proposed technique in terms of rapid learning speed, smaller computational complexity, robust performance for anti-noise conditions, and accurate identification and categorization.

Intrinsic mode ensembled statistical cepstral coefficients for feature extraction of ship-radiated noise

Effective analysis of ship underwater acoustic signals requires accurately capturing and distinguishing subtle differences between various types of signal features. This paper introduces a multi-objective feature extraction method based on intrinsic mode decomposition and statistical parameterized cepstral coefficients, aimed at identifying different ship signals. Firstly, the original sample signals are preprocessed and converted into multiple frame signals. Each acoustic signal frame is then decomposed into intrinsic mode functions (IMFs) using variational mode decomposition (VMD). Cepstral coefficients are extracted from each IMF, and the statistical parameter features of each IMF are integrated to enhance the differentiation of various types of ship-radiated noise. These features also form unique “fingerprints” for each ship type, facilitating identity accurate authentication. The performance of the proposed method is evaluated using both K-nearest neighbors (KNN) and support vector machine (SVM) classification models. Experimental results demonstrate that the synergy between the proposed method and SVM significantly outperforms KNN, effectively distinguishing between 12 types of signals, including 11 ship-radiated signals and background noise, achieving an accuracy rate exceeding 89% across 1000 random tests. This method significantly increases the number of classifiable ship targets, demonstrating its considerable potential in distinguishing various underwater acoustic signals.

A Zero-Shot Learning Approach for Blockage Detection and Identification Based on the Stacking Ensemble Model.

A data-driven approach to defect identification requires many labeled samples for model training. Yet new defects tend to appear during data acquisition cycles, which can lead to a lack of labeled samples of these new defects. Aiming at solving this problem, we proposed a zero-shot pipeline blockage detection and identification method based on stacking ensemble learning. The experimental signals were first decomposed using variational modal decomposition (VMD), and then, the information entropy was calculated for each intrinsic modal function (IMF) component to construct the feature sets. Second, the attribute matrix was established according to the attribute descriptions of the defect categories, and the stacking ensemble attribute learner was used for the attribute learning of defect features. Finally, defect identification was accomplished by comparing the similarity within the attribute matrices. The experimental results show that target defects can be identified even without targeted training samples. The model showed better classification performance on the six sets of experimental data, and the average recognition accuracy of the model for unknown defect categories reached 72.5%.

A novel spatio-temporal characteristic extraction network for bearing remaining useful life prediction

Abstract Remaining useful life (RUL) is an important index indicating the health status of equipment, which has attracted extensive attention. Nevertheless, many existing RUL prediction methods encounter difficulties in effectively capturing comprehensive degradation features hidden in the data. Moreover, within real-world industrial scenarios, noisy signals are inevitably collected in the raw signals, thereby posing a big challenge to the precision of RUL predictions. To address the aforementioned problems, a robust RUL estimation approach based on degradation intrinsic mode functions (IMFs) selection and spatio-temporal feature regression is developed in this paper. The former addresses the issue of deep learning models struggling to extract degradation features of rolling bearings due to interference factors in vibration signals, while the latter resolves the problem of incomplete degradation features extracted by traditional RUL models under complex operating conditions. Firstly, complete ensemble empirical mode decomposition with adaptive noise is adopted to process the raw signals, separating components with degradation features, ineffective components, and noise. Subsequently, an IMFs selection method employing fast dynamic time warping and cosine coefficients is designed to obtain the valuable degradation features. Finally, a spatio-temporal feature extraction network is presented to comprehensively and effectively capture both spatial and temporal features within the chosen degradation IMFs, achieving the prediction of RUL with high accuracy and strong robustness. The experimental part containing two case studies has validated the effectiveness and superiority of the proposed method.

Optimizing Electric Vehicle (EV) Charging with Integrated Renewable Energy Sources: A Cloud-Based Forecasting Approach for Eco-Sustainability

