Search results for: deterministic-stochastic subspace system

Authors: M. M. Qasaymeh, M. A. Khodeir

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Subspace channel estimation methods have been studied widely. It depends on subspace decomposition of the covariance matrix to separate signal subspace from noise subspace. The decomposition normally is done by either Eigenvalue Decomposition (EVD) or Singular Value Decomposition (SVD) of the Auto-Correlation matrix (ACM). However, the subspace decomposition process is computationally expensive. In this paper, the multipath channel estimation problem for a Slow Frequency Hopping (SFH) system using noise space based method is considered. An efficient method to estimate multipath the time delays basically is proposed, by applying MUltiple Signal Classification (MUSIC) algorithm which used the null space extracted by the Rank Revealing LU factorization (RRLU). The RRLU provides accurate information about the rank and the numerical null space which make it a valuable tool in numerical linear algebra. The proposed novel method decreases the computational complexity approximately to the half compared with RRQR methods keeping the same performance. Computer simulations are also included to demonstrate the effectiveness of the proposed scheme.

Keywords: frequency hopping, channel model, time delay estimation, RRLU, RRQR, MUSIC, LS-ESPRIT

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Authors: Mathias Marquardt, Peter Dünow, Sandra Baßler

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The paper describes the use of subspace based identification methods for auto tuning of a state space control system. The plant is an unstable but self balancing transport robot. Because of the unstable character of the process it has to be identified from closed loop input-output data. Based on the identified model a state space controller combined with an observer is calculated. The subspace identification algorithm and the controller design procedure is combined to a auto tuning method. The capability of the approach was verified in a simulation experiments under different process conditions.

Keywords: auto tuning, balanced robot, closed loop identification, subspace identification

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Authors: Somaiyeh Dehghan, Mohammad Reza Kheirkhahan Haghighi

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The rapid growth of domains that have data with a large number of features, while the number of samples is limited has caused difficulty in constructing strong classifiers. To reduce the dimensionality of the feature space becomes an essential step in classification task. Random subspace method (or attribute bagging) is an ensemble classifier that consists of several classifiers that each base learner in ensemble has subset of features. In the present paper, we introduce Random Subspace Ensemble of CMAC neural network (RSE-CMAC), each of which has training with subset of features. Then we use this model for classification task. For evaluation performance of our model, we compare it with bagging algorithm on 36 UCI datasets. The results reveal that the new model has better performance.

Keywords: classification, random subspace, ensemble, CMAC neural network

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Authors: Ci Lin, Tet Yeap, Iluju Kiringa

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This paper introduces the subspace rotation algorithm (SRA) to train the Restricted Hopfield Network (RHN) as an auto-associative memory. Subspace rotation algorithm is a gradient-free subspace tracking approach based on the singular value decomposition (SVD). In comparison with Backpropagation Through Time (BPTT) on training RHN, it is observed that SRA could always converge to the optimal solution and BPTT could not achieve the same performance when the model becomes complex, and the number of patterns is large. The AUTS case study showed that the RHN model trained by SRA could achieve a better structure of attraction basin with larger radius(in general) than the Hopfield Network(HNN) model trained by Hebbian learning rule. Through learning 10000 patterns from MNIST dataset with RHN models with different number of hidden nodes, it is observed that an several components could be adjusted to achieve a balance between recovery accuracy and noise resistance.

Keywords: hopfield neural network, restricted hopfield network, subspace rotation algorithm, hebbian learning rule

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Authors: Mojtaba Saeedinezhad, Sarah Yousefi

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In this paper, we present a hybrid subspace approach for Time Delay Estimation (TDE) in multivariable systems. While several methods have been proposed for time delay estimation in SISO systems, delay estimation in MIMO systems were always a big challenge. In these systems the existing TDE methods have significant limitations because most of procedures are just based on system response estimation or correlation analysis. We introduce a new hybrid method for TDE in MIMO systems based on subspace identification and explicit output error method; and compare its performance with previously introduced procedures in presence of different noise levels and in a statistical manner. Then the best method is selected with multi objective decision making technique. It is shown that the performance of new approach is much better than the existing methods, even in low signal-to-noise conditions.

