Variational Mode Decomposition Algorithm Research Articles

Research on spectral method of lost circulation layer located by transient pressure wave

AbstractLeakage in the wellbore annulus during drilling operations can affect normal production operations, resulting in a severe waste of resources and economic loss, so it is crucial to adopt a fast and effective leak identification method for subsequent plugging operations. For the complex problem of judging the location of the leakage layer, we proposed the method of excitation pressure wave to identify the location of the leakage layer. By analyzing the transfer of pressure waves within the annular pipe system and the pressure head response spectrum, the leak's location is identified based on the location of the resonance point and the change in resonance amplitude. The pressure wave signal contains too much noise. The variational mode decomposition (VMD) algorithm and the Hilbert joint spectrum were used to extract the main frequency components to reconstruct the signal to achieve the denoising effect. On this basis, the reconstructed signal is processed by fast Fourier transform (FFT) to obtain the pressure wave response spectrum, analyze the frequency domain features, and then determine the location of the leakage layer. The experimental results verify that: ① When a leak occurs in the wellbore annulus, the pressure wave will generate additional resonance points in the frequency domain due to the presence of the leak point. ② The combination of the VMD algorithm, FFT, and Hilbert joint spectrum can effectively remove the noise of the pressure wave signal. ③ The method effectively avoids the difficulty of identifying negative pressure waves in the time domain analysis of pressure wave signals. It can effectively locate the leaky layer in the frequency domain analysis. It is concluded that the principle of the method is feasible and has practical significance for field application.

A novel rolling bearing fault diagnosis method based on parameter optimization variational mode decomposition with feature weighted reconstruction and multi-target attention convolutional neural networks under small samples.

To enhance the precision of rolling bearing fault diagnosis, an intelligent hybrid approach is proposed in this paper for signal processing and fault diagnosis in small samples. This approach is based on advanced techniques, combining parameter optimization variational mode decomposition weighted by multiscale permutation entropy (MPE) with maximal information coefficient and multi-target attention convolutional neural networks (MTACNN). First, an improved variational mode decomposition (VMD) is developed to denoise the raw signal. The whale optimization algorithm was used to optimize the penalty factor and mode component number in the VMD algorithm to obtain several intrinsic mode functions (IMFs). Second, separate MPE calculations are performed for both the raw signal and each of the IMF components obtained from the VMD decomposition; the results are used to calculate the maximum information coefficient (MIC). Subsequently, each MIC is normalized and converted to a weight coefficient for signal reconstruction. Ultimately, the reconstructed signals serve as input to the MTACNN for diagnosing rolling bearing faults. Results demonstrate that the signal processing approach exhibits superior noise reduction capability through simple processing. Furthermore, compared to several similar approaches, The method proposed for fault diagnosis achieves superior performance levels in the fault pattern recognition target and the fault severity recognition target.

Quantitative detection of rail head internal hole defects based on laser ultrasonic bulk wave and optimized variational mode decomposition algorithm

This paper proposes a quantitative rail head internal defect detection method combining mode conversion and time-of-flight based on the theory of laser ultrasonic bulk wave scattering and diffraction. The interaction between laser ultrasonic bulk wave and rail internal hole defects is modeled using finite element simulation, and the modal conversion of bulk wave encountered defects is investigated. The feasibility of localization and the quantitative method are both confirmed. Simultaneously, an Optimized Variational Modal Decomposition (OP-VMD) method is proposed to solve the problem of low SNR of bulkwave signals and to facilitate multi-mode wave discrimination. This method can extract the defect diffraction Shear Wave (S) signal from complex ultrasonic signals. Finally, experiments are performed on the defects of artificial internal holes in rail heads with varying burial depths and sizes. The experimental results show that the method can not only detect but also quantify the defects of internal holes in rail heads. The location relative errors are within 3%, and the quantitative relative errors are within 7%.

