Joint Approximate Diagonalization Of Eigenmatrices Research Articles

Feature Extraction Based on Hierarchical Improved Envelope Spectrum Entropy for Rolling Bearing Fault Diagnosis

Bearing is the key part of mechanical equipment, which can support the rotating machinery running. It is crucial to diagnose bearing fault in time to ensure mechanical equipment working well. Effective feature extraction is an essential step in bearing fault diagnosis. However, the bearing vibration signals collected from the equipment usually contain interference, such as heavy noise. It is difficult to extract effective feature from bearing vibration signals due to the interference. To overcome this issue, a new feature extraction method for rolling bearing faults diagnosis is proposed based on hierarchical improved envelope spectrum entropy (HIESE). First, hierarchical decomposition is used to divide the bearing vibration signal into several hierarchical components. Second, the original feature set is obtained by calculating the improved envelope spectrum entropy (IESE) of each hierarchical component. Then, joint approximate diagonalization of eigenmatrices (JADE) is introduced to fuse the original features into a new one. Finally, support vector machines (SVM) is taken to identify the bearing status. Two cases are used to test the proposed method. In case 1, the bearing vibration signals composed of different fault degrees and different fault types under two speeds are used to verify the proposed method. The recognition rate achieves 100%. In case 2, the bearing vibration signals, which consist of different fault types under three operation conditions, are analyzed. The recognition rate also achieves 100% in this case. Experimental results illustrated that the proposed method has good performance in feature extraction, which can provide a new method for feature extraction of rolling bearing.

Developing a novel hybrid method based on dispersion entropy and adaptive boosting algorithm for human activity recognition

BackgroundWith the rapid development of technology, human activity recognition (HAR) from sensor data has become a key element for many real-world applications, such as healthcare, disease diagnosis and smart home systems. Although there have been several studies conducted on HAR, traditional methods remain inadequate in balancing efficiency, accuracy and speed. Moreover, existing studies have not identified a solution to managing imbalanced data in different activities groups of HAR, although that is major issue in determining satisfactory performance. Methodsthis study proposes a new hybrid approach involving hierarchical dispersion entropy (HDE) and Adaptive Boosting with convolutional neural networks (AdaB_CNN) for classifying human activities, such as running downstairs/upstairs, walking and other daily activities, from sensor data. The proposed model is comprised of the following steps: firstly, HAR data are segmented into intervals using a sliding window technique, and then the segmented data are decomposed into different frequency bands. Following this, the dispersion entropy of different frequency bands is computed to produce a feature vector set. Then, the extracted features are reduced using Joint Approximate Diagonalization of Eigenmatrices (JADE) to further eliminate redundant information. The final feature vector set is then fed into the AdaB_CNN method to classify human activities. ResultsThe proposed approach is tested on three publicly available datasets: WISDM, UCI_HAR 2012, and PAMAP2. The experimental results demonstrate that the proposed model attains a superior performance in HAR to most current methods. ConclusionsThe findings reveal that the proposed HDE based AdaB_CNN model has the capability to efficiently recognize different activities from sensor technologies. It has the potential to be implemented in a hardware system to classify human activity.

An angle error extraction algorithm based on JADE for three-channel radar seeker system with the existence of deception jamming

Mainlobe jamming always causes the degradation of signal detection ability and angle measurement precision of radar seekers. Generally, the target echo and jamming can be separated from each other through blind source separation (BSS)-based methods. However, the angle error information of target cannot be obtained just from the separated sources because of loss of amplitude information. Specially, the angle error information is of great significance for three-channel radar seeker system. Thus, in this paper, based on Joint Approximate Diagonalization of Eigenmatrices (JADE) method, we propose an angle error extraction algorithm for three-channel radar seeker system with the existence of strong deception jamming. Firstly, the model of both target echo and jamming is derived. Secondly, the target echo and jamming are separated from each other through JADE. Then, by the combination of separated target signal with Least Squares algorithm, we reconstruct the target signals of three channels, in which we get the exact specific value of sum-differential channel. Furthermore, the effectiveness of the proposed method is verified by simulations.

Cluster Migration Distance for Performance Degradation Assessment of Water Pump Bearings.

