An Improved Adaptive IVMD-WPT-Based Noise Reduction Algorithm on GPS Height Time Series

To improve the reliability of Global Positioning System (GPS) signal extraction, the traditional variational mode decomposition (VMD) method cannot determine the number of intrinsic modal functions or the value of the penalty factor in the process of noise reduction, which leads to inadequate or over-decomposition in time series analysis and will cause problems. Therefore, in this paper, a new approach using improved variational mode decomposition and wavelet packet transform (IVMD-WPT) was proposed, which takes the energy entropy mutual information as the objective function and uses the grasshopper optimisation algorithm to optimise the objective function to adaptively determine the number of modal decompositions and the value of the penalty factor to verify the validity of the IVMD-WPT algorithm. We performed a test experiment with two groups of simulation time series and three indicators: root mean square error (RMSE), correlation coefficient (CC) and signal-to-noise ratio (SNR). These indicators were used to evaluate the noise reduction effect. The simulation results showed that IVMD-WPT was better than the traditional empirical mode decomposition and improved variational mode decomposition (IVMD) methods and that the RMSE decreased by 0.084 and 0.0715 mm; CC and SNR increased by 0.0005 and 0.0004 dB, and 862.28 and 6.17 dB, respectively. The simulation experiments verify the effectiveness of the proposed algorithm. Finally, we performed an analysis with 100 real GPS height time series from the Crustal Movement Observation Network of China (CMONOC). The results showed that the RMSE decreased by 11.4648 and 6.7322 mm, and CC and SNR increased by 0.1458 and 0.0588 dB, and 32.6773 and 26.3918 dB, respectively. In summary, the IVMD-WPT algorithm can adaptively determine the number of decomposition modal functions of VMD and the optimal combination of penalty factors; it helps to further extract effective information for noise and can perfectly retain useful information in the original time series.

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A Denoising Method for Fiber Optic Gyroscope Based on Variational Mode Decomposition and Beetle Swarm Antenna Search Algorithm

Entropy ◽

10.3390/e22070765 ◽

2020 ◽

Vol 22 (7) ◽

pp. 765

Author(s):

Pengfei Wang ◽

Yanbin Gao ◽

Menghao Wu ◽

Fan Zhang ◽

Guangchun Li ◽

...

Keyword(s):

Noise Reduction ◽

Fiber Optic ◽

Search Algorithm ◽

Permutation Entropy ◽

Navigation Systems ◽

Variational Mode Decomposition ◽

Fiber Optic Gyroscope ◽

Denoising Method ◽

Mode Decomposition ◽

Penalty Factor

Fiber optic gyroscope (FOG) is one of the important components of Inertial Navigation Systems (INS). In order to improve the accuracy of the INS, it is necessary to suppress the random error of the FOG signal. In this paper, a variational mode decomposition (VMD) denoising method based on beetle swarm antenna search (BSAS) algorithm is proposed to reduce the noise in FOG signal. Firstly, the BSAS algorithm is introduced in detail. Then, the permutation entropy of the band-limited intrinsic mode functions (BLIMFs) is taken as the optimization index, and two key parameters of VMD algorithm, including decomposition mode number K and quadratic penalty factor α , are optimized by using the BSAS algorithm. Next, a new method based on Hausdorff distance (HD) between the probability density function (PDF) of all BLIMFs and that of the original signal is proposed in this paper to determine the relevant modes. Finally, the selected BLIMF components are reconstructed to get the denoised signal. In addition, the simulation results show that the proposed scheme is better than the existing schemes in terms of noise reduction performance. Two experiments further demonstrate the priority of the proposed scheme in the FOG noise reduction compared with other schemes.

