Intrinsic Mode Function Components Research Articles

Short-Term Traffic Flow Forecasting Method Based on Secondary Decomposition and Conventional Neural Network–Transformer

Because of the random volatility of traffic data, short-term traffic flow forecasting has always been a problem that needs to be further researched. We developed a short-term traffic flow forecasting approach by applying a secondary decomposition strategy and CNN–Transformer model. Firstly, traffic flow data are decomposed by using a Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm, and a series of intrinsic mode functions (IMFs) are obtained. Secondly, the IMF1 obtained from the CEEMDAN is further decomposed into some sub-series by using Variational Mode Decomposition (VMD) algorithm. Thirdly, the CNN–Transformer model is established for each IMF separately. The CNN model is employed to extract local spatial features, and then the Transformer model utilizes these features for global modeling and long-term relationship modeling. Finally, we obtain the final results by superimposing the forecasting results of each IMF component. The measured traffic flow dataset of urban expressways was used for experimental verification. The experimental results reveal the following: (1) The forecasting performance achieves remarkable improvement when considering secondary decomposition. Compared with the VMD-CNN–Transformer, the CEEMDAN-VMD-CNN–Transformer method declined by 25.84%, 23.15% and 22.38% in three-step-ahead forecasting in terms of MAPE. (2) It has been proven that our proposed CNN–Transformer model could achieve more outstanding forecasting performance. Compared with the CEEMDAN-VMD-CNN, the CEEMDAN-VMD-CNN–Transformer method declined by 13.58%, 11.88% and 11.10% in three-step-ahead forecasting in terms of MAPE.

Vibration Signal Noise-Reduction Method of Slewing Bearings Based on the Hybrid Reinforcement Chameleon Swarm Algorithm, Variate Mode Decomposition, and Wavelet Threshold (HRCSA-VMD-WT) Integrated Model

To enhance fault detection in slewing bearing vibration signals, an advanced noise-reduction model, HRCSA-VMD-WT, is designed for effective signal noise elimination. This model innovates by refining the Chameleon Swarm Algorithm (CSA) into a more potent Hybrid Reinforcement CSA (HRCSA), incorporating strategies from Chaotic Reverse Learning (CRL), the Whale Optimization Algorithm’s (WOA) bubble-net hunting, and the greedy strategy with the Cauchy mutation to diversify the initial population, accelerate convergence, and prevent local optimum entrapment. Furthermore, by optimizing Variate Mode Decomposition (VMD) input parameters with HRCSA, Intrinsic Mode Function (IMF) components are extracted and categorized into noisy and pure signals using cosine similarity. Subsequently, the Wavelet Threshold (WT) denoising targets the noisy IMFs before reconstructing the vibration signal from purified IMFs, achieving significant noise reduction. Comparative experiments demonstrate HRCSA’s superiority over Particle Swarm Optimization (PSO), WOA, and Gray Wolf Optimization (GWO) regarding convergence speed and precision. Notably, HRCSA-VMD-WT increases the Signal-to-Noise Ratio (SNR) by a minimum of 74.9% and reduces the Root Mean Square Error (RMSE) by at least 41.2% when compared to both CSA-VMD-WT and Empirical Mode Decomposition with Wavelet Transform (EMD-WT). This study improves fault detection accuracy and efficiency in vibration signals and offers a dependable and effective diagnostic solution for slewing bearing maintenance.

Early warning of systemic risk in stock market based on EEMD-LSTM.

With the increasing importance of the stock market, it is of great practical significance to accurately describe the systemic risk of the stock market and conduct more accurate early warning research on it. However, the existing research on the systemic risk of the stock market lacks multi-dimensional factors, and there is still room for improvement in the forecasting model. Therefore, to further measure the systemic risk profile of the Chinese stock market, establish a risk early warning system suitable for the Chinese stock market, and improve the risk management awareness of investors and regulators. This paper proposes a combination model of EEMD-LSTM, which can describe the complex nonlinear interaction. Firstly, 35 stock market systemic risk indicators are selected from the perspectives of macroeconomic operation, market cross-contagion and the stock market itself to build a comprehensive indicator system that conforms to the reality of China. Furthermore, based on TEI@I complex system methodology, an EEMD-LSTM model is proposed. The EEMD method is adopted to decompose the composite index sequence into intrinsic mode function components (IMF) of different scales and one trend term. Then the LSTM algorithm is used to predicted and model the decomposed sub-sequences. Finally, the forecast result of the composite index is obtained through integration. The empirical results show that the stock market systemic risk index constructed in this paper can effectively identify important risk events within the sample period. In addition, compared with the benchmark model, the EEMD-LSTM model constructed in this paper shows a stronger early warning ability for systemic financial risks in the stock market.

