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.

Landslide displacement prediction based on optimized empirical mode decomposition and deep bidirectional long short-term memory network

There are two technical challenges in predicting slope deformation.The first one is the random displacement,which could not be decomposed and predicted by numerically resolving the observed accumulated displacement and time series of a landslide.The second one is the dynamic evolution of a landslide,which could not be feasibly simulated simply by traditional prediction models.In this paper,a dynamic model of displacement prediction is introduced for composite landslides based on a combination of empirical mode decomposition with soft screening stop criteria(SSSC-EMD)and deep bidirectional long short-term memory(DBi-LSTM)neural network.In the proposed model,the time series analysis and SSSC-EMD are used to decompose the observed accumulated displacements of a slope into three components,viz.trend displacement,periodic displacement,and random displacement.Then,by analyzing the evolution pattern of a landslide and its key factors triggering landslides,appropriate influencing factors are selected for each displacement component,and DBi-LSTM neural network to carry out multi-datadriven dynamic prediction for each displacement component.An accumulated displacement prediction has been obtained by a summation of each component.For accuracy verification and engineering practicability of the model,field observations from two known landslides in China,the Xintan landslide and the Bazimen landslide were collected for comparison and evaluation.The case study verified that the model proposed in this paper can better characterize the"stepwise"deformation characteristics of a slope.As compared with long short-term memory(LSTM)neural network,support vector machine(SVM),and autoregressive integrated moving average(ARIMA)model,DBi-LSTM neural network has higher accuracy in predicting the periodic displacement of slope deformation,with the mean absolute percentage error reduced by 3.063%,14.913%,and 13.960%respectively,and the root mean square error reduced by 1.951 mm,8.954 mm and 7.790 mm respectively.Conclusively,this model not only has high prediction accuracy but also is more stable,which can provide new insight for practical landslide prevention and control engineering.

Vehicle-Bridge Interaction Simulation and Damage Identification of a Bridge Using Responses Measured in a Passing Vehicle by Empirical Mode Decomposition Method

To prevent early bridge failures, effective Structural Health Monitoring (SHM) is vital. Vibration-based damage assessment is a powerful tool in this regard, as it relies on changes in a structure’s dynamic characteristics as it degrades. By measuring the vibration response of a bridge due to passing vehicles, this approach can identify potential structural damage. This dissertation introduces a novel technique grounded in Vehicle-Bridge Interaction (VBI) to evaluate bridge health. It aims to detect damage by analyzing the response of passing vehicles, taking into account VBI. The theoretical foundation of this method begins with representing the bridge’s superstructure using a Finite Element Model and employing a half-car dynamic model to simulate the vehicle with suspension. Two sets of motion equations, one for the bridge and one for the vehicle are generated using the Finite Element Method, mode superposition, and D’Alembert’s principle. The combined dynamics are solved using the Newmark-beta method, accounting for road surface roughness. A new approach for damage identification based on the response of passing vehicles is proposed. The response is theoretically composed of vehicle frequency, bridge natural frequency, and a pseudo-frequency component related to vehicle speed. The Empirical Mode Decomposition (EMD) method is applied to decompose the signal into its constituent parts, and damage detection relies on the Intrinsic Mode Functions (IMFs) corresponding to the vehicle speed component. This technique effectively identifies various damage scenarios considered in the study.

A New Method of Wind Turbine Bearing Fault Diagnosis Based on Multi-Masking Empirical Mode Decomposition and Fuzzy C-Means Clustering

Based on Multi-Masking Empirical Mode Decomposition (MMEMD) and fuzzy c-means (FCM) clustering, a new method of wind turbine bearing fault diagnosis FCM-MMEMD is proposed, which can determine the fault accurately and timely. First, FCM clustering is employed to classify the data into different clusters, which helps to estimate whether there is a fault and how many fault types there are. If fault signals exist, the fault vibration signals are then demodulated and decomposed into different frequency bands by MMEMD in order to be analyzed further. In order to overcome the mode mixing defect of empirical mode decomposition (EMD), a novel method called MMEMD is proposed. It is an improvement to masking empirical mode decomposition (MEMD). By adding multi-masking signals to the signals to be decomposed in different levels, it can restrain low-frequency components from mixing in highfrequency components effectively in the sifting process and then suppress the mode mixing. It has the advantages of easy implementation and strong ability of suppressing modal mixing. The fault type is determined by Hilbert envelope finally. The results of simulation signal decomposition showed the high performance of MMEMD. Experiments of bearing fault diagnosis in wind turbine bearing fault diagnosis proved the validity and high accuracy of the new method.

