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The paper aims to present an innovative method for identification of flight modes in the spin maneuver, which is highly nonlinear and coupled dynamic.

To fix the mode mixing problem which is mostly happen in the EMD algorithm, the authors focused on the proposal of an optimized ensemble empirical mode decomposition (OEEMD) algorithm for processing of the flight complex signals that originate from FDR. There are two improvements with the OEEMD respect to the EEMD. First, this algorithm is able to make a precise reconstruction of the original signal. The second improvement is that the OEEMD performs the task of signal decomposition with fewer iterations and so with less complexity order rather than the competitor approaches.

By applying the OEEMD algorithm to the spin flight parameter signals, flight modes extracted, then with using systematic technique, flight modes characteristics are obtained. The results indicate that there are some non-standard modes in the nonlinear region due to couplings between the longitudinal and lateral motions.

Application of the proposed method to the spin flight test data may result accurate identification of nonlinear dynamics with high coupling in this regime.

First, to fix the mode mixing problem in EMD, an optimized ensemble empirical mode decomposition algorithm is introduced, which disturbed the original signal with a sort of white Gaussian noise, and by using white noise statistical characteristics the OEEMD fix the mode mixing problem with high precision and fewer calculations. Second, by applying the OEEMD to the flight output signals and with using the systematic method, flight mode characteristics which is very important in the simulation and controller designing are obtained.

The purpose of this paper is to develop a new structural damage detection technique based on multi-channel empirical mode decomposition (MEMD) of vibrational response data.

Empirical mode decomposition (EMD) is an empirical data-based signal decomposition method which has been applied in many engineering problems. Utilizing classical EMD to reveal the damage-indicating features of structural vibration response encounters some difficulties due to the inconsistency of modes obtained from different data channels. To overcome this problem, MEMD has been employed. To this end, MEMD algorithm has been adopted to impulse response vector of measured DOFs. The proposed method has been carried out concerning both numerical and experimental beam models. Damage has been modeled by reducing the flexural rigidity in some predefined beam sections. The effects of various factors such as measurement grid density, damage severity and damage position are investigated.

The results of both numerical and experimental case studies have been promising. The method could determine the damage location in all cases. The efficiency of method gets better when damage is located far from inflation points of the corresponding mode. In such cases, utilizing higher modes can make up the efficiency.

Since the present research is the first investigation of MEMD in damage localization, just one-dimensional structures have been studied. Extending the method to more complicated geometries needs further attempt.

Although a number of relevant studies have been carried out based on EMD, up to the author’s best knowledge, this is the first attempt to structural damage localization using MEMD.

This paper applied grey wave forecasting in a decomposition–ensemble forecasting method for modelling the complex and non-linear features in time series data. This application aims to test the advantages of grey wave forecasting method in predicting time series with periodic fluctuations.

The decomposition–ensemble method combines empirical mode decomposition (EMD), component reconstruction technology and grey wave forecasting. More specifically, EMD is used to decompose time series data into different intrinsic mode function (IMF) components in the first step. Permutation entropy and the average of each IMF are checked for component reconstruction. Then the grey wave forecasting model or ARMA is used to predict each IMF according to the characters of each IMF.

In the empirical analysis, the China container freight index (CCFI) is applied in checking prediction performance. Using two different time periods, the results show that the proposed method performs better than random walk and ARMA in multi-step-ahead prediction.

The decomposition–ensemble method based on EMD and grey wave forecasting model expands the application area of the grey system theory and graphic forecasting method. Grey wave forecasting performs better for data set with periodic fluctuations. Forecasting CCFI assists practitioners in the shipping industry in decision-making.

Embedding dimension determination in phase space reconstruction is difficult. The purpose of this paper is to present a new approach for embedding dimension determination based on empirical mode, showing that embedding dimensions for phase space reconstruction could be easily determined according to the number of intrinsic mode functions decomposed by empirical mode decomposition.

Through the relation analysis of intrinsic mode functions and embedding dimensions, the approach for embedding dimension determination by the number of intrinsic mode functions is presented. First, a time series is decomposed into several intrinsic mode functions. Second, correlation analysis between intrinsic mode functions and original signals is investigated, and then false intrinsic mode functions could be eliminated by the analysis of correlation coefficient thresholds, which makes the embedding dimension precise. Finally, the method presented is applied to the Lorenz system, Chen's system, and the Duffing equation. Simulation results prove this method is feasible.

A new approach for embedding dimension determination based on empirical mode decomposition is presented. Compared with G‐P algorithms, this new method is effective and decreases computational complexity.

