Product Function Components Research Articles

A motor imagery EEG signal optimized processing algorithm

Feature extraction and classification is a difficult area in motor imagery electroencephalogram (EEG) signal processing. In order to improve the classification accuracy of EEG signals, both a feature extraction method based on the combination of LMD-CSP and a classification algorithm based on the fusion of PSO-SVM are proposed. Firstly, the extended informax ICA algorithm is used to denoise the signal and reduce the influence of noise on the signal. Then, the pre-processed EEG signals are decomposed into multiple Product Function (PF) components by Local Mean Decomposition (LMD), and the most discriminative PF component is selected. Next, feature extraction is carried out from the selected PF components using the Common Space Pattern (CSP). Finally, the obtained features are input into a Support Vector Machine (SVM) classifier improved by Particle Swarm Optimization (PSO) for classification recognition. The experimental results show that compared with the traditional CSP-SVM method, CapsNet method, WPT-CSP+CNN method, FDCSP-SVM method, and EMD-CNN method, the classification accuracy of the proposed method is increased by 26.94 %, 14.9 %, 13.34 %, 8.34 % and 4.04 %, respectively. This further proves the superiority of the proposed method for EEG signal processing technology.

A Multi-Indicator Fusion-Based Approach for Fault Feature Selection and Classification of Rolling Bearings

Concerning the problems of harrowing extraction and poor classification accuracy of fault features in rolling bearing vibration signals, a fault feature selection and classification method based on multi-indicator fusion is proposed. Firstly, the original signal is decomposed through the improved complementary ensemble local mean decomposition (CELMD) method into several physically meaningful product functions (PF) and single residual components; then, the three indicators of kurtosis, correlation coefficient, and K-L divergence are combined to extract the most suitable PF components for signal reconstruction. Ultimately, the reconstructed signal's multi-domain characteristics and entropy value features are retrieved and fed into the LightGBM classifier for classification in order to achieve an intelligent diagnosis of rolling bearing problems. The statistical results demonstrate that the proposed method can efficiently identify the functional PF components and has notable benefits in extracting features from diverse experimental data sets and detecting faults.

A novel network traffic combination prediction model

SummaryNetwork has become an indispensable part of public life. To improve network utilization, network performance, network quality, and enhance network security, precise prediction of network traffic is an indispensable method and basis for solving the above problems. In order to accurately predict the network traffic, a novel combination prediction model for network traffic is proposed. In this model, local mean decomposition (LMD), bidirectional long short‐term memory (BiLSTM), and Bayesian optimization algorithm are combined. First, the LMD method decomposes the network traffic time series to obtain several product function (PF) components and a residual by LMD. Then, each PF component and residual is predicted with BiLSTM model. Meanwhile, the Bayesian optimization algorithm is introduced to optimize the hyperparameters of BiLSTM. Finally, the predicted value of each PF component and residual is linearly superimposed to obtain the final predicted value. Through the study of two groups of actual network traffic datasets and compared with a variety of state‐of‐the‐art prediction models, the proposed model has a preferable prediction results by comparison of the results.

Fault Diagnosis of Fracturing Vehicle Based on Local Mean Decomposition and Synchroextracting Transform

The power end of a fracturing truck is a key component that provides kinetic energy during pressure operations. Its vibration signal is collected during operation because of the complex working conditions and heavy loads, resulting in the collected signal being filled with a large amount of noise, for which it is difficult to perform effective fault feature extraction. To address this problem, a new fault diagnosis method is proposed. This method combines local mean decomposition (LMD) and synchroextracting transform (SET) for signal processing. First, LMD processing is done on the acquired signal to obtain several product function (PF) components. The cross-correlation coefficient and kurtosis value are used as references to select the true PF components. After that, the SET method is used to process the real PF components, extract the energy that is most correlated with the time-varying features of the signal, remove the fuzzy energy, improve the time-frequency resolution, and enhance the fault features contained in the signal to facilitate accurate fault diagnosis. Finally, the vibration signals collected from the power end of the fracturing vehicle are experimentally verified. The results show that the method can accurately extract the fault characteristics of bearing failure in the power end, and provide some useful reference for the diagnosis method of fracturing vehicle power system.