Remote Sensing Image Fusion Using Bidimensional Empirical Mode Decomposition and the Least Squares Theory

Due to the data acquired by most optical earth observation satellite such as IKONOS, QuickBird-2 and GF-1 consist of a panchromatic image with high spatial resolution and multiple multispectral images with low spatial resolution. Many image fusion techniques have been developed to produce high resolution multispectral image. Considering panchromatic image and multispectral images contain the same spatial information with different accuracy, using the least square theory could estimate optimal spatial information. Compared with previous spatial details injection mode, this mode is more accurate and robust. In this paper, an image fusion method using Bidimensional Empirical Mode Decomposition (BEMD) and the least square theory is proposed to merge multispectral images and panchromatic image. After multi-spectral images were transformed from RGB space into IHS space, next I component and Panchromatic are decomposed by BEMD, then using the least squares theory to evaluate optimal spatial information and inject spatial information, finally completing fusion through inverse BEMD and inverse intensity-hue-saturation transform. Two data sets are used to evaluate the proposed fusion method, GF-1 images and QuickBird-2 images. The fusion images were evaluated visually and statistically. The evaluation results show the method proposed in this paper achieves the best performance compared with the conventional method.

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.

Source Separation of Diesel Engine Vibration Based on the Empirical Mode Decomposition and Independent Component Analysis

Vibration signals from diesel engine contain many different components mainly caused by combustion and mechanism operations,several blind source separation techniques are available for decomposing the signal into its components in the case of multichannel measurements,such as independent component analysis(ICA).However,the source separation of vibration signal from single-channel is impossible.In order to study the source separation from single-channel signal for the purpose of source extraction,the combination method of empirical mode decomposition(EMD) and ICA is proposed in diesel engine signal processing.The performance of the described methods of EMD-wavelet and EMD-ICA in vibration signal application is compared,and the results show that EMD-ICA method outperforms the other,and overcomes the drawback of ICA in the case of single-channel measurement.The independent source signal components can be separated and identified effectively from one-channel measurement by EMD-ICA.Hence,EMD-ICA improves the extraction and identification abilities of source signals from diesel engine vibration measurements.

Satellite fault diagnosis method based on predictive filter and empirical mode decomposition

A novel satellite fault diagnosis scheme is presented based on the predictive filter and empirical mode composition(EMD).First,the predictive filter is utilized to obtain the fault estimation,which is corrupted by noise.Then the EMD method is introduced to decompose the fault estimation into a finite number of intrinsic mode functions and extract the trend of faults for fault diagnosis.The proposed scheme has the ability of diagnosing both abrupt and incipient faults of the actuator in a satellite attitude control subsystem.A mathematical simulation is given to illustrate the effectiveness of the proposed scheme.

A novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise,minimum mean square variance criterion and least mean square adaptive filter

Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity of marine environment and the particularity of underwater acoustic channel,noise reduction of underwater acoustic signals has always been a difficult challenge in the field of underwater acoustic signal processing.In order to solve the dilemma,we proposed a novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),minimum mean square variance criterion(MMSVC) and least mean square adaptive filter(LMSAF).This noise reduction technique,named CEEMDAN-MMSVC-LMSAF,has three main advantages:(i) as an improved algorithm of empirical mode decomposition(EMD) and ensemble EMD(EEMD),CEEMDAN can better suppress mode mixing,and can avoid selecting the number of decomposition in variational mode decomposition(VMD);(ii) MMSVC can identify noisy intrinsic mode function(IMF),and can avoid selecting thresholds of different permutation entropies;(iii) for noise reduction of noisy IMFs,LMSAF overcomes the selection of deco mposition number and basis function for wavelet noise reduction.Firstly,CEEMDAN decomposes the original signal into IMFs,which can be divided into noisy IMFs and real IMFs.Then,MMSVC and LMSAF are used to detect identify noisy IMFs and remove noise components from noisy IMFs.Finally,both denoised noisy IMFs and real IMFs are reconstructed and the final denoised signal is obtained.Compared with other noise reduction techniques,the validity of CEEMDAN-MMSVC-LMSAF can be proved by the analysis of simulation signals and real underwater acoustic signals,which has the better noise reduction effect and has practical application value.CEEMDAN-MMSVC-LMSAF also provides a reliable basis for the detection,feature extraction,classification and recognition of underwater acoustic signals.