A hybrid machine learning forecasting model for photovoltaic power

The increasing use of photovoltaic (PV) power generation presents a significant opportunity for global energy transformation. However, accurately forecasting PV power remains a challenge. This study proposes a hybrid approach that combines variational mode decomposition (VMD), whale optimization algorithm (WOA), and long short-term memory neural network (LSTM) to forecast photovoltaic (PV) power accurately. The model decomposes the time series of PV power using VMD to address the non-stationary nature of the time series. The VMD parameters are optimized using WOA. Subsequently, and the PV power time series data is then decomposed using the optimized VMD parameters to obtain multiple intrinsic mode functions (IMFs) components and a residual component. These components are then reconstructed with meteorological parameters to obtain the reconstructed IMF components and residuals. Finally, multiple LSTM sub-models are built, with each of them taking the IMF components and residual from the previous reconstruction as inputs. The sub-models are optimized using the WOA method to determine their hyperparameters and then constructed with these optimized hyperparameters. The predicted values of each IMF and residual are output and added for sequence reconstruction to derive the final predicted value of PV power. The model's effectiveness was verified for one-hour-ahead forecasting at the 1.8 MW solar system in Yulara, central Australia. The test results show that the proposed model outperforms other benchmark models, with mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and R-squared value (R2) of 15.247 kW, 19.753 kW, 4.405 % and 0.997, respectively. Compared to the LSTM, MAE, RMSE, and MAPE decreased by 84.942 %, 86.746 %, and 82.611 %, respectively, while R2 increased by 23.438 %. The proposed model has better predictive performance for both stable power changes and large fluctuations, essential for effectively integrating renewable energy sources into the power grid.

Research on rotor fault diagnosis technology of three-phase asynchronous motor based on NA-MEMD mutual information and SVM

Aiming at the problem of mode aliasing in the adaptive decomposition of nonlinear and non-stationary current signals generated by three-phase asynchronous motor faults, and the fault features contained in signals collected by a single sensor can not be accurately and comprehensively extracted and characterized when early rotor bar breakage and air gap eccentricity faults occur, A fault diagnosis method for three-phase asynchronous motor based on noise assisted multivariate empirical mode decomposition (NA-MEMD) and mutual information is proposed. Firstly, the NA-MEMD algorithm is used to decompose the three-phase stator current signal of the asynchronous motor to obtain multi-scale intrinsic mode functions (IMFs). Then, the correlation algorithm is used to screen the IMFs containing useful information. Then, the filtered IMF components are reconstructed into new signals and their features are extracted, Finally, support vector machines (SVM) are used to identify the rotor broken bars and air gap eccentric faults of the three-phase asynchronous motor. The experimental results show that the NA-MEMD method has a higher recognition rate than the traditional empirical mode decomposition (EMD) and the ensemble empirical mode decomposition (EEMD) methods.

The HWAM-EMD-GRU Forecasting Model for Short-Term Passenger Flow in an Airport Light Rail Transit Line