Fault feature extraction of rolling bearings using local mean decomposition-based enhanced sparse coding shrinkage

Rolling bearing are one of the most important rotating components in the rotating machine and they are prone to failure due to complex harsh working conditions. However, it’s a difficult issue to extract the fault feature from heavy noisy signal. In this paper, a new multilayer hybrid denoising method called local mean decomposition (LMD)-based enhanced sparse coding shrinkage (SCS) (named LMD-EnSCS) is proposed for impulse component extraction from bearing vibration signals. First, LMD is used to decompose the signal into a set of product functions (PFs) to enable impulse component as prominent as possible. Moreover, the multiple criteria is proposed to select the effective PF components. The rest filtering layer is used to enhance and extract the impulsive feature through minimum entropy deconvolution (MED) and sparse coding shrinkage (SCS) respectively. MED is able to enhance the impulsive component of noisy signal, which improve the impulsive extraction ability of SCS effectively. The simulation signal and bearing signal are used to verify the effectiveness and superiority of LMD-EnSCS, and the results show that LMD-EnSCS can extract the fault feature and perform well for bearing fault diagnosis.

Partial discharge signal denoising method based on frequency spectrum clustering and local mean decomposition

Suppressing the background noise of partial discharge (PD) is one of the key issues for accurately diagnosing the state of electrical equipment insulation. To solve this problem, this study proposes a new denoising method based on frequency spectrum clustering and local mean value decomposition. First, the K-means clustering is employed on the frequency spectrum to pick out narrow-band interference frequencies. Next, the PD signal with white noise is decomposed by local mean decomposition into different product function components, and the components contain more information about time–frequency than the intrinsic mode functions originated from empirical mode decomposition. Besides, the adaptive threshold is utilised to eliminate white noise in the components. Finally, the denoised PD signal is synthesised by these denoised components. The proposed method and three traditional methods are applied to simulated and field-detected noisy PD signals, respectively. The results of the evaluation indicators confirm that the proposed method is better than the existing PD denoising methods.

Feature Extraction of EEG Signals Based on Local Mean Decomposition and Fuzzy Entropy

An improved feature extraction method is proposed aiming at the recognition of motor imagined electroencephalogram (EEG) signals. Using local mean decomposition, the algorithm decomposes the original signal into a series of product function (PF) components, and meaningless PF components are removed from EEG signals in the range of mu rhythm and beta rhythm. According to the principle of feature time selection, 4[Formula: see text]s to 6[Formula: see text]s motor imagery EEG signals are selected as classification data, and the sum of fuzzy entropies of second-and third-order PF components of [Formula: see text], [Formula: see text] lead signals is calculated, respectively. Mean value of fuzzy entropy [Formula: see text] is used as input element to construct EEG feature vector, and support vector machine (SVM) is used to classify and predict EEG signals for recognition. The test results show that this feature extraction method has higher classification accuracy than the empirical mode decomposition method and the total empirical mode decomposition method.

Conditions of Steel Industry in Poland After Restructuring – the Analysis by Using C-D Model

Abstract The primary objective of the article is to identify conditions of restructuring from the point of view of Polish steel industry by using Cobb and Douglas model (C-D). Both in European economies and Polish economy, the steel industry is included to important branch of industry. The steel sector has been a permanent component of the Polish economy. Restructuring of metallurgy in Poland has been realized since 1990s. Finally after several years of changes (in the first decade of the 21st century) steel plants adjusted theirs operations to market economy conditions. Nowadays we think that the steel sector has competitive position on the domestic and European markets but if it is truth. On the base of C-D model, the author of the article presents results of the statistical analysis and answer the question about influence property and employment on production in steel industry. Obtained relations between particular components of production function show the condition of steel industry in Poland.

Research on Adaptive Reclosing Discriminant Method Based on LMD Sample Entropy

Based on the adaptive time-frequency analysis characteristics of local mean decomposition and the nonlinear quantization ability of sample entropy, an adaptive reclosing discriminant method based on LMD sample entropy is proposed. Firstly, the local mean decomposition method is applied to decompose the original signal of the transmission line fault into several product function components (PF component). Then calculate the sample entropy of the first three PF components to achieve feature quantization of the PF component. Finally, the sum of the sample entropy of first three PF components is used as the eigenvalue to distinguish the fault type of the transmission line. Obtained from the simulation results, the method can identify the type of fault.

