Number Of Intrinsic Mode Functions Research Articles

ANALYSIS OF THE PRECIPITATION CLIMATE SIGNAL USING EMPIRICAL MODE DECOMPOSITION (EMD) OVER THE CASPIAN CATCHMENT AREA

Abstract. In this paper, we employ Empirical Mode Decomposition (EMD) together with Hilbert Transform to analyze precipitation time series over the Caspian Sea catchment. Several studies have shown that EMD can extract nonlinear and non-stationary signals better than Fast Fourier Transform (FFT) and Wavelet Transform. EMD decomposes the time series into a finite number of Intrinsic Mode Functions (IMFs) in the time-frequency domain, while FFT helps us operate either in the time or the frequency domain, which fuels limitations such as the inability of nonstationary signal processing and the lack of time transparency. Although Wavelet Transform is shown to be better than FFT, it fails to detect the instantaneous frequencies and needs to have prior information about characteristics of the data. On the other hand, EMD has shown that it is almost able to determine the signal characteristics with no previous assumptions to estimate the instantaneous frequencies of the signal. In this work, EMD is applied to identify the main frequencies of precipitation time series. Thereafter, a statistical procedure is used to identify the prominent IMF of the original signal.We use the correlation coefficient, Minkowski distance and variance test to extract the relevant and prominent IMFs. The results show that IMF 1–3 are the relevant components and are related to annual and biennial variations of precipitation time series over the Caspian catchment during 2003–2016, respectively.

Laser self-mixing interference displacement measurement based on VMD and phase unwrapping

In order to measure displacement accurately and conveniently, the laser self-mixing interference measurement method based on variational mode decomposition (VMD) and phase unwrapping is proposed. The laser self-mixing interference technology has many advantages such as high sensitivity, ease of use and compactness. The VMD method can non-recursively decompose a self-mixing interference signal into a number of intrinsic mode functions and remove noise effectively. The linewidth enhancement factor and the optical feedback level factor are measured by the hysteresis phenomenon in the self-mixing interference. The reconstruction of displacement is implemented by phase unwrapping. The displacement measurement is carried out by the self-mixing interference experimental system. The experimental results show that the displacement measurement error is less than 80 nm, which verifies the correctness of the method.

Desert seismic signal denoising by 2D compact variational mode decomposition

AbstractNoise suppression and effective signal recovery are very important for seismic signal processing. The random noise in desert areas has complex characteristics due to the complex geographical environment; noise characteristics such as non-stationary, non-linear and low frequency. These make it difficult for conventional denoising methods to remove random noise in desert seismic records. To address the problem, this paper proposes a two-dimensional compact variational mode decomposition (2D-CVMD) algorithm for desert seismic noise attenuation. This model decomposes the complex desert seismic data into an finite number of intrinsic mode functions with specific directions and vibration characteristics. The algorithm introduces binary support functions, which can detect the edge region of the signal in each mode by penalizing the support function through the L1 and total variation (TV) norm. Finally, the signal can be reconstructed by the support functions and the decomposed modes. We apply the 2D-CVMD algorithm to synthetic and real seismic data. The results show that the 2D-CVMD algorithm can not only suppress desert low-frequency noise, but also recover the weak effective signal.

Radio Frequency Interference Suppression for HF Surface Wave Radar Using CEMD and Temporal Windowing Methods

A common source of interference in high-frequency (HF) surface wave (HFSW) radars is radio frequency interference (RFI). Its existence inhibits the detection performance of HFSW radars since its amplitude can mask the sea echoes. On the basis of the analysis of RFI characteristics, a new RFI mitigation algorithm based on inverse temporal windowing and complex empirical mode decomposition (CEMD) is proposed in this letter. In this method, echoes containing RFI are decomposed into a number of intrinsic mode functions (IMFs) via CEMD and then the inverse temporal windowing technique is applied to each IMFs in the time domain. Test results show that the proposed method outperforms the conventional method in simulated and practical conditions and can effectively mitigate RFI without losing sea echoes.

