Eigenstructure Analysis Research Articles

Granular media deformation and fluid flow as overlapping, concurrent, coupled multilayered depth-averaged framework

A novel coupled depth-averaged formulation for the combination of multilayered fluid and monolayer granular flows as a set of interpenetrating continua has been developed in this study. Granular and fluid phases are coupled through an interaction force pair comprised of fluid stresses, and drag forces. Fluid phase is discretized in the vertical direction through a set N of virtual layer interfaces to obtain a variation of flow properties along depth. A novel algorithm for mass and momentum exchange between fluid layers for flow through and over porous media has been proposed. Eigenstructure analysis of the coupled system shows that the system may be discretized in N+1 separate yet coupled Riemann problems. An improved version of well-known HLL method is developed for solution of the model (Finite Volume Method) in a regular grid. The resistive source–sink terms are embedded implicitly within the interfacial flux. Based on the choices of state variables and layer-interface porosity, four variants of the coupled system are developed. A set of benchmark experimental test-cases and a representative test involving both rigid and deformable granular media has been simulated using the four variants to establish the robustness of the model and the coupling procedure.

Superconvergence of Direct Discontinuous Galerkin Methods: Eigen-structure Analysis Based on Fourier Approach

Superconvergence of Direct Discontinuous Galerkin Methods: Eigen-structure Analysis Based on Fourier Approach

Identification of anomalies in microphone array measurements of trailing edge noise by eigenstructure analysis.

An eigenstructure analysis is used to identify anomalies in large acoustic array measurements of airfoil trailing edge noise. Cross-spectra of 102 microphones distributed in a spiral configuration were inspected considering a range of inflow conditions and airfoil configurations. A measurement expectation is set by repeat measurements of non-anomalous data and is used for the analysis of additional data. This method is based solely on the comparison between the eigenstructure of cross-spectral matrices and can be used to efficiently inspect data for anomalies without having to beamform, as is conventional. Thus, processing and reviewing beamform maps can be relegated to post-processing after the experiment when more time is available.

Amplitude semblance and its fusion with the third-generation coherence for characterization of fractured-vuggy carbonate reservoirs

Abstract In the Tarim Basin, the main hydrocarbon reservoirs of Ordovician carbonate rocks are fractured-vuggy reservoirs, of which the underground river type reservoirs are an important type. Seismic coherence attribute can highlight seismic discontinuity caused by tectonic movements, reservoir boundaries, sedimentary body boundaries or other factors. Thus, it is a widely used key technique in seismic interpretation. There are many algorithms to determine the coherence. Typically, the coherence algorithm based on eigen-structure analysis is the most robust, but is sensitive to waveform differences and insensitive to amplitude differences. This paper proposes an amplitude coherence attribute to measure semblance of root-mean-square (RMS) amplitudes of multiple traces and fuses it with the third-generation coherence (C3) to describe the boundary of underground river. Model test and case study prove that the proposed fused algorithm can effectively identify the amplitude and waveform differences in seismic data.

Data-Driven Estimation of Inertia for Multiarea Interconnected Power Systems Using Dynamic Mode Decomposition

The refined estimation of inertia can provide a reliable basis for power system operation and control. In this article, a data-driven approach for the estimation of inertia is proposed, and it can estimate the effective inertia of different areas in the interconnected power systems. Based on eigenstructure analysis, the intrinsic relationships between inertia and the eigenvalue and eigenvector are analyzed using a linearized dynamic equation. Furthermore, detailed mathematical expressions between inertia and the eigenvalue and eigenvector are established. In addition, dynamic mode decomposition is introduced to extract eigenvalues and eigenvectors from the synchronized measurements to ensure that the scheme proposed in this article can estimate the effective inertia by using only the outputs measured by the phase measurement unit. The effectiveness of the proposed approach is demonstrated through numerical simulations on the IEEE 16-machine 5-area test system and the real measurements of an actual power system.

Eigenstructure and fractionalization of the quaternion discrete Fourier transform

Quaternion signal processing has found significant application to color image processing and bivariate signal analysis. Among the studies on quaternion transforms, just a few deal with fractionalization and none does so from an eigenstructure analysis point of view. This work aims to contribute by defining a fractional quaternion discrete Fourier transform (with one or multiple parameters) out of its eigendecomposition, after proving that it shares eigenvectors with the usual unitary discrete Fourier transform. For illustrative purposes, an encryption scheme for color images with opacity layer is provided and discussed.