Regional features of the temperature trend in China based on Empirical Mode Decomposition

由实验模式分解方法，我们在超过 700 个车站分析了观察每月平均的温度从 1951 2001 在中国上。同时，每个车站的温度可变性被这个方法计算。

NON-DESTRUCTIVE PAVEMENT LAYER THICKNESS MEASUREMENT USING EMPIRICAL MODE DECOMPOSITION WITH GPR

Ground Penetrating Radar(GPR) is an effective Non-Destructive Testing(NDT) technique for highway pavement surveys, which is able to acquire continuous pavement data compared with traditional core drilling method. In this study, we proposed an accurate and efficient method to estimate the thickness of each pavement layer using an air-coupled GPR system. For this work, the main difficulties are estimating each pavement layer's time delay and dielectric constant. We first give the basic signal model for pavement evaluation, and then present an Intrinsic Mode Functions(IMFs) product detector to determine each pavement layer's time delay. This method is based on Empirical Mode Decomposition(EMD), which is an adaptive signal decomposition procedure and proved to be suitable for suppressing noises in GPR signal. The dielectric constant was determined by metal reflection measurement. The laboratory and highway experiments illustrate that the proposed thickness estimation method yields reasonable result, thus meets the requirements of practical highway pavement survey with massive GPR data.

NOISE REDUCTION METHOD FOR OCT IMAGES BASED ON EMPIRICAL MODE DECOMPOSITION

In this paper,the new method for OCT images denoizing based on empirical mode decomposition(EMD)is proposed.The noise reduction is a very important process for following operations to analyze and recognition of tissue structure.Our method does not require any additional operations and hardware modifications.The basics of proposed method is described.Quality improvement of noise suppression om example of edge detection procedure using the classical Canny's algorithm without any additional pre-and post-proc essing operations is demonstrated.Improvement of raw-segmentation in the automatic diagnostic process between a tissue and a mesh implant is shown.

Electricity Demand Time Series Forecasting Based on Empirical Mode Decomposition and Long Short-Term Memory

Load forecasting is critical for a variety of applications in modern energy systems.Nonetheless,forecasting is a difficult task because electricity load profiles are tied with uncertain,non-linear,and non-stationary signals.To address these issues,long short-term memory(LSTM),a machine learning algorithm capable of learning temporal dependencies,has been extensively integrated into load forecasting in recent years.To further increase the effectiveness of using LSTM for demand forecasting,this paper proposes a hybrid prediction model that incorporates LSTM with empirical mode decomposition(EMD).EMD algorithm breaks down a load time-series data into several sub-series called intrinsic mode functions(IMFs).For each of the derived IMFs,a different LSTM model is trained.Finally,the outputs of all the individual LSTM learners are fed to a meta-learner to provide an aggregated output for the energy demand prediction.The suggested methodology is applied to the California ISO dataset to demonstrate its applicability.Additionally,we compare the output of the proposed algorithm to a single LSTM and two state-of-the-art data-driven models,specifically XGBoost,and logistic regression(LR).The proposed hybrid model outperforms single LSTM,LR,and XGBoost by,35.19%,54%,and 49.25%for short-term,and 36.3%,34.04%,32%for longterm prediction in mean absolute percentage error,respectively.

Computational Intelligence Prediction Model Integrating Empirical Mode Decomposition,Principal Component Analysis,and Weighted k-Nearest Neighbor

On the basis of machine leaning,suitable algorithms can make advanced time series analysis.This paper proposes a complex k-nearest neighbor(KNN)model for predicting financial time series.This model uses a complex feature extraction process integrating a forward rolling empirical mode decomposition(EMD)for financial time series signal analysis and principal component analysis(PCA)for the dimension reduction.The information-rich features are extracted then input to a weighted KNN classifier where the features are weighted with PCA loading.Finally,prediction is generated via regression on the selected nearest neighbors.The structure of the model as a whole is original.The test results on real historical data sets confirm the effectiveness of the models for predicting the Chinese stock index,an individual stock,and the EUR/USD exchange rate.