Because the signal of water pump bearing is seriously disturbed by noise and the fault evolution is complex, it is difficult to describe the performance degradation trend of water pump bearing in a timely and accurate manner using the traditional performance degradation index (PDI). In this paper, a new Cluster Migration Distance (CMD) algorithm is proposed. The extraction of the indicator includes the following four steps: First, the relevant blind separation is used to extract the useful signal of the monitored bearing from the mixed signal; secondly, the impact component is further enhanced by wavelet packet analysis. Then, the redundancy of the original feature vectors is eliminated using our previously proposed KJADE (Kernel Joint Approximate Diagonalization of Eigen-matrices) method. Finally, the newly proposed CMD index is computed as PDI. By calculating the offset trajectory of the feature cluster centroid in the continuous running process of the bearing, CMD can aptly deal with the complex and variable features in the fault evolution process of the water pump bearing. The whole-life monitoring data of a 220 KW water pump system are processed. The results show that the proposed CMD index has better early-warning ability and monotonicity than the traditional kurtosis index.

Mutual information map as a new way for exploring the independence of chemically meaningful solutions in two-component analytical data

In the present contribution, a new approach based on mutual information (MI) is proposed for exploring the independence of feasible solutions in two component systems. Investigating how independent are different feasible solutions can be a way to bridge the gap between independent component analysis (ICA) and multivariate curve resolution (MCR) approaches and, to the best of our knowledge, has not been investigated before. For this purpose, different chromatographic and hyperspectral imaging (HSI) datasets were simulated, considering different noise levels and different degrees of overlap for two-component systems. Feasible solutions were then calculated by both grid search (GS) and Lawton-Sylvester (LS) plots. MI map which is the plot of MI vs. rotation matrix elements was used to estimate the degree of independence between different solutions. Inspection of the results showed that the different solutions in the feasible bands correspond to different MI values and that those values are lower for spectral profiles (more independent) than for concentration profiles (more dependent) as expected from the duality concept and the opposite is true. In addition, component profiles are found near more dependent solutions for concentration profiles and near less dependent solutions for spectral profiles which is due to the fact that “independence” constraint was applied to the spectral profiles in ICA algorithms. The performance of three well-known ICA algorithms (mean-field independent component analysis (MF-ICA), mutual information-based least dependent component analysis (MILCA) and joint approximate diagonalization of eigenmatrices (JADE)) as well as MCR-alternating least squares (MCR-ALS) were investigated. MI maps showed that the solutions of MF-ICA and MCR-ALS are in the feasible bands but the MILCA and JADE solutions which are just based on the independence maximization are outside the MI maps.

Cloud based multivariate signal based heart abnormality detection

This paper discusses the rate of heartbeat monitoring with the help of face tracking, extraction of forehead region and separation of blind source. Separation of blind source is applied for three RGB color channel. Independent Component Analysis (ICA) is a powerful tool for such acquisitions. There are mainly four ICA algorithms and these algorithms have been described in the literature. In this paper contribution of two main common ICA algorithms has been studied. These methods are compared to each other in terms of their ability to obtain independent signal from standard RGB signal of forehead region. These methods are Joint Approximate Diagonalization of Eigen matrices (JADE) and Fixed-point ICA (FastICA). Same RGB data set have been applied to these common ICA algorithms and compared with the results of blood volume pulse (BVP) sensor readings. Both methods provide equally consistent results. However, FastICA has shown better results for heart rate measurement compared to JADE.

Performance Degradation Prediction Using LSTM with Optimized Parameters.

Predicting the degradation of mechanical components, such as rolling bearings is critical to the proper monitoring of the condition of mechanical equipment. A new method, based on a long short-term memory network (LSTM) algorithm, has been developed to improve the accuracy of degradation prediction. The model parameters are optimized via improved particle swarm optimization (IPSO). Regarding how this applies to the rolling bearings, firstly, multi-dimension feature parameters are extracted from the bearing’s vibration signals and fused into responsive features by using the kernel joint approximate diagonalization of eigen-matrices (KJADE) method. Then, the between-class and within-class scatter (SS) are calculated to develop performance degradation indicators. Since network model parameters influence the predictive accuracy of the LSTM model, an IPSO algorithm is used to obtain the optimal prediction model via the LSTM model parameters’ optimization. Finally, the LSTM model, with said optimal parameters, was used to predict the degradation trend of the bearing’s performance. The experiment’s results show that the proposed method can effectively identify the trends of degradation and performance. Moreover, the predictive accuracy of this proposed method is greater than that of the extreme learning machine (ELM) and support vector regression (SVR), which are the algorithms conventionally used in degradation modeling.