Accurate forecasting of airport light rail transit line (ALRTL) outbound passenger flow is critical to the optimal operations of both light rail and airport systems. Considering the nonlinearity, non-stationarity, uncertainty, and periodicity of outbound passenger flow in the ALRTL, we propose a combined forecasting model that integrates the Holt and Winters additive model (HWAM), empirical mode decomposition (EMD) and gated recurrent unit (GRU). Firstly, the edge effect of EMD will greatly affect the performance of the forecasting model. To overcome this, we extend the passenger flow by HWAM. After that, the decomposition method, EMD, can be applied to passenger flow, and several intrinsic mode function (IMF) components can be extracted. After extracting all the IMFs, the remaining part is referred to as the residual (Res) component. Then, a correlation test is performed on all the components, followed by their aggregation. Finally, the GRU is used to predict each of the aggregated components, and the prediction of aggregated components requires reconstruction. To verify the performance of the HWAM-EMD-GRU, we conducted a comparative study on the hourly passenger flow data for Beijing Daxing International Airport Express and set the autoregressive integrated moving average model, HWAM, Prophet, and GRU as the baseline. Predictions of the HWAM-EMD-GRU combined model demonstrated higher accuracy than baseline models, with a root mean square error of 83.52 (Prophet is 110.21) and mean absolute percentage error of 8.32% (Prophet is 12.48 %). The experimental result shows that the HWAM-EMD-GRU forecasting model offers more accurate predictions.

Mid-to-long Term Wind Power Forecasting Based on ARIMA-BP Combined Model

Background: Increasing the accuracy of the output power forecasting for wind power is helpful to the improvement of the reliability of power dispatching. Objective: This study aimed to improve the forecasting accuracy of mid-to-long term wind power. Methods: A mid-to-long term wind power forecasting based on ARIMA-BP combined model was proposed. The Empirical Mode Decomposition (EMD) was used to decompose the historical wind power series and obtain the Intrinsic Mode Function (IMF) and residual components, thereby obtaining more regular components. Then, the optimum feature set was obtained based on the minimum Redundancy Maximum Relevance (mRAR) to improve the prediction accuracy for feature extraction. After that, the high-frequency components were predicted using the Back Propagation (BP) neural network model, while the low-frequency components were predicted using the Autoregressive Integrated Moving Average model (ARIMA). Finally, the predicted components obtained were superimposed to deduce the final mid- and long-term wind power prediction results. Results: An analysis was conducted according to the actual data from a typical wind farm. After comparison, it was found that, after empirical mode decomposition and feature extraction analysis, the error of the intelligent combination algorithm based on the ARIMA-BP combined model was smaller than that using only the BP neural network or only the ARIMA. Conclusion: By means of actual data analysis, the effectiveness of the method proposed by the study for mid- and long-term wind power prediction was verified.

A time-frequency-based interval decomposition ensemble method for forecasting gasoil prices under the trend of low-carbon development

Given that gasoil plays a crucial role in carbon emission reduction, in this paper we propose a time-frequency-based interval decomposition ensemble (TFIDE) learning approach to forecast gasoil prices and capture the nonlinear impact of the global trend of low-carbon development on gasoil prices. The proposed method integrates bivariate empirical mode decomposition (BEMD), an interval multilayer perceptron (IMLP) network and a threshold autoregressive interval (TARI) model. First, we use BEMD to decompose interval-valued weekly gasoil prices into a finite number of complex-valued intrinsic mode function (IMF) components and a residual component. Second, we apply the IMLP model to forecast the IMFs and the TARI model to predict the residual part with predictors of carbon reduction technology and carbon emission concerns. After that, we combine all the forecasting results to generate the final gasoil price interval forecasting results. Our empirical results show that our carbon reduction technology variable improves middle-frequency IMF forecasting and that carbon emission concerns have a nonlinear impact on long-term gasoil price intervals. Furthermore, the proposed TFIDE approach outperforms other competing methods under different accuracy measurements.

A novel learning approach for short-term photovoltaic power forecasting - A review and case studies

