Significant wave height forecasts integrating ensemble empirical mode decomposition with sequence-to-sequence model

As wave height is an important parameter in marine climate measurement,its accurate prediction is crucial in ocean engineering.It also plays an important role in marine disaster early warning and ship design,etc.However,challenges in the large demand for computing resources and the improvement of accuracy are currently encountered.To resolve the above mentioned problems,sequence-to-sequence deep learning model(Seq-to-Seq)is applied to intelligently explore the internal law between the continuous wave height data output by the model,so as to realize fast and accurate predictions on wave height data.Simultaneously,ensemble empirical mode decomposition(EEMD)is adopted to reduce the non-stationarity of wave height data and solve the problem of modal aliasing caused by empirical mode decomposition(EMD),and then improves the prediction accuracy.A significant wave height forecast method integrating EEMD with the Seq-to-Seq model(EEMD-Seq-to-Seq)is proposed in this paper,and the prediction models under different time spans are established.Compared with the long short-term memory model,the novel method demonstrates increased continuity for long-term prediction and reduces prediction errors.The experiments of wave height prediction on four buoys show that the EEMD-Seq-to-Seq algorithm effectively improves the prediction accuracy in short-term(3-h,6-h,12-h and 24-h forecast horizon)and long-term(48-h and 72-h forecast horizon)predictions.

Pressure fluctuation signal analysis of pump based on ensemble empirical mode decomposition method

Pressure fluctuations, which are inevitable in the operation of pumps, have a strong non-stationary characteristic and contain a great deal of important information representing the operation conditions. With an axial-flow pump as an example, a new method for time-frequency analysis based on the ensemble empirical mode decomposition （EEMD） method is proposed for research on the characteristics of pressure fluctuations. First, the pressure fluctuation signals are preprocessed with the empirical mode decomposition （EMD） method, and intrinsic mode functions （IMFs） are extracted. Second, the EEMD method is used to extract more precise decomposition results, and the number of iterations is determined according to the number of IMFs produced by the EMD method. Third, correlation coefficients between IMFs produced by the EMD and EEMD methods and the original signal are calculated, and the most sensitive IMFs are chosen to analyze the frequency spectrum. Finally, the operation conditions of the pump are identified with the frequency features. The results show that, compared with the EMD method, the EEMD method can improve the time-frequency resolution and extract main vibration components from pressure fluctuation signals.

Study on the Improvement of the Application of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise in Hydrology Based on RBFNN Data Extension Technology

The complex nonlinear and non-stationary features exhibited in hydrologic sequences make hydrological analysis and forecasting difficult.Currently,some hydrologists employ the complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)method,a new time-frequency analysis method based on the empirical mode decomposition(EMD)algorithm,to decompose non-stationary raw data in order to obtain relatively stationary components for further study.However,the endpoint effect in CEEMDAN is often neglected,which can lead to decomposition errors that reduce the accuracy of the research results.In this study,we processed an original runoff sequence using the radial basis function neural network(RBFNN)technique to obtain the extension sequence before utilizing CEEMDAN decomposition.Then,we compared the decomposition results of the original sequence,RBFNN extension sequence,and standard sequence to investigate the influence of the endpoint effect and RBFNN extension on the CEEMDAN method.The results indicated that the RBFNN extension technique effectively reduced the error of medium and low frequency components caused by the endpoint effect.At both ends of the components,the extension sequence more accurately reflected the true fluctuation characteristics and variation trends.These advances are of great significance to the subsequent study of hydrology.Therefore,the CEEMDAN method,combined with an appropriate extension of the original runoff series,can more precisely determine multi-time scale characteristics,and provide a credible basis for the analysis of hydrologic time series and hydrological forecasting.