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Application of improved variational mode decomposition method based on two-dimensional sparrow search algorithm in natural gas pipeline leakage signal denoising

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211063688 ◽

2021 ◽

pp. 014233122110636

Author(s):

Dongmei Wang ◽

Lijuan Zhu ◽

Jikang Yue ◽

Jingyi Lu ◽

Gongfa Li

Keyword(s):

Search Algorithm ◽

Signal To Noise Ratio ◽

Decomposition Algorithm ◽

Signal Denoising ◽

Two Dimensional ◽

Variational Mode Decomposition ◽

Denoising Method ◽

Mode Decomposition ◽

Penalty Factor ◽

Whale Optimization

To eliminate noise interference in pipeline leakage detection, a signal denoising method based on an improved variational mode decomposition algorithm is proposed. This work adopts a standard variational mode decomposition algorithm with decomposition level K and the penalty factor α. The improvements consist of using a two-dimensional sparrow search algorithm to find K and α. To verify the superiority of the sparrow search algorithm to find K and α, it is compared with three earlier studies. These studies used the firefly algorithm, particle swarm optimization, and whale optimization algorithm to perform the optimization. The main result of this study is to demonstrate that the variational mode decomposition improved by sparrow search algorithm gives a much improved signal-to-noise ratio compared to the other methods. In all other respects, the results are comparable.

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Research on a Noise Reduction Method Based on Multi-Resolution Singular Value Decomposition

Applied Sciences ◽

10.3390/app10041409 ◽

2020 ◽

Vol 10 (4) ◽

pp. 1409

Author(s):

Gang Zhang ◽

Benben Xu ◽

Kaoshe Zhang ◽

Jinwang Hou ◽

Tuo Xie ◽

...

Keyword(s):

Singular Value Decomposition ◽

Noise Reduction ◽

Signal To Noise Ratio ◽

Noise Pollution ◽

Singular Value ◽

Reduction Model ◽

Mode Decomposition ◽

Starting Point ◽

Reduction Effect ◽

Value Decomposition

Reducing noise pollution in signals is of great significance in the field of signal detection. In order to reduce the noise in the signal and improve the signal-to-noise ratio (SNR), this paper takes the singular value decomposition theory as the starting point, and constructs various singular value decomposition denoising models with multiple multi-division structures based on the two-division recursion singular value decomposition, and conducts a noise reduction analysis on two experimental signals containing noise of different power. Finally, the SNR and mean square error (MSE) are used as indicators to evaluate the noise reduction effect, it is verified that the two-division recursion singular value decomposition is the optimal noise reduction model. This noise reduction model is then applied to the diagnosis of faulty bearings. By this method, the fault signal is decomposed to reduce noise and the detail signal with maximum kurtosis is extracted for envelope spectrum analysis. Comparison of several traditional signal processing methods such as empirical modal decomposition (EMD), ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), wavelet decomposition, etc. The results show that multi-resolution singular value decomposition (MRSVD) has better noise reduction effect and can effectively diagnose faulty bearings. This method is promising and has a good application prospect.

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NOISE REDUCTION AND INTERPRETATION OF ICE-PENETRATING RADAR DATA IN ANTARCTIC ICE SHEET BASED ON VARIATIONAL MODE DECOMPOSITION

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xlii-2-w13-1787-2019 ◽

2019 ◽

Vol XLII-2/W13 ◽

pp. 1787-1791

Author(s):

X. Tang ◽

S. Cheng ◽

J. Guo

Keyword(s):