As electric vehicles (EVs) are becoming more common and the need for sustainable energy practices is growing, better management of EV charging station loads is a necessity. The simple act of folding renewable power from solar or wind in an EV charging system presents a huge opportunity to make them even greener as well as improve grid resiliency. This paper proposes an innovative EV charging station energy consumption forecasting approach by incorporating integrated renewable energy data. The optimization is achieved through the application of SARLDNet, which enhances predictive accuracy and reduces forecast errors, thereby allowing for more efficient energy allocation and load management in EV charging stations. The technique leverages comprehensive solar and wind energy statistics alongside detailed EV charging station utilization data collected over 3.5 years from various locations across California. To ensure data integrity, missing data were meticulously addressed, and data quality was enhanced. The Boruta approach was employed for feature selection, identifying critical predictors, and improving the dataset through feature engineering to elucidate energy consumption trends. Empirical mode decomposition (EMD) signal decomposition extracts intrinsic mode functions, revealing temporal patterns and significantly boosting forecasting accuracy. This study introduces a novel stem-auxiliary-reduction-LSTM-dense network (SARLDNet) architecture tailored for robust regression analysis. This architecture combines regularization, dense output layers, LSTM-based temporal context learning, dimensionality reduction, and early feature extraction to mitigate overfitting. The performance of SARLDNet is benchmarked against established models including LSTM, XGBoost, and ARIMA, demonstrating superior accuracy with a mean absolute percentage error (MAPE) of 7.2%, Root Mean Square Error (RMSE) of 22.3 kWh, and R2 Score of 0.87. This validation of SARLDNet’s potential for real-world applications, with its enhanced predictive accuracy and reduced error rates across various EV charging stations, is a reason for optimism in the field of renewable energy and EV infrastructure planning. This study also emphasizes the role of cloud infrastructure in enabling real-time forecasting and decision support. By facilitating scalable and efficient data processing, the insights generated support informed energy management and infrastructure planning decisions under dynamic conditions, empowering the audience to adopt sustainable energy practices.

Medium–Long-Term PV Output Forecasting Based on the Graph Attention Network with Amplitude-Aware Permutation Entropy

Medium–long-term photovoltaic (PV) output forecasting is of great significance to power grid planning, power market transactions, power dispatching operations, equipment maintenance and overhaul. However, PV output fluctuates greatly due to weather changes. Furthermore, it is frequently challenging to ensure the accuracy of forecasts for medium–long-term forecasting involving a long time span. In response to the above problems, this paper proposes a medium–long-term forecasting method for PV output based on amplitude-aware permutation entropy component reconstruction and the graph attention network. Firstly, the PV output sequence data are decomposed by ensemble empirical mode decomposition (EEMD), and the decomposed intrinsic mode function (IMF) subsequences are combined and reconstructed according to the amplitude-aware permutation entropy. Secondly, the graph node feature sequence is constructed from the reconstructed subsequences, and the mutual information of the node feature sequence is calculated to obtain the graph node adjacency matrix which is applied to generate a graph sequence. Thirdly, the graph attention network is utilized to forecast the graph sequence and separate the PV output forecasting results. Finally, an actual measurement system is used to experimentally verify the proposed method, and the outcomes indicate that the proposed method, which has certain promotion value, can improve the accuracy of medium–long-term forecasting of PV output.

Rolling bearing fault analysis based on variational mode decomposition and multiscale arrangement entropy

Rolling bearings in operation will appear nonlinear characteristics of the fault vibration signal. In the process of fault feature extraction, a single permutation entropy (PE) produces unsatisfactory results and low accuracy. In this paper, a new diagnostic method was proposed, which was based on variational mode decomposition (VMD) and multiscale permutation entropy (MPE) to diagnose and analyze rolling bearing faults, multi-scale aligned entropy features of intrinsic mode function (IMF) of faulty vibration signals were extracted, and then support vector machine (SVM) and K-nearest neighbor algorithm (KNN) were used to analyze these features, and the maximum attribution metrics were used to determine classification results. The test results show that this method can improve the detection accuracy by comparing with other test analysis methods.

A combined model based on decomposition and reorganization, weight optimization algorithms for carbon price point and interval prediction

With the increasing environmental and climate problems caused by global warming, more and more countries are paying attention to reducing carbon emissions. Accurately predicting carbon prices can help create a stable carbon market and mitigate global warming. Therefore, a combined model which has four modules is proposed, they are the decomposition of carbon price series, reorganization of subsequences, point forecasting, and interval forecasting. For data preprocessing of decomposition, it can reduce the non-linearity of sequences. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) decomposes the original series into multiple Intrinsic Mode Functions (IMFs). Reorganization uses SampEn (SE) and T-test to reorganize the decomposed sequence into three new sequences according to actual meanings. For point prediction, the combined prediction model uses Particle Swarm Optimization (PSO) to obtain the optimal weights of Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU), which can integrate their strengths to improve prediction accuracy. Interval prediction is based on fitting the optimal distribution function by Maximum Likelihood Estimate (MLE). Different significance intervals can be obtained from the point prediction results and the distribution function. Empirical and comparative experiments show this combined model has excellent point and interval predictions. Besides, the significance and stability are demonstrated. Finally, some valuable references are provided for policymakers.