Keywords: system identification, time delay estimation, ARX, OE, merit ratio, multi variable decision making

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Authors: Yen-Po Wang, Ming-Chih Huang, Ming-Lian Chang

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A scheme integrated with deterministic–stochastic subspace system identification and the method of damage localization vector is proposed in this study for damage detection of structures based on seismic response data. A series of shaking table tests using a five-storey steel frame has been conducted in National Center for Research on Earthquake Engineering (NCREE), Taiwan. Damage condition is simulated by reducing the cross-sectional area of some of the columns at the bottom. Both single and combinations of multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed. In addition to detecting damage(s) with respect to the intact structure, identification of new or extended damages of the as-damaged (ill-conditioned) counterpart has also been studied. The proposed scheme proves to be effective.

Keywords: damage locating vectors, deterministic-stochastic subspace system, shaking table tests, system identification

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Authors: Reza Hedayati, Meysam Jahanbakhshi

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Elastic energy absorbers which consist of a ring-liked plate and springs can be a good choice for increasing the impact duration during an accident. In the current project, an energy absorber system is optimized using four optimizing methods Kuhn-Tucker, Sequential Linear Programming (SLP), Concurrent Subspace Design (CSD), and Pshenichny-Lim-Belegundu-Arora (PLBA). Time solution, convergence, Programming Length and accuracy of the results were considered to find the best solution algorithm. Results showed the superiority of PLBA over the other algorithms.

Keywords: Concurrent Subspace Design (CSD), Kuhn-Tucker, Pshenichny-Lim-Belegundu-Arora (PLBA), Sequential Linear Programming (SLP)

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Authors: J. Y. Sun, H. Z. Shen

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We study the photon blockade at exceptional points for a non-Hermitian optomechanical system coupled to the driven whispering-gallery-mode microresonator with two nanoparticles under the weak optomechanical coupling approximation, where exceptional points emerge periodically by controlling the relative angle of the nanoparticles. We find that conventional photon blockade occurs at exceptional points for the eigenenergy resonance of the single-excitation subspace driven by a laser field and discuss the physical origin of conventional photon blockade. Under the weak driving condition, we analyze the influences of the different parameters on conventional photon blockade. We investigate conventional photon blockade at nonexceptional points, which exists at two optimal detunings due to the eigenstates in the single-excitation subspace splitting from one (coalescence) at exceptional points to two at nonexceptional points. Unconventional photon blockade can occur at nonexceptional points, while it does not exist at exceptional points since the destructive quantum interference cannot occur due to the two different quantum pathways to the two-photon state not being formed. The realization of photon blockade in our proposal provides a viable and flexible way for the preparation of single-photon sources in the non-Hermitian optomechanical system.

Keywords: optomechanical systems, photon blockade, non-hermitian, exceptional points

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Authors: Jaehong Yu, Seoung Bum Kim

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Clustering analysis can facilitate the extraction of intrinsic patterns in a dataset and reveal its natural groupings without requiring class information. For effective clustering analysis in high dimensional datasets, unsupervised dimensionality reduction is an important task. Unsupervised dimensionality reduction can generally be achieved by feature extraction or feature selection. In many situations, feature selection methods are more appropriate than feature extraction methods because of their clear interpretation with respect to the original features. The unsupervised feature selection can be categorized as feature subset selection and feature ranking method, and we focused on unsupervised feature ranking methods which evaluate the features based on their importance scores. Recently, several unsupervised feature ranking methods were developed based on ensemble approaches to achieve their higher accuracy and stability. However, most of the ensemble-based feature ranking methods require the true number of clusters. Furthermore, these algorithms evaluate the feature importance depending on the ensemble clustering solution, and they produce undesirable evaluation results if the clustering solutions are inaccurate. To address these limitations, we proposed an ensemble-based feature ranking method with random subspace and multiple-k ensemble (FRRM). The proposed FRRM algorithm evaluates the importance of each feature with the random subspace ensemble, and all evaluation results are combined with the ensemble importance scores. Moreover, FRRM does not require the determination of the true number of clusters in advance through the use of the multiple-k ensemble idea. Experiments on various benchmark datasets were conducted to examine the properties of the proposed FRRM algorithm and to compare its performance with that of existing feature ranking methods. The experimental results demonstrated that the proposed FRRM outperformed the competitors.

Keywords: clustering analysis, multiple-k ensemble, random subspace-based feature evaluation, unsupervised feature ranking

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Authors: Peyman Sheikholharam Mashhadi

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Difficulties in analyzing real world images in classical image processing and machine vision framework have motivated researchers towards considering the biology-based vision. It is a common belief that mammalian visual cortex has been adapted to the statistics of the real world images through the evolution process. There are two well-known successful models of mammalian visual cortical cells: Independent Component Analysis (ICA) and Independent Subspace Analysis (ISA). In this paper, we statistically analyze the dependencies which remain in the components after applying these models to the natural images. Also, we investigate the response of feature detectors to gratings with various parameters in order to find optimal parameters of the feature detectors. Finally, the selectiveness of feature detectors to phase, in both models is considered.