Noise Reduction ◽

Layer Structure ◽

Signal To Noise Ratio ◽

Ice Sheet ◽

Data Interpretation ◽

Radar Data ◽

Variational Mode Decomposition ◽

Intrinsic Mode Functions ◽

Antarctic Ice Sheet ◽

Mode Decomposition

<p><strong>Abstract.</strong> Ice-penetrating radar is an effective method for studying the subglacial bedrock and ice information within the Antarctic ice sheet. Because of the low conductivity of ice and the relatively uniform composition of ice sheets in the polar region, ice-penetrating radar can penetrate deeper part of the ice sheet and collect the following data. However, it is still necessary to suppress the noise from radar data to obtain more accurate and effective data. In this paper, the entirely non-recursive Variational Mode Decomposition (VMD) is applied to the data noise reduction of ice-penetrating radar data. VMD is a decomposition method of adaptive and quasi-orthogonal signals, which decomposes airborne radar data into multiple frequency-limited quasi-orthogonal Intrinsic Mode Functions (IMFs). The IMFs containing noise are then removed according to the information distribution in the IMFs component and the remaining IMFs are reconstructed. We implements the method to process the real ice-penetrating radar data, which effectively eliminates the interference noise in the data, improves the signal-to-noise ratio and characterizes the internal layer structure of ice. It is verified that the method can be applied to the noise reduction processing of polar ice-penetrating radar data successful, which provides a better basis for data interpretation. Finally, we present the internal structure within the ice sheet based on VMD denoised radar profile.</p>

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A new fault diagnosis method based on adaptive spectrum mode extraction

Structural Health Monitoring ◽

10.1177/1475921720986945 ◽

2021 ◽

pp. 147592172098694

Author(s):

Zhijian Wang ◽

Ningning Yang ◽

Naipeng Li ◽

Wenhua Du ◽

Junyuan Wang

Keyword(s):

Scale Space ◽

Variational Mode Decomposition ◽

Rolling Bearings ◽

Mode Decomposition ◽

Penalty Factor ◽

Diagnosis Method ◽

Mode Extraction ◽

Non Stationary Signal ◽

Envelope Spectrum ◽

Fault Feature Extraction

Variational mode decomposition provides a feasible method for non-stationary signal analysis, but the method is still not adaptive, which greatly limits the wide application of the method. Therefore, an adaptive spectrum mode extraction method is proposed in this article. The proposed method is mainly composed of spectral segmentation, mode extraction, and feedback adjustment. In the spectral segmentation part, considering the lack of robustness of classical scale space in a strong noise environment, this article proposes a method of fault feature mapping, which solves over-decomposition of variational mode decomposition guided by classical scale space. In the mode extraction part, for insufficient self-adaptability of the single penalty factor in the variational mode decomposition method, this article proposes a method of spectral aggregation factor, which solves multiple penalty factors that conform to different intrinsic modal functions. In the feedback adjustment part, this article proposes the method of transboundary criterion, which makes the result of variational mode decomposition within a preset range. Finally, using dispersion entropy and kurtosis indicators, intrinsic modal function components containing fault frequencies are extracted for envelope spectrum analysis to extract fault characteristic frequencies. In order to verify the effectiveness of the proposed method, the proposed method is applied to simulation signals and bearing fault signals. Comparing the decomposition results of different methods, the conclusion shows that the proposed method is more advantageous for the fault feature extraction of rolling bearings.

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Local Geometric Projection-Based Noise Reduction for Vibration Signal Analysis in Rolling Bearings

Volume 11: Mechanical Systems and Control ◽

10.1115/imece2008-66937 ◽

2008 ◽

Author(s):

Ruqiang Yan ◽

Robert X. Gao ◽

Kang B. Lee ◽

Steven E. Fick

Keyword(s):

Time Series ◽

Phase Space ◽

Noise Reduction ◽

Signal Analysis ◽

Signal To Noise Ratio ◽

Multifractal Spectrum ◽

Vibration Signal ◽

Rolling Bearings ◽

One Dimensional ◽

Vibration Signal Analysis

This paper presents a noise reduction technique for vibration signal analysis in rolling bearings, based on local geometric projection (LGP). LGP is a non-linear filtering technique that reconstructs one dimensional time series in a high-dimensional phase space using time-delayed coordinates, based on the Takens embedding theorem. From the neighborhood of each point in the phase space, where a neighbor is defined as a local subspace of the whole phase space, the best subspace to which the point will be orthogonally projected is identified. Since the signal subspace is formed by the most significant eigen-directions of the neighborhood, while the less significant ones define the noise subspace, the noise can be reduced by converting the points onto the subspace spanned by those significant eigen-directions back to a new, one-dimensional time series. Improvement on signal-to-noise ratio enabled by LGP is first evaluated using a chaotic system and an analytically formulated synthetic signal. Then analysis of bearing vibration signals is carried out as a case study. The LGP-based technique is shown to be effective in reducing noise and enhancing extraction of weak, defect-related features, as manifested by the multifractal spectrum from the signal.

