Equivariant Adaptive Separation Research Articles

Online detection of measurement error in three-phase CVT based on equivariant adaptive source separation

As a key device for signal acquisition in power systems, the capacitor voltage transformer (CVT) has been widely used in high-voltage power grids with a capacity of 110 kV and above. However, the long-term stability of error in its measurements is poor and requires effective detection work. The conventional method of regular offline detection has the problems of power failure and operation difficulty. An online method for identifying errors in measurements of the CVT based on equivariant adaptive source separation is proposed in this paper. Under normal operation, the secondary output information of three-phase CVT is linearly correlated, and equivariant adaptive separation via independence (EASI) is used to analyze the correlation of data matrix. By constructing the main space and residual space, the primary voltage fluctuation is separated from the metering error. According to the separated signal characterizing the measurement error information, the standard quantity is established to realize the online detection of measurement error of three-phase CVT. In view of the non-stationary time-varying characteristics of power system operation, the data model is continuously updated according to successively acquired, which effectively improves the accuracy of the state assessment of the three-phase CVT. The simulation and experimental results show that the proposed method outperforms the independent component analysis (ICA), which can well meet the requirements of 0.2-level accuracy and have an evaluable change in amplitude that is better than 0.05%.

Adaptive step size EASI algorithm based on nonlinear correlation for on-line separation of satellite micro-vibration sources

The on-line blind separation of satellite micro-vibration source signals can provide the basis for the on-line suppression of satellite micro-vibration from the perspective of vibration source control, which has important academic significance and remarkable engineering application value for improving the performance of satellite positioning accuracy. Focusing on the inherent contradiction between convergence rate and steady-state error in on-line separation, a novel adaptive step size EASI (Equivariant Adaptive Separation via Independence) algorithm is proposed. Since nonlinear uncorrelation of Blind Source Separation (BSS) results displays its independence equivalently, minimizing nonlinear correlation also marks the optimal state of separation. According to this basic BSS estimation principle, a separation index based on nonlinear correlation coefficients is constructed to represent the separation degree, and on-line updating equations of separation index is derived by time average technique. Then, a suitable nonlinear monotone function is adopted to map separation index to the step size, and the step size can be adaptively adjusted according to separation degree. Finally, the novel adaptive blind separation algorithm in this paper is formed by introducing the adaptive step size to traditional EASI algorithm. Compared with fixed step size EASI algorithm (FS-EASI) and several variable step size EASI algorithms, the proposed algorithm greatly improves convergence rate while ensuring high separation accuracy. Effectiveness and superiority of the proposed algorithm are verified by simulation case analysis and satellite cabin structure experimental study.

Online blind source separation method with adaptive step size in both time-invariant and time-varying cases

To effectively balance the convergence speed and steady-state error of online blind source separation, this paper develops an online blind source separation method with adaptive step size based on an equivariant adaptive separation via independence (EASI) algorithm. First, we construct a separation indicator from the convergence condition of EASI that can reveal the separation degree of mixed signals. Next, a new forgetting factor suitable for non-stationary cases is designed to reduce the error accumulation of previous data, and the separation indicator can be adaptively updated. To automatically adjust the step size according to separation degree, a nonlinear mapping between the separation indicator and step size is constructed. Finally, numerical and experimental case studies are provided to evaluate the performance of the proposed method, which comparison of results proves to be more effective. The results of numerical case studies show that the step size of the proposed method can be adaptively adjusted in the separation process and the proposed method can effectively balance convergence speed and steady-state error in both time-invariant and time-varying cases. The results of experimental case studies show that the proposed method has higher estimation accuracy.

A Modified RLS Algorithm for ICA with Weighted Orthogonal Constraint

Independent component analysis (ICA), as an important data processing technique, is widely employed in many areas. The objective of the ICA is to recover independent components from observed signals. Several algorithms, such as equivariant adaptive separation via independence algorithm, least-mean-square (LMS)-type algorithms and recursive least-squares (RLS)-type learning rules, are proposed to solve the ICA problem. In the present paper, a modified RLS algorithm for ICA with weighted orthogonal constraint is developed to implement source separation based on the local convergence analysis of the available algorithm. Comparative experiment results demonstrate that the proposed algorithm is better than existing learning rules in the aspect of the accuracy of separation and stability.

Adaptive modal identification of structures with equivariant adaptive separation via independence approach

An efficient output-only Blind Source Separation (BSS) method was recently introduced for the modal identification of structures. BSS procedures recover a set of independent sources from their unknown linear mixtures when only mixtures are observed. Batch data is required for the separation in traditional blind source separation methods. These algorithms are however unfavorable, as some sets of data are observed one after another. In this paper, an adaptive blind source separation technique - equivariant adaptive separation via independence (EASI) - is introduced to overcome the mentioned disadvantage within the structures. The EASI algorithm is beneficial as it can provide solutions to real time problems, while also update the un-mixing matrix for each step. EASI not only avoids increases in size of the relevant matrices and vectors, but also decreases the analysis time. A synthetic example and a benchmark structure have been used in this paper to better investigate the efficiency of the proposed method. The simulation results demonstrate the effectiveness of the EASI algorithm in on-line identification of modal parameters of structures.