Research on the Fault Diagnosis Method of Rotating Machinery Based on Improved Variational Modal Decomposition and Probabilistic Neural Network Algorithm

The fault diagnosis of rotating machinery is vital in industry but traditionally depends on manual expertise, requiring substantial resources. To improve diagnostic accuracy, enable effective condition monitoring, and minimize the impact of faults on operations, advanced diagnostic techniques are essential. Hence, we propose an advanced fault diagnosis framework that leverages improved particle swarm optimization (IPSO), variational mode decomposition (VMD), and probabilistic neural networks (PNN) to accurately diagnose faults in rotating machinery using gear and rolling bearing vibration signals. Initially, the vibration signals are decomposed into intrinsic mode functions via VMD, enabling the capture of subtle but critical fault features. To address parameter selection challenges in VMD, we employed IPSO to optimize the VMD parameters, ensuring the optimal decomposition effect. Further, we refined the feature set by applying Laplace fraction optimization and feature dimensionality reduction, isolating sensitive features that serve as input to a PNN-based fault classification model. Experimental results demonstrated that this IPSO-VMD-PNN framework achieves high diagnostic accuracy for various fault types, establishing it as an effective tool for fault identification in rotating machinery.

An adversarial-based domain generalization method for the health evaluation of axial piston pumps

Abstract The axial piston pump is the power component in hydraulic systems and evaluating its health status is of great importance to the safe operation of hydraulic systems. Discharge pressure signals are common monitoring signals for axial piston pumps, but it is difficult to obtain satisfactory health evaluation results by directly using raw discharge pressure signals since the degradation information lies in some specific frequency bands. Furthermore, the axial piston pump often operates under different operating conditions and most existing deep learning models have low diagnostic accuracies due to the problems of insufficient degradation data and different data distribution. This paper proposes an adversarial-based domain generalization (DG) method by integrating time-frequency analysis and data augmentation, to accurately predict the health status of axial piston pumps under unknown working conditions. First, discharge pressure signals under various operating conditions are decomposed by using the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), and effective intrinsic mode functions (IMFs) are selected to train multiple convolutional neural network (CNN) models. Second, a novel data augmentation method based on the modified discrete cosine transform-composite spectrum (DCS) algorithm is introduced to fuse the IMFs from different domains and generate pseudo data sets. Finally, the adversarial training is adopted between the real data and the pseudo data to capture domain-generalized features. The discharge pressure signal of an actual axial piston pump at different health levels were collected on a test bench to verify the effectiveness of the proposed method. Results indicate that the proposed method has a higher prediction accuracy than the comparative methods.

Short-Term Power Load Forecasting Based on Secondary Cleaning and CNN-BILSTM-Attention

Accurate power load forecasting can provide crucial insights for power system scheduling and energy planning. In this paper, to address the problem of low accuracy of power load prediction, we propose a method that combines secondary data cleaning and adaptive variational mode decomposition (VMD), convolutional neural networks (CNN), bi-directional long short-term memory (BILSTM), and adding attention mechanism (AM). The Inner Mongolia electricity load data were first cleaned use the K-means algorithm, and then further refined with the density-based spatial clustering of applications with the noise (DBSCAN) algorithm. Subsequently, the parameters of the VMD algorithm were optimized using a multi-strategy Cubic-T dung beetle optimization algorithm (CTDBO), after which the VMD algorithm was employed to decompose the twice-cleaned load sequences into a number of intrinsic mode functions (IMFs) with different frequencies. These IMFs were then used as inputs to the CNN-BILSTM-Attention model. In this model, a CNN is used for feature extraction, BILSTM for extracting information from the load sequence, and AM for assigning different weights to different features to optimize the prediction results. It is proved experimentally that the model proposed in this paper achieves the highest prediction accuracy and robustness compared to other models and exhibits high stability across different time periods.

Scale-specific controls of monthly suspended sediment load in a typical inland river

