Sparse Component Analysis Method Research Articles

Modal identification of non‐classically damped structures using generalized sparse component analysis

SummaryModal identification method based on blind source separation (BSS) technique has gained extensive attentions for civil structures. Developing the complex modes estimation method is important in practical applications because the assumption of proportional damping is not always satisfied. Sparse component analysis (SCA) performs well in underdetermined BSS problems. However, SCA is confined to the situation of proportional damping. In this study, a generalized SCA method is proposed to extend the original SCA method to both real and complex modes identification. First, the general formulation of complex modes is extended by the analytic form to eliminate the complex conjugate part in the BSS model. A new single‐source‐point detection method that is available to handle real and complex modes is proposed. Local outlier factor method is adopted to remove the outliers in single source points. Subsequently, complex‐valued modal matrix is calculated by the clustering technique. Then, modal responses are recovered using the complex version of smoothed zero norm method, where modal frequencies and damping ratios can be extracted. Finally, the effectiveness of the proposed method is demonstrated for identification of real and complex modes, close modes, and underdetermined problem. The application to a benchmark structure demonstrates the effectiveness for practical applications.

Unmixing methods based on nonnegativity and weakly mixed pixels for astronomical hyperspectral datasets

An increasing number of astronomical instruments (on Earth and space-based) provide hyperspectral images, that is three-dimensional data cubes with two spatial dimensions and one spectral dimension. The intrinsic limitation in spatial resolution of these instruments implies that the spectra associated with pixels of such images are most often mixtures of the spectra of the “pure” components that exist in the considered region. In order to estimate the spectra and spatial abundances of these pure components, we here propose an original blind signal separation (BSS), that is to say an unsupervised unmixing method. Our approach is based on extensions and combinations of linear BSS methods that belong to two major classes of methods, namely nonnegative matrix factorization (NMF) and sparse component analysis (SCA). The former performs the decomposition of hyperspectral images, as a set of pure spectra and abundance maps, by using nonnegativity constraints, but the estimated solution is not unique: It highly depends on the initialization of the algorithm. The considered SCA methods are based on the assumption of the existence of points or tiny spatial zones where only one source is active (i.e., one pure component is present). These points or zones are then used to estimate the mixture and perform the decomposition. In real conditions, the assumption of perfect single-source points or zones is not always realistic. In such conditions, SCA yields approximate versions of the unknown sources and mixing coefficients. We propose to use part of these preliminary estimates from the SCA to initialize several runs of the NMF in order to refine these estimates and further constrain the convergence of the NMF algorithm. The proposed methods also estimate the number of pure components involved in the data and they provide error bars associated with the obtained solution. Detailed tests with synthetic data show that the decomposition achieved with such hybrid methods is nearly unique and provides good performance, illustrating the potential of applications to real data.

Unbalanced responsibility division considering renewable energy integration

A reasonable division of the unbalanced contribution is the premise of responsibility division and mitigation. As a large amount of renewable energy integrates into the power system, the disturbance of the system increases and the system impedance is no longer much smaller than the load impedance. The traditional unbalanced responsibility division method is difficult to calculate accurately. This study proposes a new method for calculating unbalanced contribution, which can effectively avoid the limitations of traditional methods. The robust independent component analysis is used to estimate the equivalent source signal. The sparse component analysis method is used to construct the screening criterion to screen the equivalent source signals to obtain estimated signals that are more in line with the real source signals. Then the equivalent negative sequence impedance of upstream and downstream is calculated, and the unbalanced responsibility is divided. This method is still effective when the system impedance is not much different from the load impedance. At the same time, the calculation accuracy is high and the anti-interference ability is strong. Simulation and field test verify the correctness and effectiveness of the proposed method.

Diagnosis of Compound Fault Using Sparsity Promoted-Based Sparse Component Analysis.

Compound faults often occur in rotating machinery, which increases the difficulty of fault diagnosis. In this case, blind source separation, which usually includes independent component analysis (ICA) and sparse component analysis (SCA), was proposed to separate mixed signals. SCA, which is based on the sparsity of target signals, was developed to sever the compound faults and effectively diagnose the fault due to its advantage over ICA in underdetermined conditions. However, there is an issue regarding the vibration signals, which are inadequately sparse, and it is difficult to represent them in a sparse way. Accordingly, to overcome the above-mentioned problem, a sparsity-promoted approach named wavelet modulus maxima is applied to obtain the sparse observation signal. Then, the potential function is utilized to estimate the number of source signals and the mixed matrix based on the sparse signal. Finally, the separation of the source signals can be achieved according to the shortest path method. To validate the effectiveness of the proposed method, the simulated signals and vibration signals measured from faulty roller bearings are used. The faults that occur in a roller bearing are the outer-race flaw, the inner-race flaw and the rolling element flaw. The results show that the fault features acquired using the proposed approach are evidently close to the theoretical values. For instance, the inner-race feature frequency 101.3 Hz is very similar to the theoretical calculation 101 Hz. Therefore, it is effective to achieve the separation of compound faults utilizing the suggest method, even in underdetermined cases. In addition, a comparison is applied to prove that the proposed method outperforms the traditional SCA method when the vibration signals are inadequate.