Feature Extraction Using Hierarchical Dispersion Entropy for Rolling Bearing Fault Diagnosis

Effective feature extraction is crucial for accurate fault diagnosis of rolling bearings. A novel feature extraction method called hierarchical dispersion entropy (HDE) based on hierarchical analysis is proposed in this study. The proposed method includes the following three steps: 1) bearing vibration signal is decomposed into a series of subband signal components; 2) dispersion entropies of the components in different frequency bands are calculated as the original feature vector; and 3) joint approximate diagonalization of eigenmatrices (JADE) is used to extract fusion features from the original features. The main contributions of the proposed method are as follows: 1) the HDE method can characterize the complexity and uncertainty of the signal in full frequency band; 2) the JADE method further eliminates redundant information while greatly retaining fault-relevant information; and 3) the proposed method combines the advantages of HDE's hierarchical analysis and JADE's information fusion capabilities, so the fusion features extracted by the proposed method can be more effective for the establishment of fault pattern identification model. In the analysis of two experimental cases, the feature extracted by the proposed method shows better feature clustering effect and higher recognition rate than other methods. The results show that compared with other methods, the proposed method can more accurately characterize the health condition of the bearing.

Performance Degradation Assessment for Coaxial Bearings Using Kernel JADE and Two-Class Model

Vibration analysis is proved effective for bearing performance degradation assessment (PDA). In most of the current studies, vibration signals from one monitored bearing are collected and analyzed. However, in the real-industrial applications, bearings in pairs or even more are often mounted on the same shaft. Therefore, the collected vibration signal is actually a mixed signal from multiple bearings. In this study, our recently developed method named kernel joint approximate diagonalization of eigenmatrices (JADE) is investigated for PDA under this situation. Due to the nonlinear mapping capability of the kernel method and the blind source separation ability of the JADE algorithm, the proposed method could extract latent source features that are accurately reflecting the performance degradation from the mixed vibration signal. The method includes the following three steps: 1) statistical features are calculated and transformed into the high-dimension through nonlinear mapping. 2) Latent source features are obtained by exploiting the fourth-order moments. 3) The two-class model (SS) is proposed to assess the difference between the monitored sample and the healthy sample, which could reflect the bearing health condition. The effectiveness of this method is verified using two experimental cases within four coaxial bearings. Comparative results show that the proposed method could identify the defect earlier than the traditional rms feature and the traditional JADE method and the principal component analysis method.

Rapid Multi-Sensor Feature Fusion Based on Non-Stationary Kernel JADE for the Small-Amplitude Hunting Monitoring of High-Speed Trains

Joint Approximate Diagonalization of Eigen-matrices (JADE) cannot deal with non-stationary data. Therefore, in this paper, a method called Non-stationary Kernel JADE (NKJADE) is proposed, which can extract non-stationary features and fuse multi-sensor features precisely and rapidly. In this method, the non-stationarity of the data is considered and the data from multi-sensor are used to fuse the features efficiently. The method is compared with EEMD-SVD-LTSA and EEMD-JADE using the bearing fault data of CWRU, and the validity of the method is verified. Considering that the vibration signals of high-speed trains are typically non-stationary, it is necessary to utilize a rapid feature fusion method to identify the evolutionary trends of hunting motions quickly before the phenomenon is fully manifested. In this paper, the proposed method is applied to identify the evolutionary trend of hunting motions quickly and accurately. Results verify that the accuracy of this method is much higher than that of the EEMD-JADE and EEMD-SVD-LTSA methods. This method can also be used to fuse multi-sensor features of non-stationary data rapidly.

A New Fault Feature Extraction Method for Rotating Machinery Based on Multiple Sensors.