Voltage Disturbance Signals Identification Based on ILMD and Neural Network

In order to identify the disturbance signal in power system and reduce the influence on system security, a voltage disturbance signal classifier based on improved local mean decomposition (ILMD) and BP neural network is proposed. ILMD is used to decompose the disturbance signal in three layers, and the product function (PF) component with amplitude-frequency information of voltage signal is obtained. The signal energy value constructed by PF component is used as the input of BP neural network to identify and classify the voltage disturbance signal. Experiments on four typical voltage disturbance signals show that the signal classifiers based on ILMD and BP neural networks have high accuracy and good working efficiency for the recognition and classification of voltage disturbance signals.

Diagnosis Approach for Incipient Faults of Rolling Bearings Under Sectional Jumping Speed

Since the characteristics of the incipient faults for the rolling bearing under the sectional jumping speed are difficult to be extracted, the conventional fault diagnostic approaches usually with poor monitoring performance and low diagnostic accuracy (i.e., the ratio of samples correctly classified to total samples). This paper proposes a novel cooperative diagnostic approach for the incipient faults of the rolling bearing based on the optimized local mean decomposition (LMD) and support vector machine (SVM). First, to resolve the problem of selecting the appropriate number of product function (PF) components, an optimally weighted fusion model of PF components is established by introducing a genetic algorithm, aiming to maximize the correlation with the original incipient fault signal. Besides, in this model, a novel rule is set to calculate the weight coefficients of fusion. Second, considering the sparsity of the incipient fault characteristics caused by the sectional jumping speed, from the perspective of energy distribution, a novel characteristic extraction model is constructed based on the equal interval energy projection. This characteristic extraction model can correctly extract the fault characteristics and effectively eliminate redundant information. Moreover, the SVM has collaborated with the above-mentioned characteristic extraction model to diagnosis incipient faults. Finally, the effectiveness and correctness of the proposed approach are verified by the experimental simulation results. The comparison and analysis show that the proposed algorithm cannot only correctly extract fault characteristics but also have a high accuracy of fault characteristics recognition with good operability and scalability.

Application of an Improved Ensemble Local Mean Decomposition Method for Gearbox Composite Fault Diagnosis

In industrial production, it is highly essential to extract faults in gearbox accurately. Specifically, in a strong noise environment, it is difficult to extract the fault features accurately. LMD (local mean decomposition) is widely used as an adaptive decomposition method in fault diagnosis. In order to improve the mode mixing of LMD, ELMD (ensemble Local Mean Decomposition) is proposed as local mode mixing exists in noisy environment, but white noise added in ELMD cannot be completely neutralized leading to the influence of increased white noise on PF (product function) component. This further leads to the increase in reconstruction errors. Therefore, this paper proposes a composite fault diagnosis method for gearboxes based on an improved ensemble local mean decomposition. The idea is to add white noise in pairs to optimize ELMD, defined as CELMD (Complementary Ensemble Local Mean Decomposition) then remove the decomposed high noise component by PE (Permutation Entropy) while applying the SG (Savitzky‐Golay) filter to smooth out the low noise in PFs. The method is applied to both simulated signal and experimental signal, which overcomes mode mixing phenomenon and reduces reconstruction error. At the same time, this method avoids the occurrence of pseudocomponents and reduces the amount of calculation. Compared with LMD, ELMD, CELMD, and CELMDAN, it shows that improved ensemble local mean decomposition method is an effective method for extracting composite fault features.

Research on Weak Fault Extraction Method for Alleviating the Mode Mixing of LMD.

