Dynamic blind source separation based on source-direction prediction

The methods that can be done for the estimation of the number of source signals and separation of source signals using time‐frequency information are proposed as a method of blind source separation. In these methods, some independent conditions are assumed in a time‐frequency domain, and observed signals are expanded to time‐frequency domain using wavelet analysis. However, these methods are not considered phase differences (difference of distance) between source signals and observed signals. A new method is proposed. The method can be done not only for the source separation but also the specification of the locations of source signals considering phase differences. In this method, it is necessary to assume a rather stronger independent condition than former methods. But, on account of this assumption, a function that becomes a real value only when phase differences are coincidence in time‐frequency domain is determined. Using this function, first of all, the number of source signals is calculated, then the locations of source signals and source signals are calculated. The effectiveness of the method is shown using actual synthetic signals.

The most standard blind source separation (BSS) methods address the situation when a set of signals are available, e.g. from measurements, and all of them are linear memoryless combinations, with unknown coefficient values, of the same limited set of unknown source signals. BSS methods aim at estimating these unknown source signals and/or coefficients. This generic problem is e.g. faced in the field of Earth observation (where it is also called “unsupervised unmixing”), when considering the commonly used (over)simplified model of hyperspectral images. Each pixel of such an image has an associated reflectance spectrum derived from measurements, which is defined by the fraction of sunlight power reflected by the corresponding Earth surface at each wavelength. Each source signal is then the single reflectance spectrum associated with one of the classes of pure materials which are present in the region of Earth corresponding to the overall considered hyperspectral image. Besides, the associated coefficients define the surfaces on Earth covered with each of these pure materials in each sub-region corresponding to one pixel of the considered image. However, real hyperspectral data e.g. obtained in urban areas have a much more complex structure than the above basic model: each class of pure materials (e.g. roof tiles, trees or asphalt) has so-called spectral or intra-class variability, i.e. it yields a somewhat different spectral component in each pixel of the image. In this complex framework, this chapter shows that Principal Component Analysis (PCA) and its proposed extension are of high interest at three stages of our investigation. First, PCA allows us to analyze the above-mentioned spectral variability of real high-dimensional hyperspectral data and to propose an extended data model which is suited to these complex data. We then develop a versatile extension of BSS methods based on Nonnegative Matrix Factorization, which adds the capability to handle arbitrary forms of intra-class variability by transposing PCA concepts to this original version of the BSS tramework. Finally, PCA again proves to be very well suited to analyzing the high-dimensional data obtained as the result of the proposed BSS method.

This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method.

This paper proposes a wind turbine dynamic state prediction method using similarity matching in historical data. Because similarity matching is inefficient for large-scale multivariate time series (MTS) data, we use feature selection method based on random forest to determine main attributes and remove irrelevant attributes. Then, by using the principal component analysis, the dimension of MTS data can be reduced into one dimension. After that, we search the most similar historical data for a given current synthetic attribute time series, and then use the consequent data of the chosen historical data as the predicting state of the wind turbine. Theoretical analysis and experimental results show that the proposed method is robust and effective.

Upgrading Sparse NMF algorithm for blind source separation through Adaptive Parameterized Hybrid Kernel based approach

As sensor monitoring technology continues to evolve, structural online monitoring and health management have found numerous applications across various fields. However, challenges remain concerning the real-time diagnosis of structural damage and the accuracy of dynamic reliability predictions. In this paper, a structural online damage identification and dynamic reliability prediction method based on Unscented Kalman Filter (UKF) is presented. Specifically, in the Wiener degradation process with random effects on structural performance, the structural damage identification is initially realized using UKF. Following that, the EM algorithm is employed for estimating the performance model parameters. Eventually, dynamic reliability prediction is realized based on conditional probability. The simulation results indicate that the method effectively estimates the damage state during the structure’s use while providing accurate, real-time, and dynamic reliability predictions for the system.

Feed-Forward (FF-) and Feed-Back (FB-) structures have been proposed for Blind Source Separation (BSS). The FF-BSS systems have some degrees of freedom in the solution space, and signal distortion is likely to occur in convolutive mixtures. On the other hand, the FBBSS structure does not cause signal distortion. However, it requires a condition on the propagation delays in the mixing process. In this paper, source separation performance in the FB-BSS is theoretically analyzed taking the propagation delays into account. Simulation is carried out by using white signals and speech signals as the signal sources. The FF-BSS system and the FB-BSS system are compared. Even though the FB-BSS can provide good separation performance, there exits some limitation on location of the signal sources and the sensors.

Event-related potentials (ERPs) are a superposition of electric potential differences generated by neurophysiological activity associated with psychophysical events. Spatiotemporal dissociation of these signal sources can supplement conventional ERP analysis and improve source localization. However, results from established source separation methods applied to ERPs can be challenging to interpret. Hence, we have developed a recurrent neural network (RNN) method for blind source separation. The RNN transforms input step pulse signals representing events into corresponding ERP difference waveforms. Source waveforms are obtained from penultimate layer units and scalp maps are obtained from feed-forward output layer weights that project these source waveforms onto EEG electrode amplitudes. An interpretable, sparse source representation is achieved by incorporating L1 regularization of signals obtained from the penultimate layer of the network during training. This RNN method was applied to four ERP difference waveforms (MMN, N170, N400, P3) from the open-access ERP CORE database, and independent component analysis (ICA) was applied to the same data for comparison. The RNN decomposed these ERPs into eleven spatially and temporally separate sources that were less noisy, tended to be more ERP-specific, and were less similar to each other than ICA-derived sources. The RNN sources also had less ambiguity between source waveform amplitude, scalp potential polarity, and equivalent current dipole orientation than ICA sources. In conclusion, the proposed RNN blind source separation method can be effectively applied to grand-average ERP difference waves and holds promise for further development as a computational model of event-related neural signals.