Keywords: statistics, independent component analysis, independent subspace analysis, phase, natural images

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Authors: Rashid Ahmed , John N. Avaritsiotis

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Many signal subspace-based approaches have already been proposed for determining the fixed Direction of Arrival (DOA) of plane waves impinging on an array of sensors. Two procedures for DOA estimation based neural networks are presented. First, Principal Component Analysis (PCA) is employed to extract the maximum eigenvalue and eigenvector from signal subspace to estimate DOA. Second, minor component analysis (MCA) is a statistical method of extracting the eigenvector associated with the smallest eigenvalue of the covariance matrix. In this paper, we will modify a Minor Component Analysis (MCA(R)) learning algorithm to enhance the convergence, where a convergence is essential for MCA algorithm towards practical applications. The learning rate parameter is also presented, which ensures fast convergence of the algorithm, because it has direct effect on the convergence of the weight vector and the error level is affected by this value. MCA is performed to determine the estimated DOA. Preliminary results will be furnished to illustrate the convergences results achieved.

Keywords: Direction of Arrival, neural networks, Principle Component Analysis, Minor Component Analysis

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Authors: Kuniyoshi Abe

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Bi-conjugate gradient (Bi-CG) is a well-known method for solving linear equations Ax = b, for x, where A is a given n-by-n matrix, and b is a given n-vector. Typically, the dimension of the linear equation is high and the matrix is sparse. A number of hybrid Bi-CG methods such as conjugate gradient squared (CGS), Bi-CG stabilized (Bi-CGSTAB), BiCGStab2, and BiCGstab(l) have been developed to improve the convergence of Bi-CG. Bi-CGSTAB has been most often used for efficiently solving the linear equation, but we have seen the convergence behavior with a long stagnation phase. In such cases, it is important to have Bi-CG coefficients that are as accurate as possible, and the stabilization strategy, which stabilizes the computation of the Bi-CG coefficients, has been proposed. It may avoid stagnation and lead to faster computation. Motivated by a large number of processors in present petascale high-performance computing hardware, the scalability of Krylov subspace methods on parallel computers has recently become increasingly prominent. The main bottleneck for efficient parallelization is the inner products which require a global reduction. The resulting global synchronization phases cause communication overhead on parallel computers. The parallel variants of Krylov subspace methods reducing the number of global communication phases and hiding the communication latency have been proposed. However, the numerical stability, specifically, the convergence speed of the parallel variants of Bi-CGSTAB may become worse than that of the standard Bi-CGSTAB. In this paper, therefore, we compare the convergence speed between the standard Bi-CGSTAB and the parallel variants by numerical experiments and show that the convergence speed of the standard Bi-CGSTAB is faster than the parallel variants. Moreover, we propose the stabilization strategy for the parallel variants.

Keywords: bi-conjugate gradient stabilized method, convergence speed, Krylov subspace methods, linear equations, parallel variant

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Authors: Timir Baran Roy, Luis Guerreiro, Ashutosh Bagchi

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Dynamic study is important in order to design, repair and rehabilitation of structures. It has played an important role in the behavior characterization of structures; such as bridges, dams, high-rise buildings etc. There had been a substantial development in this area over the last few decades, especially in the field of dynamic identification techniques of structural systems. Frequency Domain Decomposition (FDD) and Time Domain Decomposition are most commonly used methods to identify modal parameters; such as natural frequency, modal damping, and mode shape. The focus of the present research is to study the dynamic characteristics of typical timber masonry walls commonly used in Portugal. For that purpose, a multi-storey structural prototypes of such walls have been tested on a seismic shake table at the National Laboratory for Civil Engineering, Portugal (LNEC). Signal processing has been performed of the output response, which is collected from the shaking table experiment of the prototype using accelerometers. In the present work signal processing of the output response, based on the input response has been done in two ways: FDD and Stochastic Subspace Identification (SSI). In order to estimate the values of the modal parameters, algorithms for FDD are formulated, and parametric functions for the SSI are computed. Finally, estimated values from both the methods are compared to measure the accuracy of both the techniques.