Integrating photovoltaic power into the power system can offer significant economic and environmental benefits. However, the intermittent and random nature of photovoltaic power generation poses a challenge to the current power system's planning and operation. Accurate photovoltaic power generation forecasting is crucial for delivering high-quality electric energy to consumers and increasing system reliability.In this study, a multi-stage approach is proposed. In the first stage, three decomposition techniques (Iterative Filtering decomposition, Variational Mode Decomposition, and Wavelet Packet Decomposition) are employed for time series decomposition. Then, for each Intrinsic Mode Function (IMF) component resulting from the decomposition block, five machine learning and three deep learning algorithms are utilized, serving as local forecasting models. In the final forecast phase, the best forecasting result for each regressor is selected during the reconstruction phase. Two years of photovoltaic power data recorded in three grid-connected photovoltaic systems installed in South Algeria were utilized for training and testing the proposed forecasting models. Upon comprehensive analysis and examination of the outcomes, the proposed method exhibits the lowest normalized Root Mean Square Error values across all forecast horizons and monitoring stations. Particularly, for forecasting steps at time intervals +1, +3, and +5, the proposed method attains an average normalized Root Mean Square Error, showcasing its efficacy: 0.709%, 2.097%, and 3.241% for station 1; 1.147%, 3.546%, and 5.347% for station 2; and 0.922%, 2.158%, and 4.539% for station 3. The experimental results underscore the superiority of our approach over conventional regression algorithms, thus substantiating its prowess in delivering robust and competitive performance outcomes.

Impact of the water-wedge deterioration effect of pulsating water injection on AE waveforms and crack propagation during fracturing processes

Pulsating hydraulic fracturing (PHF) is a promising technology for enhancing the extraction of coalbed methane. In this study, the effects of pulsating water response of coal fractures were investigated. Prior to quasi-static fracturing, coal samples were subjected to pulsating water injection for 120 min. The fracturing process was monitored using an acoustic emission (AE) system and compared with direct fracturing without pulsating water injection. The Hilbert–Huang transform theory was employed for the analysis. The AE signals were examined in time and frequency domains, across various parameters, including intrinsic mode function (IMF) components, energy, three-dimensional spectrum, location features, and crack development. The results indicated a 37.82 % reduction in initiation pressure, accompanied by decreased AE counts and the promotion of gradual fracture initiation. Initially, the AE waveform amplitudes decreased, followed by an increase in distinctive patterns. Water injection primarily reduced the amplitudes during unstable fracturing, shifting the extreme IMF component forward. Moreover, it decreased the peak energy, shortened the energy release duration, and improved the signal-to-noise ratio during crack propagation. Water injection also narrowed the frequency distribution range, concentrated the energy distribution, expanded the extent of the fracture, increased the number of location points, and induced more macroscopic cracks within the coal body.

EMD-based noise reduction study of steel cored conveyor belt containing slag signal

This paper proposes a noise reduction technique that combines empirical mode decomposition (EMD) and wavelet thresholding to eliminate the noise interference caused by metal slag in the steel cord conveyor belt damage signal. Initially, the original signal undergoes decomposition by EMD into high- and low-frequency intrinsic mode function (IMF) components based on metal slag signal feature analysis. The wavelet threshold de-noising method is then applied to filter out the high-frequency noise while preserving the low-frequency IMF components. The IMF components containing slag noise are discarded, and the filtered signal and the low-frequency IMF components are used for signal reconstruction to obtain an optimal noise reduction effect. The study demonstrates that this method is more effective in suppressing metal slag noise, environmental noise, and other noise interferences than traditional EMD decomposition noise reduction and wavelet threshold noise reduction methods. This research provides a valuable reference for noise reduction in steel cord conveyor belt detection data.

Research on a Sound Source Localization Method for UAV Detection Based on Improved Empirical Mode Decomposition.

To address the challenge of accurately locating unmanned aerial vehicles (UAVs) in situations where radar tracking is not feasible and visual observation is difficult, this paper proposes an innovative acoustic source localization method based on improved Empirical Mode Decomposition (EMD) within an adaptive frequency window. In this study, the collected flight signals of UAVs undergo smoothing filtering. Additionally, Robust Empirical Mode Decomposition (REMD) is applied to decompose the signals into Intrinsic Mode Function (IMF) components for spectrum analysis. We introduce a sliding frequency window with adjustable bandwidth, which is automatically determined using a Grey Wolf Optimizer (GWO) with a sliding index. This window is used to lock and extract specific frequencies from the IMFs. Based on predefined criteria, the extracted IMF components are reconstructed, and trigger signal times are analyzed and recorded from these reconstructed IMFs. The time differences between sensor receptions are then calculated. Furthermore, this study introduces the Chan-Taylor localization algorithm based on weighted least squares. This advanced algorithm takes sensor time delay parameters as input and solves a set of nonlinear equations to determine the target's location. Simulations and real-world signal tests are used to validate the robustness and performance of the proposed method. The results indicate that the localization error remains below 5% within a 15 m × 15 m measurement area. This provides an efficient and real-time method for detecting the location of small UAVs.