Ill-posedness in modeling mixed sediment river morphodynamics

In this paper we analyze the Hirano active layer model used in mixed sediment river morphodynamics concerning its ill-posedness. Ill-posedness causes the solution to be unstable to short-wave perturbations. This implies that the solution presents spurious oscillations, the amplitude of which depends on the domain discretization. Ill-posedness not only produces physically unrealistic results but may also cause failure of numerical simulations. By considering a two-fraction sediment mixture we obtain analytical expressions for the mathematical characterization of the model. Using these we show that the ill-posed domain is larger than what was found in previous analyses, not only comprising cases of bed degradation into a substrate finer than the active layer but also in aggradational cases. Furthermore, by analyzing a three-fraction model we observe ill-posedness under conditions of bed degradation into a coarse substrate. We observe that oscillations in the numerical solution of ill-posed simulations grow until the model becomes well-posed, as the spurious mixing of the active layer sediment and substrate sediment acts as a regularization mechanism. Finally we conduct an eigenstructure analysis of a simplified vertically continuous model for mixed sediment for which we show that ill-posedness occurs in a wider range of conditions than the active layer model.

The eigenvalue shift technique and its eigenstructure analysis of a matrix

The eigenvalue shift technique is the most well-known and fundamental tool for matrix computations. Applications include the search of eigeninformation, the acceleration of numerical algorithms, the study of Google’s PageRank. The shift strategy arises from the concept investigated by Brauer (1952) [11] for changing the value of an eigenvalue of a matrix to the desired one, while keeping the remaining eigenvalues and the original eigenvectors unchanged. The idea of shifting distinct eigenvalues can easily be generalized by Brauer’s idea. However, shifting an eigenvalue with multiple multiplicities is a challenge issue and worthy of our investigation. In this work, we propose a new way for updating an eigenvalue with multiple multiplicities and thoroughly analyze its corresponding Jordan canonical form after the update procedure.

Dealing with project complexity by matrix-based propagation modelling for project risk analysis

Engineering projects are facing a growing complexity and are thus exposed to numerous and interdependent risks. In this paper, we present a quantitative method for modelling propagation behaviour in the project risk network. The construction of the network requires the involvement of the project manager and related experts using the design structure matrix method. A matrix-based risk propagation model is introduced to calculate risk propagation and thus to re-evaluate risk characteristics such as probability and criticality. An eigenstructure analysis is also used based on the risk network, with the goal of measuring and prioritising risks with respect to their importance in terms of influence in the network. These supplemental project risk analyses provide project managers with improved insights into risks considering complexity and help them to design more effective response actions. An example of an application to a real urban transportation system implementation project is presented to illustrate the utility of the proposed approach.

Eigenvector Sensitivity: A Kharitonov Result

This study is motivated by a need to effectively determine the difference between a system fault and normal system operation under parametric uncertainty using eigenstructure analysis. This involves computational robustness of eigenvectors in linear state space systems dependent upon uncertain parameters. The work involves the development of practical algorithms which provide for computable robustness measures on the achievable set of eigenvectors associated with certain state space matrix constructions. To make connections to a class of systems for which eigenvalue and characteristic root robustness are well understood, the work begins by focusing on companion form matrices associated with a polynomial whose coefficients lie in specified intervals. The work uses an extension of the well known theories of Kharitonov that provides computational efficient tests for containment of the roots of the polynomial (and eigenvalues of the companion matrices) in “desirable” regions, such as the left half of the complex plane.

Superconvergence of discontinuous Galerkin and local discontinuous Galerkin methods: Eigen-structure analysis based on Fourier approach

Various superconvergence properties of discontinuous Galerkin (DG) and local DG (LDG) methods for linear hyperbolic and parabolic equations have been investigated in the past. Due to these superconvergence properties, DG and LDG methods have been known to provide good wave resolution properties, especially for long time integrations (Zhong and Shu, 2011) [26]. In this paper, under the assumption of uniform mesh and via Fourier approach, we observe that the error of the DG or LDG solution can be decomposed into three parts: (1) dissipation and dispersion errors of the physically relevant eigenvalue; this part of error will grow linearly in time and is of order: 2k+1 for DG method and 2k+2 for LDG method (2) projection error: there exists a special projection of the exact solution such that the numerical solution is much closer to this special projection than the exact solution itself; this part of error will not grow in time (3) the dissipation of non-physically relevant eigenvectors; this part of error will be damped exponentially fast with respect to the spatial mesh size Δx. Along this line, we analyze the error for a fully discrete Runge–Kutta (RK) DG scheme. A collection of numerical examples for linear equations are presented to verify our observations above. We also provide numerical examples based on non-uniform mesh, nonlinear Burgers’ equation, and high-dimensional Maxwell equations to explore superconvergence properties of DG methods in a more general setting.