A method for extracting human gait series from accelerometer signals based on the ensemble empirical mode decomposition

In this paper, the ensemble empirical mode decomposition （EEMD） is applied to analyse accelerometer signals collected during normal human walking. First, the self-adaptive feature of EEMD is utilised to decompose the ac- celerometer signals, thus sifting out several intrinsic mode functions （IMFs） at disparate scales. Then, gait series can be extracted through peak detection from the eigen IMF that best represents gait rhythmicity. Compared with the method based on the empirical mode decomposition （EMD）, the EEMD-based method has the following advantages： it remarkably improves the detection rate of peak values hidden in the original accelerometer signal, even when the signal is severely contaminated by the intermittent noises; this method effectively prevents the phenomenon of mode mixing found in the process of EMD. And a reasonable selection of parameters for the stop-filtering criteria can improve the calculation speed of the EEMD-based method. Meanwhile, the endpoint effect can be suppressed by using the auto regressive and moving average model to extend a short-time series in dual directions. The results suggest that EEMD is a powerful tool for extraction of gait rhythmicity and it also provides valuable clues for extracting eigen rhythm of other physiological signals.

De-noising of radiation pressure signal generated by bubble oscillation based on ensemble empirical mode decomposition

The radiation pressure signals generated by the bubble oscillation are often utilized to recognize the characteristics of the target objects in many fields.However,these signals are easily contaminated by complex background noises.In order to accurately extract the effective components of the radiation pressure signal generated by the bubble oscillation,this paper proposes a de-noising procedure for the radiation pressure signal,based on the ensemble empirical mode decomposition(EEMD),the autocorrelation function and the modified wavelet soft-threshold de-noising method.In order to verify the effectiveness of the procedure,the typical radiation pressure signal generated based on the Keller-Miksis model under the acoustic excitation is employed for the subsequent de-noising analysis.The results of the qualitative analysis show that the amplitude and the period of the bubble oscillation can be clearly observed in the time-domain diagram of the de-noised signal based on the EEMD.In the quantitative analysis,the de-noised signal based on the EEMD has better performance with higher signal-to-noise ratio(SNR),smaller root-mean-square error,and larger correlation coefficient than that based on the wavelet transform(WT)and the empirical mode decomposition(EMD).Furthermore,with the increase of the complexity of the radiation pressure signal(e.g.,the increase of the dimensionless pressure amplitude of the acoustic wave and the decrease of the SNR of the input signal),the above three evaluation indexes of the de-noised signal based on the EEMD are all better than those based on the other two methods.When the signal is more complex,the de-noising capabilities of the WT,the EMD are greatly reduced,but the EEMD can still maintain the good de-noising capability,which shows the superiority of the signal de-noising procedure proposed in the present paper.

Regional features of topographic relief over the Loess Plateau,China:evidence from ensemble empirical mode decomposition

Landforms with similar surface matter compositions,endogenic and exogenic forces,and development histories tend to exhibit significant degrees of self-similarity in morphology and spatial variation.In loess hill-gully areas,ridges and hills have similar topographic relief characteristics and present nearly periodic variations of similar repeating structures at certain spatial scales,which is termed the topographic relief period(TRP).This is a relatively new concept,which is different from the degree of relief,and describes the fluctuations of the terrain from both horizontal and vertical(cross-section)perspectives,which can be used for in-depth analysis of 2-D topographic relief features.This technique provides a new perspective for understanding the macro characteristics and differentiation patterns of loess landforms.We investigate TRP variation features of different landforms on the Loess Plateau,China,by extracting catchment boundary profiles(CBPs)from 5 m resolution digital elevation model(DEM)data.These profiles were subjected to temporal-frequency analysis using the ensemble empirical mode decomposition(EEMD)method.The results showed that loess landforms are characterized by significant regional topographic relief;the CBP of 14 sample areas exhibited an overall pattern of decreasing TRPs and increasing topographic relief spatial frequencies from south to north.According to the TRPs and topographic relief characteristics,the topographic relief of the Loess Plateau was divided into four types that have obvious regional differences.The findings of this study enrich the theories and methods for digital terrain data analysis of the Loess Plateau.Future study should undertake a more in-depth investigation regarding the complexity of the region and to address the limitations of the EEMD method.

The Modified Ensemble Empirical Mode Decomposition Method and Extraction of Oceanic Internal Wave from Synthetic Aperture Radar Image

In this paper a modified ensemble empirical mode decomposition(EEMD) method is presented, which is named winning-EEMD(W-EEMD). Two aspects of the EEMD, the amplitude of added white noise and the number of intrinsic mode functions(IMFs), are discussed in this method. The signal-to-noise ratio(SNR) is used to measure the amplitude of added noise and the winning number of IMFs(which results most frequency) is used to unify the number of IMFs. By this method, the calculation speed of decomposition is improved, and the relative error between original data and sum of decompositions is reduced. In addition, the feasibility and effectiveness of this method are proved by the example of the oceanic internal solitary wave.

