Product Function Components Research Articles

Classification of Seismic Events and Quarry Blasts Using Singular Value Decomposition and Support Vector Machine

Abstract Investigating two types of seismic signals often misclassified in practice, seismic events and quarry blasts, two novel approaches using singular value decomposition (SVD) to extract features of the main wavelet coefficients (WCs) and product function components (PFs) and the support vector machine (SVM) to classify them are proposed. This research collected and preprocessed 200 seismic events and 200 quarry blasts from the Yongshaba mine, China. Discrete wavelet transform (DWT) and local mean decomposition (LMD) were used to decompose the signals into several WCs and PFs, respectively, and the correlation coefficient and variance contribution ratio were used to select the main WCs and PFs. Finally, the singular value features of the selected six WCs and PFs, which can discriminate between seismic events and quarry blasts, were extracted, and the features were input to backpropagation (BP) neural network, Bayes, SVM, and logistic regression (LR) classifiers. The results show that SVD can effectively extract signal features, and that the SVM classifier offers better classification results than the BP neural network, Bayes, and LR classifiers. In addition, the LMD-SVD-SVM-based method is better than the DWT-SVD-SVM-based method in accuracy, specificity, and sensitivity, with values of 96.0 %, 97.0 %, and 95.0 %, and 95.5 %, 97.0 %, and 94.0 %, respectively. Therefore, DWT and LMD based on SVD and SVM techniques provide useful approaches to seismic event and quarry-blast classification.

Product function correntropy and its application in rolling bearing fault identification

Abstract Rolling bearing as one of the key mechanical components plays a significant role in the field of industrial. To improve the ability of rolling bearing fault diagnosis under multi-rotating situation, this paper proposes a novel rolling bearing fault characteristic product function correntropy (PFC), and employs Least Square Support Vector Machine (LSSVM) to implement intelligent fault identification of rolling bearings under multi-stationary working situations. Firstly, rolling bearing vibration acceleration signal is decomposed by Local Mean Decomposition (LMD) to extract product functions (PF). Secondly, PFC needs to be obtained. PFC is the solution of the correntropy mathematical model of primary signal and PF component that is modified by Correlation Coefficient Entropy (CCE) as amplitude modulation operator. Finally, drawing support from LSSVM, the fault identification is achieved. Through the bearing identification experiments in different rotating situations, it is verified that PFC generates higher diagnosis accuracy than traditional fault features. Meanwhile, it is proved that PFC has more robustness than traditional fault features under cross-mixed roller bearing rolling status. Above all, the higher efficiency and availability of LMD-PFC-LSSVM are confirmed from the experiment consequence. It can be concluded that LMD-PFC-LSSVM is a reliable technology for rolling bearing fault diagnosis online under complicated rolling conditions and possesses the broad application prospect.

Gas pipeline small leakage feature extraction based on LMD envelope spectrum entropy and PCA–RWSVM

This paper presents a novel intelligent method based on local mean decomposition and multi-class reproducing wavelet support vector machines (RWSVMs), which are applied to detect leakage in natural gas pipelines. First, local mean decomposition is used to construct product function components to decompose the leakage signals. Then, we select the leakage signals which contain the most leakage information, according to the kurtosis features of these signals, through principal component analysis. Next, we reconstruct the principal product function components in order to acquire the envelope spectrum. Finally, we confirm the leak aperture by inputting envelope spectrum entropy features, as feature vectors, into the RWSVMs. Through analysing the pipeline leakage signals, the experiments show that this method can effectively identify different leak categories.

Numerical and experimental analysis of vibratory signals for rolling bearing fault diagnosis

The detecting technique of the mechanical anomaly has been a hot topic in the scientific and engineering community. Vibration analysis has been frequently applied in the condition monitoring and fault diagnosis of rolling element bearings. Unfortunately, the vibration signals collected from a faulty bearing are generally nonstationary, nonlinear and with strong noise interference, so it is essential to obtain the fault features correctly. In this paper, a novel numerical analysis method that combines the singular value decomposition (SVD) and local mean decomposition (LMD) is proposed. SVD is a non-parametric technique which has been widely used to eliminate the noise and enhance the impulsive features, then LMD decompose the purified signal into a series of product functions (PFs), each of which is the product of an envelope signal and a purely frequency modulated FM signal. The envelope of a PF is the instantaneous amplitude (IA) and the derivative of the unwrapped phase of a purely flat frequency demodulated (FM) signal is the IF. After that the fault characteristic frequency of the roller bearing can be extracted by performing spectrum analysis to the instantaneous amplitude of PF component containing dominant fault information. Finally, the proposed method is applied to experimental data and the results show the effectiveness of the proposed technique in fault detection and diagnosis of rolling element bearing.DOI: http://dx.doi.org/10.5755/j01.mech.22.3.11962