Compared with the strong background noise, the energy entropy of early fault signals of bearings are weak under actual working conditions. Therefore, extracting the bearings’ early fault features has always been a major difficulty in fault diagnosis of rotating machinery. Based on the above problems, the masking method is introduced into the Local Mean Decomposition (LMD) decomposition process, and a weak fault extraction method based on LMD and mask signal (MS) is proposed. Due to the mode mixing of the product function (PF) components decomposed by LMD in the noisy background, it is difficult to distinguish the authenticity of the fault frequency. Therefore, the MS method is introduced to deal with the PF components that are decomposed by the LMD and have strong correlation with the original signal, so as to suppress the modal aliasing phenomenon and extract the fault frequencies. In this paper, the actual fault signal of the rolling bearing is analyzed. By combining the MS method with the LMD method, the fault signal mixed with the noise is processed. The kurtosis value at the fault frequency is increased by eight-fold, and the signal-to-noise ratio (SNR) is increased by 19.1%. The fault signal is successfully extracted by the proposed composite method.

A compound interpolation envelope local mean decomposition and its application for fault diagnosis of reciprocating compressors

Abstract Local mean decomposition (LMD) is a self-adaptive analysis method which can decompose a signal into a set of product function (PF) components, and the construction of envelope function plays an important role in the accuracy of its PF components. According to the local nonstationary characteristics of vibration signals, a compound interpolation envelope (CIE) LMD was proposed through a novel envelope construction method. By defining an nonstationary coefficient to evaluate the local nonstationary characteristics of vibration signals, an compound envelope construction method which use Monotonic Piecewise Cubic Hermite Interpolation (MPCHI) for nonstationary part and Cubic spline interpolation (CSI) for smooth part was proposed, and an CIE LMD algorithm was give based on the novel envelope construction method. A numerical example simulation was conducted to verify the performance of CIE LMD, results indicated that CIE LMD outperforms three other methods. The CIE LMD was employed to diagnose the oversized bearing clearance fault in reciprocating compressor, and the envelope frequency spectrum of PF component gives a more significant peak of fault frequency than that of original signal, which further indicates that this proposed method is competent for the diagnosis of reciprocating compressor oversized bearing clearance fault.

Weak Fault Feature Extraction of Rolling Bearings Using Local Mean Decomposition-Based Multilayer Hybrid Denoising

Extraction of the weak fault features under strong background noise is crucial to early fault diagnosis in bearings. A new method called local mean decomposition (LMD)-based multilayer hybrid denoising (LMD-MHD) is proposed for signal denoising in this paper. LMD is a novel self-adaptive time-frequency analysis method. It can decompose the signal into a set of product functions (PFs), and is thus particularly suitable for processing of multicomponent amplitude-modulated and frequency-modulated signals. The first filtering layer of LMD-MHD is to use a multiple criteria decision to select the effective PF components. The second filtering layer is to use the wavelet threshold denoising (WTD) as the prefilter of singular value decomposition (SVD) implementation, which enables the preserved singular values to consist of the most important information of the PFs. The final denoising layer of LMD-MHD is to use SVD to extract the most important principal features from Hankel matrix of the PFs. The order of effective ranks of the Hankel matrix is determined by the number of main frequencies in the fast Fourier transformation (FFT) result of the signal. The filtering is finished based on the reconstructed signal from the decomposition result of SVD. The results of experimental analysis on the simulation signals and vibration signal collected from rolling bearings indicate that LMD-MHD is effective for extracting the weak fault features and performs well for bearing fault diagnosis.

Early Fault Diagnosis of Rotating Machinery by Combining Differential Rational Spline-Based LMD and K–L Divergence

First, an improved local mean decomposition (LMD) method called differential rational spline-based LMD (DRS) is developed for signal decomposition. Differential and integral operations are introduced in LMD, which can weaken the mode mixing problem. Meanwhile, an optimized rational spline interpolation is proposed to calculate the envelope functions aiming to reduce the large errors caused by moving average in the traditional LMD. A series of product functions (PFs) is obtained after the application of the proposed DRS-LMD. Then, Kullback–Leibler (K–L) divergence is adopted to select main PF components that contain most fault information. The machine fault can be easily identified from the amplitude spectrum of the selected PF component. The effectiveness of the proposed DRS-LMD and K–L strategy is tested on simulated vibration signals and experimental vibration signals. Results show that the proposed method can increase the decomposition accuracy of the signals and can be used to detect early faults on the gears and rolling bearings.