During the operation of rotating machinery, the vibration signals measured by sensors are the aliasing signals of various vibration sources, and they contain strong noises. Conventional signal processing methods have difficulty separating the aliasing signals, which causes great difficulties in the condition monitoring and fault diagnosis of the equipment. The principle and method of blind source separation are introduced, and it is pointed out that the blind source separation algorithm is invalid in strong pulse noise environments. In these environments, the vibration signals are first de-noised with the median filter (MF) method and the de-noised signals are separated with an improved joint approximate diagonalization of eigenmatrices (JADE) algorithm. The simulation results found here verify the effectiveness of the proposed method. Finally, the vibration signal of the hybrid rotor is effectively separated by the proposed method. A new separation approach is thus provided for vibration signals in strong pulse noise environments.

HKF-SVR Optimized by Krill Herd Algorithm for Coaxial Bearings Performance Degradation Prediction.

In real industrial applications, bearings in pairs or even more are often mounted on the same shaft. So the collected vibration signal is actually a mixed signal from multiple bearings. In this study, a method based on Hybrid Kernel Function-Support Vector Regression (HKF–SVR) whose parameters are optimized by Krill Herd (KH) algorithm was introduced for bearing performance degradation prediction in this situation. First, multi-domain statistical features are extracted from the bearing vibration signals and then fused into sensitive features using Kernel Joint Approximate Diagonalization of Eigen-matrices (KJADE) algorithm which is developed recently by our group. Due to the nonlinear mapping capability of the kernel method and the blind source separation ability of the JADE algorithm, the KJADE could extract latent source features that accurately reflecting the performance degradation from the mixed vibration signal. Then, the between-class and within-class scatters (SS) of the health-stage data sample and the current monitored data sample is calculated as the performance degradation index. Second, the parameters of the HKF–SVR are optimized by the KH (Krill Herd) algorithm to obtain the optimal performance degradation prediction model. Finally, the performance degradation trend of the bearing is predicted using the optimized HKF–SVR. Compared with the traditional methods of Back Propagation Neural Network (BPNN), Extreme Learning Machine (ELM) and traditional SVR, the results show that the proposed method has a better performance. The proposed method has a good application prospect in life prediction of coaxial bearings.

A Method for the Micro-Motion Signal Separation and Micro-Doppler Extraction for the Space Precession Target

Aiming at the problem of micro-motion signal separation and micro-Doppler extraction of the precession target, a new method based on singular value decomposition (SVD) and joint approximate diagonalization of eigen-matrices (JADE) is proposed in this paper. Firstly, the micro-motion model of space precession target is established, and the micro-Doppler and scattering characteristics are analyzed to establish the echo signal model of the target. Secondly, through simplifying the signal model of scattering point and building the signal matrix of different signal lengths, the singular value ratio sequence is constructed by the method of SVD to estimate the precession period of the target. Thirdly, the singular vectors of different observation periods are extracted, the observation matrix is constructed, and then the JADE algorithm is adopted to separate the micro-motion signal of each scattering point. Finally, the clustering analysis is used to denoise the time-frequency graph and the centroid calculation is employed to extract the micro-Doppler of each scattering point. Simulation results show that this method of good robustness can effectively separate and extract the micro-Doppler of the scattering points.

Electroencephalogram Signal Eye Blink Rejection Improvement Based on the Hybrid Stone Blind Origin Separation and Particle Swarm Optimization Technique

Electroencephalogram (EEG) extraction has widely used Stone's Blind Source Separation (Stone's BSS) algorithm. However, Stone's BSS algorithm is sensitive to the initial half-life (hlong, hshort) and weight vector W parameters, which affect the convergence of the algorithm. This paper proposes a hybridization of Stone's BSS with Particle Swarm Optimization (PSO) to boost the separation process. An improved Stone's BSS (ISBSS) method is employed to reject eye blinking from the electroencephalogram (EEG) mixture. The electroencephalogram (EEG) mixed-signal is first centralized and whitened; then, it is incorporated into the particle swarm optimization (PSO) iterative algorithm to process the initial (hlong, hshort) and generate the weight vector W parameters randomly. Finally, the generalized eigenvalue decomposition (GEVD) method is applied to extract EEG singles to obtain a clean EEG signal. A clinical EEG database is used to test the improved and other algorithms. The GEVD method estimates the measurement performance of the proposed algorithm using a carrier-to-interference ratio and integral square error and compares the proposed algorithm with the conventional Stone's BSS, fast independent component analysis (FastICA), evolutionary fast independent component analysis (EFICA), and joint approximate diagonalization of eigen matrices (JADE) algorithms to check its effectiveness. The results show that the suggested hybrid method has a better performance and decreasing elapsed time than conventional Stone's BSS and other algorithms.