Modern bridges are monitored by an increasing network of sensors that produce massive data for bridge performance prediction. Reasonably and dynamically predicting with monitored data for the time-variant reliability of the existing bridges has become one of the urgent problems in structural health monitoring (SHM). This study, taking the dynamic measure of structural stress over time as a time series, proposes a data assimilation approach to predicting reliability based on extreme stress data with cyclicity. To this aim, the objectives of this article are to present the following: (a) a Gaussian mixture model-based Bayesian cyclical dynamic linear model (GMM-BCDLM) based on extreme stress data with cyclicity and (b) a dynamic reliability prediction method in the combination of GMM-BCDLM and SHM data via first-order second-moment (FOSM) method. An in-service bridge for providing real-time monitored stress data is applied to illustrate the application and feasibility of the proposed method. Then, the effectiveness and prediction precision of the proposed models are proved to be superior compared to other prediction approaches to extreme stress data with cyclicity.

Blind source separation has found applications in various areas including biomedical signal processing and genomic signal processing. Often, blind source separation is solved via independent component analysis (ICA) by assuming and utilizing mutual independence among source signals. However, in bio-signal and genomic signal processing, the assumption of independence is often untrue, and the performance of the ICA approach is not as good. Much effort has been devoted to searching alternative approaches to blind source separation without the independence assumption. One idea known as network component analysis (NCA) is developed to identify the underlying regulatory signals of transcription factors in the gene regulatory network. In this paper we show that NCA is a general method for blind source separation using a priori information on the mixing matrix. An alternative proof of identifiability using NCA is proposed and a novel method to solve the problem is developed. Validation is made through computer simulations.

Blind image restoration is a great part of image processing, which refers to the technology field that study how to restore the original image from the observed image without sufficient prior knowledge about the degradation process. Recently, as a novel method for blind source separation based on high statistics, Independent Component Analysis (ICA)'s computation algorithms and applications are widely studied. In this paper, we present a Non-negative ICA algorithm which is used to the blind image restoration with the constraint of non-negativity. Besides this, through a matrix of de-correlation, it can reduce the requirements to the independence of the source signals in ICA algorithm. Through some computer simulation and experiments for real images, we show the effectiveness of the presented method.

We present a new approach to independent component analysis (ICA) by extending the formulation of univariate source signals to multivariate source signals. The new approach is termed independent vector analysis (IVA). In the model, we assume that linear mixing model exists in each dimension separately, and the latent sources are independent of the others. In contrast to ICA, the sources are random vectors, not just single variables, which means the elements of a random vector are closely related to the others. Thus, we assume the dependency between the elements of a source vector. In this manner, we define dependence between vectors as Kullback-Leibler divergence between the total joint probability of vectors and the product of marginal probabilities of vectors. Then, the model allows independence between multivariate source signals represented as random vectors, and dependence between the source signals within the vector representation. The proposed vector density model can for example capture variance dependencies within a vector source signal. There are several applications of this new formulation. In the separation of acoustic sources, the algorithm mitigates the permutation problem, i.e. the usual ICA algorithms applied in to the frequency domain mixture data suffer from the unknown permutation of the output signals. Although there are several engineering solutions to fix this problem after the ICA stage, the proposed method provides a natural solution to the problem by capturing the inherent dependencies of the acoustic signals. It therefore avoids the permutation problem and allows the separation of sources in very challenging environments for many sound sources.

Blind source separation and feature extraction in concurrent control charts pattern recognition: Novel analyses and a comparison of different methods

Drive system is one of most important key equipment to guarantee safe and stable operation in locomotive. With time variation, unpredictability and nonstationary, fault source of drive system is not obtained by traditional fault diagnosis method. Blind source separation is a kind of method on source signals separation under transmission channel unknown instance. The method of Blind source separation based on variable metric empirical mode decomposition is proposed. Intrinsic mode function is built, redundancy factors are reduced, and recurrent neural network is used to adaptive blind separation. The method is verified by data analysis of on-line measuring. The results show that separation efficiency is improved and unaffected with iteration time in the process of fault information separation, which will be better for further fundamental research and provide technique support for the locomotive.

We propose a new method for blind source separation of cyclostationary sources, whose cyclic frequencies are unknown and may share one or more common cyclic frequencies. The suggested method exploits the cyclic correlation function of observation signals to compose a set of matrices which has a particular algebraic structure. The aforesaid matrices are automatically selected by proposing two new criteria. Then, they are jointly diagonalized so as to estimate the mixing matrix and retrieve the source signals as a consequence. The nonunitary joint diagonalization (NU‐JD) is ensured by Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) method which is the most commonly used update strategy for implementing a quasi‐Newton technique. The efficiency of the method is illustrated by numerical simulations in digital communications context, which show good performances comparing to other state‐of‐the‐art methods.