Singular Value Decomposition Approach Research Articles

Finite-time stabilization for nonlinear discrete-time singular Markov jump systems with piecewise-constant transition probabilities subject to average dwell time

In this paper, the finite-time boundedness and stabilization issues for nonlinear discrete-time singular Markov jump systems with time-varying transition probabilities subject to average dwell time switching are studied for the first time. The finite piecewise homogeneous character of transition probabilities is taken into account. Firstly, by using average dwell time approach and implicit function theorem, a sufficient condition is presented such that the nonlinear discrete-time singular Markov jump systems are singular finite-time bounded and of a unique solution. Secondly, according to the singular value decomposition approach, a linear matrix inequality (LMI) finite-time boundedness criterion is developed, which can be used for constructing state feedback controllers directly. Based on this LMI finite-time boundedness criterion, the state feedback controller design is handled. Finally, three numerical examples are presented to illustrate the validity and advantage of the proposed methods.

Metabolomic Biomarker Identification in Presence of Outliers and Missing Values.

Metabolomics is the sophisticated and high-throughput technology based on the entire set of metabolites which is known as the connector between genotypes and phenotypes. For any phenotypic changes, potential metabolite (biomarker) identification is very important because it provides diagnostic as well as prognostic markers and can help to develop new biomolecular therapy. Biomarker identification from metabolomics data analysis is hampered by the use of high-throughput technology that provides high dimensional data matrix which contains missing values as well as outliers. However, missing value imputation and outliers handling techniques play important role in identifying biomarker correctly. Although several missing value imputation techniques are available, outliers deteriorate the accuracy of imputation as well as the accuracy of biomarker identification. Therefore, in this paper we have proposed a new biomarker identification technique combining the groupwise robust singular value decomposition, t-test, and fold-change approach that can identify biomarkers more correctly from metabolomics dataset. We have also compared the performance of the proposed technique with those of other traditional techniques for biomarker identification using both simulated and real data analysis in absence and presence of outliers. Using our proposed method in hepatocellular carcinoma (HCC) dataset, we have also identified the four upregulated and two downregulated metabolites as potential metabolomic biomarkers for HCC disease.

A Truncated Singular Value Decomposition approach for locating a magnetic dipole with Euler's equation

It is known that Euler's homogeneity equation provides a system of linear equations for localizing a magnetic dipole from measurements of the magnetic field and its gradients. In this paper, we show that a solution of the equations obtained by Truncated Singular Value Decomposition (TSVD) always gi ves the true position of the dipole regardless of the singularity of the coefficient matrix. Hence, we can localize a magnetic dipole robustly without estimation bias by TSVD.

Optimal Joint Design of Hermitian Transform Matrix and Corresponding Mask Coefficients for Multi-Digital Demodulation Systems

Nowadays, signals are transmitted using different digital modulation systems according to different channel conditions. Different digital modulation systems transmit signals using different frequency bands. To demodulate the signals and decode the corresponding digital symbols, different filters with different frequency bands are employed. This paper explores the possibility of performing the digital demodulation in a general energy preserved transform domain instead of in the conventional frequency domain. In particular, instead of performing the multiplication in the frequency domain for performing the conventional filtering, this paper proposes to perform the multiplication in an optimal Hermitian transform domain for performing the optimal mask operation. The joint design of the Hermitian transform matrix and the corresponding mask coefficients is formulated as a least squares optimization problem subject to the Hermitian condition. This is actually a complex-valued quadratic matrix equality constrained least squares optimization problem. A condition on an optimal solution is derived via a singular value decomposition approach. Based on the derived condition, an iterative approach is proposed for finding the solution of the optimization problem. Computer numerical simulation results show that our proposed approach outperforms the conventional filtering approach.

Improving accuracy in the MPM method using a null space filter

The material point method (MPM) has been very successful in providing solutions to many challenging problems involving large deformations. Nevertheless there are some important issues that remain to be resolved with regard to its analysis. One key challenge applies to both MPM and particle-in-cell (PIC) methods and arises from the difference between the number of particles and the number of the nodal grid points to which the particles are mapped. This difference between the number of particles and the number of grid points gives rise to a non-trivial null space of the linear operator that maps particle values onto nodal grid point values. In other words, there are non-zero particle values that when mapped to the grid point nodes result in a zero value there. Moreover, when the nodal values at the grid points are mapped back to particles, part of those particle values may be in that same null space. Given positive mapping weights from particles to nodes such null space values are oscillatory in nature. While this problem has been observed almost since the beginning of PIC methods there are still elements of it that are problematical today as well as methods that transcend it. The null space may be viewed as being connected to the ringing instability identified by Brackbill for PIC methods. It will be shown that it is possible to remove these null space values from the solution using a null space filter. This filter improves the accuracy of the MPM methods using an approach that is based upon a local singular value decomposition (SVD) calculation. This local SVD approach is compared against the global SVD approach previously considered by the authors and to a recent MPM method by Zhang and colleagues.