Sediment transport is a multi-scale and non-linear process controlled by multiple variables. Given the intricate nature of sediment transport mechanisms and the overlap of different factors’ effects on it at various time scales, unraveling the relationship between sediment load and its influencing factors is challenging. This study aimed to elucidate the multi-timescale effects of factors on monthly suspended sediment load in a seasonal inland river. In this study, monthly sediment loads measured by the depth-integrating method were obtained from the Tabu River Basin in northern China from 2007 to 2021, alongside data on four controlling factors: runoff, precipitation, water surface evaporation, and the normalized difference vegetation index (NDVI). The results showed that sediment load, runoff, and precipitation showed strong variability during 2007–2021, while water surface evaporation and NDVI exhibited moderate variability. Multivariate empirical mode decomposition (MEMD) decomposed the temporal patterns of sediment load and associated variables into five intrinsic mode functions (IMF) and a residue. IMF1 (4.7 months), IMF2 (9.0 months) and IMF3 (14.2 months) collectively explained 115.88 %, 91.73 %, 91.28 %, 107.69 %, and 106.09 % of the total variability in sediment load, runoff, precipitation, water surface evaporation, and NDVI, respectively. Subsequently, the time-dependent intrinsic correlation (TDIC) was utilized to illustrate the inherent relationships between sediment load and its controlling factors across various time scales. The associations between sediment load and the controlling factors changed significantly with the scale. Runoff was the dominant factor controlling sediment load at IMF1 (4.7 months), IMF2 (9.0 months), IMF3 (14.2 months), and IMF4 (25.1 months). Water surface evaporation controlled the sediment transport process at IMF5 (63.6 months). The prediction of sediment load on the measurement scale, using scale-specific controls analyzed with MEMD (R2 = 0.993), demonstrated superior performance compared to traditional multiple linear regression prediction (R2 = 0.748). This study will provide a theoretical basis for effective prevention and control of soil erosion and watershed management in inland river basins.

Multi-scale prediction of remaining useful life of lithium-ion batteries based on variational mode decomposition and integrated machine learning

Accurate and reliable prediction of the remaining useful life (RUL) of lithium-ion batteries (LIB) is very important for the safety of power systems. To solve the nonlinear and time-varying problems of LIB aging trajectories, an RUL prediction method based on variational mode decomposition (VMD) and integrated machine learning is proposed. First, the VMD algorithm is used to mine the internal information in LIB data to capture the long-term downward trend and capacity regeneration hidden in the capacity degradation. After that, the Elman neural network optimized by the gray wolf algorithm and Gaussian process regression were used to model and predict the intrinsic mode function (IMF) and residual sequence respectively. Next, the predicted IMF component and residual sequence are fused to obtain the LIB aging trajectory, and the capacity prediction error is corrected through the bidirectional long short-term memory network. Finally, the LIB data set is used as the test data of the algorithm. The results show that the proposed method has better robustness and nonlinear tracking ability, the mean absolute error is controlled within 1.5 %, and the RUL prediction error is within 3 cycles.

Energy efficiency identification and surface roughness prediction using cutting force signal for computer numerical controlled machine systems

The energy efficiency identification of machining process plays an indispensable part in achieving energy-efficient manufacturing and improving energy utilization as well as productivity and surface quality. However, there is a great difficulty to track energy efficiency in real-time based on one kind of traditional power signal. Because energy consumption is affected by many factors such as machine tool current performance, tool wear conditions and cutting parameters selection. This paper puts forward an energy efficiency recognition method as well as surface roughness prediction model based on the cutting force signals. The CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) algorithm is employed to decompose the cutting force signal into multiple IMF (intrinsic mode function) components; and characterization of energy efficiency of machining process is recognized through proportion of components based on PCA—Fast ICA algorithm. Then, a surface roughness prediction model is proposed using support vector regression (SVR) based on specific cutting energy consumption (SCEC). The orthogonal test is designed considering spindle speed, feed rate, depth of cutting and width of cutting in 3 levels to obtain the influence degree of cutting parameters on cutting force, specific energy consumption, and the surface roughness. The energy efficiency of 27 group experiments is classified into high, medium and low levels according to energy efficiency value. Finally, using the data of orthogonal test, energy efficiency state was identified. The result show that time–frequency of cutting force signals for high, medium and low energy efficiency could be extracted, and the average absolute error of surface roughness predict is 0.058. That illustrated that the proposed method could meet the industry requirement for energy efficiency monitoring and surface roughness prediction to achieve sustainable manufacturing.

A data-driven method with sample entropy and CEEMDAN for short-term performance degradation prediction of dynamic hydrogen fuel cells

Short-term degradation prediction plays a crucial role in enhancing the reliability, safety, and cost-effectiveness of hydrogen fuel cells. A data-driven method for short-term degradation prediction is proposed based on Sample Entropy (SE), Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), and a varying-depth Gated Recurrent Unit (GRU). CEEMDAN decomposes the voltage sequence into Intrinsic Mode Functions (IMFs), which are then reconstructed into three meaningful combined Intrinsic Mode Functions (co-IMFs) using SE. The varying-depth GRU is employed to predict these co-IMFs. Results show that under dynamic conditions, the proposed method achieves an RMSE of 0.0012 for 1-h ahead predictions and 0.0151 for 35-h ahead predictions. Under static conditions, the RMSE for 1-h ahead is 0.0012, and for 35-h ahead prediction, it is 0.0097. Comparative analysis with hybrid models using the same dataset reveals that this novel approach demonstrates superior accuracy and efficiency.