Optimizing condition monitoring of ball bearings: An integrated approach using decision tree and extreme learning machine for effective decision-making

Abstract This article presents a study on condition monitoring and predictive maintenance, highlighting the importance of tracking ball bearing condition to estimate their Remaining Useful Life (RUL). The study proposes a methodology that combines three algorithms, namely Variational Mode Decomposition (VMD), Decision Tree (DT), and Extreme Learning Machine (ELM), to extract pertinent features and estimate RUL using vibration signals. To improve the accuracy of the method, the VMD algorithm is used to reduce noise from the original vibration signals. The DT algorithm is then employed to extract relevant features, which are fed into the ELM algorithm to estimate the RUL of the ball bearings. The effectiveness of the proposed approach is evaluated using ball bearing data sets from the PRONOSTIA platform. Overall, the results demonstrate that the suggested methodology successfully tracks the ball bearing condition and estimates RUL using vibration signals. This study provides valuable insights into the development of predictive maintenance systems that can assist decision-makers in planning maintenance activities. Further research could explore the potential of this methodology in other industrial applications and under different operating conditions.

Research on Long-Term Tidal-Height-Prediction-Based Decomposition Algorithms and Machine Learning Models

Tidal-level prediction is crucial for ensuring the safety and efficiency of offshore marine activities, port and channel management, water transportation resource development, and life-saving operations. Although tidal harmonic analysis is among the most prevalent methods for predicting tidal water level fluctuations, it relies on extensive data, and its long-term prediction accuracy can be limited. To enhance prediction performance, this paper proposes a model that combines the variational mode decomposition (VMD) algorithm with the long short-term memory (LSTM) neural network. The initial step involves decomposing the original data using the VMD algorithm, followed by applying the LSTM to each decomposition component. Finally, all prediction results are superimposed and summed. The model is tested using the 2018 tidal time series data from the Lvsi station in Zhoushan City and the 2020 tidal time series data from the Ganpu station. The results are compared with those from the classical harmonic analysis model, the traditional machine learning model, and the decomposition-based machine learning method. The experimental outcomes demonstrate the superior predictive capabilities of the proposed model.

Rolling bearing faults identification based on multiscale singular value

To solve the vulnerability of singular value denoising to the effective number of singular value orders and influence of Hankel matrix structure, the paper has proposed a multiscale singular value denoising algorithm (M-SVD). Meanwhile, in concerning that when a fault of bearing occurs, the fault feature information contained in vibration signal tends to be weak and complex, the M-SVD method is blended with variational mode decomposition (VMD) algorithm in identification. Firstly, when bearing faults occur, raw vibration acceleration signals are decomposed using the superiority of VMD algorithm for non-stationary signal; in addition, considering that with the larger difference between singular values of signal, feature information will be more obvious, the method takes advantage of sensibility of variance to signal intensity and proposes to constitute Hankel matrix based on variance feature of signal. During the construction of Hankel matrix, the method to determine effective length of variance sequence (optimal scale) has been brought forward by sample entropy which is able to precisely measure the regularity of signal and detect the weak change of signal. Furthermore, component signals are denoised in line with reconstructed Hankel matrix and the spectrum of signals denoised are selected to describe fault characteristic information and judge the failure types. For the sake of verification of the accuracy and effectiveness of proposed method, the paper has analyzed and verified the data of rolling bearing in 3 different failure types and 2 different installation positions of accelerometers. The comparative analysis with classical singular value difference spectrum (SVDS) and singular value median decomposition (SVMD) denoising has further proved that presented VMD combined M-SVD method can effectively restrain noise while retaining fault characteristic information of signal. Therefore, the identification for rolling bearing fault types can be implemented, accurately.