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BP-AdaBoost Algorithm Based on Variational Mode Decomposition Optimized by Envelope Entropy for Diagnosing the Working Conditions of a Slideway Seedling-Picking Mechanism

Applied Engineering in Agriculture ◽

10.13031/aea.14124 ◽

2021 ◽

Vol 37 (4) ◽

pp. 665-675

Author(s):

Zhitao He ◽

Haiyang Zhang ◽

Jun Wang ◽

Xin Jin ◽

Song Gao ◽

...

Keyword(s):

Empirical Mode Decomposition ◽

Working Conditions ◽

Working Condition ◽

Recognition Accuracy ◽

Variational Mode Decomposition ◽

Adaboost Algorithm ◽

Layer Number ◽

Entropy Minimization ◽

Mode Decomposition ◽

Penalty Factor

Highlights A method of monitoring the working conditions of a slideway seedling-picking mechanism based on variational mode decomposition (VMD), envelope entropy, and energy entropy is proposed. Based on the criterion of envelope entropy minimization, the combination of the decomposition layer number and penalty factor in VMD is optimized to yield a satisfactory decomposition effect of the analyzed vibration signal. The BP-AdaBoost algorithm is used to improve the working condition classification performance for the slideway seedling-picking mechanism. The working-condition identification effect with the proposed method are compared with those through EMD-based, LMD-based, and EEMD-based methods. Abstract . The slideway seedling-picking mechanism is a type of rotating machinery. This study proposes a novel method of identifying the working conditions of slideway seedling-picking mechanisms for early fault diagnosis by utilizing a back-propagation adaptive boosting (BP-AdaBoost) algorithm based on variational mode decomposition (VMD) optimized by the envelope entropy. The experimental results demonstrate that the proposed method can effectively verify the four working conditions (normal state, slideway failure, cam failure, and spring failure). The overall recognition accuracy reaches 90.0% under the optimal combination of the decomposition layer number K and penalty factor a in VMD determined through the envelope entropy minimization criterion. Classification comparisons with empirical mode decomposition (EMD), local mean decomposition (LMD) and ensemble empirical mode decomposition (EEMD) integrated into the BP-AdaBoost algorithm indicate that the overall recognition accuracy of the proposed method is 18.1%, 16.9%, and 15.6% higher than the accuracies of the three conventional methods, respectively. Compared with the K-means, support vector machine (SVM) algorithms, BP-AdaBoost algorithm demonstrates a more dependable capability for identifying the working conditions. This study provides a useful reference for monitoring the working conditions of slideway seedling-picking mechanisms. Keywords: BP-AdaBoost algorithm, Energy entropy, Envelope entropy, Slideway seedling-picking mechanism, Variational mode decomposition, Working conditions.

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Research on Fault Diagnosis of Gearbox with Improved Variational Mode Decomposition

Sensors ◽

10.3390/s18103510 ◽

2018 ◽

Vol 18 (10) ◽

pp. 3510 ◽

Cited By ~ 24

Author(s):

Zhijian Wang ◽

Junyuan Wang ◽

Wenhua Du

Keyword(s):