Keywords: frequency domain decomposition (fdd), modal parameters, signal processing, stochastic subspace identification (ssi), time domain decomposition

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Authors: Arpita Mondal, Aurobinda Routray, Sreeraj Puravankara, Rajashree Biswas

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The most difficult part of designing a battery management system (BMS) is battery modeling. A good battery model can capture the dynamics which helps in energy management, by accurate model-based state estimation algorithms. So far the most suitable and fruitful model is the equivalent circuit model (ECM). However, in real-time applications, the model parameters are time-varying, changes with current, temperature, state of charge (SOC), and aging of the battery and this make a great impact on the performance of the model. Therefore, to increase the equivalent circuit model performance, the parameter estimation has been carried out in the frequency domain. The battery is a very complex system, which is associated with various chemical reactions and heat generation. Therefore, it’s very difficult to select the optimal model structure. As we know, if the model order is increased, the model accuracy will be improved automatically. However, the higher order model will face the tendency of over-parameterization and unfavorable prediction capability, while the model complexity will increase enormously. In the time domain, it becomes difficult to solve higher order differential equations as the model order increases. This problem can be resolved by frequency domain analysis, where the overall computational problems due to ill-conditioning reduce. In the frequency domain, several dominating frequencies can be found in the input as well as output data. The selective frequency domain estimation has been carried out, first by estimating the frequencies of the input and output by subspace decomposition, then by choosing the specific bands from the most dominating to the least, while carrying out the least-square, recursive least square and Kalman Filter based parameter estimation. In this paper, a second order battery model consisting of three resistors, two capacitors, and one SOC controlled voltage source has been chosen. For model identification and validation hybrid pulse power characterization (HPPC) tests have been carried out on a 2.6 Ah LiFePO₄ battery.

Keywords: equivalent circuit model, frequency estimation, parameter estimation, subspace decomposition

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Authors: Alexander Vaninsky

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The objective of this paper is finding the way of economic restructuring - that is, change in the shares of sectoral gross outputs - resulting in the maximum possible increase in the gross domestic product (GDP) combined with decreases in energy consumption and CO2 emissions. It uses an input-output model for the GDP and factorial models for the energy consumption and CO2 emissions to determine the projection of the gradient of GDP, and the antigradients of the energy consumption and CO2 emissions, respectively, on a subspace formed by the structure-related variables. Since the gradient (antigradient) provides a direction of the steepest increase (decrease) of the objective function, and their projections retain this property for the functions' limitation to the subspace, each of the three directional vectors solves a particular problem of optimal structural change. In the next step, a type of factor analysis is applied to find a convex combination of the projected gradient and antigradients having maximal possible positive correlation with each of the three. This convex combination provides the desired direction of the structural change. The national economy of the United States is used as an example of applications.

Keywords: economic restructuring, input-output analysis, divisia index, factorial decomposition, E3 models

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Authors: Yanping Liao, Zenan Wu, Ruigang Zhao

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Frequency diverse array (FDA) beamforming is a technology developed in recent years, and its antenna pattern has a unique angle-distance-dependent characteristic. However, the beam is always required to have strong concentration, high resolution and low sidelobe level to form the point-to-point interference in the concentrated set. In order to eliminate the angle-distance coupling of the traditional FDA and to make the beam energy more concentrated, this paper adopts a multi-carrier FDA structure based on proposed power exponential frequency offset to improve the array structure and frequency offset of the traditional FDA. The simulation results show that the beam pattern of the array can form a dot-shape beam with more concentrated energy, and its resolution and sidelobe level performance are improved. However, the covariance matrix of the signal in the traditional adaptive beamforming algorithm is estimated by the finite-time snapshot data. When the number of snapshots is limited, the algorithm has an underestimation problem, which leads to the estimation error of the covariance matrix to cause beam distortion, so that the output pattern cannot form a dot-shape beam. And it also has main lobe deviation and high sidelobe level problems in the case of limited snapshot. Aiming at these problems, an adaptive beamforming technique based on exponential correction for multi-carrier FDA is proposed to improve beamforming robustness. The steps are as follows: first, the beamforming of the multi-carrier FDA is formed under linear constrained minimum variance (LCMV) criteria. Then the eigenvalue decomposition of the covariance matrix is ​​performed to obtain the diagonal matrix composed of the interference subspace, the noise subspace and the corresponding eigenvalues. Finally, the correction index is introduced to exponentially correct the small eigenvalues ​​of the noise subspace, improve the divergence of small eigenvalues ​​in the noise subspace, and improve the performance of beamforming. The theoretical analysis and simulation results show that the proposed algorithm can make the multi-carrier FDA form a dot-shape beam at limited snapshots, reduce the sidelobe level, improve the robustness of beamforming, and have better performance.