Diagnosing planetary gear faults using the fuzzy entropy of LMD and ANFIS

The small size, low weight, and large transmission ratio of planetary gear have resulted in large-scale use, low speed, and heavy-duty mechanical systems. Poor working conditions of planetary gear lead to frequent occurrence of faults. A method is proposed for diagnosing faults in planetary gear based on fuzzy entropy of Local mean decomposition (LMD) and Adaptive neuro-fuzzy inference system (ANFIS). The original vibration signal is decomposed into six Product function (PF) components and a residual using LMD. Given that decomposed PF components contain the main fault feature information, fuzzy entropy is used to reflect the complexity and irregularity of each PF component. The fuzzy entropies of each PF component are defined as the input of the ANFIS model, and its parameters and membership functions are adaptively adjusted based on training samples. Finally, fuzzy inference rules are determined, and the optimal ANFIS model is obtained. Testing samples are used to verity the trained ANFIS model. The overall fault recognition rate reaches 88.8%, and the fault recognition rate for gear with wear reaches 96%. Therefore, the proposed method is effective at diagnosing planetary gear faults.

An improved local mean decomposition method and its application for fault diagnosis of reciprocating compressor

Local mean decomposition (LMD) is a new time–frequency analysis method which can decompose a signal adaptively into a set of product function (PF) components, and the construction of local mean function and envelope function plays an important role in the accuracy of its PF components. Aiming at the strong nonstationarity, nonlinearity and multi-component coupling characteristics of reciprocating compressor vibration signals, an improved LMD was proposed by a novel construction method of local mean function and envelope function. By introducing an extreme symmetrical point between two extreme points and using the Monotone Piecewise Cubic Hermite Interpolation (MPCHI) instead of Cubic Spline Interpolation (CSI) to construct the envelopes, a novel construction method of local mean function and envelope function was proposed, and then the improved LMD algorithm was given based on this novel construction method. The improved LMD was applied to decompose the vibration signals of reciprocating compressor fault states, and the comparison of details between different LMD decomposition results verified the superiority of this improved method. 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.

Improved LMD, Permutation Entropy and Optimized K-Means to Fault Diagnosis for Roller Bearings

A novel bearing vibration signal fault feature extraction and recognition method based on the improved local mean decomposition (LMD), permutation entropy (PE) and the optimized K-means clustering algorithm is put forward in this paper. The improved LMD is proposed based on the self-similarity of roller bearing vibration signal extending the right and left side of the original signal to suppress its edge effect. After decomposing the extended signal into a set of product functions (PFs), the PE is utilized to display the complexity of the PF component and extract the fault feature meanwhile. Then, the optimized K-means algorithm is used to cluster analysis as a new pattern recognition approach, which uses the probability density distribution (PDD) to identify the initial centroid selection and has the priority of recognition accuracy compared with the classic one. Finally, the experiment results show the proposed method is effectively to fault extraction and recognition for roller bearing.

Natural gas pipeline leak aperture identification and location based on local mean decomposition analysis

When a gas pipeline leaks, the leak aperture and its position cannot be easily identified. This paper proposed a leak aperture recognition and location method based on root mean square (RMS) entropy of local mean deposition (LMD) and Wigner–Ville time-frequency analysis. Firstly, wavelet packet energy analysis is employed to remove noise and extract the primary energy leak bands to reconstruct. The reconstructed signal is then decomposed using LMD, and the RMS entropy of PF components is calculated. The RMS entropies of multiple groups are used to build the feature vector, and it is then input into support vector machines (SVMs) to achieve the aperture recognition. An adaptive method based on mutual information is proposed to select the sensitive product function (PF) components, and the time-frequency parameters of the sensitive PF components are then calculated using Wigner–Ville distribution (WVD) method. The time delays are obtained by analyzing the time-frequency parameters. Finally the leak location was achieved by combining time delay with leak signal propagation velocity. The experimental results show that the proposed method can effectively identify different leak apertures, and the leak location accuracy is better than that of the direct cross-correlation method.