Effective Hybrid Method for the Detection and Rejection of Electrooculogram (EOG) and Power Line Noise Artefacts From Electroencephalogram (EEG) Mixtures

Electrooculogram (EOG) and power line noise artefact detection and rejection have commonly utilized Stone's blind source separation (Stone's BSS) algorithm. The paper suggests a hybrid method between particle swarm optimization (PSO) and Stone's BSS for the detection and rejection of electrooculogram (EOG) and power line noise in the single-channel without the use of a notch filter. The proposed method contains three major steps: centralizing and whitening of the input EEG signal, incorporating the processing EEG signal into the iterative algorithm of the particle swarm optimization (PSO) to randomly generate the optimal value of (h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">short</sub> , h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">long</sub> ) and weight vector W parameters, and applying Stone's BSS using the generalized eigenvalue decomposition (GEVD) method to eliminate electrooculogram (EOG) and power line noise artefacts to obtain a clean EEG signal. The authors assess the robustness of the suggested method evaluated using real and simulated electroencephalogram (EEG) data sets. The simulated electroencephalogram (EEG) data and electrooculogram (EOG) and line noise (LN) artefacts are produced and mixed randomly in the MATLAB program; two types of real EEG data are taken in 9 and 19 channels. Evaluation results show the proposed algorithms as effective techniques for extracting both the power line noise and electrooculogram (EOG) artefacts from brain mixtures compared to specific BSS algorithms (e.g., Stone's BSS, evolutionary fast independent component analysis (EFICA), fast independent component analysis (FastICA), and joint approximate diagonalization of Eigen matrices (JADE)) while preserving the clinical features of the reconstructed EEG signal.

Fault Diagnosis of Bearings Based on KJADE and VNWOA-LSSVM Algorithm

In order to accurately diagnose the faulty parts of the rolling bearing under different operating conditions, the KJADE (Kernel Function Joint Approximate Diagonalization of Eigenmatrices) algorithm is proposed to reduce the dimensionality of the high-dimensional feature data. Then, the VNWOA (Von Neumann Topology Whale Optimization Algorithm) is used to optimize the LSSVM (Least Squares Support Vector Machine) method to diagnose the fault type of the rolling bearing. The VNWOA algorithm is used to optimize the regularization parameters and kernel parameters of LSSVM. The low-dimensional nonlinear features contained in the multidomain feature set are extracted by KJADE and compared with the results of PCA, LDA, KPCA, and JADE methods. Finally, VNWOA-LSSVM is used to identify bearing faults and compare them with LSSVM, GA-LSSVM, PSO-LSSVM, and WOA-LSSVM. The results show that the recognition rate of fault diagnosis is up to 98.67% by using VNWOA-LSSVM. The method based on KJADE and VNWOA-LSSVM can diagnose and identify fault signals more effectively and has higher classification accuracy.

Independent component analysis for multivariate functional data

We extend two methods of independent component analysis, fourth order blind identification and joint approximate diagonalization of eigen-matrices, to vector-valued functional data. Multivariate functional data occur naturally and frequently in modern applications, and extending independent component analysis to this setting allows us to distill important information from this type of data, going a step further than the functional principal component analysis. To allow the inversion of the covariance operator we make the assumption that the dependency between the component functions lies in a finite-dimensional subspace. In this subspace we define fourth cross-cumulant operators and use them to construct the two novel, Fisher consistent methods for solving the independent component problem for vector-valued functions. Both simulations and an application on a hand gesture data set show the usefulness and advantages of the proposed methods over functional principal component analysis.