A coarse-to-fine demodulation frequency band selection strategy for multi-fault detection of rotating machinery

The most critical issue of envelope demodulation analysis for rotating machinery fault diagnosis is to identify the fault-induced informative frequency bands. However, the majority of currently used blind or targeted demodulation methods either only focus on selecting a single frequency band as the best (which may result in unexpected missed diagnosis in the case of multiple faults) or require prior fault knowledge (this is unfeasible for most blind cases). To address this issue, this study proposes a coarse-to-fine demodulation frequency band selection strategy for multi-fault detection of rotating machines. A reweighted Variational Mode Decomposition algorithm, aided by a new evaluation indicator coined fault information correlation index (CFII), is first proposed to coarsely select the useful frequency bands for signal initial denoising and reconstruction. Then, Cyclic Spectral Coherence (CSCoh), a powerful cyclic spectral analysis tool, is implemented to further process the reconstructed signal for fine demodulation analysis. To solve the problem of selecting the spectral frequency band of CSCoh, a practical guideline is established together with the cyclic-frequency-domain fault information index (αFII) for the automatic determination of informative frequency bands to be integrated. Benefiting from the above two stages and developed indicators, the proposed method can effectively detect features of incipient and multiple faults under complex interferences without requiring any prior candidate fault period. Its effectiveness and advancements over several commonly used demodulation techniques are validated using simulation and experimental scenarios involving multi-fault gears and bearings.

Short-term traffic flow prediction: An ensemble machine learning approach

The inconvenience of travel, air pollution and consequent economic losses caused by traffic congestion have seriously restricted the healthy and sustainable development of cities in China. In this context, as the main component of current and future urban traffic management measures, intelligent transportation system is an important means to improve the traffic efficiency of road network and alleviate urban traffic congestion. Traffic flow prediction plays an important role in this connection. In this paper, an ensemble short-term traffic flow prediction method based on optimized variational mode decomposition (OVMD) and combined long short-term memory network (LSTM) is proposed. The method consists of three main components: 1. Use the improved bat algorithm to optimize the parameters of VMD to achieve better decomposition effect; 2. Use the optimized variational mode decomposition algorithm (OVMD) to decompose the unstable original traffic flow time series data into relatively stable multiple Intrinsic Mode Functions (IMFs); 3. The optimized L-BILSTM model is established by combining the basic long short-term memory network with the bidirectional long short-term memory network. It can better extract information from traffic flow data and improve the accuracy of prediction results.In the empirical study part, the traffic flow data of Changsha City is used to verify the prediction model proposed in this paper. The influence of the application of the variational mode decomposition algorithm to the training set data and the overall data on the final prediction results is also compared and analysed.

Transient simulation of reversible pump turbine during pump mode's starting up

A pumped storage power station is an electric power system that utilizes low-peak electricity to pump water into a high-altitude reservoir and releases water to generate electricity during high-peak electricity demand. The pump mode's starting up impacts the operational stability and lifespan of the reversible pump turbine (RPT). Especially, the pressure pulsation signal during the pump mode's starting up is a typical non-stationary signal in RPT, which is an important basis for judging the operation status of the unit. In this study, the time-varying boundary conditions are used to calculate the pressure fluctuation and flow pattern evolution for a prototype RPT. This paper analyzed and compared the time-frequency characteristics of pressure fluctuations by continuous wavelet transform (CWT) and by variational mode decomposition (VMD). And the internal flow of RPT was also visualized using entropy generation theory. In this study, the effect of the penalty coefficient on the VMD algorithm is investigated in the form of a signal-noise ratio (SNR). With the increase of the penalty coefficient, the SNR of the signal gradually decreases and tends to be stable. Several modal components with strong physical significance and center frequency separation are obtained. Influenced by the boundary conditions that change with time, the pressure fluctuation presents a five-stage trend of “descending - ascending - descending - ascending - descending”. There are three main types of high-flow energy dissipation (FED) areas during this process of the RPT. The research and analysis in this paper will provide a good reference for the stable and safe operation of RPT and pumped storage power stations.