Keywords: adaptive beamforming, correction index, limited snapshot, multi-carrier frequency diverse array, robust

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Authors: Carlos Vera, Tetyana Baydyk, Ernst Kussul, Graciela Velasco, Miguel Aparicio

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This article describes the Random Subspace Neural Classifier (RSC) for the recognition of meteors in the night sky. We used images of meteors entering the atmosphere at night between 8:00 p.m.-5: 00 a.m. The objective of this project is to classify meteor and star images (with stars as the image background). The monitoring of the sky and the classification of meteors are made for future applications by scientists. The image database was collected from different websites. We worked with RGB-type images with dimensions of 220x220 pixels stored in the BitMap Protocol (BMP) format. Subsequent window scanning and processing were carried out for each image. The scan window where the characteristics were extracted had the size of 20x20 pixels with a scanning step size of 10 pixels. Brightness, contrast and contour orientation histograms were used as inputs for the RSC. The RSC worked with two classes and classified into: 1) with meteors and 2) without meteors. Different tests were carried out by varying the number of training cycles and the number of images for training and recognition. The percentage error for the neural classifier was calculated. The results show a good RSC classifier response with 89% correct recognition. The results of these experiments are presented and discussed.

Keywords: contour orientation histogram, meteors, night sky, RSC neural classifier, stars

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Authors: Sandeep Santosh, O. P. Sahu

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In this paper, performance comparison of wideband covariance matrix sparse representation (W-CMSR) method with other existing wideband Direction of Arrival (DOA) estimation methods has been made.W-CMSR relies less on a priori information of the incident signal number than the ordinary subspace based methods.Consider the perturbation free covariance matrix of the wideband array output. The diagonal covariance elements are contaminated by unknown noise variance. The covariance matrix of array output is conjugate symmetric i.e its upper right triangular elements can be represented by lower left triangular ones.As the main diagonal elements are contaminated by unknown noise variance,slide over them and align the lower left triangular elements column by column to obtain a measurement vector.Simulation results for W-CMSR are compared with simulation results of other wideband DOA estimation methods like Coherent signal subspace method (CSSM), Capon, l1-SVD, and JLZA-DOA. W-CMSR separate two signals very clearly and CSSM, Capon, L1-SVD and JLZA-DOA fail to separate two signals clearly and an amount of pseudo peaks exist in the spectrum of L1-SVD.

Keywords: W-CMSR, wideband direction of arrival (DOA), covariance matrix, electrical and computer engineering

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Authors: Ardalan Sabamehr, Ashutosh Bagchi

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Recently, Structural Health Monitoring (SHM) based on the vibration of structures has attracted the attention of researchers in different fields such as: civil, aeronautical and mechanical engineering. Operational Modal Analysis (OMA) have been developed to identify modal properties of infrastructure such as bridge, building and so on. Frequency Domain Decomposition (FDD), Stochastic Subspace Identification (SSI) and Continuous Wavelet Transform (CWT) are the three most common methods in output only modal identification. FDD, SSI, and CWT operate based on the frequency domain, time domain, and time-frequency plane respectively. So, FDD and SSI are not able to display time and frequency at the same time. By the way, FDD and SSI have some difficulties in a noisy environment and finding the closed modes. CWT technique which is currently developed works on time-frequency plane and a reasonable performance in such condition. The other advantage of wavelet transform rather than other current techniques is that it can be applied for the non-stationary signal as well. The aim of this paper is to compare three most common modal identification techniques to find modal properties (such as natural frequency, mode shape, and damping ratio) of three story steel frame which was built in Concordia University Lab by use of ambient vibration. The frame has made of Galvanized steel with 60 cm length, 27 cm width and 133 cm height with no brace along the long span and short space. Three uniaxial wired accelerations (MicroStarin with 100mv/g accuracy) have been attached to the middle of each floor and gateway receives the data and send to the PC by use of Node Commander Software. The real-time monitoring has been performed for 20 seconds with 512 Hz sampling rate. The test is repeated for 5 times in each direction by hand shaking and impact hammer. CWT is able to detect instantaneous frequency by used of ridge detection method. In this paper, partial derivative ridge detection technique has been applied to the local maxima of time-frequency plane to detect the instantaneous frequency. The extracted result from all three methods have been compared, and it demonstrated that CWT has the better performance in term of its accuracy in noisy environment. The modal parameters such as natural frequency, damping ratio and mode shapes are identified from all three methods.

