Long-term wave height forecasting using VMD-informer

The time series of blood glucose concentration in diabetic patients are time-varying, nonlinear, and non-stationary. In order to improve the accuracy of blood glucose prediction, a multi-scale combination short-term blood glucose prediction model was constructed by combining the variational mode decomposition (VMD) method, the kernel extreme learning machine (KELM), and the AdaBoost algorithm (VMD-ELM-AdaBoost). Firstly, the blood glucose concentration series were decomposed into a set of intrinsic modal functions (IMFs) with different scales by the VMD method. On this basis, the KELM neural network and AdaBoost algorithm are combined to predict each IMF component. Finally, the cumulative blood glucose concentration prediction value is obtained by accumulating the KELM-AdaBoost prediction results of each IMF. The time series of measured blood glucose concentration were used for experimental analysis; the experimental results show that the proposed VMD-KELM-AdaBoost method has higher prediction accuracy compared with the classical prediction models such as ELM, KELM, SVM, and LSTM. The proposed VMD-KELM-AdaBoost model can still achieve high prediction accuracy 60 min in advance (the mean values of RMSE, MAPE, and CC are about 10.1422, 4.8629%, and 0.8737 respectively); in Clarke error mesh analysis, the proportion of falling into A region is about 95.7%; the sensitivity and false alarm rate of early alarm of hypoglycemia were 94.8% and 7.7%, respectively. Graphical abstract We have proposed a new prediction model. In the first part, for reducing thenon-stationarity, the data of blood glucose concentration was decomposed as a series ofIMF by VMD. In the second part, a prediction model based KELM and Adaboost wasestablished. In the third part, the KELM-Adaboost model was used to predict each IMF,and the predicted values of all IMFS were superimposed to obtain the final predictionresult of blood glucose concentration.

PurposeThis paper aims to reduce the impact of noise on the prediction accuracy of remaining useful life (RUL) for supercapacitor. First, Savitzky–Golay (SG) smoothing filter method (Savitzky and Golay, 1964) is used to eliminate the local small fluctuation and high-frequency noises that are generated by the capacity drop and rebound during the charging and discharging process of supercapacitor. Then, the variational mode decomposition (VMD) method is used to eliminate large fluctuation noises that are caused by internal temperature change of supercapacitor and chemical reaction of the supercapacitor. Its parameters are optimized by using marine predators algorithm (MPA), and the capacity sequence after denoising is reconstructed. Finally, long short term memory neural networks (LSTM) is used to predict the performance degradation law (PDL) and remaining useful life (RUL) of supercapacitor for the reconstructed sequence, then the comparative analysis is conducted with other methods, which results show this method improves the prediction accuracy effectively, and provides theoretical support for timely and accurately understanding the PDL and RUL of supercapacitor backup power supply.Design/methodology/approachFirst, SG smoothing filter method is used to eliminate the local small fluctuation and high-frequency noises that are generated by the capacity drop and rebound during the charging and discharging process of supercapacitor. Then, the VMD method is used to eliminate large fluctuation noises that are caused by internal temperature change of supercapacitor and chemical reaction of the supercapacitor. Its parameters are optimized by using MPA, and the capacity sequence after denoising is reconstructed. Finally, LSTM is used to predict the PDL and RUL of supercapacitor for the reconstructed sequence, then the comparative analysis is conducted with other methods, the results show that this method improves the prediction accuracy effectively, and provides theoretical support for timely and accurate understanding the PDL and RUL of supercapacitor backup power supply.FindingsThese factors will bring different types of noise during the service process of supercapacitor backup power supply, such as capacity regeneration, differences of charging and discharging rate, internal temperature change of supercapacitor, chemical reaction and external electromagnetic interference. Therefore, the paper proposes an LSTM prediction method of supercapacitor’s PDL and RUL based on composite denoising, which is divided into three stages: smoothing, noise reduction and prediction. First, SG smoothing filter method is used to eliminate the local small fluctuation and high-frequency noises, and MPA-VMD method is used to eliminate the nonlinear and nonstationary noises. Then, the capacity sequence after denoising is reconstructed, LSTM is used to predict PDL and RUL of supercapacitor. Finally, the comparative analysis with other methods is carried out. The results show that SG-VMD-LSTM method has higher prediction accuracy, which can accurately predict PDL and RUL of supercapacitor backup power supply, and improve the safety and reliability of wind turbine operation under the severe wind conditions.Originality/valueThe comparative analysis with other methods is carried out. The results show that SG-VMD-LSTM method has higher prediction accuracy, which can accurately predict PDL and RUL of supercapacitor backup power supply, and improve the safety and reliability of wind turbine operation under the severe wind conditions.