Electric shock fault diagnosis of low‐voltage residual current‐operated protective device

In order to diagnose the electric shock fault types of new‐generation adaptive residual current operated protective devices (RCDs), a combination method based on local mean decomposition (LMD) amount of energy and support vector machine (SVM) is proposed in this study. First, LMD is applied to decompose the original electric shock signals into a finite number of product functions (PFs); then the former PFs containing the main features are selected to calculate the total energy. Second, SVM is used to solve the multi‐class classification problem. The amount of energy of the PF component is considered as the input vector of the SVM, and particle swarm optimization (PSO) is used to optimize the model parameters. Experimental results show that the proposed method is effective in diagnosing animal or plant electric shock fault type, which provides a reliable theoretical basis for developing a new generation of adaptive RCDs. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Weak Fault Diagnosis of Wind Turbine Gearboxes Based on MED-LMD

In view of the problem that the fault signal of the rolling bearing is weak and the fault feature is difficult to extract in the strong noise environment, a method based on minimum entropy deconvolution (MED) and local mean deconvolution (LMD) is proposed to extract the weak fault features of the rolling bearing. Through the analysis of the simulation signal, we find that LMD has many limitations for the feature extraction of weak signals under strong background noise. In order to eliminate the noise interference and extract the characteristics of the weak fault, MED is employed as the pre-filter to remove noise. This method is applied to the weak fault feature extraction of rolling bearings; that is, using MED to reduce the noise of the wind turbine gearbox test bench under strong background noise, and then using the LMD method to decompose the denoised signals into several product functions (PFs), and finally analyzing the PF components that have strong correlation by a cyclic autocorrelation function. The finding is that the failure of the wind power gearbox is generated from the micro-bending of the high-speed shaft and the pitting of the #10 bearing outer race at the output end of the high-speed shaft. This method is compared with LMD, which shows the effectiveness of this method. This paper provides a new method for the extraction of multiple faults and weak features in strong background noise.

Leakage aperture recognition based on ensemble local mean decomposition and sparse representation for classification of natural gas pipeline

Leakage in a natural gas pipeline is influenced by many factors, including aperture, distance from sensors, and pressure inside the pipeline. The feature extraction and recognition algorithm is complex; thus, a new leakage aperture recognition method is proposed that presents a feature extraction algorithm based on the Ensemble Local Mean Decomposition (ELMD)-K-L (Kullback-Leibler) model and Sparse Representation for Classification. This method applied ELMD to perform adaptive decomposition of the leakage signals and obtain feature information of the leakage signals with different apertures. It then selected the product function components that contained major leakage information according to the K-L divergence from which we extracted a variety of time-frequency feature parameters to obtain the comprehensive and accurate eigenvector of the leakage signal. Realization of an accurate classification of leakage aperture using sparse representation classifiers was proposed to classify small samples of the complex signals. The classifiers obtained the sparsest solution of the test signal through the over-complete dictionary and used this solution as the sparse reconstruction coefficients of the test signal to obtain the reconstructed signal of this test signal under different categories. Finally, it completed the classification by determining the residuals of the test and the reconstructed signals. The experimental results showed that the proposed algorithm can achieve higher accuracy than the traditional support vector machine and Back-Propagation classification algorithms.

Fault diagnosis for rotating machinery based on Local Mean Decomposition morphology filtering and Least Square Support Vector Machine

In order to improve the accuracy of fault diagnosis, a fault diagnosis method for rotating machinery based on Local Mean Decomposition (LMD) morphological filtering and Least Square Support Vector Machine(LS-SVM) is proposed. Firstly, the collected vibration signals are processed by LMD which decom poses them into a series of product function (PF) components, and PF components are carried out by method of the morphological filtering and signal recombination. Then, the feature vector is obtained from the new PF components by LMD method. Secondly, a new kernel function is proposed to improve LS-SVM, which can solve the problem of kernel function parameters selection. Further, Lagrange parameters are processed by feature weighting method, and the weighted average value of the Lagrange parameters is calculated as the threshold value of Pruning algorithm, which can solve sparsity problem in LS-SVM. Thirdly, Energy features are inputted into the new LS-SVM to recognize machinery faults according to LS-SVM parameters. Finally, the performance of the proposed method was verified by a fault diagnosis case in a rolling element bearing. The results indicated that this new method could judge and classify the multi-fault of rotating machinery quickly and effectively.