This method provides an effective qualitative criterion to the selection of embedding dimensions in phase space reconstruction.

This method could be used to determine embedding dimensions of phase space reconstruction and degree‐of‐freedom of nonlinear dynamical systems.

The paper proposes a new method of embedding dimension determination in phase space reconstruction.

Despite the widespread use of univariate empirical mode decomposition (EMD) in financial market forecasting, the application of multivariate empirical mode decomposition (MEMD) has not been fully investigated. The purpose of this study is to forecast the stock price index more accurately, relying on the capability of MEMD in modeling the dependency between relevant variables.

Quantitative and comprehensive assessments were carried out to compare the performance of some selected models. Data for the assessments were collected from three major stock exchanges, namely, the standard and poor 500 index from the USA, the Hang Seng index from Hong Kong and the Shanghai Stock Exchange composite index from China. MEMD-based support vector regression (SVR) was used as the modeling framework, where MEMD was first introduced to simultaneously decompose the relevant covariates, including the opening price, the highest price, the lowest price, the closing price and the trading volume of a stock price index. Then, SVR was used to set up forecasting models for each component decomposed and another SVR model was used to generate the final forecast based on the forecasts of each component. This paper named this the MEMD-SVR-SVR model.

The results show that the MEMD-based modeling framework outperforms other selected competing models. As per the models using MEMD, the MEMD-SVR-SVR model excels in terms of prediction accuracy across the various data sets.

This research extends the literature of EMD-based univariate models by considering the scenario of multiple variables for improving forecasting accuracy and simplifying computability, which contributes to the analytics pool for the financial analysis community.

The electromechanical brake system is leading the latest development trend in railway braking technology. The tolerance stack-up generated during the assembly and production process catalyzes the slight geometric dimensioning and tolerancing between the motor stator and rotor inside the electromechanical cylinder. The tolerance leads to imprecise brake control, so it is necessary to diagnose the fault of the motor in the fully assembled electromechanical brake system. This paper aims to present improved variational mode decomposition (VMD) algorithm, which endeavors to elucidate and push the boundaries of mechanical synchronicity problems within the realm of the electromechanical brake system.

The VMD algorithm plays a pivotal role in the preliminary phase, employing mode decomposition techniques to decompose the motor speed signals. Afterward, the error energy algorithm precision is utilized to extract abnormal features, leveraging the practical intrinsic mode functions, eliminating extraneous noise and enhancing the signal’s fidelity. This refined signal then becomes the basis for fault analysis. In the analytical step, the cepstrum is employed to calculate the formant and envelope of the reconstructed signal. By scrutinizing the formant and envelope, the fault point within the electromechanical brake system is precisely identified, contributing to a sophisticated and accurate fault diagnosis.

This paper innovatively uses the VMD algorithm for the modal decomposition of electromechanical brake (EMB) motor speed signals and combines it with the error energy algorithm to achieve abnormal feature extraction. The signal is reconstructed according to the effective intrinsic mode functions (IMFS) component of removing noise, and the formant and envelope are calculated by cepstrum to locate the fault point. Experiments show that the empirical mode decomposition (EMD) algorithm can effectively decompose the original speed signal. After feature extraction, signal enhancement and fault identification, the motor mechanical fault point can be accurately located. This fault diagnosis method is an effective fault diagnosis algorithm suitable for EMB systems.

By using this improved VMD algorithm, the electromechanical brake system can precisely identify the rotational anomaly of the motor. This method can offer an online diagnosis analysis function during operation and contribute to an automated factory inspection strategy while parts are assembled. Compared with the conventional motor diagnosis method, this improved VMD algorithm can eliminate the need for additional acceleration sensors and save hardware costs. Moreover, the accumulation of online detection functions helps improve the reliability of train electromechanical braking systems.

Early fault detection of bearing plays an increasingly important role in the operation of rotating machinery. Based on the properties of early fault signal of bearing, this paper aims to describe a novel hybrid early fault detection method of bearings.

In adaptive variational mode decomposition (AVMD), an adaptive strategy is proposed to select the optimal decomposition level K of variational mode decomposition. Then, a criterion based on envelope entropy is applied to select the optimal intrinsic mode functions (OIMF), which contains most useful fault information. Afterwards, local tangent space alignment (LTSA) is used to denoising of OIMF. The envelope spectrum of the OIMF is used to analyze the fault frequency, thereby detecting the fault. Experiments are conducted in a simulated signal and two experimental vibration signals of bearings to verify the effect of the new method.