Rolling Bearing Fault Feature Extraction Method based on SSA-VMD and MOMEDA

To address the challenge of extracting bearing fault features, this study proposes a new rolling bearing fault feature extraction method based on the Sparrow Search Algorithm (SSA) to optimize Variational Mode Decomposition (VMD) and Multipoint Optimal Minimum Entropy Deconvolution with Convolution Adjustment (MOMEDA). Firstly, SSA is employed to identify optimal parameters in VMD, followed by the utilization of correlation coefficients and kurtosis to filter relevant Intrinsic Mode Function (IMF) components. Subsequently, MOMEDA is applied to denoise the reconstructed signal, mitigating the interference caused by pulse fault signals. Finally, the envelope spectrum analysis is conducted on the denoised signal. Experimental results demonstrate the efficacy of the proposed method in extracting fault features and mitigating noise interference.

Research on Annual Runoff Prediction Model Based on Adaptive Particle Swarm Optimization–Long Short-Term Memory with Coupled Variational Mode Decomposition and Spectral Clustering Reconstruction

Accurate medium- and long-term runoff prediction models play crucial guiding roles in regional water resources planning and management. However, due to the significant variation in and limited amount of annual runoff sequence samples, it is difficult for the conventional machine learning models to capture its features, resulting in inadequate prediction accuracy. In response to the difficulties in leveraging the advantages of machine learning models and limited prediction accuracy in annual runoff forecasting, firstly, the variational mode decomposition (VMD) method is adopted to decompose the annual runoff series into multiple intrinsic mode function (IMF) components and residual sequences, and the spectral clustering (SC) algorithm is applied to classify and reconstruct each IMF. Secondly, an annual runoff prediction model based on the adaptive particle swarm optimization–long short-term memory network (APSO-LSTM) model is constructed. Finally, with the basis of the APSO-LSTM model, the decomposed and clustered IMFs are predicted separately, and the predicted results are integrated to obtain the ultimate annual runoff forecast results. By decomposing and clustering the annual runoff series, the non-stationarity and complexity of the series have been reduced effectively, and the endpoint effect of modal decomposition has been effectively suppressed. Ultimately, the expected improvement in the prediction accuracy of the annual runoff series based on machine learning models is achieved. Four hydrological stations along the upper reaches of the Fen River in Shanxi Province, China, are studied utilizing the method proposed in this paper, and the results are compared with those obtained from other methods. The results show that the method proposed in this article is significantly superior to other methods. Compared with the APSO-LSTM model and the APSO-LSTM model based on processed annual runoff sequences by single VMD or Wavelet Packet Decomposition (WPD), the method proposed in this paper reduces the RMSE by 40.95–80.28%, 25.26–57.04%, and 15.49–40.14%, and the MAE by 24.46–80.53%, 16.50–59.30%, and 16.58–41.80%, in annual runoff prediction, respectively. The research has important reference significance for annual runoff prediction and hydrological prediction in areas with data scarcity.

Damage Identification of Simple Supported Bridges Under Moving Loads Based on Variational Mode Decomposition and Deep Learning