A new rolling bearing fault diagnosis method based on multiscale permutation entropy and improved support vector machine based binary tree

A new bearing vibration feature extraction method based on multiscale permutation entropy (MPE) and improved support vector machine based binary tree (ISVM-BT) is put forward in this paper. Local mean decomposition (LMD), a new self-adaptive time–frequency analysis method, is utilized to decompose the roller bearing vibration signal into a set of product functions (PFs) and then MPE method is used to characterize the complexity of the principal PF component in different scales. After the feature extraction, a new pattern recognition approach called ISVM-BT is introduced to accomplish the fault identification automatically, which has the priority of high recognition accuracy compared with other classifiers. Besides, the Laplacian score (LS) is introduced to refine the fault feature by sorting the scale factors. Finally, the rolling bearing fault diagnosis method based on LMD, MPE, LS and ISVM-BT is proposed and the experimental results indicate the proposed method is effective in identifying the different categories of rolling bearings.

Production Functions in Identifying the Specifics of Producing Gross Regional Product of Russian Federation

The paper presents the results of research about specifics of gross domestic product production in Russia using the tool of econometrics – production functions apparatus. Also, there are quantitatively found answers on questions, which have theoretical and methodological significance. First question – what has a decisive influencing on the production of gross domestic product in Russia, whether it is stocks or investments into the main fund? It was found that the decisive influence on the production of gross domestic product in Russia comes from investments into the main fund. Weak dependency of gross domestic product in Russia on capital stocks explains the inappropriateness of using capital stocks as a parameter of fund in production functions. Second question – what is the exact type of indicators that is preferred to use for characterizing the components of production function in conditions of the Russian economy – cost or natural? It is defined that is it possible to use both – cost terms indicators and indexes of physical volume. However, mining specifics of Russian economy defines the preference of using indexes of physical volume. Third question – what is the quality of economic growth of Russian economy during the period between 1996 and 2013? The intensive character of economic growth was found and the input of main factors of production into economic growth of Russian economy was measured. DOI: 10.5901/mjss.2015.v6n5s3p265

A fault diagnosis method combined with LMD, sample entropy and energy ratio for roller bearings

Since the vibration signals of roller bearings are non-linear and non-stationary, the fault diagnosis of roller bearings is very difficult to determine. Characterized by the self-adaptive time–frequency, local mean decomposition (LMD) is suitable for analyzing this kind of complex signals. By using LMD method, vibration signals of roller bearings can be decomposed into a number of product functions (PFs) and a residual trend. In order to diagnose the fault of roller bearings, the PF components derived from LMD method are used to extract the features of fault signals. Considering the fact that sample entropy and energy ratio can reflect the regularity and characteristics of vibration signals to some extent, the two factors are chosen as PFs’ feature vectors. Thus, a novel fault diagnosis method combining LMD method, sample entropy and energy ratio for roller bearings is put forward. By using the Support Vector Machine (SVM) classifier to make classification, the analysis results demonstrate that the proposed fault diagnosis and feature extraction method is effective.

Research on Fault Diagnosis for Rotor System based on Improved LMD and Singular Value Decomposition

Based on the disadvantages of the original LMD algorithm in terms of smoothing method and end effect, this paper puts forward a fault diagnosis method of rotor system based on the improved LMD and singular value decomposition. The PF (Product function) component obtained after applying the improved LMD method is able to separate the aliasing modes while maintaining the natures and features of the original PF component. Thus, the system’s real information can be grasped more effectively. According to the experimental analysis, this method can be applied to fault diagnosis of rotor system effectively.