A hybrid Elman recurrent neural network, group search optimization, and refined VMD-based framework for multi-step ahead electricity price forecasting

This paper presents a synergy of three methods for training the Elman recurrent neural network to forecast the multi-step-ahead electricity price in an electric power system. Electricity prices are characterized as non-stationary time series data that entail vigorous learning model for predicting the future electricity price from past data. To accomplish this, an enhanced hybrid framework that integrates the refined variational mode decomposition method and the group search optimization algorithm is proposed for training the Elman recurrent neural network. The variational mode decomposition method is optimized using a complement particle swarm optimization method so as to decompose the non-stationary pricing data into optimum number of intrinsic mode functions. Subsequently, based on the power values of intrinsic mode, functions are further filtered and used as the input data to train the Elman neural network. The group search optimization algorithm is used to optimize the weights of the Elman neural network. Three real-time time series non-stationary data for multi-step ahead price prediction are adopted from Australian, British, and Indian power markets and experimented using the proposed forecasting model.

Time-varying system identification by enhanced Empirical Wavelet Transform based on Synchroextracting Transform

In this paper, an enhanced Empirical Wavelet Transform (EWT) approach based on Synchroextracting Transform (SET) is proposed for time-varying system identification. When a structure of time-varying physical properties, i.e. mass, stiffness or damping, is under external excitations, structural dynamic responses are usually non-stationary because the system has time-varying dynamic vibration characteristics. Under this circumstance, it would be difficult to determine the number of Intrinsic Mode Functions (IMFs) included in structural dynamic responses by using Fourier spectrum. Considering that the filtering boundaries of traditional EWT method are defined based on the segmental Fourier Spectrum of a processed signal, directly using it for non-stationary signal decomposition may not be effective and accurate. To apply the EWT method for time-varying system identification, in this study, time-frequency analysis based on SET is first performed to determine the frequency components of a non-stationary vibration signal instead of using Fourier spectrum. The filtering boundaries for EWT analysis are determined based on the time-frequency representation. Then, the IMFs are extracted from the non-stationary vibration signals by using EWT with the above defined filtering boundaries. When the IMFs are accurately obtained, the instantaneous frequencies of IMFs are identified by using Hilbert Transform (HT). In numerical simulations, a simulated signal with a high level noise is analyzed to verify the feasibility of using SET to define the filtering boundaries. Then the proposed approach is used to identify the instantaneous frequencies of a time-varying two-storey shear type building under earthquake and Gaussian white noise excitations, respectively. Experimental investigations on a time-varying bridge-vehicle system are conducted to verify the effectiveness of the proposed approach. The results in both numerical simulations and experimental validations demonstrate that the enhanced EWT approach can effectively and reliably identify the instantaneous frequencies of time-varying systems.

Decomposition-ANN Methods for Long-Term Discharge Prediction Based on Fisher’s Ordered Clustering with MESA

Precise and reliable long-term streamflow prediction contributes to water resources planning and management. Artificial neural network (ANN) have shown its remarkable ability in forecasting non-linear hydrological processes without involvement of complex, dynamic, hydrological and hydro-climatologic physical process in the water shed. To improve its non-stationary responses, decomposition methods are adopted as pre-processing methods in this study including Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD) and Seasonal-Trend decomposition using Loess (STL). The original time sequence is decomposed to several components, which are then taken as the inputs of the ANN model. EMD and EEMD are data- adaptable methods, and thus the number of Intrinsic Mode Functions (IMFs) might differ for different sequences, leading to the discrepancy of the input number for ANN model in training and predicting. Fisher’s ordered clustering is thus used to classify the IMFs into a determined number of classes based on their frequency spectrum resulting from Maximum Entropy Spectral Analysis (MESA). The proposed methodology is applied on four important hydrological stations on the upper stream of the Yellow River and the Yangtze River in China, respectively, to forecast the streamflow of the next whole year with the historical daily data of the past 6 years. The Nash-Sutcliffe efficiencies of the monthly prediction are higher than 0.85 for all of the four cases, and various indicators indicates that the proposed hybrid method of STL-ANN performs better than other compared methods. The highlights of this study lies in that only historical daily streamflow data is used to derive an accurate long-term prediction by data mining based on decomposition technology and mapping relationships between the decomposed components and the original sequence in the future.