Aiming at rapid and economical damage detection of a large number of simple supported bridges, a new structural damage identification method under moving load based on variational mode decomposition (VMD) and deep learning is proposed. Firstly, a moving vehicle is used as an exciting load to invoke structural damage feature and enhance the signal-to-noise ratio, and the structural vertical acceleration response is extracted by a finite element simulating analysis under various damage cases. In order to simulate the influence of noise and expand the samples, Gaussian white noise is added to the extracted data, and then the response signal is decomposed into a series of intrinsic mode functions (IMFs) using VMD, and the optimal IMF component is selected as the damage sample of the structure. Then, a one-dimensional convolutional neural network (CNN) model is built and trained by the various samples of damage. The vibration response of the practical bridge is processed and inputted by the trained CNN model to identify the location of the damage and degree of the structure. Finally, the effectiveness and anti-noise performance of the proposed method are verified through numerical analysis and a simply supported beam bridge model experiment. The results show that the average identification accuracy of the numerical simulations and experimental is 93.4% and 86.8% with 20% Gaussian white noise, respectively. Sensors at different locations have almost the same identification effect for various cases of damage, so it is possible to identify structural damage only using a small amount of accelerometer.

Load forecasting for regional integrated energy system based on two-phase decomposition and mixture prediction model

Current load forecasting methods struggle with the randomness and complexity of multiple loads in regional integrated energy systems, resulting in less accurate predictions. To address this problem, this paper proposes a novel two-phase decomposition hybrid forecasting model that combines complementary ensemble empirical mode decomposition, sample entropy, variational mode decomposition, and genetic algorithm-bidirectional long short term memory. The proposed approach begins by decomposing the load sequence into multiple intrinsic mode function components at different frequencies using complementary ensemble empirical mode decomposition. Afterward, the sample entropy values are calculated for each intrinsic mode function. The intrinsic mode function with the highest sample entropy value is subjected to a two-stage decomposition using the variational mode decomposition method. Through this technique, a series of stationary components is acquired. Subsequently, the bidirectional long short term memory model is optimized using the genetic algorithm, and the genetic algorithm-bidirectional long short term memory approach is employed to predict all the decomposed components. Finally, the prediction results are combined and reconstructed to obtain the final prediction value. Experimental results demonstrate the effective handling of non-stationary load sequences by the forecasting model, showcasing the highest level of accuracy in regional integrated energy system multiple loads forecasting.

Research on Speech Denoising Algorithm for Equipment Trains in Fully Mechanized Mining Working Faces based on CEEMDAN High and Low Frequency Filtering

This paper proposes a high and low frequency filtering denoising algorithm based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). CEEMDAN to address the issue of noise in speech signals obtained in the environment of fully mechanized mining face equipment trains. This algorithm first decomposes speech signals into multiple Intrinsic Mode Functions (IMFs) in different frequency domains through CEEMDAN, then uses Hilbert-Huang Transform (HHT) to obtain the instantaneous frequency and amplitude of IMFs, calculates the Euclidean distance between IMFs, normalizes it to obtain the average distance between IMFs, and divides the IMFs components into high and low frequency categories based on the average distance. Next, Optimally Modified Log Spectral Amplitude (OMLSA) algorithm and Kalman filtering algorithm are used for the high-frequency and low-frequency IMF components, respectively. Finally, the processed IMF components are reconstructed to obtain a denoised signal. After comparative experiments, the noise reduction algorithm proposed in this paper significantly improves the Signal to Noise Ratio (SNR), Peak Signal to Noise Ratio (PSNR), Mean Square Error (RMSE), and Mean Absolute Distance (MAE) of speech signals obtained in the environment of fully mechanized mining face equipment trains compared to other commonly used noise reduction algorithms.

Ship Shaft-Rate Electric Field Signal Denoising Method Based on VMD-MSS

The presence of complex electromagnetic noise in the ocean significantly impacts the accuracy of ship shaft-rate electric field signal detection, necessitating the development of an effective denoising method to enhance detection precision. Nevertheless, traditional denoising methods encounter issues like low frequency resolution, challenging threshold configuration, and mode mixing. This study introduces a method that integrates variational mode decomposition (VMD) with multi-window spectral subtraction (MSS). The intrinsic mode functions (IMFs) of noisy signals are extracted using VMD, and the noise components within different IMFs are identified. The spectral features of both signal and noise within different IMFs are leveraged to eliminate noise signals via MSS. Subsequently, the denoised components of IMFs are rearranged to derive the denoised ship shaft-rate electric field signals, achieving noise reduction across various frequency bands. Following validation using simulation signals and empirical data, the noise reduction efficacy of VMD-MSS surpasses that of alternative methods, demonstrating robust performance even at low signal-to-noise ratios. The marine electromagnetic noise is effectively suppressed in the empirical data, while preserving the characteristics of ship’s shaft-rate signals, thereby validating the method’s efficacy and demonstrating its practical engineering value.