Decoupling of Multiple Concurrent Faults for Diagnosing Coal Cutter Gearboxes: An Extensive Experimental Investigation With Multichannel Sensor Measurements

Abstract Due to harsh operating environments in underground coal seams, the key components (e.g., gear pairs and bearings) in the power transmission systems of coal cutters suffer from extreme wear and functional damages. To guarantee the safe and reliable operation of the coal cutters, it is important to monitor the condition of their transmission systems and detect possible faults in a timely manner. A challenging task here is to diagnose multiple concurrent faults. A literature review indicates that the current interests lie on the decoupling of multiple co-existing faults and that the very limited work has been done to deal with the dependence/correlation between the fault signals. To address this issue, this work extends our previous work on gear crack detection using the bounded component analysis (BCA) and proposes an improved BCA-based approach for decoupling hybrid faults with high dependence/correlation in coal cutter transmission systems. The proposed approach incorporates the Vold–Kalman order tracking and spectral kurtosis into an improved BCA framework (OTBCA-SK). Owing to the uniform sampling of order tracking, the influence of background noise and rotational speed variation on vibration signals can be effectively reduced. Since BCA is capable of handling vibration sources that are statistically dependent, OTBCA-SK can decouple both independent and dependent source signals. As a result, the vibration sources excited by hybrid faults, although maybe dependent/correlated, can be fully decoupled into single-fault vibration source signals. Three specially designed case studies were used to evaluate the effectiveness of the proposed OTBCA-SK approach in decoupling hybrid gear faults. The analysis results demonstrate better performance of hybrid fault decoupling using OTBCA-SK than that of three representative techniques, i.e., Erdogan's BCA (E-BCA), joint approximate diagonalization of eigen matrices (JADE) and fast independent component analysis (FastICA). These case studies also suggest that the proposed OTBCA-SK approach can retain the physical meaning of the original vibration and is hence suitable for hybrid fault diagnosis in practical applications.

Independent component analysis: A statistical perspective

Independent component analysis (ICA) is a data analysis tool that can be seen as a refinement of principal component analysis or factor analysis. ICA recovers the structures in the data which stay hidden if only the covariance matrix is used in the analysis. The ICA problem is formulated as a latent variable model where the observed variables are linear combinations of unobserved mutually independent non‐Gaussian variables. The goal is to recover linear transformations back to these latent independent components (ICs). As a statistical tool, the unmixing procedure is expressed as a functional in a relevant semiparametric model which further allows a careful formulation of the inference problem and the comparison of competing estimation procedures. For most approaches, the ICs are found in two steps, (a) by standardizing the random vector and then (b) by rotating the standardized vector to the ICs. In the projection pursuit, the ICs can be found either one‐by‐one or simultaneously and this is discussed in detail when the convex combination of the squared third and fourth cumulants is used as a projection index. Alternative projection indices and their use are also explained. The classical fourth‐order blind identification (FOBI) and joint approximate diagonalization of eigenmatrices (JADE) are described as well. The statistical tools for the comparison of consistent and asymptotically multivariate normal unmixing matrix estimates are discussed. Finally, recent extensions for times series, matrix‐ and tensor‐valued and functional data are reviewed.This article is categorized under: Statistical and Graphical Methods of Data Analysis &gt; Modeling Methods and Algorithms Statistical Models &gt; Multivariate Models Statistical and Graphical Methods of Data Analysis &gt; Dimension Reduction Statistical and Graphical Methods of Data Analysis &gt; Information Theoretic Methods

JADE for Tensor-Valued Observations

ABSTRACTIndependent component analysis is a standard tool in modern data analysis and numerous different techniques for applying it exist. The standard methods however quickly lose their effectiveness when the data are made up of structures of higher order than vectors, namely, matrices or tensors (e.g., images or videos), being unable to handle the high amounts of noise. Recently, an extension of the classic fourth-order blind identification (FOBI) specially suited for tensor-valued observations was proposed and showed to outperform its vector version for tensor data. In this article, we extend another popular independent component analysis method, the joint approximate diagonalization of eigen-matrices (JADE), for tensor observations. In addition to the theoretical background, we also provide the asymptotic properties of the proposed estimator and use both simulations and real data to show its usefulness and superiority over its competitors. Supplementary material including the proofs of the theorems and the codes for running the simulations and the real data example are available online.