An EMD-MRLS de-noising method for fiber optic gyro Signal

In order to reduce the influence of fiber optic gyroscope (FOG) random drift error on inertial navigation systems (INS), a novel de-noising method is proposed in this paper, which based on an improved empirical mode decomposition (EMD) and modified recursive least square (RLS). Referred to as the EMD-MRLS method, it is developed to decompose the FOG outputs into a number of intrinsic mode functions (IMFs) after which mode manipulations are divided into three parts, noise IMFs, mixed IMFs, and information IMFs by two index parameters based on mahalanobis distance (MD). A modified RLS algorithm is then employed to process the mixed IMFs, from which the refined IMFs components are reconstructed to produce the final de-noising results. Other traditional methods, such as RLS, and EMD are investigated to provide a comparison with the proposed one through both simulated signals and experimental FOG outputs. Compared with the EMD method, the results show that the error mean is reduced by 27.01%, and the horizontal position error is reduced by 106.75m, when the INS lasts for 1000s.

Operational modal identification of structures based on improved empirical wavelet transform

This paper proposes an improved Empirical Wavelet Transform (EWT) approach for structural operational modal identification based on measured dynamic responses of structures under ambient vibrations. Two steps are involved in the improved EWT approach. In the first step, the standardized autoregressive power spectrum of the measured response is calculated to define the boundaries of frequency components for the subsequent EWT analysis. The second step is to decompose the measured response into a number of Intrinsic Mode Functions (IMFs) by using EWT. When the Intrinsic Mode Functions are obtained, structural modal information such as natural frequencies, mode shapes, and damping ratios can be identified by using Hilbert transform and Random Decrement Technique. In numerical studies, a simulated signal is used to investigate the effectiveness of the proposed approach. Operational modal identification based on the proposed approach and procedure is conducted to identify the modal parameters of a simulated spatial frame structure under the ambient excitations. The proposed approach is further used for operational modal identification of a seven-storey shear type steel frame structure in the laboratory and a real footbridge under ambient vibrations to verify the accuracy and performance. The modal identification results from both numerical simulations and experimental validations demonstrate that the proposed approach can effectively and accurately decompose the vibration responses and identify the structural modal parameters under operational conditions.

High-Intensity Focused Ultrasound Lesion Detection Using Adaptive Compressive Sensing Based on Empirical Mode Decomposition.

Background:The main goal of ultrasound therapy is to have clinical effects in the tissue without damage to the intervening and surrounding tissues. Treatments have been developed for both in vitro and in clinical applications. HIFU therapy is one of these. Non-invasive surgeries, such as HIFU, have been developed to treat tumors or to stop bleeding. In this approach, an adequate imaging method for monitoring and controlling the treatment is required.Methods:In this paper, an adaptive compressive sensing representation of ultrasound RF echo signals is presented based on empirical mode decomposition (EMD). According to the different numbers of intrinsic mode functions (IMFs) produced by the EMD, the ultrasound signals is adaptively compressive sampled in the source and then adaptively reconstructed in the receiver domains. In this paper, a new application of compressive sensing based on EMD (CS-EMD) in the monitoring of high-intensity focused ultrasound (HIFU) treatment is presented. Non-invasive surgeries such as HIFU have been developed for various therapeutic applications. In this technique, a suitable imaging method is necessary for monitoring of the treatment to achieve adequate treatment safety and efficacy. So far, several methods have been proposed, such as ultrasound radiofrequency (RF) signal processing techniques, and imaging methods such as X-ray, MRI, and ultrasound to monitor HIFU lesions.Results:In this paper, a CS-EMD method is used to detect the HIFU thermal lesion dimensions using different types of wavelet transform. The results of the processing on the real data demonstrate the potential for this technique in image-guided HIFU therapy.Conclusions:In this study, a new application of compressive sensing in the field of monitoring of the HIFU treatment is presented. To the best of our knowledge, so far no studies on compressive sensing have been carried out in the monitoring of the HIFU. Based on the results obtained, it was showed that the number of measurements and Intrinsic Mode Functions have the function of noise reduction. In addition, results were shown that the successful reconstruction of the compressive sensing signals can be gained using a threshold based algorithm. To this end, in this paper it was shown that by selecting an suitable number of measurements, the sparse transform, and a thresholding algorithm, we can achieve a more accurate detection of the HIFU thermal lesion size.