Exponential stability and L1-gain performance analysis for continuous-time delayed switched positive singular systems

The problem of exponential stability and L1-gain performance is solved for continuous-time delayed switched positive singular systems. First, a necessary and sufficient condition of positivity is established for the system via the singular value decomposition approach. Then, based on the co-positive Lyapunov function tool, we develop a sufficient condition for the switched positive singular system to be exponentially stable and meet a prescribed L1-gain performance. Based on this condition, the optimal system performance level can be determined by solving a convex optimization problem. All the obtained conditions are in linear programming form, which suggests a good scalability and applicability to high-dimensional systems. Finally, a numerical example is given to illustrate the applicability of the obtained results.

Algebraic method to speed up robust algorithms: example of laser-scanned point clouds

Surface reconstruction from point clouds generated by laser scanning technology has become a fundamental task in many fields of geosciences, such as robotics, computer vision, digital photogrammetry, computational geometry, digital building modelling, forest planning and operational activities. Point clouds produced by laser scanning, however, are limited due to the occurrence of occlusions, multiple reflectance and noise, and off-surface points (outliers), thus necessitating the need for robust fitting techniques. In this contribution, a fast, non-iterative and data invariant algebraic algorithm with constant O(1) complexity that fits planes to point clouds in the total least squares sense using Gaussian-type error distribution is proposed. The maximum likelihood estimator method is used, resulting in a multivariate polynomial system that is solved in an algebraic way. It is shown that for plane fitting when datasets are affected heavily by outliers, the proposed algebraic method can be embedded into the framework of robust methods like the Danish or the RANdom SAmple Consensus methods and computed in parallel to provide rigorous algebraic fitting with significantly reduced running times. Compared to the embedded traditional singular value decomposition and principal component analysis approaches, the performance of the proposed algebraic algorithm demonstrated its efficiency on both synthetic data and real laser-scanned measurements. The evaluation of a symbolic algebraic formula is practically independent of the values of its coefficients; however, the computation of the coefficients depends on the complexity of the data. Since the main advantage of the symbolic solution is its non-requirement of numerical iteration, the data complexity will have weak influence on the speed-up. The novelty of the proposed method is the use of algebraic technique in a robust plane fitting algorithm that could be applied to remote sensing data analysis/delineation/classification. In general, the method could be applied to most plane fitting problems in the geoscience field.

Robust H∞ control for uncertain singular discrete T–S fuzzy time-delay systems with actuator saturation

In this paper, the problem of robust H∞ control for uncertain singular discrete T–S fuzzy time-delay systems with actuator saturation is addressed. Based on singular value decomposition approach, a delay-dependent sufficient condition for the H∞ control problem is obtained by constructing multiple Lyapunov–Krasovskii function and a latest difference inequality. Meanwhile, a parallel-distributed compensation (PDC) state feedback H∞ controller design problem is solved by linear matrices inequalities (LMIs) to guarantee the closed-loop system not only is admissible but also possesses H∞ performance index γ. Moreover, the problem of estimating the domain of attraction for the discrete T–S fuzzy closed-loop system is formulated and solved as a LMI optimization problem. Finally, numerical examples demonstrate the obtained estimation of the domain of attraction and H∞ performance index γ less conservative than some result reported in the literature.

Detecting heart rate while jogging: blind source separation of gait and heartbeat

A blind source signal separation problem that was brought to a Study Group in Limerick in 2013 required a way to prevent the gait of a jogger from masking the heartbeat, when detected by a simple photodiode that measures light transmission through a jogger’s wrist tissues. The group was successful in discovering a singular value decomposition (SVD) approach, which not only allows accurate detection of heart rate but also allows recovery of a good facsimile of the entire blood pressure time series from the mixed photodiode signal.

Modeling and Forecasting Mortality Using the Lee-Carter Model for Indian Population Based on Decade-wise Data

The stochastic mortality model given by Lee and Carter (1992) has been used in literature for fitting and forecasting the human mortality. We have modeled mortality rates of Indian population using the Lee-Carter (LC) model based on decade-wise data available separately for Indian female and male populations in the form of life tables for the period 1901-2011. The Singular Value Decomposition (SVD) approach is used for estimation of the parameters of the LC model. Forecasted values of time dependent parameter of the LC model are obtained for next five decades using best fitted auto regressive integrated moving average (ARIMA) model. Forecasted values of life expectancy at different ages with 95% confidence intervals are also reported for the next five decades. As an application, using forecasted mortality rates for the next five decades, net single premium for whole life and term insurance, actuarial present values of life annuities for some selected ages are also evaluated