A hybrid approach based on complete ensemble empirical mode decomposition with adaptive noise for multi-step-ahead solar radiation forecasting

Accurate measurements of solar radiation are required to ensure that power and energy systems continue to function effectively and securely.On the other hand,estimating it is extremely challenging due to the non-stationary behaviour and randomness of its components.In this research,a novel hybrid forecasting model,namely complete ensemble empirical mode decomposition with adaptive noise-Gaussian process regression(CEEMDAN-GPR),has been developed for daily global solar radiation prediction.The non-stationary global solar radiation series is transformed by CEEMDAN into regular subsets.After that,the GPR model uses these subsets as inputs to perform its prediction.According to the results of this research,the performance of the developed hybrid model is superior to two widely used hybrid models for solar radiation forecasting,namely wavelet-GPR and wavelet packet-GPR,in terms of mean square error,root mean square error,coefficient of determination and relative root mean square error values,which reached 3.23 MJ/m^(2)/day,1.80 MJ/m^(2)/day,95.56%,and 8.80%,respectively(for one-step forward forecasting).The proposed hybrid model can be used to ensure the safe and reliable operation of the electricity system.

An Enhanced Ensemble-Based Long Short-Term Memory Approach for Traffic Volume Prediction

With the advancement of artificial intelligence,traffic forecasting is gaining more and more interest in optimizing route planning and enhancing service quality.Traffic volume is an influential parameter for planning and operating traffic structures.This study proposed an improved ensemble-based deep learning method to solve traffic volume prediction problems.A set of optimal hyperparameters is also applied for the suggested approach to improve the performance of the learning process.The fusion of these methodologies aims to harness ensemble empirical mode decomposition’s capacity to discern complex traffic patterns and long short-term memory’s proficiency in learning temporal relationships.Firstly,a dataset for automatic vehicle identification is obtained and utilized in the preprocessing stage of the ensemble empirical mode decomposition model.The second aspect involves predicting traffic volume using the long short-term memory algorithm.Next,the study employs a trial-and-error approach to select a set of optimal hyperparameters,including the lookback window,the number of neurons in the hidden layers,and the gradient descent optimization.Finally,the fusion of the obtained results leads to a final traffic volume prediction.The experimental results show that the proposed method outperforms other benchmarks regarding various evaluation measures,including mean absolute error,root mean squared error,mean absolute percentage error,and R-squared.The achieved R-squared value reaches an impressive 98%,while the other evaluation indices surpass the competing.These findings highlight the accuracy of traffic pattern prediction.Consequently,this offers promising prospects for enhancing transportation management systems and urban infrastructure planning.

Missing interpolation model for wind power data based on the improved CEEMDAN method and generative adversarial interpolation network

Randomness and fluctuations in wind power output may cause changes in important parameters(e.g.,grid frequency and voltage),which in turn affect the stable operation of a power system.However,owing to external factors(such as weather),there are often various anomalies in wind power data,such as missing numerical values and unreasonable data.This significantly affects the accuracy of wind power generation predictions and operational decisions.Therefore,developing and applying reliable wind power interpolation methods is important for promoting the sustainable development of the wind power industry.In this study,the causes of abnormal data in wind power generation were first analyzed from a practical perspective.Second,an improved complete ensemble empirical mode decomposition with adaptive noise(ICEEMDAN)method with a generative adversarial interpolation network(GAIN)network was proposed to preprocess wind power generation and interpolate missing wind power generation sub-components.Finally,a complete wind power generation time series was reconstructed.Compared to traditional methods,the proposed ICEEMDAN-GAIN combination interpolation model has a higher interpolation accuracy and can effectively reduce the error impact caused by wind power generation sequence fluctuations.