Keywords: ambient vibration, frequency domain decomposition, stochastic subspace identification, continuous wavelet transform

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Authors: A. K. Borah, A. K. Singh

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In this paper we deal building blocks of the computer simulation of the multiphase flows. Whole simulation procedure can be viewed as two super procedures; The implementation of VOF method and the solution of Navier Stoke’s Equation. Moreover, a sequential code for a Navier Stoke’s solver has been studied.

Keywords: Bi-conjugate gradient stabilized (Bi-CGSTAB), ILUT function, krylov subspace, multifluid flows preconditioner, simple algorithm

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Authors: Rubin Dan, Xingcai Wang, Ziyang Chen

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A chaotic time series noise reduction method based on the fusion of the local projection method, wavelet transform, and particle swarm algorithm (referred to as the LW-PSO method) is proposed to address the problem of false recognition due to noise in the recognition process of chaotic time series containing noise. The method first uses phase space reconstruction to recover the original dynamical system characteristics and removes the noise subspace by selecting the neighborhood radius; then it uses wavelet transform to remove D1-D3 high-frequency components to maximize the retention of signal information while least-squares optimization is performed by the particle swarm algorithm. The Lorenz system containing 30% Gaussian white noise is simulated and verified, and the phase space, SNR value, RMSE value, and K value of the 0-1 test method before and after noise reduction of the Schreiber method, local projection method, wavelet transform method, and LW-PSO method are compared and analyzed, which proves that the LW-PSO method has a better noise reduction effect compared with the other three common methods. The method is also applied to the classical system to evaluate the noise reduction effect of the four methods and the original system identification effect, which further verifies the superiority of the LW-PSO method. Finally, it is applied to the Chengdu rainfall chaotic sequence for research, and the results prove that the LW-PSO method can effectively reduce the noise and improve the chaos recognition rate.

Keywords: Schreiber noise reduction, wavelet transform, particle swarm optimization, 0-1 test method, chaotic sequence denoising

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Authors: Doyoung Kim, Hyo Seon Park

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Studies of System Identification(SI) based on Structural Health Monitoring(SHM) have actively conducted for structural safety. Recently SI techniques have been rapidly developed with output-only SI paradigm for estimating modal parameters. The features of these output-only SI methods consist of Frequency Domain Decomposition(FDD) and Stochastic Subspace Identification(SSI) are using the algorithms based on orthogonal decomposition such as singular value decomposition(SVD). But the SVD leads to high level of computational complexity to estimate modal parameters. This paper proposes the technique to estimate mode shape with lower computational cost. This technique shows pseudo modal Operating Deflections Shape(ODS) through bandpass filter and suggests time history Modal Assurance Criterion(MAC). Finally, mode shape could be estimated from pseudo modal ODS and time history MAC. Analytical simulations of vibration measurement were performed and the results with mode shape and computation time between representative SI method and proposed method were compared.

Keywords: modal assurance criterion, mode shape, operating deflection shape, system identification

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Authors: Manal Azzidani

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This research consideres the extension of special functions called Positive Linear Operators. the bounded linear operator which defined from normed space to Banach space will extend to the closure of the its domain, And extend identified linear functional on a vector subspace by Hana-Banach theorem which could be generalized to the positive linear operators.

Keywords: extension, positive operator, Riesz space, sublinear function

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Authors: Mouhamadou Dosso

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This paper presents methods of spectral dichotomy of a matrix which compute spectral projectors on the subspace associated with the eigenvalues external to the parabolas described by a general equation. These methods are modifications of the one proposed in [A. N. Malyshev and M. Sadkane, SIAM J. MATRIX ANAL. APPL. 18 (2), 265-278, 1997] which uses the spectral dichotomy method of a matrix with respect to the imaginary axis. Theoretical and algorithmic aspects of the methods are developed. Numerical results obtained by applying methods presented on matrices are reported.