Knock recognition of knock sensor signal based on wavelet transform and variational mode decomposition algorithm

Natural gas has become the most widely used alternative energy for engines because of its low emission pollution and sufficient energy reserve. In order to improve the thermal efficiency of the natural gas engine, it is necessary to increase the compression ratio, but knock restricts the increase of the engine compression ratio. The main knock detection method of engine is to use knock sensor. However, the body vibration detected by the knock sensor contains a lot of interference noise, which brings bad effect on the accuracy of knock detection. Thus, in this paper, a knock recognition method based on wavelet transform (WT) and variational mode decomposition (VMD) algorithm is proposed to process the knock sensor signal and extract the knock feature. Based on the test bench of natural gas engine, experimental investigation of knock combustion characteristics was conducted by adjusting the spark timing, and simultaneously collects cylinder pressure signal and knock sensor signal. Burg algorithm based on Auto-regressive (AR) model was used to extract the knock characteristic frequency of the research engine. Then, wavelet transform and variational mode decomposition algorithm were employed to process the knock sensor signal to remove the interference noise and extract the knock feature. Maximum amplitude of pressure oscillation (MAPO) was selected as the knock intensity evaluation index of cylinder pressure signal. Then, taking the evaluation result of the knock intensity of cylinder pressure signal as reference, the root-mean-square of the knock characteristic signal was used as knock intensity evaluation index of knock sensor signal to determine the knock intensity classification of the knock sensor signal. The results show that the proposed method can effectively extract the knock feature from the knock sensor signal and realize the accurate engine knock recognition. The recognition accuracy is higher than the most existing knock recognition methods.

Fault Diagnosis of Rolling Bearings in VMD and GWO-ELM

Strong noise, nonlinearity, and complex frequency are the remarkable symbols of vibration signals when rolling bearing failure. So a new method that improved the accuracy of rolling bearing fault diagnosis is proposed based on variational mode decomposition (VMD) and grey wolf algorithm optimized extreme learning machine (GWO-ELM). The bearing vibration signal is decomposed by VMD, and decomposed Intrinsic Mode Component (IMF) is used for fuzzy entropy calculation to construct a multi-scale complexity eigenvector. The fault pattern recognition is carried out in the extreme learning machine afterward. The parameter selection problem in VMD and fuzzy entropy algorithm is analysed through the experimental fault data of the rolling bearing, and the noise robustness of the experimental data is verified. Through fault data of rolling bearings on site, the comparison of the results shows that the GWO-ELM model can effectively identify the abnormal conditions, and has a faster training and learning speed in diagnosing the faults.

Fault diagnosis model of rolling bearing based on parameter adaptive VMD algorithm and Sparrow Search Algorithm-Based PNN

Fault diagnosis of rolling bearings is essential to ensure the proper functioning of the entire machinery and equipment. Variational mode decomposition (VMD) and neural networks have gained widespread attention in the field of bearing fault diagnosis due to their powerful feature extraction and feature learning capacity. However, past methods usually utilize experiential knowledge to determine the key parameters in the VMD and neural networks, such as the penalty factor, the smooth factor, and so on, so that generates a poor diagnostic result. To address this problem, an Adaptive Variational Mode Decomposition (AVMD) is proposed to obtain better features to construct the fault feature matrix and Sparrow probabilistic neural network (SPNN) is constructed for rolling bearing fault diagnosis. Firstly, the unknown parameters of VMD are estimated by using the genetic algorithm (GA), then the suitable features such as kurtosis and singular value entropy are extracted by automatically adjusting the parameters of VMD. Furthermore, a probabilistic neural network (PNN) is used for bearing fault diagnosis. Meanwhile, embedding the sparrow search algorithm (SSA) into PNN to obtain the optimal smoothing factor. Finally, the proposed method is tested and evaluated on a public bearing dataset and bearing tests. The results demonstrate that the proposed method can extract suitable features and achieve high diagnostic accuracy.