A Hybrid BPNN-GARF-SVR Prediction Model Based on EEMD for Ship Motion

Accurate prediction of shipmotion is very important for ensuringmarine safety,weapon control,and aircraft carrier landing,etc.Ship motion is a complex time-varying nonlinear process which is affected by many factors.Time series analysis method and many machine learning methods such as neural networks,support vector machines regression(SVR)have been widely used in ship motion predictions.However,these single models have certain limitations,so this paper adopts amulti-model prediction method.First,ensemble empirical mode decomposition(EEMD)is used to remove noise in ship motion data.Then the randomforest(RF)prediction model optimized by genetic algorithm(GA),back propagation neural network(BPNN)prediction model and SVR prediction model are respectively established,and the final prediction results are obtained by results of three models.And the weights coefficients are determined by the correlation coefficients,reducing the risk of prediction and improving the reliability.The experimental results show that the proposed combined model EEMD-GARF-BPNN-SVR is superior to the single predictive model and more reliable.The mean absolute percentage error(MAPE)of the proposed model is 0.84%,but the results of the single models are greater than 1%.

基于EEMD、相关系数、排列熵和小波阈值去噪的新型水下声学信号去噪方法

The complexities of the marine environment and the unique characteristics of underwater channels pose challenges in obtaining reliable signals underwater,necessitating the filtration of underwater acoustic noise.Herein,an underwater acoustic signal denoising method based on ensemble empirical mode decomposition(EEMD),correlation coefficient(CC),permutation entropy(PE),and wavelet threshold denoising(WTD)is proposed.Furthermore,simulation experiments are conducted using simulated and real underwater acoustic data.The experimental results reveal that the proposed denoising method outperforms other previous methods in terms of signal-to-noise ratio,root mean square error,and CC.The proposed method eliminates noise and retains valuable information in the signal.

Price prediction of power transformer materials based on CEEMD and GRU

The rapid growth of the Chinese economy has fueled the expansion of power grids.Power transformers are key equipment in power grid projects,and their price changes have a significant impact on cost control.However,the prices of power transformer materials manifest as nonsmooth and nonlinear sequences.Hence,estimating the acquisition costs of power grid projects is difficult,hindering the normal operation of power engineering construction.To more accurately predict the price of power transformer materials,this study proposes a method based on complementary ensemble empirical mode decomposition(CEEMD)and gated recurrent unit(GRU)network.First,the CEEMD decomposed the price series into multiple intrinsic mode functions(IMFs).Multiple IMFs were clustered to obtain several aggregated sequences based on the sample entropy of each IMF.Then,an empirical wavelet transform(EWT)was applied to the aggregation sequence with a large sample entropy,and the multiple subsequences obtained from the decomposition were predicted by the GRU model.The GRU model was used to directly predict the aggregation sequences with a small sample entropy.In this study,we used authentic historical pricing data for power transformer materials to validate the proposed approach.The empirical findings demonstrated the efficacy of our method across both datasets,with mean absolute percentage errors(MAPEs)of less than 1%and 3%.This approach holds a significant reference value for future research in the field of power transformer material price prediction.

基于CEEMDAN-HT的永磁同步电机匝间短路振动信号故障特征提取研究

由于长时间处于高负荷运行状态,永磁同步电机(permanent magnet synchronous motor, PMSM)定子绕组线圈匝与匝之间的绝缘性能容易降低,导致出现匝间短路,此时电机的振动强度会发生改变。针对此现象,提出将自适应噪声完备经验模态分解(complete ensemble empirical mode decomposition with adaptive noise, CEEMDAN)与希尔伯特变换(Hilbert transform, HT)结合,构成一种CEEMDAN-HT非线性信号分析方法,并将其应用于提取振动信号故障特征。首先,利用CEEMDAN算法分解振动信号,得到一系列本征模态函数(intrinsic mode function, IMF),并将主元分析中的方差贡献率用于识别包含故障特征信息的IMF。其次,使用HT对方差贡献率较高的IMF进行分析,并以三维联合时频图呈现时间、瞬时频率与幅值,得到了主要故障特征。最后,使用ANSYS有限元软件建立了电机短路故障模型,并搭建了短路故障试验平台,通过对比有限元仿真结果与试验结果,对提出的方法进行了有效性和准确性验证。

Characteristics of the dynamic changes in active accumulated temperature in Sichuan,China in the last 51 years against the background of climate change

