Eigenvalue Decomposition Technique Research Articles

Wave mode computing method using the step-split Padé parabolic equation

Models based on a parabolic equation (PE) can accurately predict sound propagation problems in range-dependent ocean waveguides. Consequently, this method has developed rapidly in recent years. Compared with normal mode theory, PE focuses on numerical calculation, which is difficult to use in the mode domain analysis of sound propagation, such as the calculation of mode phase velocity and group velocity. To broaden the capability of PE models in analyzing the underwater sound field, a wave mode calculation method based on PE is proposed in this study. Step-split Padé PE recursive matrix equations are combined to obtain a propagation matrix. Then, the eigenvalue decomposition technique is applied to the matrix to extract sound mode eigenvalues and eigenfunctions. Numerical experiments on some typical waveguides are performed to test the accuracy and flexibility of the new method. Discussions on different orders of Padé approximant demonstrate angle limitations in PE and the missing root problem is also discussed to prove the advantage of the new method. The PE mode method can be expanded in the future to solve smooth wave modes in ocean waveguides, including fluctuating boundaries and sound speed profiles.

Fault Detection in Industrial Systems Using Maximized Divergence Analysis Approach

Dimensionality reduction techniques including partial least-squares (PLS) and principal component analysis (PCA) have been widely applied for data-driven process monitoring. However, the objectives of PCA- and PLS-based techniques are not specific for fault detection where a superior detection performance results from a large divergence (i.e., difference) between normal operating data and faulty data. In this article, a maximized divergence analysis (MDA) method is proposed to detect faults in industrial systems. The objective of MDA is to directly maximizes the Kullback-Leibler (KL) divergence corresponding to the distributions of normal operating data and faulty data during the procedure of dimensionality reduction. An algorithm using eigenvalue-decomposition technique is put forward to efficiently solve the optimization problem of maximizing KL-divergence. Two-dimensional synthetic data and Tennessee Eastman process are used to demonstrate the effectiveness of the proposed MDA-based detection approach.

A linearized non-isothermal general rate model for studying thermal effects in liquid chromatographic columns

A linearized non-isothermal general rate model is formulated and analytically solved to quantify the effects of temperature variations in fixed-bed chromatographic columns. The model contains a set of four coupled PDE accounting for energy transfer resistances, inner and outer particle-pore diffusions, and interfacial mass and axial dispersion. The Laplace transform, the eigenvalue-decomposition technique, and a conventional technique for the solutions of ODE are jointly employed for the solution of the model equations. A few numerical test studies are considered to assess the impact of system parameters on the performance of packed-bed adsorption columns. To access the range of applicability and to get the scope of the appropriateness of calculated analytical results, the numerical results are also obtained by applying a high resolution finite volume scheme. The analytical solutions obtained can be used as an invaluable tool for analyzing, optimizing, and upgrading the non-isothermal liquid chromatographic procedures.

Volume coherence function optimization method for extracting vegetation and terrain parameters from polarimetric synthetic aperture radar interferometry images

An advanced algorithm is introduced to enhance the efficiency in measuring vegetation parameters using L-band polarimetric synthetic aperture radar interferometry data. In this method, the combination of the eigenvalue decomposition technique and the coherence matrix optimization method is to achieve higher accuracy for ground phase estimation. Then an exhaustive search method based on the optimal polarization coherence channel is developed to retrieve the forest parameters. To evaluate the effectiveness of this method, we first apply it to simulated data obtained from PolSARProSim software. Next, the experimental L-band single-baseline single-frequency polarimetric interferometric data are used to assess the applicability of the proposed method for the actual forest topography in Malaysia and Kudara, Lake Baikal, Russia. The obtained results indicate that the proposed algorithm significantly overcomes the disadvantages of the recently published methods.