Standing tree health assessment using contact–ultrasonic testing and machine learning

The problem of hole-defect detection in standing trees is solved. An ultrasonic device (Pundit PL-200) was employed to collect ultrasonic signals from various wood specimens both in the lab and field. The collected ultrasonic signals were then processed through the Variational Mode Decomposition algorithm to derive effective features. In order to solve the classification problem more efficiently, the obtained characteristics were then analyzed through PCA to determine the most useful features. Several machine learning algorithms and a one-dimensional convolutional neural network (1D-CNN) were employed to solve a set of classification problems based on data collected from (1) specimens with artificial defects in the lab and (2) billets with natural defects selected from trees harvested at sites in the two states of WA and NSW, Australia. The results demonstrate the effectiveness of the proposed method for classifying wood materials based on their health state, where testing accuracy results of 100% in the lab and at least 92.2% in fields were achieved. The Fine Gaussian SVM was found to perform most effectively on data derived from specimens in the lab and fields. It was also shown that 1D-CNN results were more reliable for generalizing the solution to the classification problem of standing trees in fields.

Runoff prediction based on a VMD-LSTM model considering the decomposition error

For increasing the forecasting accuracy of runoff, a combined prediction model composed of the variational mode decomposition (VMD) and long short-term memory network (LSTM) is investigated in our manuscript. Firstly, data from the runoff is decomposed into three modal components via the VMD algorithm, for reducing the complexity of the original data. In addition, decomposition error is also been considered in this paper, and the hidden information in the series is extracted. Three subsequences and the decomposition error are handled by the LSTM method, respectively. Superimposing the prediction results, the prediction result of the runoff is thus derived. Experimental analysis is carried out, and a comparison of the VMD-LSTM model and other algorithmic indicates that the model constructed in our manuscript is more valid for predicting the runoff.

Analysis of pipeline leakage signal based on adaptive weighted frequency band entropy optimized VMD algorithm

The influence of pressure and environment on urban polyethylene (PE) gas pipeline makes structural deterioration and leaking to the pipeline and pipeline easy. This paper proposes an analysis method for optimizing Variational Mode Decomposition (VMD) algorithm. Firstly, the optimal bandwidth is obtained by using the adaptive weighted frequency band entropy (AFBE), and the optimal quadratic penalty factor is obtained by curve fitting. Then, the AFBE is used as the fitness function, and the optimal decomposition level is obtained by the optimized beetle whisker search algorithm. Experimental results show that the signal-to-noise ratio (SNR) is improved by 12.74% on average.

Fault location of flexible grounding distribution system based on multivariate modes and kurtosis calibration

Aiming at the problems of large fault location errors when the traditional traveling wave fault location is applied to flexible ground distribution systems. This paper proposed the fault location of flexible grounding distribution system based on multivariate modes and kurtosis calibration. Firstly, a disturbance signal is generated by putting a small resistor in parallel. This signal reaches the fault point and undergoes a sudden change, generating an aerial mode traveling wave signal. Secondly, it used the multivariate variational mode decomposition algorithm to decompose the aerial mode current and extracts the fault features. Then, the discrete kurtosis value is calculated for the highest frequency intrinsic mode function component. The moment of maximum kurtosis is the arrival time of the aerial mode current. Finally, it adopted the head-end detection device to calculate the fault distance. For the complex topology of the flexible ground distribution systems, the localization equation of the overhead line, cable line, and hybrid lines are studied, and the pseudo-fault points are excluded by adding auxiliary devices at the branch end. The simulation results demonstrate that the proposed method can accurately locate faults and is not affected by the fault's initial phase angle, transition resistance, and location.

Study on Denoising Method of Vibration Signal Induced by Tunnel Portal Blasting Based on WOA-VMD Algorithm

Because of the impact of the complex environment of tunnel portals, the measured blasting vibration signals in a tunnel portal contains a lot of high-frequency noise. To achieve effective noise reduction, a novel method of noise reduction for blasting vibration signals based on the whale optimization algorithm (WOA) optimized with the variational mode decomposition (VMD) algorithm was proposed. The WOA algorithm is used to optimize globally for the mode number K and penalty factor α of VMD for measured signals and to determine the optimal parameters of [K, α], and to obtain the intrinsic mode function (IMF). Multi-scale permutation entropy (MPE) was used to identify and remove noise components in IMF, and then the reserved IMF was reconstructed to achieve a denoised signal. The method is applied to the blasting vibration analysis of the Xiali tunnel of the Jixin expressway in the Henan Province. Results indicate that the novel method can acquire the optimal decomposition mode number and identify the high frequency noise. Its denoising effect is better than the conventional VMD algorithm and the complete ensemble empirical mode decomposition with adaptive ability (CEEMDAN), which verifies the self-adaptivity and effectiveness of the WOA-VMD denoising method.

