Underwater acoustic signal denoising model based on secondary variational mode decomposition

A new denoising algorithm and feature extraction algorithm that combine a new kind of permutation entropy (NPE) and variational mode decomposition (VMD) are put forward in this paper. VMD is a new self-adaptive signal processing algorithm, which is more robust to sampling and noise, and also can overcome the problem of mode mixing in empirical mode decomposition (EMD) and ensemble EMD (EEMD). Permutation entropy (PE), as a nonlinear dynamics parameter, is a powerful tool that can describe the complexity of a time series. NPE, a new version of PE, is interpreted as distance to white noise, which shows a reverse trend to PE and has better stability than PE. In this paper, three kinds of ship-radiated noise (SN) signal are decomposed by VMD algorithm, and a series of intrinsic mode functions (IMF) are obtained. The NPEs of all the IMFs are calculated, the noise IMFs are screened out according to the value of NPE, and the process of denoising can be realized by reconstructing the rest of IMFs. Then the reconstructed SN signal is decomposed by VMD algorithm again, and one IMF containing the most dominant information is chosen to represent the original SN signal. Finally, NPE of the chosen IMF is calculated as a new complexity feature, which constitutes the input of the support vector machine (SVM) for pattern recognition of SN. Compared with the existing denoising algorithms and feature extraction algorithms, the effectiveness of proposed algorithms is validated using the numerical simulation signal and the different kinds of SN signal.

Multistep short-term wind power forecasting model based on secondary decomposition, the kernel principal component analysis, an enhanced arithmetic optimization algorithm, and error correction

Dissolved oxygen is one of the important comprehensive indicators of river water quality, which reflects the degree of pollution in the water body. Monitoring and predicting dissolved oxygen are an important tool for water quality management, which helps to effectively maintain water ecological balance and prevent environmental problems. A single model cannot describe the dynamic characteristics of dissolved oxygen sequence, which affects the prediction accuracy. In order to obtain more accurate dissolved oxygen prediction results, decomposition techniques are commonly used to extract the main fluctuations and trends of water quality sequences. However, the high-frequency modes obtained from decomposition are still unstable. To solve this problem, this paper proposed a hybrid prediction model of dissolved oxygen concentration based on secondary decomposition and bidirectional gate recurrent unit. Firstly, dissolved oxygen sequence is preliminarily decomposed by complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and obtain several intrinsic mode functions (IMF). The fuzzy entropy (FE) is calculated to quantify the complexity of the IMF. Then, variational mode decomposition improved by northern goshawk optimization is used to decompose the IMF with higher entropy. The nonlinearity and instability of the sequence are further weakened. Finally, the bidirectional gate recurrent unit (BiGRU) neural network is used to predict each IMF component, and the final prediction result is obtained by reconstructing the prediction results of each component. In order to verify the effectiveness of the proposed model, this paper selects the dissolved oxygen data of Xin'anjiang Reservoir as the research object. The experimental results show that the RMSE, MAE, MAPE, and R2 of the proposed model are 0.1164, 0.0894, 1.0403%, and 0.9939, respectively, which is best among other comparative prediction models (BP, LSTM, GRU, BiGRU, EMD-BiGRU, CEEMDAN-BiGRU, VMD-BiGRU, and GNO-VMD-BiGRU). Therefore, this model effectively deals with high volatility and nonlinear dissolved oxygen data and provides reference for water environment management and ecological protection.

A novel secondary decomposition method for forecasting crude oil price with twitter sentiment

This paper proposes a novel method to improve the variational mode decomposition (VMD) method and to automatically acquire the sensitive intrinsic mode function (IMF). First, since fault signals are impulsive and periodic, a weighted autocorrelative function maximum (AFM) indicator is constructed based on the Gini index and autocorrelation function to serve as the optimization objective function. The mode number K and the penalty parameter α of VMD are automatically obtained through an optimal parameter searching process underpinned by the improved particle swarm optimization (PSO) algorithm with a variety of inertia weights. This improvement solves one of the major drawbacks of the conventional VMD method, that is, the need to manually set parameters. Then, an optimal IMF automatic selecting process is performed for single-failure faults and compound faults, according to the principles of the maximum weighted AFM indicator and maximum spectrum peak ratio (SPR), respectively. The sensitive IMFs are then subjected to an envelope demodulation analysis to obtain the fault characteristic frequency. The results of simulations and experiments show that the proposed method can effectively identify fault characteristics early, especially compound faults, demonstrating great potential for real-world applications.

The research about online monitoring and leakage automatic location of water distribution networks (WDN) has a wide range of applications that include water resource protection, monitoring, and allocation. Variational mode decomposition (VMD) and cross-correlation (CC) based leakage location is a popular and effective method in WDN. However, the value of K intrinsic mode functions (IMFs) based on VMD decomposition needs to be determined artificially, which affects the separation effect of signal frequency band characteristics directly. Hence, this work proposes an adaptive method to determine the parameter K of leakage vibration signal’s IMFs, which will be applied to automatic leakage location in WDN. Firstly, the number of saddle points in the frequency domain envelope of the sampled signal in different step sizes is calculated. The parameter K is determined according to the curvature change of the number of saddle points and the sampled signal. Finally, the selective IMFs are reconstituted into a new signal, which can determine a leak position using CC based time-delay estimation (TDE). To verify the effectiveness of the proposed algorithm, the different methods based on EMD and Fast ICA are compared. The experimental results demonstrate that the proposed parameter K value adaptive VMD (KVA-VMD) decomposition method is more suitable for leakage location in WDN.