In this research, the variational mode decomposition (VMD) method is used for the drive-by health monitoring of bridges. Firstly, the problem of a half-trailer tractor moving over a bridge is formulated. Next, a Finite Element (FE) code is developed and verified against modal analysis results where complete agreement is found. The vehicle's output signals are decomposed through VMD and then analyzed to identify and precisely locate damage in the bridge structure. The range of applicability of this technique is examined from different perspectives by including various road classes, damage severity and location, and noise. The results prove the robustness and reliability of using VMD for drive-by damage detection. The method outcomes indicate that through the VMD method, cracks with a depth of 10% to 20% of the beam height can be detected even in the case of a rough road profile. A comparison of the results of the VMD and the well-known empirical mode decomposition (EMD) method has also been conducted. This comparison reveals that by implementing the VMD, precise damage locations can be determined, whereas the EMD fails to detect any damage under the conditions considered in this study. The effects of noise and moving vehicle speed are also investigated in the research, and it is found that processing the output signals using VMD can yield reliable estimates of the damage location(s).

Variational mode decomposition (VMD) has been applied in the field of rolling bearing fault diagnosis because of its good ability of frequency segmentation. Mode number K and quadratic penalty term α have a significant influence on the decomposition result of VMD. At present, the commonly used method is to determine these two parameters adaptively through intelligent optimization algorithm, namely, the parameter‐adaptive VMD (PAVMD) method. The key of the PAVMD method is the setting of an objective function, and the traditional PAVMD method is prone to overdecomposition or underdecomposition. To solve these problems, an improved parameter‐adaptive VMD (IPAVMD) method is proposed. A new objective function, the maximum average envelope kurtosis (MAEK), is proposed in this paper. The new objective function fully considers the equivalent filtering characteristics of VMD, and squared envelope kurtosis has good antinoise performance. In the optimization method, this paper uses an improved particle swarm optimization (PSO) algorithm. The MAEK and PSO can make sure the IPAVMD method reaches the best complete decomposition of the signal without an underdecomposition or overdecomposition problem. Through the analysis of simulation data and experimental data, the performance of the IPAVMD and the traditional PAVMD is compared. The comparison results show that the proposed IPAVMD has better performance and stronger robustness than the traditional method and is suitable for both single‐fault and multiple‐fault cases of rolling bearings. The research results have certain theoretical significance and application value for improving the fault diagnosis effect of rolling bearings.

Nuclear magnetic resonance (NMR) relaxometry, a noninvasive and nondestructive method, is a key technique for unconventional reservoir evaluation. Echo data detected from NMR instrument, a kind of weak signal, however, is characterized by a low signal-to-noise ratio (SNR). The achievement of NMR relaxation spectra inversion of a high precision, for echo data with a low SNR, is a challenge, which will also affect the unconventional reservoir evaluation of NMR logging. In this article, a variational mode decomposition (VMD) method was proposed for NMR echo data denoising. NMR echo data were decomposed into an ensemble of intrinsic mode functions (IMFs) by the VMD method. The IMF number is an important parameter for VMD, and VMD results are different with various IMF numbers. An optimal selection method for the IMF number was proposed. The decomposed IMFs compose of signals with different frequencies. Noise is from high-frequency signal, but valuable data are from low-frequency signal. The effective IMFs in VMD were selected and summed as the denoised echo data. Numerical simulations and field NMR logging data processing were undertaken to evaluate the NMR echo data denoising effectiveness and practicality of the proposed VMD-based method. The results showed that the inverted NMR spectra exhibit a higher quality after the VMD-based denoise, compared with those for raw echo data and after the empirical mode decomposition (EMD) denoise. This indicates that a higher denoising quality is achieved by the VMD-based method than by the EMD-based method for NMR echo data.