A new result on finite-time control of singular linear time-delay systems

In this paper, problem of robust finite-time stability and control is first time discussed for singular linear time-delay systems subject to disturbance. By developing delay singular value decomposition approach combining with linear matrix inequality (LMI) technique, new sufficient conditions for the existence of such controllers are proposed in terms of the solvability to a set of LMIs. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Weighting variables in Kohonen competitive learning algorithms

ABSTRACTThis paper presents a new variable weight method, called the singular value decomposition (SVD) approach, for Kohonen competitive learning (KCL) algorithms based on the concept of Varshavsky et al. [18]. Integrating the weighted fuzzy c-means (FCM) algorithm with KCL, in this paper, we propose a weighted fuzzy KCL (WFKCL) algorithm. The goal of the proposed WFKCL algorithm is to reduce the clustering error rate when data contain some noise variables. Compared with the k-means, FCM and KCL with existing variable-weight methods, the proposed WFKCL algorithm with the proposed SVD's weight method provides a better clustering performance based on the error rate criterion. Furthermore, the complexity of the proposed SVD's approach is less than Pal et al. [17], Wang et al. [19] and Hung et al. [9].

Fast SVD Computations for Synchrophasor Algorithms

Many singular value decomposition (SVD) problems in power system computations require only a few largest singular values of a large-scale matrix for the analysis. This letter introduces two fast SVD approaches recently developed in other domains to power systems for speeding up phasor measurement unit (PMU) based online applications. The first method is a randomized SVD algorithm that accelerates computation by introducing a low-rank approximation of a given matrix through randomness. The second method is the augmented Lanczos bidiagonalization, an iterative Krylov subspace technique that computes sequences of projections of a given matrix onto low-dimensional subspaces. Both approaches are illustrated on SVD evaluation within an ambient oscillation monitoring algorithm, namely stochastic subspace identification (SSI).

Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems

This paper investigates the stochastic stability and the state feedback control design for a class of nonlinear continuous-time descriptor semi-Markov jump systems whose transition rates are time-varying, which are more general than the descriptor Markov jump systems. First, by deriving the infinitesimal generator for stochastic Lyapunov functional of descriptor semi-Markov jump systems, a stochastic stability condition is established, which guarantees this kind of systems are regular, impulse-free, have a unique solution, and are stochastically stable. In order to design the state feedback controller, a linear matrix inequality (LMI) stability condition is developed based on the lower and upper bounds of the time-varying transition probability and singular value decomposition approach. Furthermore, the state feedback controller design is developed in terms of LMI approach. Last, numerical examples are given to demonstrate the effectiveness of the obtained methods.

LLE for submersible plunger pump fault diagnosis via joint wavelet and SVD approach

Locally linear embedding (LLE) is a classical non-linear dimension reduction algorithm. LLE can deal with a nonlinear dataset and extract the significant feature from the dataset. However, LLE may fail, when signal is non-stationary or contains strong noise. In this paper, wavelet transformation, singular value decomposition (SVD), and LLE are assembled to extract the feature of a dataset based on which a new fault diagnosis method is developed for submersible plunger pump fault recognition. First, each sample is preprocessed by wavelet transformation and SVD, upon which a new feature space is constructed; then, LLE is utilized to reduce the dimensions of the feature space; finally, support vector machines (SVM) is invoked to recognize the device status. The experiments performed on submersible plunger pump dataset and bearing dataset demonstrate that the proposed method is effective and can achieve a high diagnosis accuracy.

A Split-and-Merge Approach for Singular Value Decomposition of Large-Scale Matrices.

We propose a new SVD algorithm based on the split-and- merge strategy, which possesses an embarrassingly parallel structure and thus can be efficiently implemented on a distributed or multicore machine. The new algorithm can also be implemented in serial for online eigen-analysis. The new algorithm is particularly suitable for big data problems: Its embarrassingly parallel structure renders it usable for feature screening, while this has been beyond the ability of the existing parallel SVD algorithms.

A computational system biology approach to construct gene regulatory networks for salinity response in rice (Oryza sativa)

Salinity is one of the most common abiotic stress which limits agricultural crop production. Salinity stress tolerance in rice (Oryza sativa L.) is an important trait controlled by various genes. The mechanism of salinity stress response in rice is quite complex. Modelling and construction of genetic regulatory networks is an important tool and can be used for understanding this underlying mechanism. This paper considers the problem of modeling and construction of Gene Regulatory Networks using Multiple Linear Regression and Singular Value Decomposition approach coupled with a number of computational tools. The gene networks constructed by using this approach satisfied the scale free property of biological networks and such networks can be used to extract valuable information on the transcription factors, which are salt responsive. The gene ontology enrichment analysis of selected nodes is performed. The developed model can also be used for predicting the gene responses under stress condition and the result shows that the model fits well for the given gene expression data in rice. In this paper, we have identified ten target genes and a series of potential transcription factors for each target gene in rice which are highly salt responsive.