Output-only modal identification with limited sensors using sparse component analysis

Blind source separation (BSS) based methods have been shown to be efficient and powerful to perform output-only modal identification. Existing BSS modal identification methods, however, require the number of sensors at least equal to that of sources (active modes).This paper proposes a new modal identification algorithm based on a novel BSS technique termed sparse component analysis (SCA) to handle even the underdetermined problem where sensors may be highly limited compared to the number of active modes. The developed SCA method reveals the essence of modal expansion that the monotone modal responses with disjoint sparsest representations in frequency domain naturally cluster in the directions of the mode matrix's columns (modeshapes), which are readily extracted from the measured system responses using a simple clustering algorithm. Then, in determined case where sensor number equals that of modes, the estimated square mode matrix directly decouples the system responses to obtain the modal responses, whereby computing their frequencies and damping ratios; whereas with limited sensors, the modal responses are efficiently recovered via the ℓ1-minimization sparse recovery technique from the incomplete knowledge of the partial mode matrix and the system responses of inadequate sensors. Numerical simulations and experimental example show that whether in determined or underdetermined situations, the SCA method performs accurate and robust identification of a wide range of structures including those with closely-spaced and highly-damped modes. The SCA method is simple and efficient to conduct reliable output-only modal identification even with limited sensors.

Separation of individual operation signals from mixed sensor measurements

Sensor system measurements are generally mixed signals measured from multiple independent/dependent operations embedded in a complex system. In this article, a novel method is developed to separate the source signals of individual operations from the mixed sensor measurements by integrating the independent component analysis method and the Sparse Component Analysis (SCA) method. The proposed method can efficiently estimate the source signals that include both independent signals and dependent signals that have some dominant components in the time or some linear transform domains (e.g., frequency domain, time/frequency domain, or wavelet domain). In addition, an SCA method is also developed in this article that can automatically identify the dominant components in multiple linear transform domains. A case study of a forging process is conducted to demonstrate the effectiveness of the proposed methods.

A new blind image source separation algorithm based on feedback sparse component analysis

In this paper, a new blind source separation (BSS) algorithm for mixed images, called feedback sparse component analysis (FSCA), is proposed. The algorithm develops the sparse component analysis (SCA) and utilizes feedback mechanism to extract the image sources which are not sufficiently sparse to the SCA method, such as noise or complex images with low sparseness. It is experimentally shown that the proposed method does not need vast iteration and can effectively separate all un-sparse sources from the mixtures. Compared to classic fast independent component analysis (FastICA) algorithm, the presented algorithm has better accuracy.

Blind spatial unmixing of multispectral images: New methods combining sparse component analysis, clustering and non-negativity constraints

Remote sensing has become an unavoidable tool for better managing our environment, generally by realizing maps of land cover using classification techniques. Traditional classification techniques assign only one class (e.g., water, soil, grass) to each pixel of remote sensing images. However, the area covered by one pixel contains more than one surface component and results in the mixture of these surface components. In such situations, classical classification is not acceptable for many major applications, such as environmental monitoring, agriculture, mineral exploration and mining, etc. Most methods proposed for treating this problem have been developed for hyperspectral images. On the contrary, there are very few automatic techniques suited to multispectral images. In this paper, we propose new unsupervised spatial methods (called 2D-Corr-NLS and 2D-Corr-NMF) in order to unmix each pixel of a multispectral image for better recognizing the surface components constituting the observed scene. These methods are related to the blind source separation (BSS) problem, and are based on sparse component analysis (SCA), clustering and non-negativity constraints. Our approach consists in first identifying the mixing matrix involved in this BSS problem, by using the first stage of a spatial correlation-based SCA method with very limited source sparsity constraints, combined with clustering. Non-negative least squares (NLS) or non-negative matrix factorization (NMF) methods are then used to extract spatial sources. An important advantage of our proposed methods is their applicability to the possibly globally underdetermined, but locally (over)determined BSS model in multispectral remote sensing images. Experiments based on realistic synthetic mixtures and real multispectral images collected by the Landsat ETM+ and the Formosat-2 sensors are performed to evaluate the performance of the proposed approach. We also show that our methods significantly outperform the sequential maximum angle convex cone (SMACC) method.

Precession missile feature extraction using sparse component analysis of radar measurements

According to the working mode of the ballistic missile warning radar (BMWR), the radar return from the BMWR is usually sparse. To recognize and identify the warhead, it is necessary to extract the precession frequency and the locations of the scattering centers of the missile. This article first analyzes the radar signal model of the precessing conical missile during flight and develops the sparse dictionary which is parameterized by the unknown precession frequency. Based on the sparse dictionary, the sparse signal model is then established. A nonlinear least square estimation is first applied to roughly extract the precession frequency in the sparse dictionary. Based on the time segmented radar signal, a sparse component analysis method using the orthogonal matching pursuit algorithm is then proposed to jointly estimate the precession frequency and the scattering centers of the missile. Simulation results illustrate the validity of the proposed method.

Advances in Nonnegative Matrix and Tensor Factorization

Advances in Nonnegative Matrix and Tensor Factorization

Novel sparse component analysis approach to free radical EPR spectra decomposition

Free radicals play important roles in many physiological and pathological pathways in biological systems. These free radicals can be detected and quantified by their EPR spectra. The measured EPR spectra are often mixtures of pure spectra of several different free radicals and other chemicals. Blind source separation can be applied to estimate the pure spectra of interested free radicals. However, since the pure EPR spectra are often not independent of each other, the approach based on independent component analysis (ICA) cannot accurately extract the required spectra. In this paper, a novel sparse component analysis method for blind source separation, which exploits the sparsity of the EPR spectra, is presented to reliably extract the pure source spectra from their mixtures with high accuracy. This method has been applied to the analysis of EPR spectra of superoxide, hydroxyl, and nitric oxide free radicals, for both simulated data and real world ex vivo experiment. Compared to the traditional self-modeling method and our previous ICA-based blind source separation method, the proposed sparse component analysis approach gives much better results and can give perfect separation for mixtures of superoxide spectrum and hydroxyl spectrum in the ideal noise-free case. This method can also be used in other similar applications of quantitative spectroscopy analysis.