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

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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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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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 Extraction Method of Variational Mode Decomposition Based on Immunized Fruit Fly Optimization Algorithm

Entropy ◽

10.3390/e21040400 ◽

2019 ◽

Vol 21 (4) ◽

pp. 400 ◽

Cited By ~ 7

Author(s):

Zhou ◽

Guo ◽

Wang ◽

Du ◽

Wang ◽

...

Keyword(s):

Optimization Algorithm ◽

Fruit Fly ◽

Permutation Entropy ◽

Measured Signal ◽

Fruit Fly Optimization Algorithm ◽

Variational Mode Decomposition ◽

Fruit Fly Optimization ◽

Mode Decomposition ◽

Penalty Factor ◽

Combined Parameters

In recent years, a new method of fault diagnosis, named variational mode decomposition (VMD), has been widely used in industrial production, but the decomposition accuracy of VMD is determined by two parameters, which are respectively the decomposition layer number k and the penalty factor α, if the parameters are not properly selected, there will be over-decomposition or under-decomposition. In order to find an approach to determine the parameters adaptively, a method to optimize VMD by using the immune fruit fly optimization algorithm (IFOA) is proposed in this paper. In this method, permutation entropy is used as the fitness function, firstly, the immune fruit fly optimization algorithm is used to search the combined parameters of k and α in VMD, searching for the best combination parameters of k and α by iteration, and then uses the combined parameters to perform VMD, finally, the center frequency is determined through frequency spectrum analysis. The method mentioned is applied to the fault extraction of a simulated signal and a measured signal of a wind turbine gearbox, and the fault frequency is successfully extracted. Using ensemble empirical mode decomposition (EEMD) and singular spectrum decomposition (SSD) to compare with the proposed method, which validated feasibility of the proposed method.

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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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An optimized variational mode decomposition method and its application in vibration signal analysis of bearings

Structural Health Monitoring ◽

10.1177/14759217211057444 ◽

2021 ◽

pp. 147592172110574

Author(s):

Jun Gu ◽

Yuxing Peng ◽

Hao Lu ◽

Xiangdong Chang ◽

Shuang Cao ◽

...

Keyword(s):

Mean Squared Error ◽

Input Parameter ◽

Vibration Signal ◽

Rolling Bearing ◽

Permutation Entropy ◽

Support Vector ◽

Svm Classifier ◽

Variational Mode Decomposition ◽

Mode Decomposition ◽

Penalty Factor

The performance of the rolling bearing of a spindle device is directly related to the safety and reliability of the operation of a mine hoist. To extract bearing vibration signal features effectively for fault diagnosis, a feature extraction method based on the parameter optimization of a variational mode decomposition (VMD) method and permutation entropy (PE) is proposed. In addition, a support vector machine (SVM) classifier is used to identify bearing fault types. An analogue signal is used to test the effect of noise and sampling frequency on VMD performance. Focused on the problem of the VMD method needing to determine the number of mode components K and a penalty factor α during the signal decomposition process, a genetic algorithm is used to optimize the parameter combination [K,α] with the minimum sample entropy as the indicator. By using mean squared error (MSE) and correlation coefficient, an evaluation indicator is constructed to determine the decomposition effects of the optimized VMD, centre frequency, empirical mode decomposition (EMD) and ensemble EMD (EEMD) methods. The normalized PE of the five mode components is used as an eigenvalue, which is used as the input parameter of the SVM. Two different experimental datasets are used to verify the effectiveness of the proposed method. The results show that the proposed method has better diagnostic accuracy than EMD, EEMD and a BP neural network in the case of limited samples and unknown sample inputs. It can provide a good reference for the diagnosis of a rolling bearing and has practical application value.

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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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A Hybrid Model for Forecasting Sunspots Time Series Based on Variational Mode Decomposition and Backpropagation Neural Network Improved by Firefly Algorithm

Computational Intelligence and Neuroscience ◽

10.1155/2018/3713410 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9 ◽

Cited By ~ 8

Author(s):

Guohui Li ◽

Xiao Ma ◽

Hong Yang

Keyword(s):

Neural Network ◽

Time Series ◽

Hybrid Model ◽

Bp Neural Network ◽

Firefly Algorithm ◽

Variational Mode Decomposition ◽

Intrinsic Mode Functions ◽

Mode Decomposition ◽

Earth’S Climate ◽

Bp Model

The change of the number of sunspots has a great impact on the Earth’s climate, agriculture, communications, natural disasters, and other aspects, so it is very important to predict the number of sunspots. Aiming at the chaotic characteristics of monthly mean of sunspots, a novel hybrid model for forecasting sunspots time-series based on variational mode decomposition (VMD) and backpropagation (BP) neural network improved by firefly algorithm (FA) is proposed. Firstly, a set of intrinsic mode functions (IMFs) are obtained by VMD decomposition of the monthly mean time series of the sunspots. Secondly, the firefly algorithm is introduced to initialize the weights and thresholds of the BP neural network, and a prediction model is established for each IMF. Finally, the predicted values of these components are calculated to obtain the final predict results. Comparing BP model, FA-BP model, EMD-BP model, and VMD-BP model, the simulation results show that the proposed algorithm has higher prediction accuracy and can be used to forecast the time series of sunspots.