Fault Diagnosis ◽

Signal To Noise Ratio ◽

Optimal Number ◽

Original Signal ◽

Variational Mode Decomposition ◽

Intrinsic Mode Functions ◽

Multiple Fault ◽

Mode Decomposition ◽

Fault Features ◽

Reconstructed Signal

Variational Mode Decomposition (VMD) can decompose signals into multiple intrinsic mode functions (IMFs). In recent years, VMD has been widely used in fault diagnosis. However, it requires a preset number of decomposition layers K and is sensitive to background noise. Therefore, in order to determine K adaptively, Permutation Entroy Optimization (PEO) is proposed in this paper. This algorithm can adaptively determine the optimal number of decomposition layers K according to the characteristics of the signal to be decomposed. At the same time, in order to solve the sensitivity of VMD to noise, this paper proposes a Modified VMD (MVMD) based on the idea of Noise Aided Data Analysis (NADA). The algorithm first adds the positive and negative white noise to the original signal, and then uses the VMD to decompose it. After repeated cycles, the noise in the original signal will be offset to each other. Then each layer of IMF is integrated with each layer, and the signal is reconstructed according to the results of the integrated mean. MVMD is used for the final decomposition of the reconstructed signal. The algorithm is used to deal with the simulation signals and measured signals of gearbox with multiple fault characteristics. Compared with the decomposition results of EEMD and VMD, it shows that the algorithm can not only improve the signal to noise ratio (SNR) of the signal effectively, but can also extract the multiple fault features of the gear box in the strong noise environment. The effectiveness of this method is verified.

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Non-local mean filtering algorithm based on deep learning

MATEC Web of Conferences ◽

10.1051/matecconf/201823203025 ◽

2018 ◽

Vol 232 ◽

pp. 03025

Author(s):

Baozhong Liu ◽

Jianbin Liu

Keyword(s):

Deep Learning ◽

Noise Reduction ◽

Image Denoising ◽

Signal To Noise Ratio ◽

Denoising Method ◽

Filtering Algorithm ◽

Local Mean ◽

Non Local ◽

Reduction Effect ◽

Mean Filtering

Aimed at the problem that the traditional image denoising algorithm is not effective in noise reduction, a new image denoising method is proposed. The method combines deep learning and non-local mean filtering algorithms to denoise the noisy image to obtain better noise reduction effect. By comparing with Gaussian filtering algorithm, median filtering algorithm, bilateral filtering algorithm and early non-local mean filtering algorithm, the noise reduction effect of the new algorithm is better than the traditional method and the peak signal to noise ratio is compared with the early non-local mean algorithm. The performance is better.

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Optimal Kernel ELM and Variational Mode Decomposition for Probabilistic PV Power Prediction

Energies ◽

10.3390/en13143592 ◽

2020 ◽

Vol 13 (14) ◽

pp. 3592 ◽

Cited By ~ 1

Author(s):

Xiaomei Wu ◽

Chun Sing Lai ◽

Chenchen Bai ◽

Loi Lei Lai ◽

Qi Zhang ◽

...

Keyword(s):

Power Output ◽

Firefly Algorithm ◽

Prediction Models ◽

Prediction Interval ◽

Spline Interpolation ◽

Variational Mode Decomposition ◽

Probabilistic Prediction ◽

Mode Decomposition ◽

Penalty Factor ◽

Kernel Parameter

A probabilistic prediction interval (PI) model based on variational mode decomposition (VMD) and a kernel extreme learning machine using the firefly algorithm (FA-KELM) is presented to tackle the problem of photovoltaic (PV) power for intra-day-ahead prediction. Firstly, considering the non-stationary and nonlinear characteristics of a PV power output sequence, the decomposition of the original PV power output series is carried out using VMD. Secondly, to further improve the prediction accuracy, KELM is established for each decomposed component and the firefly algorithm is introduced to optimize the penalty factor and kernel parameter. Finally, the point predicted value is obtained through the summation of predicted results of each component and then using the nonlinear kernel density estimation to fit it. The cubic spline interpolation algorithm is applied to obtain the shortest confidence interval. Results from practical cases show that this probabilistic prediction interval could achieve higher accuracy as compared with other prediction models.

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