An optimized VMD method and its applications in bearing fault diagnosis

High-G MEMS accelerometer (HGMA) is a new type of sensor; it has been widely used in high precision measurement and control fields. Inevitably, the accelerometer output signal contains random noise caused by the accelerometer itself, the hardware circuit and other aspects. In order to denoise the HGMA’s output signal to improve the measurement accuracy, the improved VMD and TFPF hybrid denoising algorithm is proposed, which combines variational modal decomposition (VMD) and time-frequency peak filtering (TFPF). Firstly, VMD was optimized by the multi-objective particle swarm optimization (MOPSO), then the best decomposition parameters [kbest, abest] could be obtained, in which the permutation entropy (PE) and fuzzy entropy (FE) were selected for MOPSO as fitness functions. Secondly, the accelerometer voltage output signals were decomposed by the improved VMD, then some intrinsic mode functions (IMFs) were achieved. Thirdly, sample entropy (SE) was introduced to classify those IMFs into information-dominated IMFs or noise-dominated IMFs. Then, the short-window TFPF was selected for denoising information-dominated IMFs, while the long-window TFPF was selected for denoising noise-dominated IMFs, which can make denoising more targeted. After reconstruction, we obtained the accelerometer denoising signal. The denoising results of different denoising algorithms in the time and frequency domains were compared, and SNR and RMSE were taken as denoising indicators. The improved VMD and TFPF denoising method has a smaller signal distortion and stronger denoising ability, so it can be adopted to denoise the output signal of the High-G MEMS accelerometer to improve its accuracy.

This paper proposes a new criterion for selecting the optimum number of Intrinsic Mode Functions (IMFs) from vibration signals measured on rotating machines. The criterion is based on calculating the variation of normalized Shannon entropy ([Formula: see text]) between two successive IMFs, enabling the optimization of the number of processed IMFs. The method combines Variational Mode Decomposition (VMD) with Wavelet Multi-Resolution Analysis (WMRA) using the newly introduced criterion. The key steps involve determining the optimal number of IMFs, decomposing the vibration signals using VMD, and applying WMRA to the selected IMFs. Numerical simulations and experimental results demonstrate its effectiveness in identifying various faults, including gear defects, shaft misalignment, insufficient backlash, and belt defects. These latter flaws are the primary cause of the elevated noise levels in the measured signals. Finally, to validate our approach in an industrial setting, we diagnosed a turbofan, which revealed the presence of several typical faults for this type of installation. The proposed approach addresses a critical industry need by increasing fault diagnosis accuracy in noisy environments. Its practical impact stems from its ability to improve early fault detection, which is critical for predictive maintenance strategies aimed at reducing equipment downtime and extending its lifespan.

Background/Objectives: This paper introduced an image fusion algorithm based on Variational Mode Decomposition (VMD). Methods/Statistical Analysis: Image fusion is one of the image enhancement methods which results the image with better quality derived from a set of degraded images. Fused image contains more information than input images and it is efficient for visual perception and computer vision applications. This paper proposed an image fusion technique based on VMD for multi focus images. VMD has been a recently introduced non-recursive decomposition method, which decomposes the image into separate spectral bands called Intrinsic Mode Function (IMF) or modes. The modes are generated with respect to the associated central frequencies and they are band limited. Findings: A fusion rule based on weighing scheme is performed at the decomposition level for increasing the features by decreasing the mutual information. The reconstruction of the IMFs results the final fused image. The performance analysis of the proposed fusion method is experimented using standard objective quality metrics. The efficiency of the proposed method is determined by comparing the method with some state of the art methods. Application/Improvements: The image fusion using VMD is applicable to multi-resolution, multi model multi-sensor images.

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

Recently, magnetocardiography (MCG) has attracted increasing attention as a non-invasive and non-contact technique for detecting electrocardioelectric functions. However, the severe background noise makes it difficult to extract information. Variational Mode Decomposition (VMD), which is an entirely non-recursive model, is used to decompose the non-stationary signal into the intrinsic mode functions (IMFs). Traditional VMD algorithms cannot control the bandwidth of each IMF, whose quadratic penalty lacks adaptivity. As a result, baseline drift noise is still present or medical information is lost. In this paper, to overcome the unadaptable quadratic penalty problem, an improved VMD model via correlation coefficient and new update formulas are proposed to decompose MCG signals. To improve the denoising precision, this algorithm is combined with the interval threshold algorithm. First, the correlation coefficient is calculated, to determine quadratic penalty, in order to extract the first IMF made up of baseline drift. Then, the new update formulas derived from the variance that describes the noise level are used, to perform decomposition on the rest signal. Finally, the Interval thresholding algorithm is performed on each IMF. Theoretical analysis and experimental results show that this algorithm can effectively improve the output signal-to-noise ratio and has superior performance.

Fault detection of rotating machinery under heavy noise background, is a significant but difficult issue, and traditional fault detection approaches are difficult to apply. To address this problem, a novel approach that combines variational mode decomposition (VMD), L-Kurtosis and random decrement technique (RDT) is proposed, which procedures are summarized as follows. First, the raw vibration signal collected from the rotating component is decomposed using VMD into a set of intrinsic mode functions (IMFs), and the noise components can be separated from the raw signal. Second, the L-Kurtosis indicator is introduced to solve the problem that the fault information is difficult to track, and the optimal intrinsic mode function (IMF) can be determined according to the maximum L-Kurtosis value. Then, RDT is further employed to purify the optimal IMF to eliminate the other unknown interference sources. Finally, a Hilbert envelope spectrum analysis is used for detecting the fault type. In order to validate the proposed approach, the numerical simulations and real experimental investigations about rolling element bearing and gear are conducted. The results illustrate that the proposed approach can effectively detect faults of rotating components.

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A new hybrid prediction model of air quality index based on secondary decomposition and improved kernel extreme learning machine