Efficient, Fair, and QoS-Aware Policies for Wirelessly Powered Communication Networks

In this paper, we propose efficient wireless power transfer (WPT) policies for various practical scenarios in wirelessly powered communication networks (WPCNs). First, we consider WPT from an energy access point (E-AP) to multiple energy receivers (E-Rs). We formulate the problem of maximizing the total average received power of the E-Rs subject to power constraints of the E-AP, which is a non-convex stochastic optimization problem. Using eigenvalue decomposition techniques, we derive a closed-form expression for the optimal policy, which requires the distribution of the channel state information (CSI) in the network. We then propose a near-optimal policy that does not require this knowledge and prove that its optimality gap can be decreased at the cost of increment in its convergence time. Next, we consider fairness among the E-Rs and propose a quality of service (QoS) aware fair policy that provides fairness and guarantees the required QoS of each E-R. Finally, we study a WPCN where the E-Rs utilize their received energy to transmit information to the E-AP. We maximize a generic fair network utility under the E-Rs’ QoS constraints and the E-AP’s power constraints. Numerical results show a significant improvement of $O(\log {N})$ in the total throughput compared to the state-of-the-art baselines.

A propagation matrix method for the solution of the parabolic equation in ocean acoustics.

A propagation matrix method for the solution of the parabolic equation in ocean acoustics is presented, where the sound fields at an arbitrary distance are expressed as a product of the initial fields and a sequential multiplication of the propagation matrices. The method contains two main calculation steps, i.e., producing and multiplying the propagation matrices. The first step allows a two-level parallel algorithm. In the second step an eigenvalue decomposition technique is developed to improve the efficiency in the case of a range-independent waveguide. The efficiency of the parallelized algorithm shall be tested in the future.

Oriented grouping-constrained spectral clustering for medical imaging segmentation

Original medical images are often inadequate for clinical diagnosis. Certain prior information can be used as an important basis for disease diagnosis and prevention. In this study, an oriented grouping-constrained spectral clustering method, OGCSC, is proposed to deal with medical image segmentation problems. OGCSC propagates the group information from the affinity matrix and subdivides the group information into two constraints. By adopting the normalized framework, OGCSC can be transformed into normalized spectral clustering. The solution of OGSCSC can be viewed as a generalized eigenvalue problem that can be solved using eigenvalue decomposition techniques. The significance of our work is that the use of group information and constraints information to analyse image data can greatly enhance the results achieved using the clustering segmentation method. The empirical experimental results reveal that the proposed method achieves robust and effective performance for medical image segmentation.

Small Signal Stability Analysis of Multi-Infeed Power Electronic Systems Based on Grid Strength Assessment

The increasing penetration of renewable energy resources, such as wind and solar, is changing AC grid dynamics. Potential dynamic stability issues such as small signal instability may occur when these resources are connected to a grid with low strength, i.e., a weak grid. In this paper, the relationships between small signal stability and grid strength measured with short circuit ratio (SCR), along with the relationships between the stability boundary and critical SCR (CSCR) are analytically studied in a single-infeed power electronic system (SIPES). On this basis, these relationships are extended to a multi-infeed power electronic system (MIPES) through eigenvalue decomposition techniques to define the so-called generalized short circuit ratio (gSCR) and critical gSCR (CgSCR) for small signal stability analysis. The defined gSCR and CgSCR are the generalized representation of SCR and CSCR for SIPESs in MIPESs. The gSCR can assess the grid strength of a MIPES in terms of its small signal stability while the CgSCR can characterize the stability boundary of a MIPES. In addition, the condition of CgSCR = CSCR is satisfied for a MIPES with homogeneous power electronic devices. This enables the proposed method based on the gSCR to simplify the complex stability analysis of MIPESs into the stability study of SIPESs. The efficacy of the proposed gSCR and CgSCR is validated with eigenvalue analysis and time-domain simulations.

Validation of beat by beat fetal heart signals acquired from four-channel fetal phonocardiogram with fetal electrocardiogram in healthy late pregnancy