Energy Time Series Forecasting Based on Empirical Mode Decomposition and FRBF-AR Model

Energy time series forecasting is challenging due to its uncertainty of natural factor. Energy time series has nonlinear and non-stationary characteristics and not normally distributed, which makes it difficult to be forecast by statistical or computational intelligent methods. A set of locally linear fuzzy radial basis function (FRBF) to approximate the functional coefficients of the state-dependent autoregressive (SD-AR) model and the proposed model is called FRBF-AR model, which combines the advantage of FRBF in function approximation and the merit of SD-AR model in nonlinear dynamics description. Empirical mode decomposition (EMD) is a powerful tool to decompose a complex time series into a number of intrinsic mode functions (IMFs) and one residual series. Then, these sub-series are predicted by the FRBF-AR model. Finally, the prediction results of the IMFs and residual series are added to formulate an ensemble forecast for the original energy time series. Furthermore, energy time series data sets from the generated electricity and load demand time series are used to test the effectiveness of the proposed hybrid modeling method. The simulation results demonstrate the effectiveness of the proposed hybrid modeling method compared with other forecasting methods.

A multi-source fusion algorithm for high-accuracy signal reconstruction of vehicle interior noise on passenger ear-sides

The use of reconstructed noise signal as a primary reference signal is critical toactive noise control in passenger ear-sides under high-speed conditions. A signal decomposition optimisation-based BP neural network for ear-side noise reconstruction (DBENR) algorithm is proposed. This algorithm contains the processes of signal decomposition optimisation (SDO), component fitness calculation (CFC) and ear-side noise reconstruction (ENR). The SDO method is divided into two steps. Firstly, multi-source noise signals are decomposed into a finite number of intrinsic mode function (IMF) components by empirical mode decomposition. Secondly, according to a proposed energy-extreme division method, the IMFs are reconstructed into three signal components, namely, high-, intermediate- and low-frequency components. CFC calculates the fitness of a component in each forward training process of a signal reconstruction BP network to obtain the optimal fitness value. The ENR model is obtained by regarding the optimal fitness values as the initial weights and the thresholds of the signal reconstruction BP network and training. The effectiveness of the proposed DBENR algorithm is validated using five noise signal sources collected from a vehicle. Compared with the signal reconstruction BP algorithm, the proposed algorithm is superior in reconstruction accuracy.

Dynamic fluctuations of cross-correlations in multi-time scale

With the empirical mode decomposition, we investigate the dynamic fluctuations of cross-correlations in multi-time scale. In this approach, the time series of price returns in financial markets is decomposed into a small number of intrinsic mode functions, and the corresponding time series of phases can be obtained with the Hilbert transform. Through the empirical mode decomposition, we uncover that the cross-correlations between stocks change significantly for different time scales and exhibit singular behaviors during a financial crisis. With the phase correlation analysis, we observe that the cross-correlations between market indices vary also for different time scales. Dividing the total time interval into two sub-intervals by the year 2007, we detect that the market indices are much more correlated after 2007.