Meta-model structural monitoring with cutting-edge AAE-VMD fusion alongside optimized machine learning methods

Transfer learning significantly enhances machine learning by leveraging knowledge from one dataset to boost performance on another, which is particularly beneficial when labelled data ares limited or costly. Sensor fusion, an essential technique in structural health monitoring, improves the effectiveness of transfer learning by combining data from multiple sensors to extract more informative features. This article proposes a novel meta-model structural monitoring using a new data fusion method named the adversarial autoencoder (AAE)–variational mode decomposition (VMD) algorithm, which integrates optimization algorithms, transfer learning, and machine learning techniques for damage detection tasks. The proposed meta-model combines transfer learning with an optimized machine learning framework for training and employs pretrained models for testing across diverse datasets. First, the tensors are fused using the AAE approach into 300 data points, reducing noise and outliers, performing dimensionality reduction, and enriching the training and test datasets. Then, a preprocessing step involves decomposing and denoising tensors using the VMD algorithm, followed by selecting the most informative intrinsic mode functions (IMFs) based on their variance. These selected IMFs are concatenated, and 13 statistical features are extracted from them and used as inputs for machine learning models. Various optimization algorithms are employed to fine-tune the hyperparameters of the machine learning models for optimal classification results. Validation of this meta-model utilizes the dataset collected from a steel grandstand structure, available in benchmark dataset format. For decomposed fused tensors, both particle swarm optimization and covariance matrix adaptation evolution strategy emerge as equally effective optimization techniques for K-nearest neighbours (KNN), consistently achieving the highest mean test accuracy and F1 score of 99.5%. Conversely, KNN stands out as a robust and reliable classification algorithm for denoised fused tensors in transfer learning classification problems, consistently demonstrating perfect accuracy and an F1 score of 1.0 ± 0.0 across all optimization techniques.

Wind Speed Forecasting Based on Phase Space Reconstruction and a Novel Optimization Algorithm

The wind power generation capacity is increasing rapidly every year. There needs to be a corresponding development in the management of wind power. Accurate wind speed forecasting is essential for a wind power management system. However, it is not easy to forecast wind speed precisely since wind speed time series data are usually nonlinear and fluctuant. This paper proposes a novel combined wind speed forecasting model that based on PSR (phase space reconstruction), NNCT (no negative constraint theory) and a novel GPSOGA (a hybrid optimization algorithm that combines global elite opposition-based learning strategy, particle swarm optimization and the genetic algorithm) optimization algorithm. SSA (singular spectrum analysis) is firstly applied to decompose the original wind speed time series into IMFs (intrinsic mode functions). Then, PSR is employed to reconstruct the intrinsic mode functions into input and output vectors of the forecasting model. A combined forecasting model is proposed that contains a CBP (cascade back propagation network), RNN (recurrent neural network), GRU (gated recurrent unit), and CNNRNN (convolutional neural network combined with recurrent neural network). The NNCT strategy is used to combine the output of the four predictors, and a new optimization algorithm is proposed to find the optimal combination parameters. In order to validate the performance of the proposed algorithm, we compare the forecasting results of the proposed algorithm with different models on four datasets. The experimental results demonstrate that the forecasting performance of the proposed algorithm is better than other comparison models in terms of different indicators. The DM (Diebold–Mariano) test, Akaike’s information criterion and the Nash–Sutcliffe efficiency coefficient confirm that the proposed algorithm outperforms the comparison models.

Copyright Protection Based on Hybrid Image Watermark (DCT) with Audio Watermark (EMD)

A digital watermark is a type of security that incorporates data into a signal, making it difficult to erase and showing ownership and validity. An important issue brought about by the growing use of the Internet is illicit copyright infringement and authentication. Previous research has proposed several techniques for this problem but has proven them to be either robust, difficult to detect, or fragile and easy to break. Because of this, in this paper, we use two separate kinds of watermarks—one for image and one for audio—to merge these two purposes into one. The image watermark discrete cosine transform (DCT) is renowned for its robustness. It is embedded in an audio watermarking algorithm based on empirical mode decomposition (EMD), ensuring a safe and fragile embedding process. The audio signal was divided into frames, and each one was decomposed by EMD into intrinsic mode functions (IMFs). The DCT watermark bits and the synchronization codes are embedded into the extrema of the first IMF, a high frequency mode sensitive to any small changes in the audio signal. The experimental outcomes suggest that while using two separate kinds of watermarks may seem like a comprehensive solution, it shows the flexibility of EMD and the limits of the DCT watermark technique in different scenarios.