Optimal placement of piezoelectric actuators on plate structures for active vibration control via modified control matrix and singular value decomposition approach using modified heuristic genetic algorithm

ABSTRACTThe present work deals with the optimal placement of piezoelectric actuators on a thin plate using modified control matrix and singular value decomposition (MCSVD) approach. The MCSVD is considered as the fitness function and optimal positions of the actuators are obtained by maximizing it with MHGA (modified heuristic genetic algorithm). Vibration suppression has been studied for simply supported plate with piezoelectric patches in optimal positions to suppress first specified modes using LQR (linear quadratic regulator) controller. It is observed that the positions of patches obtained with this approach give greater vibration suppression, reduced computational requirements, and provide global optimum solution only.

Application of singular value decomposition (SVD) in extraction of gravity components indicating the deeply and shallowly buried granitic complex associated with tin polymetallic mineralization in the Gejiu tin ore field, Southwestern China

The Gejiu tin polymetallic ore deposit, located at the westernmost end of the Cathaysia Block, is one of the largest tin polymetallic ore deposits in the world. It is associated with a magmatic-hydrothermal ore-forming system triggered by the deeply buried geological structures and concealed granites. A singular value decomposition (SVD) program on a MATLAB platform was effectively used to extract deeply buried geological information reflecting deep-seated geological structures and the concealed granites by decomposing gravity signals within the Gejiu tin polymetallic ore field. Firstly, the gravity signals were decomposed into a few components with different eigenvalues using a singular value decomposition (SVD) approach. Secondly, the thresholds between the eigenvalues of gravity components reflecting deeply and shallowly buried ore-controlling geological structures and/or geological bodies were established by a multifractal method. Finally, the images of gravity components reflecting deeply and shallowly buried ore-controlling geological structures and/or geological bodies were reconstituted. This yielded two layers of significant two dimensional singular value gravity component images that indicate deeply and shallowly buried ore-controlling geological structures and/or geological bodies, respectively. The deep layer of gravity component image reveals a negative gravity anomaly (I) which indicates that the granites exposed in the west ore field, bounded by the Gejiu Fault, may be extended to the east ore field at depth, forming concealed granites (Fig. 4). The shallow layer of gravity component image reveals a structural framework created by two groups of NW-trending and three groups of NE-trending positive gravity component images defining two negative gravity anomalies (I and II), which may reflect existence of the exposed granites in the western ore field (I) and the concealed granites in the eastern ore field (II) (Figs. 5 and 6). Almost all tin polymetallic deposits are located within the negative gravity anomalies (Figs. 4 and 5). This approach, combined with the identification of geochemical anomalies plays an important role in the discovery of deeply buried tin polymetallic ore deposits, including the 0.78milliontons of tin reserves over the last ten years.

Estimation of the local convective heat transfer coefficient in pipe flow using a 2D thermal Quadrupole model and Truncated Singular Value Decomposition

The techniques for solving the Inverse Heat Conduction Problem represent useful tools for designing heat transfer apparatuses. One of their most challenging applications derives from the necessity of catching what happens inside a heat transfer apparatus by monitoring the temperature distribution on the external wall of the device, possibly by means of contactless experimental methodologies. The research presented here deals with the application of a solution strategy of the Inverse Heat Conduction Problem (IHCP) aimed at estimating the local heat transfer coefficient on the internal wall surface of a pipe, under a forced convection problem. The solution strategy, formulated for a 2D model, is based on the Quadrupole Method (QM) coupled to the Truncated Singular Value Decomposition approach, used to cope with the ill-conditioning of the problem. QM presents some advantages over the more classical domain or boundary discretization methods as for instance the fact that, being meshless, brings to a reduction of the computational cost. The analytical model, built under the QM, is validated by means of numerical simulations and the numerical outputs are then used as synthetic data inputs to solve the IHCP. The estimation methodology is also applied to experimental data regarding a forced convection problem in coiled pipes. Moreover, the adopted solution technique is compared to other two well-known and consolidated approaches: Finite Element Method coupled to the Tikhonov Regularization Method and Gaussian Filtering Technique. The comparison highlights that, for the problem here investigated, the Quadrupole Method coupled to the Truncated Singular Value Decomposition and Finite Element Method coupled to the Tikhonov Regularization Method perform better than the Gaussian Filtering Technique when the noise level is low, while, for higher noise level values, their efficiency is almost comparable, as it happens in the considered experimental study case.