A general method for mode decomposition on additive mixture: Generalized Variational Mode Decomposition and its sequentialization

Application of the Variational Mode Decomposition (VMD) method to river tides

A parameter-adaptive VMD method based on grasshopper optimization algorithm to analyze vibration signals from rotating machinery

Machines learning models have recently been proposed for predicting rivers water temperature (Tw) using only air temperature (Ta). The proposed models relied on a nonlinear relationship between the Tw and Ta and they have proven to be robust modelling tools. The main motivation for this study was to evaluate how the variational mode decomposition (VMD) contributed to the improvement of machines learning performances for river Tw modelling. Measured data collected at five stations located in Poland from 1987 to 2014 were acquired and used for the analysis. Six machines learning models were used and compared namely, K-nearest neighbor's regression (KNNR), least square support vector machine (LSSVM), generalized regression neural network (GRNN), cascade correlation artificial neural networks (CCNN), relevance vector machine (RVM), and locally weighted polynomials regression (LWPR). The six models were developed according to three scenarios. First, the models were calibrated using only the Ta as input and obtained results show that the models were able to predict consistently water temperature, showing a high determination coefficient (R2) and Nash-Sutcliffe efficiency (NSE) with values near or above 0.910 and 0.915, respectively, and in overall the six models worked equally without clear superiority of one above another. Second, the air temperature was combined with the periodicity (i.e., day, month and year number) as input variable and a significant improvement was achieved. Both models show their ability to accurately predict river Tw with an overall accuracy of 0.956 for R2 and 0.955 for NSE values, but the LSSVM2 have some advantages such as a small errors metrics, and high fitting capabilities and it slightly surpasses the others models. Thirdly, air temperature was decomposed into several intrinsic mode functions (IMF) using the VMD method and the performances of the models were evaluated. The VMD parameters appeared to cause much influence on the prediction accuracy, exhibiting an improvement of about 40.50% and 39.12% in terms of RMSE and MAE between the first and the third scenarios, however, some models, i.e., GRNN and KNNR have not benefited from the VMD. This research has demonstrated the high capability of the VMD algorithm as a preprocessing approach in improving the accuracies of the machine learning models for river water temperature prediction.

To solve the problem of micro‐electro‐mechanical system (MEMS) gyroscope noise, this paper presents a variational mode decomposition (VMD) method based on crow search algorithm. First, the signal was decomposed by variational mode decomposition for optimization of crow search algorithm (CSA‐VMD) method. The parameters required by the VMD method (penalty parameter α and decomposition number K) are given by the crow search algorithm, and then the signal is decomposed into the superposition of multiple subsignals, called intrinsic mode functions (IMFs). The sample entropy (SE) corresponding to each IMF is then obtained. By calculating the sample entropy, the noise signal can be divided into pure noise part, mixing part, and temperature drift part. Second, Savitzky–Golay smoothing denoising (SG) is used to filter the mixed noise signal to eliminate the influence of noise. Third, for the filtering of the drift part, the least square support vector machine optimized by the crow search algorithm (CSA‐LSSVM) was used to filter, so as to reduce the effect of temperature drift. Finally, the processed signal is reconstructed to achieve the goal of denoising. Through the results, it can be found that the optimized VMD and LSSVM using CSA algorithm can achieve more effective denoising. After using the method proposed in this paper, the angular random walk value is 1.1175 ∗ 10−4°/h/√Hz, and the bias stability is 0.0017°/h. Compared with the original signal, the two signals are optimized by 98.1% and 98.2%, respectively. It can be seen from the experimental results that the proposed CSA‐VMD method, SG method, and CSA‐LSSVM method can effectively eliminate noise effects.

BACKGROUND: Ultrasound computed tomography (USCT) is a promising technique for improving the detection of breast cancer. Image quality of USCT has a major impact on the breast cancer diagnosis.OBJECTIVE: This paper investigates the combination of variational mode decomposition (VMD) and coherent factor method for USCT image quality enhancement.METHODS: The signals can be decomposed into multiple intrinsic mode functions (IMFs) sifting through the frequency by VMD method. Refactoring the remaining IMFs, spatio-temporally smoothed coherence factor (STSCF) beamforming method is applied to reconstructed data for USCT.RESULTS: The validation of combination the VMD and STSCF is described through the breast phantom experiment and in vivo experiments. The evaluation indicators such as contrast ratio (CR), contrast to noise ratio (CNR) and signal to noise ratio (SNR) have been better improved in the experimental results. For the breast phantom, the proposed method gives a higher resolution and the better contrast properties for the hyperechoic cyst. The borders of cysts and tumors in the breast phantom can be distinguished clearly. For volunteer breast experiments, artifacts are removed more efficiently while the clutters are suppressed simultaneously.CONCLUSION: The combination of VMD and STSCF can further reduce the noise and suppress the side lobes.