It is of utmost necessity to understand the dynamics of regional active accumulated temperature(AAT)to cope with the negative impacts of global warming on agroforestry development and food security and to provide a real-time and effective reference basis for regional agroforestry planning.The daily temperature data from 30 meteorological stations in Sichuan Province from 1970 to 2020,and sea surface temperature(SST)index data from the Atlantic Multiphase Oscillation(AMO)and Pacific Decadal Oscillation(PDO)were used for the study.Sichuan Province was divided into the western region(WS)and the eastern region(ES),considering 1000 m above sea level as the boundary.The spatiotemporal characteristics of≥0℃ and≥10℃ active accumulated temperature(AAT0,AAT10)in WS and ES were analyzed comprehensively using 5-day average sliding,empirical orthogonal function(EOF),ensemble empirical mode decomposition(EEMD),and multiple mutation tests.The results show that(1)AAT0 and AAT10 of WS ranged from 3034℃ to 3586℃ and 1971℃ to 2636℃,respectively,while the AAT0 and AAT10 of ES ranged from 5863℃ to 6513℃ and 4847℃ to 5875℃,respectively.The period around 1997 was a significant abrupt change,and the AAT in the province generally increased during the subsequent time period(2)AAT in the study area is mainly driven by the fluctuations of AMO,as reflected by the low-to-high variation of AAT coinciding with the jump of the cold-to-warm phase of AMO.Considering different time scale fluctuations in the past 51 years,the major cycle for both AAT0 and AAT10 in WS is 3.40 a,while the major cycles in ES are 3.64 a and 3.19 a,respectively with a sub-cycle of 7.29 a.AAT fluctuation has an insignificant periodic characteristic of 25.50 a on the interdecadal scale(3)The spatial heterogeneity of AAT in WS is prominent and is mainly reflected by the significantly warm conditions in the south of the WS region and relatively slight warm conditions in the north,as well as by the isolated cooling area in the form of"freezing point",i.e.,Xiaojin county.In contrast,the spatial variability of AAT in ES is more or less consistent,with the warming areas concentrated in the foothills of the western edge of the basin and a slight increase in AAT observed in the central part of the basin.

Extraction of Strain Characteristic Signals from Wind Turbine Blades Based on EEMD-WT

Analyzing the strain signal of wind turbine blade is the key to studying the load of wind turbine blade,so as to ensure the safe and stable operation of wind turbine in natural environment.The strain signal of the wind turbine blade under continuous crosswind state has typical non-stationary and unsteady characteristics.The strain signal contains a lot of noise,which makes the analysis error.Therefore,it is very important to denoise and extract features of measured signals before signal analysis.In this paper,the joint algorithm of ensemble empirical mode decomposition(EEMD)and wavelet transform(WT)is used for the first time to achieve sufficient noise reduction and effectively extract the feature signals of non-stationary strain signals.The application process of EEMD-WT is optimized.This optimization can avoid the repeated selection of wavelet basis function and the number of decomposition layers due to different crosswind conditions.EEMD adaptively decomposes the strain signal into intrinsic mode functions,to judge the frequency of IMFs,remove the high-frequency noise components,retain the useful components.The useful components are denoised twice by the wavelet transform,the components and residual terms after the secondary denoising are reconstructed to obtain the characteristic signal.The EEMD-WT was applied to process the simulating signals andmeasured the strain signals.The results were compared with the results of the EEMD.The results showed that the EEMD-WTmethod has better noise reduction performance,and can effectively extract the characteristics of strain signals,which lays a solid foundation for accurate analysis of wind turbine blade strain signals under crosswind conditions.

Prediction of seawater pH by bidirectional gated recurrent neural network with attention under phase space reconstruction:case study of the coastal waters of Beihai,China

Marine life is very sensitive to changes in pH.Even slight changes can cause ecosystems to collapse.Therefore,understanding the future pH of seawater is of great significance for the protection of the marine environment.At present,the monitoring method of seawater pH has been matured.However,how to accurately predict future changes has been lacking effective solutions.Based on this,the model of bidirectional gated recurrent neural network with multi-headed self-attention based on improved complete ensemble empirical mode decomposition with adaptive noise combined with phase space reconstruction(ICPBGA)is proposed to achieve seawater pH prediction.To verify the validity of this model,pH data of two monitoring sites in the coastal sea area of Beihai,China are selected to verify the effect.At the same time,the ICPBGA model is compared with other excellent models for predicting chaotic time series,and root mean square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE),and coefficient of determination(R2)are used as performance evaluation indicators.The R2 of the ICPBGA model at Sites 1 and 2 are above 0.9,and the prediction errors are also the smallest.The results show that the ICPBGA model has a wide range of applicability and the most satisfactory prediction effect.The prediction method in this paper can be further expanded and used to predict other marine environmental indicators.