Analysis of cardiovascular function in diabetic patients using EEMD-ICA fusion multi-scale percussion entropy.

Diabetes is a chronic disease that can lead to a variety of complications and even cause death. The signal characteristics of the photoplethysmography signals (PPG) and electrocardiogram signals (ECG) can reflect the autonomic and vascular aspects of the effects of diabetes on the body. Based on the complex mechanism of interaction between PPG and ECG, a set of ensemble empirical mode decomposition-independent component analysis (EEMD-ICA) fusion multi-scale percussion entropy index (MSPEI) method was proposed to analyze cardiovascular function in diabetic patients. Firstly, the original signal was decomposed into multiple Intrinsic Mode Function (IMFs) by ensemble empirical mode decomposition EEMD, principal components of IMF were extracted by independent component analysis (ICA), then the extracted principal components were reconstructed to eliminate the complex high and low frequency noise of physiological signals. In addition, the MSPEI was calculated for the ECG R-R interval and PPG amplitude sequence.(RRI and Amp) The results showed that, compared with EEMD method, the SNR of EEMD-ICA method increases from 2.1551 to 11.3642, and the root mean square error (RMSE) decreases from 0.0556 to 0.0067. This algorithm can improve the performance of denoising and retain more feature information. The large and small scale entropy of MSPEI (RRI,Amp) was significantly different between healthy and diabetic patients (p< 0.01). Compared with arteriosclerosis index (AI) and multi-scale cross-approximate entropy (MCAE): MSPEISS (RRI,Amp) indicated that diabetes can affect the activity of human autonomic nervous system, while MSPEILS (RRI,Amp) indicated that diabetes can cause or worsen arteriosclerosis. Multi-scale Percussion Entropy algorithm has more advantages in analyzing the influence of diabetes on human cardiovascular and autonomic nervous function.

A hybrid prediction model of dissolved oxygen concentration based on secondary decomposition and bidirectional gate recurrent unit.

Dissolved oxygen is one of the important comprehensive indicators of river water quality, which reflects the degree of pollution in the water body. Monitoring and predicting dissolved oxygen are an important tool for water quality management, which helps to effectively maintain water ecological balance and prevent environmental problems. A single model cannot describe the dynamic characteristics of dissolved oxygen sequence, which affects the prediction accuracy. In order to obtain more accurate dissolved oxygen prediction results, decomposition techniques are commonly used to extract the main fluctuations and trends of water quality sequences. However, the high-frequency modes obtained from decomposition are still unstable. To solve this problem, this paper proposed a hybrid prediction model of dissolved oxygen concentration based on secondary decomposition and bidirectional gate recurrent unit. Firstly, dissolved oxygen sequence is preliminarily decomposed by complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and obtain several intrinsic mode functions (IMF). The fuzzy entropy (FE) is calculated to quantify the complexity of the IMF. Then, variational mode decomposition improved by northern goshawk optimization is used to decompose the IMF with higher entropy. The nonlinearity and instability of the sequence are further weakened. Finally, the bidirectional gate recurrent unit (BiGRU) neural network is used to predict each IMF component, and the final prediction result is obtained by reconstructing the prediction results of each component. In order to verify the effectiveness of the proposed model, this paper selects the dissolved oxygen data of Xin'anjiang Reservoir as the research object. The experimental results show that the RMSE, MAE, MAPE, and R2 of the proposed model are 0.1164, 0.0894, 1.0403%, and 0.9939, respectively, which is best among other comparative prediction models (BP, LSTM, GRU, BiGRU, EMD-BiGRU, CEEMDAN-BiGRU, VMD-BiGRU, and GNO-VMD-BiGRU). Therefore, this model effectively deals with high volatility and nonlinear dissolved oxygen data and provides reference for water environment management and ecological protection.