Fetal heart rate monitoring is an essential obstetric procedure, however, false-positive results cause unnecessary obstetric interventions and healthcare cost. In this study, we propose a low cost and non-invasive fetal phonocardiography based signal system to measure the fetal heart sounds and fetal heart rate. Phonocardiogram (PCG) signals contain acoustic information reflecting the contraction and relaxation of the heart. We have developed a four-channel recording device with four separated piezoelectric sensors harnessed by a cloth sheet to record abdominal phonogram signals. A multi-lag covariance matrix based eigenvalue decomposition technique was used to extract fetal and maternal heart sounds as well as maternal breathing movement. In order to validate the fetal heart sounds extracted by PCG signal processing, 10 minutes’ simultaneous recordings of fetal Electrocardiogram (fECG) and abdominal phonogram from 15 pregnant women (27 ± 5-year-old) with fetal gestation ages between 33 and 40 weeks were obtained and processed. Highly significant (p < 0.01) correlation (r = 0.96; N = 270) was found between beat to beat fetal heart rate (FHRECG) from fECG and the same (FHRPCG) from fetal PCG signals. Bland–Altman plot of FHRECG and FHRPCG shows good agreement (<5% difference). We conclude that the proposed beat to beat fetal heart rate measurement system would be useful for monitoring fetal neurological wellbeing as a better alternative to traditional cardiotocogram based antenatal fetal heart rate monitoring.

Study on fault diagnosis algorithm in WSN nodes based on RPCA model and SVDD for multi-class classification

For characteristics of the wireless sensor network (WSN) nodes data streaming in the application environment, the limitations of conventional principal component analysis (PCA) method which depend on the static model in practical application are discussed, an online fault diagnosis algorithm in WSN nodes based on recursive PCA (RPCA) model and support vector data description (SVDD) for multi-class classification is proposed in this paper. The main contents of the method include:The algorithm first applies recursive eigenvalue decomposition techniques based on first-order perturbation (FOP) analysis to update the PCA model adaptively and realize the online fault detection, and then uses SVDD based multi-class classification algorithm to diagnose the fault types. Experimental results show that the algorithm can satisfy the real time needs of data stream processing, but also can track the data changes well. The experimental results based on data sets in real field and experimental data off our typical node failures demonstrate the effectiveness of the proposed algorithm. The algorithm proposed in this paper would improve the safety factor of monitoring sites and it can allows us to know the working state of the node in time and repair or replace it at first time.

Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

SummaryThis manuscript aims to investigate a new approach based on the modal series method and eigenvalue decomposition technique to solve a class of nonlinear optimal control problems. For this purpose, a sequence of decoupled linear two‐point boundary value problems is solved iteratively instead of solving the coupled nonlinear two‐point boundary value problem derived from the maximum principle. The convergence analysis of the suggested technique is also investigated. In addition, the problem that needs to be solved at each iteration is composed of lower‐order decoupled subproblems; hence, they can be solved in parallel. Thus, the new scheme has a parallel computing property improving its computational effectiveness. Numerical simulations and comparative results show that the proposed approach is efficient and provides satisfactory results.

Optimization of Size and Cost of Static VAR Compensator using Dragonfly Algorithm for Voltage Profile Improvement in Power Transmission Systems

Voltage stability is a major concern in power transmission systems due to mismatch between power generation and demand. Hence maintenance of voltage profile within the acceptable limit becomes a challenging task. In this paper the weakest buses for implementing the reactive power compensators are identified by eigenvalue decomposition technique on partitioned Y-admittance matrix. The size and cost of the SVC are optimized using dragonfly algorithm. The algorithm is implemented on IEEE 14 and 30 bus systems and the results obtained with and without the placement of Static VAR Compensators are compared with the results of other algorithms to show its effectiveness. The further scope of this work is to extend this to renewable energy by implementing the wind generators at the weakest buses there by reducing the electrical distance between the generators and the farthest load buses and securing the system from voltage collapse.

Modal Analysis of Fluid Flows: An Overview

Modal Analysis of Fluid Flows: An Overview

A Comparative Study on Fetal Heart Rates Estimated from Fetal Phonography and Cardiotocography.