Chirplet Signal and Empirical Mode Decompositions of Ultrasonic Signals for Echo Detection and Estimation

In this study, the performance of chirplet signal decomposition (CSD) and empirical mode decomposition (EMD) coupled with Hilbert spectrum have been evaluated and compared for ultrasonic imaging applications. Numerical and experimental results indicate that both the EMD and CSD are able to decompose sparsely distributed chirplets from noise. In case of signals consisting of multiple interfering chirplets, the CSD algorithm, based on successive search for estimating optimal chirplet parameters, outperforms the EMD algorithm which estimates a series of intrinsic mode functions (IMFs). In particular, we have utilized the EMD as a signal conditioning method for Hilbert time-frequency representation in order to estimate the arrival time and center frequency of chirplets in order to quantify the ultrasonic signals. Experimental results clearly exhibit that the combined EMD and CSD is an effective processing tools to analyze ultrasonic signals for target detection and pattern recognition.

FAST IMPLEMENTATION OF ORTHOGONAL EMPIRICAL MODE DECOMPOSITION AND ITS APPLIGA-TION INTO HARMONIC DETECTION

Since the empirical mode decomposition (EMD) lacks strict orthogonality,the method of orthogonal empirical mode decomposition (OEMD) is innovationally proposed.The primary thought of this method is to obtain the intrinsic mode function (IMF) and the residual function by auto-adaptive band-pass filtering.OEMD is proved to preserve strict orthogonality and completeness theoretically,and the orthogonal basis function of OEMD is generated,then an algorithm to implement OEMD fast,IMF binary searching algorithm is built based on the point that the analytical band-pass filtering preserves perfect band-pass feature in the frequency domain.The application into harmonic detection shows that OEMD successfully conquers mode aliasing,avoids the occurrence of false mode,and is featured by fast computing speed.Furthermore,it can achieve harmonic detection accurately combined with the least square method.

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.

Application of empirical mode decomposition based energy ratio to vortex flowmeter state diagnosis

To improve the measurement performance, a method for diagnosing the state of vortex flowmeter under various flow conditions was presented. The raw sensor signal of the vortex flowmeter was adaptively decomposed into intrinsic mode functions using the empirical mode decomposition approach. Based on the empirical mode decomposition results, the energy of each intrinsic mode function was extracted, and the vortex energy ratio was proposed to analyze how the perturbation in the flow affected the measurement performance of the vortex flowmeter. The relationship between the vortex energy ratio of the signal and the flow condition was established. The results show that the vortex energy ratio is sensitive to the flow condition and ideal for the characterization of the vortex flowmeter signal. Moreover, the vortex energy ratio under normal flow condition is greater than 80%, which can be adopted as an indicator to diagnose the state of a vortex flowmeter.

GEARBOX FAULTDIAGNOSIS BASED ON EMPIRICAL MODE DECOMPOSITION

Time synchronous averaging of vibration data is a fundament technique for gearbox diagnosis. Currently, this technique relies on hardware tachometer to give phase synchronous information. Empirical mode decomposition (EMD) is introduced to replace time synchronous averaging of gearbox vibration signal. With it, any complicated dataset can be decomposed into a finite and often small number of intrinsic mode functions (IMF). The key problem is how to assure that vibration signals deduced by gear defects could be sifted out by EMD. The characteristic vibration signals of gear defects are proved IMFs, which makes it possible to utilize EMD for the diagnosis of gearbox faults. The method is validated by data from recordings of the vibration of a single-stage spiral bevel gearbox with fatigue pitting. The results show EMD is powerful to extract characteristic information from noisy vibration signals.

Improvement of the Mirror Extending in Empirical Mode Decomposition Method and the Technology for Eliminating Frequency Mixing

The mirror extending approach proposed by Zhao and Huang in EMD method is improved in this paper. Mirror extending manner of data is kept unchanged, but the approach for determining envelopes is changed. When the end of data is obviously not extremum, the envelope is determined by the first inner extremum and the image value in the mirror, ignoring the value on the end. This improvement eliminates the frequency compression near the end and decreases the error. Meanwhile, tridiagonal equations are used and the calculation speed is much increased. The temporal process curve is more important in reflecting the real physical process and comparable with other phenomena. Frequency mixing in IMFs makes it impossible. A high frequency reconstruction (HFR) approach is proposed to eliminate common frequency mixing and reconstruct an IMF with all high frequency portions. By this approach, the IMFs without frequency mixing are obtained to express significative processes. The high frequency information restored in high frequency IMF can be extracted by general spectrum method. After obtaining IMFs by EMD method, some of the theoretical and technological issues still exist when using the IMFs. The consistency of IMFs with real physical process is discussed in detail. By virtue of the approach proposed in this paper, the EMD method can be widely used in various fields.