An efficient equivariant adaptive separation via independence algorithm for acoustical source separation and identification

To balance the convergence rate and steady-state error of blind source separation (BSS) algorithms, an efficient equivariant adaptive separation via independence (Efficient EASI) algorithm is proposed based on separating indicator, which was derived from the convergence condition of EASI, and can be used to evaluate the separation degree of separated signals. Furthermore, a nonlinear monotone increasing function between suitable step sizes and separating indicator is constructed to adaptively adjust step sizes, and forgetting factor is employed to weaken effects of data at the initial stage. Numerical case studies and experimental studies on a test bed with shell structures are provided to validate the efficiency improvement of the proposed method. This study can benefit for vibration & acoustic monitoring and control, and machinery condition monitoring and fault diagnosis.

The Research and Simulation of Blind Source Separation Algorithm

When the original source signals and input channel are unknown, blind source separation (BSS) tries decomposing the mixed signals observed to obtain the original source signals, as seems mysterious. BSS has found many applications in biomedicine science, image processing, wireless communication and speech enhancement. In this paper the basic theory of blind source separation is described, which consists of the mathematical model, knowledge, performance evaluation index, and so on. And a further research on blind source separation algorithm has done when the number of source signals is more than (equal) the number of the signals observed, including the traditional ways of BSS—fast independent component analysis (FastICA) algorithm and equivariant adaptive separation via independence (EASI) algorithm, as well as the SOBI algorithm which is based on the joint diagonalization of matrices.

An optimized EASI algorithm

This paper addresses the problem of blind source separation and presents a kind of optimized equivariant adaptive separation via independence (EASI) algorithms. According to the cumulant based approximation to the mutual information contrast function, the EASI learning rule is optimized by multiplying the symmetric part with an optimal time variant weight coefficient. Simulation results show the proposed optimized EASI algorithms outperform the existing algorithms in convergent speed and steady-state accuracy.

Source separation and tracking for time-varying systems

Many situations arise when it is desired to recover from a noisy mixture of data both an estimate of a propagating source signal as well as its angular position. Accordingly, the problem of source separation and tracking for time-varying systems of moving sources is studied. Using techniques borrowed from independent component analysis (ICA) and numerical linear algebra, a processing solution is formulated. The ULV decomposition (ULVD), a member of the complete orthogonal decompositions (CODs) family is used to normalize and decorrelate the data. Since the ULVD is known to stably update and downdate with time-varying data, this step is named ULVD adaptive whitening. The ICA-based EASI (equivariant adaptive separation based on independence) algorithm is adapted to provide not only separated sources but direction-of-arrival (DOA) estimates. Developed improvements to this technique are an adaptive filter method for estimating the mixing matrix from the newly estimated signals as well as a simple cross-over detection scheme. Finally, the developed solutions are tested in simulation examples using meaningful performance measures.

FPGA implementation of EASI algorithm

Using chaotic signals, we evaluate the performance of the EASI(Equivariant Adaptive Separation via Independence) algorithm, which is a basic algorithm among various on-line ICA (Independent Component Analysis) algorithms. We found that the EASI algorithm in fixed-point (16-bit) arithmetic can recover the chaotic signals successfully as well as the algorithm in floating-point arithmetic. We can implement the algorithm in fixed-point arithmetic to Virtex-IV SX25 FPGA (Field Programmable Gate Arrays) up to the 4x4 design.

Quasi-optimal EASI algorithm based on the Score Function Difference (SFD)

Equivariant adaptive separation via independence (EASI) is one of the most successful algorithms for blind source separation (BSS). However, the user has to choose non-linearities, and usually simple (but non-optimal) cubic polynomials are applied. In this paper, the optimal choice of these non-linearities is addressed. We show that this optimal non-linearity is the output score function difference (SFD). Contrary to simple non-linearities usually used in EASI (such as cubic polynomials), the optimal choice is neither component-wise nor fixed: it is a multivariate function which depends on the output distributions. Finally, we derive three adaptive algorithms for estimating the SFD and achieving “quasi-optimal” EASI algorithms, whose separation performance is much better than “standard” EASI and which especially converges for any sources.

Robust rank-EASI algorithm for blind source separation

Robustness against deviations from nominal source pdf assumptions is very desirable in blind source separation (BSS) algorithms. In the paper, a new approach for robust BSS is proposed. The EASI (equivariant adaptive separation by independence) algorithm (Cardoso and Laheld, 1996) is modified to use ranks of observed signals. The modified EASI algorithm can be applied to both real-valued and complex-valued data. Design guidelines are discussed for the nonlinear rank weighting functions in the modified EASI algorithm. Simulation results for two examples are given, showing very good performance.

Median equivariant adaptive separation via independence: application to communications

The authors propose a family of algorithms to solve the blind source separation (BSS) problem, focusing on digital communications. We first include a revision of the equivariant adaptive separation via independence (EASI). These results provide a better characterization of the stability condition. Starting from this analysis we propose a new method, the Median EASI, whose stability condition presents useful properties. Next, we prove this method to be more noise-robust for some sources such as digitally modulated signals. Some experiments are included to show how the Median EASI allows phase recovering, an important issue in communications. Finally, we propose the median EASI as a blind asynchronous CDMA multiuser detector.

Equivariant adaptive source separation

Source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence (EASI). The EASI algorithms are based on the idea of serial updating. This specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures. Most importantly, the performance of an EASI algorithm does not depend on the mixing matrix. In particular, convergence rates, stability conditions, and interference rejection levels depend only on the (normalized) distributions of the source signals. Closed-form expressions of these quantities are given via an asymptotic performance analysis. The theme of equivariance is stressed throughout the paper. The source separation problem has an underlying multiplicative structure. The parameter space forms a (matrix) multiplicative group. We explore the (favorable) consequences of this fact on implementation, performance, and optimization of EASI algorithms.