The aim of this study is to investigate that fetal heart rates (fHR) extracted from fetal phonocardiography (fPCG) could convey similar information of fHR from cardiotocography (CTG). Four-channel fPCG sensors made of low cost (<$1) ceramic piezo vibration sensor within 3D-printed casings were used to collect abdominal phonogram signals from 20 pregnant mothers (>34 weeks of gestation). A novel multi-lag covariance matrix-based eigenvalue decomposition technique was used to separate maternal breathing, fetal heart sounds (fHS) and maternal heart sounds (mHS) from abdominal phonogram signals. Prior to the fHR estimation, the fPCG signals were denoised using a multi-resolution wavelet-based filter. The proposed source separation technique was first tested in separating sources from synthetically mixed signals and then on raw abdominal phonogram signals. fHR signals extracted from fPCG signals were validated using simultaneous recorded CTG-based fHR recordings.The experimental results have shown that the fHR derived from the acquired fPCG can be used to detect periods of acceleration and deceleration, which are critical indication of the fetus' well-being. Moreover, a comparative analysis demonstrated that fHRs from CTG and fPCG signals were in good agreement (Bland Altman plot has mean = −0.21 BPM and ±2 SD = ±3) with statistical significance (p < 0.001 and Spearman correlation coefficient ρ = 0.95). The study findings show that fHR estimated from fPCG could be a reliable substitute for fHR from the CTG, opening up the possibility of a low cost monitoring tool for fetal well-being.

Full-Diversity QO-STBC Technique for Large-Antenna MIMO Systems

The need to achieve high data rates in modern telecommunication systems, such as 5G standard, motivates the study and development of large antenna and multiple-input multiple-output (MIMO) systems. This study introduces a large antenna-order design of MIMO quasi-orthogonal space-time block code (QO-STBC) system that achieves better signal-to-noise ratio (SNR) and bit-error ratio (BER) performances than the conventional QO-STBCs with the potential for massive MIMO (mMIMO) configurations. Although some earlier MIMO standards were built on orthogonal space-time block codes (O-STBCs), which are limited to two transmit antennas and data rates, the need for higher data rates motivates the exploration of higher antenna configurations using different QO-STBC schemes. The standard QO-STBC offers a higher number of antennas than the O-STBC with the full spatial rate. Unfortunately, also, the standard QO-STBCs are not able to achieve full diversity due to self-interference within their detection matrices; this diminishes the BER performance of the QO-STBC scheme. The detection also involves nonlinear processing, which further complicates the system. To solve these problems, we propose a linear processing design technique (which eliminates the system complexity) for constructing interference-free QO-STBCs and that also achieves full diversity using Hadamard modal matrices with the potential for mMIMO design. Since the modal matrices that orthogonalize QO-STBC are not sparse, our proposal also supports O-STBCs with a well-behaved peak-to-average power ratio (PAPR) and better BER. The results of the proposed QO-STBC outperform other full diversity techniques including Givens-rotation and the eigenvalue decomposition (EVD) techniques by 15 dB for both MIMO and multiple-input single-output (MISO) antenna configurations at 10 − 3 BER. The proposed interference-free QO-STBC is also implemented for 16 × N R and 32 × N R MIMO systems, where N R ≤ 2 . We demonstrate 8, 16 and 32 transmit antenna-enabled MIMO systems with the potential for mMIMO design applications with attractive BER and PAPR performance characteristics.

Characteristic Mode and Reduced Order Modeling at Low Frequencies

We present a stabilized theory to address the breakdown or inaccuracy issue for low-frequency (LF) characteristic mode analysis (CMA). At LFs, to properly preserve the governing quasi-static circuit physics, the eigenvalue decomposition technique is leveraged to formulate a stabilized eigenvalue problem regarding low-order CMs, which dominate the scattering, radiation, and energy storage properties of arbitrarily shaped conducting bodies. Several efficient schemes are introduced for the computation of the low-order CMs in the LF regime, including the augmented electric-field integral equation, the potential ( $\mathbf {A}$ - $\Phi$ )-based integral equation, and the Calderon multiplicative preconditioner. The LF stabilized CMA enables one to understand and interpret the behaviors of complicated conducting objects with a reduced “modal” representation at LFs, which offers an insightful tool for reduced order modeling in circuit design and analysis.