The Application of Local Mean Decomposition and Variable Predictive Model-Based Class Discriminate in Gear Fault Diagnosis

The time-domain energy message conveyed by vibration signals of different gear fault are different, so a method based on local mean decomposition (LMD) and variable predictive model-based class discriminate (VPMCD) is proposed to diagnose gear fault model. The vibration signal of gear which is the research object in this paper is decomposed into a series of product functions (PF) by LMD method. Then a further analysis is to select the PF components which contain main fault information of gear, the energy feature parameters of the selected PF components are used to form a fault feature vector. The variable predictive model-based class discriminate is a new multivariate classification approach for pattern recognition, through taking fully advantages of the fault feature vector. Finally, gear fault diagnosis is distinguished into normal state, inner race fault and outer race fault. The results show that LMD method can decompose a complex non-stationary signal into a number of PF components whose frequency is from high to low. And the method based on LMD and VPMCD has a high fault recognition function by analyzing the fault feature vector of PF.

Natural gas pipeline small leakage feature extraction and recognition based on LMD envelope spectrum entropy and SVM

As it is difficult to identify the scale and aperture of small leaks occurring in a natural gas pipeline, this paper proposes a small leak feature extraction and recognition method based on local mean decomposition (LMD) envelope spectrum entropy and support vector machine (SVM). First, LMD is used to decompose the leakage signals into several FM–AM signals, i.e. into product function (PF) components. Then, based on their kurtosis features, the principal PF components that contain most of the leakage information are selected. Wavelet packet decomposition and energy methods are used to analyze and then reconstruct the principal PF components. The Hilbert transform is applied to these reconstructed principal PF components in order to acquire the envelope spectrum, from which the envelope spectrum entropy is obtained. Finally the normalized envelope spectrum entropy features are input into the SVM as leakage feature vectors in order to enable leak aperture category identification. By analyzing the acquired pipeline leakage signals in field experiments, it shows that this method can effectively identify different leak categories.

Fault Diagnosis Method of Gear Based on Local Mean Decomposition and Least Squares Support Vector Machine

For differences of time-domain energy distribution of different gear fault vibration signal, an analytical method based on local mean decomposition (LMD) and least squares support vector machine (LS-SVM) is proposed to apply to gear fault diagnosis. First vibrational signal of gear is decomposed into a series of product functions (PF) by LMD method. Then extracting energy characteristic parameters of PF components which contain main fault information to constitute a fault feature vectors, which is considered as input sample of well-trained LS-SVM, and then identifying working state and fault type of different gear can be identified accurately and effectively by diagnostic method based on LMD and LS-SVM.

Fault Diagnosis Method of Rolling Bearing Based on Ensemble Local Mean Decomposition and Neural Network

For a problem of mode mixing occurs in implementation process of local mean decomposition (LMD) method, an analytical method based on ensemble local mean decomposition (ELMD) and neural network is proposed to apply to fault diagnosis of rolling bearing, the vibrational signal of rolling bearing is decomposed into a series of product functions(PF) by ELMD method. The PF components which contain main fault information are selected to perform a further analysis. The kurtosis coefficient and energy characteristic parameters extracted from these PF components can be used as the input parameters of the neural network to identify the working status and fault types of rolling bearing. Through the analysis of rolling bearing with fault-free, inner-race fault and outer-race fault, the results indicate that the method based on ELMD and neural network has a higher failure recognition rate than the method based on wavelet packet analysis and neural network, and the working status and fault types of rolling bearing can be identified accurately and effectively.

An ensemble local means decomposition method and its application to local rub-impact fault diagnosis of the rotor systems

Targeting the shock characteristics of the vibration signal of a rotor system with local rub-impact fault, a local rub-impact fault diagnosis method of rotor system based on ELMD (ensemble local means decomposition) is proposed in this paper. The local mean decomposition (LMD) is a newly self-adaptive time–frequency analysis method, by which any complicated multi-component signal could be decomposed into a set of product functions (PFs) whose instantaneous frequencies in theory have physical significance. Unfortunately, mode mixing phenomenon which makes the decomposition results devoid of physical meaning is common when LMD is performed in practice. Targeting this shortcoming, the filter bank structure of white noise by LMD is obtained by numerical experiments, and then an improved method based upon noise-assisted analysis, ensemble local mean decomposition, is put forward. In ELMD, firstly, different white noise is added to the targeted signal; secondly, LMD is used to decompose the noise-added signal into product functions (PFs); finally, the ensemble means of corresponding PF components derived from LMD is regarded as the final decomposition result. The analytical results from simulation signal and experimental rotor local rub-impact signal demonstrate that the ELMD approach can be used to overcome the mode mixing of the original LMD method effectively.