Short-Term Wind Speed Forecasting Based on Signal Decomposing Algorithm and Hybrid Linear/Nonlinear Models

Accurate wind speed forecasting is a significant factor in grid load management and system operation. The aim of this study is to propose a framework for more precise short-term wind speed forecasting based on empirical mode decomposition (EMD) and hybrid linear/nonlinear models. Original wind speed series is decomposed into a finite number of intrinsic mode functions (IMFs) and residuals by using the EMD. Several popular linear and nonlinear models, including autoregressive integrated moving average (ARIMA), support vector machine (SVM), random forest (RF), artificial neural network with back propagation (BP), extreme learning machines (ELM) and convolutional neural network (CNN), are utilized to study IMFs and residuals, respectively. An ensemble forecast for the original wind speed series is then obtained. Various experiments were conducted on real wind speed series at four wind sites in China. The performance and robustness of various hybrid linear/nonlinear models at two time intervals (10 min and 1 h) are compared comprehensively. It is shown that the EMD based hybrid linear/nonlinear models have better accuracy and more robust performance than the single models with/without EMD. Among the five hybrid models, EMD-ARIMA-RF has the best accuracy on the whole for 10 min data, and the mean absolute percentage error (MAPE) is less than 0.04. However, for the 1 h data, no model can always perform well on the four datasets, and the MAPE is around 0.15.

A Novel Adaptive Signal Processing Method Based on Enhanced Empirical Wavelet Transform Technology.

Empirical wavelet transform (EWT) is a novel adaptive signal decomposition method, whose main shortcoming is the fact that Fourier segmentation is strongly dependent on the local maxima of the amplitudes of the Fourier spectrum. An enhanced empirical wavelet transform (MSCEWT) based on maximum-minimum length curve method is proposed to realize fault diagnosis of motor bearings. The maximum-minimum length curve method transforms the original vibration signal spectrum to scale space in order to obtain a set of minimum length curves, and find the maximum length curve value in the set of the minimum length curve values for obtaining the number of the spectrum decomposition intervals. The MSCEWT method is used to decompose the vibration signal into a series of intrinsic mode functions (IMFs), which are processed by Hilbert transform. Then the frequency of each component is extracted by power spectrum and compared with the theoretical value of motor bearing fault feature frequency in order to determine and obtain fault diagnosis result. In order to verify the effectiveness of the MSCEWT method for fault diagnosis, the actual motor bearing vibration signals are selected and the empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) methods are selected for comparative analysis in here. The results show that the maximum-minimum length curve method can enhance EWT method and the MSCEWT method can solve the shortcomings of the Fourier spectrum segmentation and can effectively decompose the bearing vibration signal for obtaining less number of intrinsic mode function (IMF) components than the EMD and EEMD methods. It can effectively extract the fault feature frequency of the motor bearing and realize fault diagnosis. Therefore, the study provides a new method for fault diagnosis of rotating machinery.

Selecting effective intrinsic mode functions of empirical mode decomposition and variational mode decomposition using dynamic time warping algorithm for rolling element bearing fault diagnosis

Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) are data-driven self-adaptive signal processing methods to decompose a complex signal into different modes of separate spectral bands, in to a number of Intrinsic Mode Functions (IMFs). While the EMD extracts modes recursively and empirically, the VMD extracts modes non-recursively and concurrently. In this paper, both the EMD and the VMD have been applied to examine their efficacy in fault diagnosis of rolling element bearing. However, all the IMFs do not contain necessary information regarding fault characteristic signature of the bearing. In order to select the effective IMF, the Dynamic Time Warping (DTW) algorithm has been employed here, which gives a measurement of similarity index between two signals. Also, correlation analysis has been carried out to select the appropriate IMFs. Finally, out of the selected IMFs, bearing characteristic fault frequencies have been determined with the envelope spectrum.

Radio Frequency Interference Mitigation for High-Frequency Surface Wave Radar

Radio frequency interference (RFI) is a common source of interference for high-frequency surface wave radar (HFSWR) since the HF band is shared among many radio services. The existence of RFI greatly degrades the detection performance of HFSWR. On the basis of a detailed analysis of the characteristics of RFI, a new RFI mitigation method based on joint fractional Fourier transform (FRFT) and complex empirical mode decomposition (CEMD) is proposed in this letter. In this method, the optimum transform order of the FRFT is obtained through a two-level peak search. Subsequently, echoes that contain RFI are transformed into the fractional Fourier domain and are then decomposed into a number of intrinsic mode functions (IMFs) via CEMD. The RFI is mitigated by implementing detection and localization in each IMF. The reconstructed signal is then transformed into the time domain via an inverse FRFT, and the mitigated signal is finally obtained. Processing results using experimental data indicate that the proposed method can effectively suppress RFI without losing echoes.