Maintenance planning plays a critical role in the process industry, where any unplanned maintenance may lead to a significant loss. Condition monitoring happens to aid maintenance planning and has become an inherent part of the maintenance activity. Physical parameters such as vibration, acoustic emission, current, etc., are used for condition monitoring, out of which vibration is the most preferred parameter and is widely used in the industry. Vibration data is measured near to bearings, which themselves are monitored for their condition, and hence rolling element bearing (REB) is the focus of this study. REBs are monitored for the presence of a fault in them as well as for their severity. Fault diagnosis of REB using harmonic product spectrum (HPS) is proposed in this study. The proposed methodology's novelty lies in the signal pre-processing step, whose output is fed to the HPS method, which is used for defective raceway identification. The efficacy of HPS is assessed with parameter optimized Variational mode decomposition (VMD) and classical bandpass filtering method as pre-processors. It is observed that the HPS delivers better diagnostic results with the VMD method than the bandpass filtering method. Non-dominated sorting particle swarm optimization algorithm is deployed for parameter optimization of VMD. HPS combined with VMD as pre-processor forms an autonomous HPS(AHPS) algorithm, whose input is measured signal and output is defect frequency. The process is so designed that a raw signal, when fed to the algorithm, delivers the result as identification of a defective raceway. Unlike previously developed methods, the proposed method needs no manual intervention. Results obtained from simulated signals and signals recorded through experiments validate that the proposed methodology can be used effectively for fault diagnosis of REB.

The variational mode decomposition (VMD) method for signal decomposition is severely affected by the number of components of the VMD method. In order to determine the decomposition modal number, K, in the VMD method, a new center frequency method of the multi-threshold is proposed in this paper. Then, an improved VMD (MTCFVMD) algorithm based on the center frequency method of the multi-threshold is obtained to decompose the vibration signal into a series of intrinsic modal functions (IMFs). The Hilbert transformation is used to calculate the envelope signal of each IMF component, and the maximum frequency value of the power spectral density is obtained in order to effectively and accurately extract the fault characteristic frequency and realize the fault diagnosis. The rolling element vibration data of the motor bearing is used to test the effectiveness of proposed methods. The experiment results show that the center frequency method of the multi-threshold can effectively determine the number, K, of decomposed modes. The proposed fault diagnosis method based on MTCFVMD and Hilbert transformation can effectively and accurately extract the fault characteristic frequency, rotation frequency, and frequency doubling, and can obtain higher diagnostic accuracy.

The failure of rotating machinery applications has major time and cost effects on the industry. Condition monitoring helps to ensure safe operation and also avoids losses. The signal processing method is essential for ensuring both the efficiency and accuracy of the monitoring process. Variational mode decomposition (VMD) is a signal processing method which decomposes a non-stationary signal into sets of variational mode functions (VMFs) adaptively and non-recursively. The VMD method offers improved performance for the condition monitoring of rotating machinery applications. However, determining an accurate number of modes for the VMD method is still considered an open research problem. Therefore, a selection method for determining the number of modes for VMD is proposed by taking advantage of the similarities in concept between the original signal and VMF. Simulated signal and online gearbox vibration signals have been used to validate the performance of the proposed method. The statistical parameters of the signals are extracted from the original signals, VMFs and intrinsic mode functions (IMFs) and have been fed into machine learning algorithms to validate the performance of the VMD method. The results show that the features extracted from VMD are both superior and accurate for the monitoring of rotating machinery. Hence the proposed method offers a new approach for the condition monitoring of rotating machinery applications.

The failure of rotating machinery applications has major time and cost effects on the industry. Condition monitoring helps to ensure safe operation and also avoids losses. The signal processing method is essential for ensuring both the efficiency and accuracy of the monitoring process. Variational mode decomposition (VMD) is a signal processing method which decomposes a non-stationary signal into sets of variational mode functions (VMFs) adaptively and non-recursively. The VMD method offers improved performance for the condition monitoring of rotating machinery applications. However, determining an accurate number of modes for the VMD method is still considered an open research problem. Therefore, a selection method for determining the number of modes for VMD is proposed by taking advantage of the similarities in concept between the original signal and VMF. Simulated signal and online gearbox vibration signals have been used to validate the performance of the proposed method. The statistical parameters of the signals are extracted from the original signals, VMFs and intrinsic mode functions (IMFs) and have been fed into machine learning algorithms to validate the performance of the VMD method. The results show that the features extracted from VMD are both superior and accurate for the monitoring of rotating machinery. Hence the proposed method offers a new approach for the condition monitoring of rotating machinery applications.