Bounded Component Analysis Research Articles

Underdetermined RFID tag anti-collision based on bounded component analysis

Underdetermined RFID tag anti-collision based on bounded component analysis

A Blind Source Separation Method Based on Bounded Component Analysis Optimized by the Improved Beetle Antennae Search.

Currently, the widely used blind source separation algorithm is typically associated with issues such as a sluggish rate of convergence and unstable accuracy, and it is mostly suitable for the separation of independent source signals. Nevertheless, source signals are not always independent of one another in practical applications. This paper suggests a blind source separation algorithm based on the bounded component analysis of the enhanced Beetle Antennae Search algorithm (BAS). Firstly, the restrictive assumptions of the bounded component analysis method are more relaxed and do not require the signal sources to be independent of each other, broadening the applicability of this blind source separation algorithm. Second, the objective function of bounded component analysis is optimized using the improved Beetle Antennae Search optimization algorithm. A step decay factor is introduced to ensure that the beetle does not miss the optimal point when approaching the target, improving the optimization accuracy. At the same time, since only one beetle is required, the optimization speed is also improved. Finally, simulation experiments show that the algorithm can effectively separate independent and dependent source signals and can be applied to blind source separation of images. Compared to traditional blind source separation algorithms, it has stronger universality and has faster convergence speed and higher accuracy compared to the original independent component analysis algorithm.

IDENTIFIABLE BOUNDED COMPONENT ANALYSIS VIA MINIMUM VOLUME ENCLOSING PARALLELOTOPE.

In this paper, we revisit bounded component analysis (BCA) and formulate it as a geometric problem of finding the minimum volume enclosing parallelotope (MVEP) of a set of data points in the Euclidean space. A parallelotope is an affine transformation of the standard box, also known as the -norm ball. An immediate benefit of the novel formulation is that the bounds on the supports of the latent components can be arbitrary, unlike most existing BCA works that assume the bounds are symmetric around zero. The main contribution is that the MVEP solution exactly recovers the latent components, up to the inherent (and inconsequential) permutation, shift, and scaling ambiguities, if the groundtruth components satisfy a so-called "sufficiently scattered" condition in the standard box. This is a great improvement to the existing result that requires all vertices of the box are contained in the data set, which requires exponentially many data points, or that of ICA, which essentially requires infinite amount of data points to guarantee exact recovery. We also present a new learning algorithm to solve the (NP-hard) MVEP problem based on Frank-Wolfe, and show numerically that the performance is surprisingly effective.

Frequency-Domain Convolutive Bounded Component Analysis Algorithm for the Blind Separation of Dependent Sources

Frequency-Domain Convolutive Bounded Component Analysis Algorithm for the Blind Separation of Dependent Sources

Convolutive blind source separation in the frequency domain of mechanical noise for gas turbines based on bounded component analysis

Noise source identification of gas turbines can provide the basis and guidance for vibration and noise reduction of gas turbines. Independent component analysis (ICA) is one of the most popular techniques for blind source separation (BSS) widely used in vibration and noise source separation in mechanical systems. ICA is suitable for independent source signals. However, in order to identify dependent mechanical noise sources in gas turbines, a convolutive BSS in the frequency domain based on bounded component analysis (BCA) is proposed. First, the basic theory of BSS and BCA is introduced in detail. The convolutive mixing in the time domain is transformed into an instantaneous mixing in the frequency domain by short time Fourier transform (STFT), and complex BCA is performed at each frequency bin. Second, a permutation alignment method based on local and global optimization is proposed to solve the problem of the permutation ambiguity. Finally, the accuracy and robustness of the proposed method are comparatively studied through typical numerical and experimental studies on a three-rotor experimental bench. The results show that the proposed method can effectively separate and identify independent and dependent source signals.

Quantitative identification of independent and dependent sources based on bounded component analysis

The quantitative identification of vibration sources can provide the basis and guidance for the vibration and noise reduction of mechanical systems. Since the vibration sources in a mechanical system are not necessarily mutually independent, this paper proposes a quantitative identification method suitable for both independent and dependent sources based on bounded component analysis (BCA). Firstly, the new BCA algorithm is adopted to separate source signals and normalized boundary minimization is used as the objective function, which is optimized by a modified subgradient method with the introduction of the probability mass function and an adaptive step size, and thus the noise resistance and convergence performance are enhanced. Secondly, the source contribution is extracted by taking the separated signal as the input and boundary minimization of the residual signal as the criterion. Thirdly, the projection of the source contribution in the mixed signal is calculated by the inner product and the proportion of the calculated projection on the mixed signal is taken as the contribution index to evaluate the influence of the vibration source on the vibration of the observation point of the system. Finally, the effectiveness and superiority of the proposed method are tested by simulation analysis and experimental verification. The results show that the proposed method has high accuracy in the quantitative identification of both independent and dependent sources.