Critical dynamics and asynchronous rate propagation in homogenous feedforward networks

Event Abstract Back to Event Critical dynamics and asynchronous rate propagation in homogenous feedforward networks Natasha A. Cayco Gajic1* and Eric Shea-Brown1 1 University of Washington, Applied Mathematics, United States Recent experimental and computational evidence suggests that the brain may operate at a critical state characterized by complex dynamics, significant higher-order correlations, and optimal computational properties. We investigate the emergence of critical activity in a homogeneous, feedforward network of McCullochs-Pitts neurons. By applying an eigenstructure analysis of a mean-field Markov chain model, we explain the emergence of persistence, complexity, and higher-order correlations characteristic of criticality. We extend our analysis from an initial treatment of purely excitatory networks to more complex models that include inhibition and noise: excitatory-inhibitory networks display enhanced robustness of the critical state, and noisy networks exhibit stochastic resonance as the addition of some noise mitigates the effect of harsh thresholding. Keywords: Criticality, feedforward networks, rate coding, stochastic resonance, Markov chain Conference: Bernstein Conference 2012, Munich, Germany, 12 Sep - 14 Sep, 2012. Presentation Type: Poster Topic: Other Citation: Cayco Gajic NA and Shea-Brown E (2012). Critical dynamics and asynchronous rate propagation in homogenous feedforward networks. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference 2012. doi: 10.3389/conf.fncom.2012.55.00022 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 18 Sep 2012; Published Online: 12 Sep 2012. * Correspondence: Ms. Natasha A Cayco Gajic, University of Washington, Applied Mathematics, Seattle, Washington, 98195-2420, United States, caycogajic@gmail.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Natasha A Cayco Gajic Eric Shea-Brown Google Natasha A Cayco Gajic Eric Shea-Brown Google Scholar Natasha A Cayco Gajic Eric Shea-Brown PubMed Natasha A Cayco Gajic Eric Shea-Brown Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Intelligent data analysis and model interpretation with spectral analysis fuzzy symbolic modeling

This paper proposes fuzzy symbolic modeling as a framework for intelligent data analysis and model interpretation in classification and regression problems. The fuzzy symbolic modeling approach is based on the eigenstructure analysis of the data similarity matrix to define the number of fuzzy rules in the model. Each fuzzy rule is associated with a symbol and is defined by a Gaussian membership function. The prototypes for the rules are computed by a clustering algorithm, and the model output parameters are computed as the solutions of a bounded quadratic optimization problem. In classification problems, the rules’ parameters are interpreted as the rules’ confidence. In regression problems, the rules’ parameters are used to derive rules’ confidences for classes that represent ranges of output variable values. The resulting model is evaluated based on a set of benchmark datasets for classification and regression problems. Nonparametric statistical tests were performed on the benchmark results, showing that the proposed approach produces compact fuzzy models with accuracy comparable to models produced by the standard modeling approaches. The resulting model is also exploited from the interpretability point of view, showing how the rule weights provide additional information to help in data and model understanding, such that it can be used as a decision support tool for the prediction of new data.

Mixed Loop Scheme and it’s Industry Application

This paper presents a unified and mixed interpolatory and approximation subdivision scheme for triangular meshes. It can be used to solve the "popping effect" problem when switching between meshes at different levels of resolution. The scheme generates surfaces coincidence with the Loop subdivision scheme in the limit condition having the coefficient k equal 0. When k equal 1, it will be changed into a new interpolatory subdivision scheme. A new set of rules is designed for computing the newly inserted vertices around extraordinary masks. Eigen-structure analysis demonstrates that subdivision surfaces generated using the new schemes are C1 continuous. The method is a completely simple one without constructing and solving equations. The example of British Museum shell design show the great flexibility advantage of mixed subdivision design method in shell architecture, even in other industry design field.

Numerical Method of Symplectic State Transition Matrix and Application to Fully Perturbed Earth Orbit

This paper presents a numerical method for deriving a symplectic state transition matrix for high-fidelity Earth orbits subject to non-dissipative perturbation forces. By taking advantage of properties of Hamiltonian systems, this method provides an exact solution space mapping of linearized orbital dynamics, preserving the symplectic structure that all Hamiltonian systems should possess by nature. This method can be applied to accurate, yet computationally efficient dynamic filters, long-term propagations of the motions of formation flying spacecraft and the eigenstructure analysis of N-body dynamics, etc., when the exact structure-preserving property is crucial. We show the derivation of the numerical method of symplectic state transition matrix, and apply it to Earth orbits with perturbation forces based on real ephemerides. These numerical examples reveal that this method shows improvements in preserving the structural properties of the state transition matrix, and in the computational efficiency compared to the conventional linear state transition matrix with Euler or Runge-Kutta integration.