Keywords: spectral dichotomy method, spectral projector, eigensubspaces, eigenvalue

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Authors: Olga Hernán-Vega, Patricia López-Rodríguez, David Escot-Bocanegra, Raúl Fernández-Recio, Ignacio Bravo

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Non-Cooperative Target Identification has become a key research domain in the Defense industry since it provides the ability to recognize targets at long distance and under any weather condition. High Resolution Range Profiles, one-dimensional radar images where the reflectivity of a target is projected onto the radar line of sight, are widely used for identification of flying targets. According to that, to face this problem, an approach to Non-Cooperative Target Identification based on the exploitation of Singular Value Decomposition to a matrix of range profiles is presented. Target Identification based on one-dimensional radar images compares a collection of profiles of a given target, namely test set, with the profiles included in a pre-loaded database, namely training set. The classification is improved by using Singular Value Decomposition since it allows to model each aircraft as a subspace and to accomplish recognition in a transformed domain where the main features are easier to extract hence, reducing unwanted information such as noise. Singular Value Decomposition permits to define a signal subspace which contain the highest percentage of the energy, and a noise subspace which will be discarded. This way, only the valuable information of each target is used in the recognition process. The identification algorithm is based on finding the target that minimizes the angle between subspaces and takes place in a transformed domain. Two metrics, F1 and F2, based on Singular Value Decomposition are accomplished in the identification process. In the case of F2, the angle is weighted, since the top vectors set the importance in the contribution to the formation of a target signal, on the contrary F1 simply shows the evolution of the unweighted angle. In order to have a wide database or radar signatures and evaluate the performance, range profiles are obtained through numerical simulation of seven civil aircraft at defined trajectories taken from an actual measurement. Taking into account the nature of the datasets, the main drawback of using simulated profiles instead of actual measured profiles is that the former implies an ideal identification scenario, since measured profiles suffer from noise, clutter and other unwanted information and simulated profiles don't. In this case, the test and training samples have similar nature and usually a similar high signal-to-noise ratio, so as to assess the feasibility of the approach, the addition of noise has been considered before the creation of the test set. The identification results applying the unweighted and weighted metrics are analysed for demonstrating which algorithm provides the best robustness against noise in an actual possible scenario. So as to confirm the validity of the methodology, identification experiments of profiles coming from electromagnetic simulations are conducted, revealing promising results. Considering the dissimilarities between the test and training sets when noise is added, the recognition performance has been improved when weighting is applied. Future experiments with larger sets are expected to be conducted with the aim of finally using actual profiles as test sets in a real hostile situation.

Keywords: HRRP, NCTI, simulated/synthetic database, SVD

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Authors: Dawood Al Chanti, Alice Caplier

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Sparse representations of signals have received a great deal of attention in recent years. In this paper, the interest of using sparse representation as a mean for performing sparse discriminative analysis between spontaneous facial expressions is demonstrated. An automatic facial expressions recognition system is presented. It uses a KSVD-SVM approach which is made of three main stages: A pre-processing and feature extraction stage, which solves the problem of shared subspace distribution based on the random projection theory, to obtain low dimensional discriminative and reconstructive features; A dictionary learning and sparse coding stage, which uses the KSVD model to learn discriminative under or over dictionaries for sparse coding; Finally a classification stage, which uses a SVM classifier for facial expressions recognition. Our main concern is to be able to recognize non-basic affective states and non-acted expressions. Extensive experiments on the JAFFE static acted facial expressions database but also on the DynEmo dynamic spontaneous facial expressions database exhibit very good recognition rates.

Keywords: dictionary learning, random projection, pose and spontaneous facial expression, sparse representation

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Authors: Md Monir Hossain, Anne Staples, Kuya Takami, Tomonari Furukawa

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Tire noise has a significant impact on ride quality and vehicle interior comfort, even at low frequency. Reduction of tire noise is especially important due to strict state and federal environmental regulations. The primary sources of tire noise are the low frequency structure-borne noise and the noise that originates from the release of trapped air between the tire tread and road surface during each revolution of the tire. The frequency response of the tire changes at low and high frequency. At low frequency, the tension and bending moment become dominant, while the internal structure and local deformation become dominant at higher frequencies. Here, we analyze tire response in terms of deformation and rolling velocity at low revolution frequency. An Abaqus FEA finite element model is used to calculate the static and dynamic response of a rolling tire under different rolling conditions. The natural frequencies and mode shapes of a deformed tire are calculated with the FEA package where the subspace-based steady state dynamic analysis calculates dynamic response of tire subjected to harmonic excitation. The analysis was conducted on the dynamic response at the road (contact point of tire and road surface) and side nodes of a static and rolling tire when the tire was excited with 200 N vertical load for a frequency ranging from 20 to 200 Hz. The results show that frequency has little effect on tire deformation up to 80 Hz. But between 80 and 200 Hz, the radial and lateral components of displacement of the road and side nodes exhibited significant oscillation. For the static analysis, the fluctuation was sharp and frequent and decreased with frequency. In contrast, the fluctuation was periodic in nature for the dynamic response of the rolling tire. In addition to the dynamic analysis, a steady state rolling analysis was also performed on the tire traveling at ground velocity with a constant angular motion. The purpose of the computation was to demonstrate the effect of rotating motion on deformation and rolling velocity with respect to a fixed Newtonian reference point. The analysis showed a significant variation in deformation and rolling velocity due to centrifugal and Coriolis acceleration with respect to a fixed Newtonian point on ground.