Time and frequency based sparse bounded component analysis algorithms for convolutive mixtures

In this paper, we introduce time-domain and frequency-domain versions of a new Blind Source Separation (BSS) approach to extract bounded magnitude sparse sources from convolutive mixtures. We derive algorithms by maximization of the proposed objective functions that are defined in a completely deterministic framework, and prove that global maximums of the objective functions yield perfect separation under suitable conditions. The derived algorithms can be applied to temporal or spatially dependent sources as well as independent sources. We provide experimental results to demonstrate some benefits of the approach, also including an application on blind speech separation.

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.

An Algorithmic Framework for Sparse Bounded Component Analysis

Bounded component analysis (BCA) is a recent approach that enables the separation of both dependent and independent signals from their mixtures. This paper introduces a novel deterministic instantaneous BCA framework for the separation of sparse bounded sources. The framework is based on a geometric maximization setting, where the objective function is defined as the volume ratio of two objects, namely, the principal hyperellipsoid and the bounding $\ell _1$ -norm ball, defined over the separator output samples. It is shown that all global maxima of this objective are perfect separators. This paper also provides the corresponding iterative algorithms for both real and complex sparse sources. The numerical experiments illustrate the potential benefits of the proposed approach, with applications on image separation and neuron identification.

A new proof of a contrast function for bounded component analysis and further analysis

Bounded Component Analysis (BCA) solves the Blind Source Separation (BSS) problem based on geometric assumptions. This paper introduces a new proof of a BCA contrast function, derived from elementary matrices, Gauss–Jordan elimination and convex geometry. The new proof and further analysis provide additional insight into a key assumption of BCA. In addition, an interpretation is presented to clarify one of the limitations of the instantaneous BCA algorithm. Experiments on audio sources support our analysis.

A Comprehensive Survey on Blind Source Separation for Wireless Adaptive Processing: Principles, Perspectives, Challenges and New Research Directions

With the rapid proliferation of wireless services, the frequency spectrum has become increasingly crowded, and the interferences and composite signals will be ubiquitous in the wireless receiver. For deeply dissecting and detecting the expected signals, the research community has to investigate the smart signal processing technology to resisting the influence of detrimental signals. For this purpose, blind source separation has been shown to be a promising method for achieving simultaneous spectrum utilization and wireless adaptive interference cancellation. The attractive features and appealing advantages of blind source separation make it an attractive theory for source extraction or recovery, which plays a crucial role in helping realize intelligent signal processing for wireless communication. It can recover the unobserved sources only from the wireless received mixed signals based on the features of the source signal exempted from channel estimation and synchronization manipulation. Wireless communication systems can benefit the high spectrum efficiency, strong anti-interference, and adaptive signal processing through the blind separation mechanism. So far, numerous researchers have made tremendous efforts to investigate this field for enhancing spectrum efficiency, anti-interference ability, and signal detection performance through employing the philosophy of blind separation. These meaningful and appealing research works motivate us to make a comprehensive survey with regard to this area. In this paper, the fundamental principle of the blind separation mechanism, involving independent component analysis, sparse component analysis, non-negative matrix factorization, and bounded component analysis will be reviewed briefly, and then, the critical technologies applied in various wireless communication systems will be overviewed, such as in direct-sequence code division multiplexing access, frequency hopping, orthogonal frequency-division multiplexing, multiple input multiple output, wireless sensor networks, cognitive radio networks, radio frequency identification devices, and communication security. In addition, the important research challenges and meaningful research directions pertaining to the area of blind separation applied in wireless communications systems are also discussed.

Stationary Point Characterization for a Class of BCA Algorithms

Bounded component analysis (BCA) is a recently introduced approach including independent component analysis as a special case under the assumption of source boundedness. In this paper, we provide a stationary point analysis for the recently proposed instantaneous BCA algorithms that are capable of separating dependent, even correlated as well as independent sources from their mixtures. The stationary points are identified and characterized as either perfect separators, which are the global maxima of the proposed optimization scheme or saddle points. The important result emerging from the analysis is that there are no local optima that can prevent the proposed BCA algorithms from converging to perfect separators.