The results show that the proposed method yields a good capability of detecting bearing fault at an early stage. The new method can extract more useful information and can reduce noise, which can provide better detection accuracy compared with the other two methods.

An adaptive strategy based on center frequency is proposed to select the optimal decomposition level of variational mode decomposition. Envelope entropy is used to fault feature selection. Combining the advantage of the AVMD-envelope entropy and LTSA, which suits the nature of the early fault signal. So, the proposed method has better detection accuracy, which provides a good alternative for early fault detection of bearings.

The purpose of this paper is to provide a shorter time cost, high-accuracy fault diagnosis method for water pumps. Water pumps are widely used in industrial equipment and their fault diagnosis is gaining increasing attention. Considering the time-consuming empirical mode decomposition (EMD) method and the more efficient classification provided by the convolutional neural network (CNN) method, a novel classification method based on incomplete empirical mode decomposition (IEMD) and dual-input dual-channel convolutional neural network (DDCNN) composite data is proposed and applied to the fault diagnosis of water pumps.

This paper proposes a data preprocessing method using IEMD combined with mel-frequency cepstrum coefficient (MFCC) and a neural network model of DDCNN. First, the sound signal is decomposed by IEMD to get numerous intrinsic mode functions (IMFs) and a residual (RES). Several IMFs and one RES are then extracted by MFCC features. Ultimately, the obtained features are split into two channels (IMFs one channel; RES one channel) and input into DDCNN.

The Sound Dataset for Malfunctioning Industrial Machine Investigation and Inspection (MIMII dataset) is used to verify the practicability of the method. Experimental results show that decomposition into an IMF is optimal when taking into account the real-time and accuracy of the diagnosis. Compared with EMD, 51.52% of data preprocessing time, 67.25% of network training time and 63.7% of test time are saved and also improve accuracy.

This method can achieve higher accuracy in fault diagnosis with a shorter time cost. Therefore, the fault diagnosis of equipment based on the sound signal in the factory has certain feasibility and research importance.

This method provides a feasible method for mechanical fault diagnosis based on sound signals in industrial applications.

This paper proposes an intelligent fault diagnosis method, which aims to obtain the outstanding fault diagnosis results of the gearbox.

An intelligent fault diagnosis method based on energy entropy-weighted complementary ensemble empirical mode decomposition (EWCEEMD) and support vector machine (SVM) optimized by whale optimization algorithm (WOA) is proposed. The raw signal is first denoised by the wavelet noise reduction method. Then, complementary ensemble empirical mode decomposition (CEEMD) is used to generate several intrinsic mode functions (IMFs). Next, energy entropy is used as an indicator to measure the sensibility of the IMF and converted into a weight coefficient by function. After that, IMFs are linearly weighted to form the reconstruction signal, and several features are extracted from the new signal. Finally, the support vector machine optimized by the whale optimization algorithm (WOA-SVM) model is used for gearbox fault classification using feature vectors.

The fault features extracted by this method have a better clustering effect and clear boundaries under each fault mode than the unimproved method. At the same time, the accuracy of fault diagnosis is greatly improved.

In most studies of fault diagnosis, the sensitivity of IMF has not been appreciated. In this paper, energy entropy is chosen to quantify sensitivity. In addition, high classification accuracy can be achieved by applying WOA-SVM as the final classification model, improving the efficiency of fault diagnosis as well.

This paper aims to present a new method for identification of some flight modes, including natural and non-standard modes, and extraction of their characteristics, directly from measurements of flight parameters in the time domain.

The Hilbert-Huang transform (HHT), as a novel prevailing tool in the signal analysis field, is used to attain the purpose. The study shows that the HHT has superior potential capabilities to improve the airplane flying quality analysis and to conquer some drawbacks of the classical method in flight dynamics.

The proposed method reveals the existence of some non-standard modes with small damping ratios at non-linear flight regions and obtains their characteristics.

The paper examines only airplane longitudinal dynamics. Further research is needed regarding lateral-directional dynamic modes and coupling effects of the longitudinal and lateral modes.

Application of the proposed method to the flight test data may result in real-time flying quality analysis, especially at the non-linear flight regions.

First, to utilize the empirical mode decomposition (EMD) capabilities in real time, a local-online algorithm is introduced which estimates the signal trend by the Savitzky-Golay sifting process and eliminates it from the signal in the EMD algorithm. Second, based on the local-online EMD algorithm, a systematic method is proposed to identify flight modes from flight parameters in the time domain.