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Application of Parameter Optimized Variational Mode Decomposition Method in Fault Feature Extraction of Rolling Bearing

Entropy ◽

10.3390/e23050520 ◽

2021 ◽

Vol 23 (5) ◽

pp. 520

Author(s):

Tao Liang ◽

Hao Lu ◽

Hexu Sun

Keyword(s):

Feature Extraction ◽

Empirical Method ◽

Variational Mode Decomposition ◽

Intrinsic Mode Functions ◽

Feature Extraction Method ◽

Time Frequency ◽

Bearing Fault ◽

Mode Decomposition ◽

Penalty Factor ◽

Reconstructed Signal

The decomposition effect of variational mode decomposition (VMD) mainly depends on the choice of decomposition number K and penalty factor α. For the selection of two parameters, the empirical method and single objective optimization method are usually used, but the aforementioned methods often have limitations and cannot achieve the optimal effects. Therefore, a multi-objective multi-island genetic algorithm (MIGA) is proposed to optimize the parameters of VMD and apply it to feature extraction of bearing fault. First, the envelope entropy (Ee) can reflect the sparsity of the signal, and Renyi entropy (Re) can reflect the energy aggregation degree of the time-frequency distribution of the signal. Therefore, Ee and Re are selected as fitness functions, and the optimal solution of VMD parameters is obtained by the MIGA algorithm. Second, the improved VMD algorithm is used to decompose the bearing fault signal, and then two intrinsic mode functions (IMF) with the most fault information are selected by improved kurtosis and Holder coefficient for reconstruction. Finally, the envelope spectrum of the reconstructed signal is analyzed. The analysis of comparative experiments shows that the feature extraction method can extract bearing fault features more accurately, and the fault diagnosis model based on this method has higher accuracy.

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An Adaptive Variational Mode Decomposition Technique with Differential Evolution Algorithm and Its Application Analysis

Shock and Vibration ◽

10.1155/2021/2030128 ◽

2021 ◽

Vol 2021 ◽

pp. 1-5

Author(s):

Yuanxin Wang

Keyword(s):

Differential Evolution ◽

Differential Evolution Algorithm ◽

Decomposition Technique ◽

Variational Mode Decomposition ◽

Mode Decomposition ◽

Penalty Factor ◽

Application Analysis ◽

Evolution Algorithm ◽

Decomposition Number ◽

Selection Of

Variational mode decomposition is an adaptive nonrecursive signal decomposition and time-frequency distribution estimation method. The improper selection of the decomposition number will cause under decomposition or over decomposition, and the improper selection of the penalty factor will affect the bandwidth of modal components, so it is very necessary to look for the optimal parameter combination of the decomposition number and the penalty factor of variational mode decomposition. Hence, differential evolution algorithm is used to look for the optimization combination of the decomposition number and the penalty factor of variational mode decomposition because differential evolution algorithm has a good ability at global searching. The method is called adaptive variational mode decomposition technique with differential evolution algorithm. Application analysis and discussion of the adaptive variational mode decomposition technique with differential evolution algorithm are employed by combining with the experiment. The conclusions of the experiment are that the decomposition performance of the adaptive variational mode decomposition technique with differential evolution algorithm is better than that of variational mode decomposition.

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A Hybrid Forecasting Method for Solar Output Power Based on Variational Mode Decomposition, Deep Belief Networks and Auto-Regressive Moving Average

Applied Sciences ◽

10.3390/app8101901 ◽

2018 ◽

Vol 8 (10) ◽

pp. 1901 ◽

Cited By ~ 11

Author(s):

Tuo Xie ◽

Gang Zhang ◽

Hongchi Liu ◽

Fuchao Liu ◽

Peidong Du

Keyword(s):

Power Generation ◽

Time Series ◽

Empirical Mode Decomposition ◽

Prediction Models ◽

Moving Average ◽

Variational Mode Decomposition ◽

Mode Decomposition ◽

Forecasting Method ◽

Auto Regressive ◽

Pv Power Generation

Due to the existing large-scale grid-connected photovoltaic (PV) power generation installations, accurate PV power forecasting is critical to the safe and economical operation of electric power systems. In this study, a hybrid short-term forecasting method based on the Variational Mode Decomposition (VMD) technique, the Deep Belief Network (DBN) and the Auto-Regressive Moving Average Model (ARMA) is proposed to deal with the problem of forecasting accuracy. The DBN model combines a forward unsupervised greedy layer-by-layer training algorithm with a reverse Back-Projection (BP) fine-tuning algorithm, making full use of feature extraction advantages of the deep architecture and showing good performance in generalized predictive analysis. To better analyze the time series of historical data, VMD decomposes time series data into an ensemble of components with different frequencies; this improves the shortcomings of decomposition from Empirical Mode Decomposition (EMD) and Ensemble Empirical Mode Decomposition (EEMD) processes. Classification is achieved via the spectrum characteristics of modal components, the high-frequency Intrinsic Mode Functions (IMFs) components are predicted using the DBN, and the low-frequency IMFs components are predicted using the ARMA. Eventually, the forecasting result is generated by reconstructing the predicted component values. To demonstrate the effectiveness of the proposed method, it is tested based on the practical information of PV power generation data from a real case study in Yunnan. The proposed approach is compared, respectively, with the single prediction models and the decomposition-combined prediction models. The evaluation of the forecasting performance is carried out with the normalized absolute average error, normalized root-mean-square error and Hill inequality coefficient; the results are subsequently compared with real-world scenarios. The proposed approach outperforms the single prediction models and the combined forecasting methods, demonstrating its favorable accuracy and reliability.

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