MEEMD-DBA-based short term traffic flow prediction

Aiming at the problem that ensemble empirical mode decomposition(EEMD)method can not completely neutralize the added noise in the decomposition process,which leads to poor reconstruction of decomposition results and low accuracy of traffic flow prediction,a traffic flow prediction model based on modified ensemble empirical mode decomposition(MEEMD),double-layer bidirectional long-short term memory(DBiLSTM)and attention mechanism is proposed.Firstly,the intrinsic mode functions(IMFs)and residual components(Res)are obtained by using MEEMD algorithm to decompose the original traffic data and separate the noise in the data.Secondly,the IMFs and Res are put into the DBiLSTM network for training.Finally,the attention mechanism is used to enhance the extraction of data features,then the obtained results are reconstructed and added.The experimental results show that in different scenarios,the MEEMD-DBiLSTM-attention(MEEMD-DBA)model can reduce the data reconstruction error effectively and improve the accuracy of the short-term traffic flow prediction.

An Analysis of Historical and Future Temperature Fluctuations over China Based on CMIP5 Simulations

The trends and fluctuations of observed and CMIP5-simulated yearly mean surface air temperature over China were analyzed.In general,the historical simulations replicate the observed increase of temperature,but the multi-model ensemble （MME） mean does not accurately reproduce the drastic interannual fluctuations.The correlation coefficient of the MME mean with the observations over all runs and all models was 0.77,which was larger than the largest value （0.65） from any single model ensemble.The results showed that winter temperatures are increasing at a higher rate than summer temperatures,and that winter temperatures exhibit stronger interannual variations.It was also found that the models underestimate the differences between winter and summer rates.The ensemble empirical mode decomposition technique was used to obtain six intrinsic mode functions （IMFs） for the modeled temperature and observations.The periods of the first two IMFs of the MME mean were 3.2 and 7.2,which represented the cycle of 2-7-yr oscillations.The periods of the third and fourth IMFs were 14.7 and 35.2,which reflected a multi-decadal oscillation of climate change.The corresponding periods of the first four IMFs were 2.69,7.24,16.15 and 52.5 in the observed data.The models overestimate the period of low frequency oscillation of temperature,but underestimate the period of high frequency variation.The warming rates from different representative concentration pathways （RCPs） were calculated,and the results showed that the temperature will increase by approximately 0.9℃,2.4℃,3.2℃ and 6.1℃ in the next century under the RCP2.6,RCP4.5,RCP6.0 and RCP8.5 scenarios,respectively.

On Multi-Timescale Variability of Temperature in China in Modulated Annual Cycle Reference Frame

The traditional anomaly （TA） reference frame and its corresponding anomaly for a given data span changes with the extension of data length. In this study, the modulated annual cycle （MAC）, instead of the widely used climatological mean annual cycle, is used as an alternative reference frame for computing climate anomalies to study the multi-timescale variability of surface air temperature （SAT） in China based on homogenized daily data from 1952 to 2004. The Ensemble Empirical Mode Decomposition （EEMD） method is used to separate daily SAT into a high frequency component, a MAC component, an interannual component, and a decadal-to-trend component. The results show that the EEMD method can reflect historical events reasonably well, indicating its adaptive and temporally local characteristics. It is shown that MAC is a temporally local reference frame and will not be altered over a particular time span by an exten-sion of data length, thereby making it easier for physical interpretation. In the MAC reference frame, the low frequency component is found more suitable for studying the interannual to longer timescale variability （ILV） than a 13-month window running mean, which does not exclude the annual cycle. It is also better than other traditional versions （annual or summer or winter mean） of ILV, which contains a portion of the annual cycle. The analysis reveals that the variability of the annual cycle could be as large as the magnitude of interannual variability. The possible physical causes of different timescale variability of SAT in China are further discussed.