Detection of gear cracks in a complex gearbox of wind turbines using supervised bounded component analysis of vibration signals collected from multi-channel sensors

In the complex gear transmission systems, in wind turbines a crack is one of the most common failure modes and can be fatal to the wind turbine power systems. A single sensor may suffer with issues relating to its installation position and direction, resulting in the collection of weak dynamic responses of the cracked gear. A multi-channel sensor system is hence applied in the signal acquisition and the blind source separation (BSS) technologies are employed to optimally process the information collected from multiple sensors. However, literature review finds that most of the BSS based fault detectors did not address the dependence/correlation between different moving components in the gear systems; particularly, the popular used independent component analysis (ICA) assumes mutual independence of different vibration sources. The fault detection performance may be significantly influenced by the dependence/correlation between vibration sources. In order to address this issue, this paper presents a new method based on the supervised order tracking bounded component analysis (SOTBCA) for gear crack detection in wind turbines. The bounded component analysis (BCA) is a state of art technology for dependent source separation and is applied limitedly to communication signals. To make it applicable for vibration analysis, in this work, the order tracking has been appropriately incorporated into the BCA framework to eliminate the noise and disturbance signal components. Then an autoregressive (AR) model built with prior knowledge about the crack fault is employed to supervise the reconstruction of the crack vibration source signature. The SOTBCA only outputs one source signal that has the closest distance with the AR model. Owing to the dependence tolerance ability of the BCA framework, interfering vibration sources that are dependent/correlated with the crack vibration source could be recognized by the SOTBCA, and hence, only useful fault information could be preserved in the reconstructed signal. The crack failure thus could be precisely identified by the cyclic spectral correlation analysis. A series of numerical simulations and experimental tests have been conducted to illustrate the advantages of the proposed SOTBCA method for fatigue crack detection. Comparisons to three representative techniques, i.e. Erdogan’s BCA (E-BCA), joint approximate diagonalization of eigen-matrices (JADE), and FastICA, have demonstrated the effectiveness of the SOTBCA. Hence the proposed approach is suitable for accurate gear crack detection in practical applications.

Convergence study of a Bounded Component Analysis algorithm

This work presents the convergence study of a component analysis algorithm that is designed for extracting a source from a linear mixture of bounded sources. The algorithm implements the parsimonious criterion of finding the linear projection of observations whose convex support has the minimum normalised perimeter. In a noiseless situation, our stability analysis provides recommendations for setting the step size of the algorithm. These recommendations are designed to guarantee the global monotonic convergence to the source that is closest to the algorithm׳s initialisation (in a given sense) while at the same time maintaining a fast local convergence rate in the neighborhood of this solution. In the absence of noise, these theoretical results have been corroborated by means of computer simulations. Furthermore, we have shown that in noisy mixtures, the performance of the algorithms is improved by eliminating the bias that noise creates.

The minimum risk principle that underlies the criteria of bounded component analysis.

This paper studies the problem of the blind extraction of a subset of bounded component signals from the observations of a linear mixture. In the first part of this paper, we analyze the geometric assumptions of the observations that characterize the problem, and their implications on the mixing matrix and latent sources. In the second part, we solve the problem by adopting the principle of minimizing the risk, which refers to the encoding complexity of the observations in the worst admissible situation. This principle provides an underlying justification of several bounded component analysis (BCA) criteria, including the minimum normalized volume criterion of the estimated sources or the maximum negentropy-likelihood criterion with a uniform reference model for the estimated sources. This unifying framework can explain the differences between the criteria in accordance with their considered hypotheses for the model of the observations. This paper is first presented for the case of the extraction of a complex and multidimensional source, and later is particularized for the case of the extraction of subsets of 1-D complex sources. The results also hold true in the case of real signals, where the obtained criteria for the extraction of a set of 1-D sources usually coincide with the existing BCA criteria.