Incipient fault feature extraction of rolling bearings based on the MVMD and Teager energy operator

Aiming at the problems that the incipient fault of rolling bearings is difficult to recognize and the number of intrinsic mode functions (IMFs) decomposed by variational mode decomposition (VMD) must be set in advance and can not be adaptively selected, taking full advantages of the adaptive segmentation of scale spectrum and Teager energy operator (TEO) demodulation, a new method for early fault feature extraction of rolling bearings based on the modified VMD and Teager energy operator (MVMD-TEO) is proposed. Firstly, the vibration signal of rolling bearings is analyzed by adaptive scale space spectrum segmentation to obtain the spectrum segmentation support boundary, and then the number K of IMFs decomposed by VMD is adaptively determined. Secondly, the original vibration signal is adaptively decomposed into K IMFs, and the effective IMF components are extracted based on the correlation coefficient criterion. Finally, the Teager energy spectrum of the reconstructed signal of the effective IMF components is calculated by the TEO, and then the early fault features of rolling bearings are extracted to realize the fault identification and location. Comparative experiments of the proposed method and the existing fault feature extraction method based on Local Mean Decomposition and Teager energy operator (LMD-TEO) have been implemented using experimental data-sets and a measured data-set. The results of comparative experiments in three application cases show that the presented method can achieve a fairly or slightly better performance than LMD-TEO method, and the validity and feasibility of the proposed method are proved.

Long term rolling prediction model for solar radiation combining empirical mode decomposition (EMD) and artificial neural network (ANN) techniques

Long-term prediction of solar radiation intensity plays an important role in the planning and design of photovoltaic power stations. Unlike previous research on solar radiation prediction requiring various meteorological and topographic data, this study proposed a rolling prediction model combining Empirical Mode Decomposition (EMD) and Artificial Neural Network (ANN) techniques with the need for historical solar radiation data only. To overcome the inconsistency problem of the number of intrinsic mode functions derived from the EMD, they are classified into high-frequency term, low-frequency term, and trend item, which are taken as the input parameters of the ANN model. With the historical data one-year after as the output parameter, the ANN model implies the complex, non-linear relationship between the adjacent periods, and it can be used to predict long-term solar radiation. The proposed methodology is applied to Gonghe county in the Qinghai province of China, where a large-scale photovoltaic power plant is under planning. The results indicate that the correlation coefficients between the daily and monthly predicted value and the historical data are 0.698 and 0.930, respectively, which are comparable to previous studies with a greater data requirement and a simpler model.

Fault Diagnosis of Electromechanical Actuator Based on VMD Multifractal Detrended Fluctuation Analysis and PNN

Electromechanical actuators (EMAs) are more and more widely used as actuation devices in flight control system of aircrafts and helicopters. The reliability of EMAs is vital because it will cause serious accidents if the malfunction of EMAs occurs, so it is significant to detect and diagnose the fault of EMAs timely. However, EMAs often run under variable conditions in realistic environment, and the vibration signals of EMAs are nonlinear and nonstationary, which make it difficult to effectively achieve fault diagnosis. This paper proposed a fault diagnosis method of electromechanical actuators based on variational mode decomposition (VMD) multifractal detrended fluctuation analysis (MFDFA) and probabilistic neural network (PNN). First, the vibration signals were decomposed by VMD into a number of intrinsic mode functions (IMFs). Second, the multifractal features hidden in IMFs were extracted by using MFDFA, and the generalized Hurst exponents were selected as the feature vectors. Then, the principal component analysis (PCA) was introduced to realize dimension reduction of the extracted feature vectors. Finally, the probabilistic neural network (PNN) was utilized to classify the fault modes. The experimental results show that this method can effectively achieve the fault diagnosis of EMAs even under diffident working conditions. Simultaneously, the diagnosis performance of the proposed method in this paper has an advantage over that of EMD‐MFDFA method for feature extraction.