Novel Decomposition and Ensemble Model with Attention Mechanism for Container Throughput Forecasting at Four Ports in Asia

Container shipping has suffered a sharp decline since COVID-19, and risks associated with container transit will persist in the future. The decrease in container transportation has caused a ripple impact on the global supply chain. However, container throughput forecasting is both critical and complicated under the circumstances of economic uncertainty and the outbreak of the COVID-19 pandemic. A novel model propounded in this paper for container throughput forecasting to assist the port management bureau and container shipping industry integrates with the variational mode decomposition (VMD) algorithm, SARIMA technique, convolutional neural network (CNN) method, long short-term memory (LSTM) approach, and attention mechanism, among others. In this model, there are three stages: (i) data decomposition, (ii) component prediction, and (iii) ensemble output. In the first stage, the original data of the container throughput time series is decomposed into several different components using the VMD algorithm. Next, from low frequency to high frequency, each component is modeled by the corresponding prediction approach. Subsequently, the prediction results of each component generated by the previous stage are integrated into the final forecasting results by addition strategy. To enhance the prediction accuracy in the second stage, the attention mechanism is adopted in the CNN-bidirectional LSTM method. Finally, six measurement criteria, the container throughput times series at four ports, and a statistical evaluation approach are applied to comprehensively evaluate the proposed model compared with seven benchmark models. The empirical analysis demonstrates that the proposed model significantly outperforms other comparable models with regard to prediction results, level, and directional prediction accuracy.

An optimized zonal deformation prediction model for super-high arch dams

The previous zonal deformation prediction models for super-high arch dams focus on the measured deformation law, which cannot capture the trend, periodic and fluctuating characteristics. This greatly limits their physical interpretation and practical applications. To address this issue, this paper proposes an optimized zonal deformation prediction model. First, the variational mode decomposition algorithm is applied to split displacement into trend, periodic and fluctuating components. Representative environmental and load factors are determined by the hierarchical clustering on principal components, and then also decomposed into the trend, low- and high-frequency components according to their physical meanings. Second, an optimized dynamic time warping (DTW) based on shape-based distance is employed to divide the displacement components of measured points into different zones. The centroid sequences are calculated to capture the shared characteristics of the corresponding deformation zones. The zonal data sets of the centroid sequences of displacement components and their strongly related influencing factor components are established. Third, the optimized zonal deformation prediction models using three machine learning algorithms (random forest, least squares support vector machines, and boosted regression tree) and the improved hydrostatic-thermal-time model are constructed. The effectiveness of the optimized model is verified using the measured data collected from the Xiluodu dam. The case study shows that the optimized model can well explain the spatio-temporal characteristics of the trend, periodic and fluctuating displacements. Affected by the geological condition, the radial displacement distribution is not completely symmetrical under high reservoir water level.

A robust areal residual-restrained variational mode decomposition for filtering on surface texture analysis

This study proposes a novel filter, namely areal RrVMD based on Variational Mode Decomposition (VMD), for decomposing surface areal texture into the form, waviness and roughness. VMD is one of the latest signal decomposition techniques and has been introduced into the field of surface metrology recently. The paper develops a residual-restrained method to further improved the VMD algorithm. It consists of three processing steps: firstly, calculating the robust weight function; secondly, decomposing the surface into the corresponding k modes and a residual by using the devised areal residual-restrained VMD; thirdly, identifying different surface topography features by different wavelengths of modes. This study also proposes a robust algorithm to handle outliers and defects on the measured surface. The experimental results demonstrate that the robust areal residual-restrained VMD can precisely separate form, waviness and roughness and eliminate outliers efficiently.