Keywords: natural frequency, rotational motion, steady state rolling, subspace-based steady state dynamic analysis

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Authors: A: Annis Fathima, V. Vaidehi, S. Ajitha

Abstract:

Face recognition system finds many applications in surveillance and human computer interaction systems. As the applications using face recognition systems are of much importance and demand more accuracy, more robustness in the face recognition system is expected with less computation time. In this paper, a hybrid approach for face recognition combining Gabor Wavelet and Linear Discriminant Analysis (HGWLDA) is proposed. The normalized input grayscale image is approximated and reduced in dimension to lower the processing overhead for Gabor filters. This image is convolved with bank of Gabor filters with varying scales and orientations. LDA, a subspace analysis techniques are used to reduce the intra-class space and maximize the inter-class space. The techniques used are 2-dimensional Linear Discriminant Analysis (2D-LDA), 2-dimensional bidirectional LDA ((2D)2LDA), Weighted 2-dimensional bidirectional Linear Discriminant Analysis (Wt (2D)2 LDA). LDA reduces the feature dimension by extracting the features with greater variance. k-Nearest Neighbour (k-NN) classifier is used to classify and recognize the test image by comparing its feature with each of the training set features. The HGWLDA approach is robust against illumination conditions as the Gabor features are illumination invariant. This approach also aims at a better recognition rate using less number of features for varying expressions. The performance of the proposed HGWLDA approaches is evaluated using AT&T database, MIT-India face database and faces94 database. It is found that the proposed HGWLDA approach provides better results than the existing Gabor approach.

Keywords: face recognition, Gabor wavelet, LDA, k-NN classifier

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Authors: Yanisa Chaiya, Jintana Sanwong

Abstract:

Let V be a vector space over a field and W a subspace of V. Let Fix(V,W) denote the set of all linear transformations on V with fix all elements in W. In this paper, we show that Fix(V,W) is a semigroup under the composition of maps and describe Green’s relations on this semigroup in terms of images, kernels and the dimensions of subspaces of the quotient space V/W where V/W = {v+W : v is an element in V} with v+W = {v+w : w is an element in W}. Let dim(U) denote the dimension of a vector space U and Vα = {vα : v is an element in V} where vα is an image of v under a linear transformation α. For any cardinal number a let a'= min{b : b > a}. We also show that the ideals of Fix(V,W) are precisely the sets. Fix(r) ={α ∊ Fix(V,W) : dim(Vα/W) < r} where 1 ≤ r ≤ a' and a = dim(V/W). Moreover, we prove that if V is a finite-dimensional vector space, then every ideal of Fix(V,W) is principle.

Keywords: Green’s relations, ideals, linear transformation semi-groups, principle ideals

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Authors: Neil M. Mame

Abstract:

We consider only finite graphs without loops nor multiple edges. Let G be a graph with E(G) = {e1, e2, …., em}. The edge space of G, denoted by ε(G), is a vector space over the field Z2. The elements of ε(G) are all the subsets of E(G). Vector addition is defined as X+Y = X Δ Y, the symmetric difference of sets X and Y, for X, Y ∈ ε(G). Scalar multiplication is defined as 1.X =X and 0.X = Ø for X ∈ ε(G). The set S ⊆ ε(G) is called a generating set if every element ε(G) is a linear combination of the elements of S. For a non-empty set X ∈ ε(G), the smallest subgraph with edge set X is called edge-induced subgraph of G, denoted by G[X]. The set EH(G) = { A ∈ ε(G) : G[A] ≅ H } denotes the uniform set of H with respect to G and εH(G) denotes the subspace of ε(G) generated by EH(G). If εH(G) is generating set, then we call H a generator subgraph of G. This paper gives the characterization for the generator subgraphs of the wheel that contain cycles and gives the necessary conditions for the acyclic generator subgraphs of the wheel.

Keywords: edge space, edge-induced subgraph, generator subgraph, wheel

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