Bounded Component Analysis of Noisy Underdetermined and Overdetermined Mixtures

Our paper addresses the problem of the bounded component analysis of the observations in noisy mixtures. We present an original set of assumptions that guarantee the identifiability of the mixture in underdetermined mixtures and the separability of the sources in overdetermined mixtures. These assumptions are especially well suited for the blind identification of communication channels. Our proof of the identifiability of the mixing system is non-constructive. Thus, we develop a novel blind identification criterion for underdetermined and overdetermined mixtures, which is based on the least square fit of the perimeter of a set of projections of the observations. For the optimization of this criterion we propose the BCA-PM algorithm, which implements the natural gradient descent, along with an acceleration of the convergence designed for the neighbourhood of the solution. In situations of isotropic Gaussian noise and for reasonable signal to noise ratio, BCA-PM compares favorably with respect to other state-of-the-art methods, such as the ICA simultaneous diagonalization algorithms for underdetermined and overdetermined mixtures. The simulations also corroborate the advantages of using bounded component analysis for the blind identification of the channel with small datasets or when the transmitters cannot be regarded as statistically independent.

Convolutive bounded component analysis algorithms for independent and dependent source separation.

Bounded component analysis (BCA) is a framework that can be considered as a more general framework than independent component analysis (ICA) under the boundedness constraint on sources. Using this framework, it is possible to separate dependent as well as independent components from their mixtures. In this paper, as an extension of a recently introduced instantaneous BCA approach, we introduce a family of convolutive BCA criteria and corresponding algorithms. We prove that the global optima of the proposed criteria, under generic BCA assumptions, are equivalent to a set of perfect separators. The algorithms introduced in this paper are capable of separating not only the independent sources but also the sources that are dependent/correlated in both component (space) and sample (time) dimensions. Therefore, under the condition that the sources are bounded, they can be considered as extended convolutive ICA algorithms with additional dependent/correlated source separation capability. Furthermore, they have potential to provide improvement in separation performance, especially for short data records. This paper offers examples to illustrate the space-time correlated source separation capability through a copula distribution-based example. In addition, a frequency-selective Multiple Input Multiple Output equalization example demonstrates the clear performance advantage of the proposed BCA approach over the state-of-the-art ICA-based approaches in setups involving convolutive mixtures of digital communication sources.

A Convolutive Bounded Component Analysis Framework for Potentially Nonstationary Independent and/or Dependent Sources

Bounded Component Analysis (BCA) is a recent framework which enables development of methods for the separation of dependent as well as independent sources from their mixtures. This paper extends a recent geometric BCA approach introduced for the instantaneous mixing problem to the convolutive mixing problem. The paper proposes novel deterministic convolutive BCA frameworks for the blind source extraction and blind source separation of convolutive mixtures of sources which allows the sources to be potentially nonstationary. The global maximizers of the proposed deterministic BCA optimization settings are proved to be perfect separators. The paper also illustrates that the iterative algorithms corresponding to these frameworks are capable of extracting/separating convolutive mixtures of not only independent sources but also dependent (even correlated) sources in both component (space) and sample (time) dimensions through simulations based on a Copula distributed source system. In addition, even when the sources are independent, it is shown that the proposed BCA approach have the potential to provide improvement in separation performance especially for short data records based on the setups involving convolutive mixtures of digital communication sources.

A Class of Bounded Component Analysis Algorithms for the Separation of Both Independent and Dependent Sources

Bounded Component Analysis (BCA) is a recent approach which enables the separation of both dependent and independent signals from their mixtures. In this approach, under the practical source boundedness assumption, the widely used statistical independence assumption is replaced by a more generic domain separability assumption. This article introduces a geometric framework for the development of Bounded Component Analysis algorithms. Two main geometric objects related to the separator output samples, namely Principal Hyper-Ellipsoid and Bounding Hyper-Rectangle, are introduced. The maximization of the volume ratio of these objects, and its extensions, are introduced as relevant optimization problems for Bounded Component Analysis. The article also provides corresponding iterative algorithms for both real and complex sources. The numerical examples illustrate the potential advantage of the proposed BCA framework in terms of correlated source separation capability as well as performance improvement for short data records.

Blind Separation of Dependent Sources With a Bounded Component Analysis Deflationary Algorithm

The problem of blind source separation of complex-valued sources from a linear mixture is addressed. We propose a deflationary algorithm for the sequential recovery of a set of communication signals, where each source is extracted by performing a Bounded Component Analysis of the linear mixture. The contribution of each recovered source to the observations is removed by minimizing its convex perimeter, without using second-order statistics. This implies to run a gradient descent algorithm several times. In order to accelerate the convergence, we have derived a fast step size that exploits the second-order information of the cost function by means of the augmented Hessian matrix. Computer simulations show that the proposed method is able to blindly separate even dependent sources, as long as they satisfy the BCA separability conditions. Also, the speed of convergence of this novel step size is compared with other classical approaches.