Voltage stability assessment and identification of important nodes in power transmission network through network response structural characteristics

Electrical power grids are often susceptible to voltage instability and have been a growing concern. In this study, the authors propose techniques based on network response structural characteristics for voltage stability assessment and for the identification of important nodes in electrical power grids. First, the network response structural characteristic indices (NRSCIs) which are inherent in the conventional power grids in terms of the Kirchhoff matrix is formulated. The eigenvalue decomposition (ED) technique is then applied to a submatrix of the Kirchhoff matrix to determine the topological strength of the electrical network graph. The vertex (node) that has a minimum eigenvalue is taken as the critical mode, from which its contributions to the entire graph is identified using the proposed network response structural characteristics theory participation factor (NRSCTPF). To demonstrate the magnitude of the concept formulated, the known degree centrality is modified in terms of the established NRSCI, which are then used to determine the important nodes of the network graph. The results obtained show that the proposed NRSCTPF and the degree centrality based on the NRSCI can be used for voltage stability assessment and identification of important nodes. The proposed approach is also less computationally intensive compared with the traditional approach.

Semi-blind simplified mean value channel estimator for MC-IDMA systems

The Multi-Carrier Interleave Division Multiple Access (MC-IDMA) scheme combines Orthogonal Frequency Division Multiplexing and IDMA. The scheme combats both Inter-Symbol Interference (ISI) and Multiple Access Interference (MAI). For coherent detection of the transmitted signals at the receiver, Channel State Information (CSI) is crucial. There are several schemes that can be used to obtain CSI at the receiver, such as pilot-based schemes and decision directed scheme, semi-blind and as blind channel estimation schemes. This paper focuses on developing semi-blind channel estimation scheme for the MC-IDMA systems. The developed scheme is based on Minimum Mean Square Error (MMSE) algorithm. The estimator employs applications of the eigenvalue and eigenvector decomposition (EVD) techniques to simplify the MMSE algorithm, and is named Simplified Mean Value Estimator (SMVE). Simulation results show that the proposed SMVE-based estimator outperforms Least Mean Square (LMS) algorithm-based estimator, Modified Minimized Mean Value Estimator (MMMVE), and the Minimized Mean Value-MMSE Estimator (MMVE).

Memory Efficient PCA Methods for Large Group ICA.

Principal component analysis (PCA) is widely used for data reduction in group independent component analysis (ICA) of fMRI data. Commonly, group-level PCA of temporally concatenated datasets is computed prior to ICA of the group principal components. This work focuses on reducing very high dimensional temporally concatenated datasets into its group PCA space. Existing randomized PCA methods can determine the PCA subspace with minimal memory requirements and, thus, are ideal for solving large PCA problems. Since the number of dataloads is not typically optimized, we extend one of these methods to compute PCA of very large datasets with a minimal number of dataloads. This method is coined multi power iteration (MPOWIT). The key idea behind MPOWIT is to estimate a subspace larger than the desired one, while checking for convergence of only the smaller subset of interest. The number of iterations is reduced considerably (as well as the number of dataloads), accelerating convergence without loss of accuracy. More importantly, in the proposed implementation of MPOWIT, the memory required for successful recovery of the group principal components becomes independent of the number of subjects analyzed. Highly efficient subsampled eigenvalue decomposition techniques are also introduced, furnishing excellent PCA subspace approximations that can be used for intelligent initialization of randomized methods such as MPOWIT. Together, these developments enable efficient estimation of accurate principal components, as we illustrate by solving a 1600-subject group-level PCA of fMRI with standard acquisition parameters, on a regular desktop computer with only 4 GB RAM, in just a few hours. MPOWIT is also highly scalable and could realistically solve group-level PCA of fMRI on thousands of subjects, or more, using standard hardware, limited only by time, not memory. Also, the MPOWIT algorithm is highly parallelizable, which would enable fast, distributed implementations ideal for big data analysis. Implications to other methods such as expectation maximization PCA (EM PCA) are also presented. Based on our results, general recommendations for efficient application of PCA methods are given according to problem size and available computational resources. MPOWIT and all other methods discussed here are implemented and readily available in the open source GIFT software.

Admissible output consensus control for singular swarm systems

For swarm systems consisting of agents described by high-order linear singular systems, admissible output consensus problems are investigated. By using observability decomposition and eigenvalue decomposition techniques, a sufficient condition for admissible output consensus and a necessary and sufficient condition for admissible limited control energy output consensus are obtained. Furthermore, it is shown that stabilisability of the agents is a sufficient condition for admissible output consensualisability, and an approach to solve the protocol design problem is presented. Finally, a numerical example is provided to demonstrate the effectiveness of protocol design approach.