Optimum design of three-dimensional behavioural decentralized controller for UAV formation flight

This article proposes a behavioural decentralized approach that allows an unmanned aerial vehicle (UAV) formation flight to carry out a waypoint-passing mission effectively. The objective of the proposed controller is to make each UAV in the formation fly through predefined waypoints while maintaining its distance from other UAVs. To perform these two tasks, which can conflict with each other, coupled dynamics of UAVs is considered; this combines the dynamics of all the members in the formation. To apply the behavioural decentralized controller on the basis of the coupled dynamics, a feedback linearization technique with a diffeomorphic transfer map is derived for a three-dimensional UAV kinematics model. A behavioural approach in which the control input is decided by the relative weight of each UAV's desired behaviour is considered, so that the UAVs can react promptly in various situations. Optimization techniques of the gain matrices are also performed to improve the performance of the formation flight using eigen-structure analysis and Cholesky decomposition. To verify the performance of the proposed controller, numerical simulation is performed for a waypoint-passing mission of multiple UAVs.

Design of interpretable fuzzy rule-based classifiers using spectral analysis with structure and parameters optimization

This paper presents a design method for fuzzy rule-based systems that performs data modeling consistently according to the symbolic relations expressed by the rules. The focus of the model is the interpretability of the rules and the model's accuracy, such that it can be used as tool for data understanding. The number of rules is defined by the eigenstructure analysis of the similarity matrix, which is computed from data. The rule induction algorithm runs a clustering algorithm on the dataset and associates one rule to each cluster. Each rule is selected among all possible combinations of one-dimensional fuzzy sets, as the one nearest to a cluster's center. The rules are weighted in order to improve the classifier performance and the weights are computed by a bounded quadratic optimization problem. The model complexity is minimized in a structure selection search, performed by a genetic algorithm that selects simultaneously the most representative subset of variables and also the number of fuzzy sets in the fuzzy partition of the selected variables. The resulting model is evaluated on a set of benchmark datasets for classification problems. The results show that the proposed approach produces accurate and yet compact fuzzy classifiers. The resulting model is also evaluated from an interpretability point of view, showing how the rule weights provide additional information to help data understanding and model exploitation.

A modified eigen-structure analyzer to lower SNR DS-SS signals under narrow band interferences

This paper proposes a modified approach to eigen-structure analysis of direct sequence spread spectrum (DS-SS) signals under narrow-band interferences (NBIs), which can estimate the pseudo noise (PN) sequence blindly in lower signal-to-noise ratio (SNR) and signal-to-interference ratio (SIR) DS-SS signals. Of course, some parameters of DS-SS signals (such as the period and chip interval of PN sequences) need to be known. The received signal is divided into continuous non-overlapping temporal vectors according to two periods (not the one period before in [T. Zhang, A. Mu, C. Zhang, Analyze the eigen-structure of DS-SS signals under narrow band interferences, Digital Signal Process. 16 (6) (2006) 746-753]) of PN sequence, after which their correlation matrix is calculated and accumulated vector by vector. An eigenvalue decomposition operation can be applied to the matrices to analyze blindly the eigen-structure (including the NBI eigen-structures and PN sequences) of received signals from the principal component eigenvectors. Since the duration of temporal window is two periods of PN sequence, the PN sequence can be reconstructed by one principal eigenvector (not the two component eigenvectors before in [T. Zhang, A. Mu, C. Zhang, Analyze the eigen-structure of DS-SS signals under narrow band interferences, Digital Signal Process. 16 (6) (2006) 746-753]) only. Theoretic analysis and experimental results show that the approach is more effective than the method before in [T. Zhang, A. Mu, C. Zhang, Analyze the eigen-structure of DS-SS signals under narrow band interferences, Digital Signal Process. 16 (6) (2006) 746-753]. It can also work well in the lower SNR and SIR environments.

Boundary conditions in a two-layer geomorphological model. Application to a

The one-dimensional numerical model presented in the present paper divides the flow in two fully coupled layers, a water layer and a water-sediment transport layer. Initially, this model was used to depict dam-break flows, which do not require a specific treatment of boundary conditions. The aim of the present research is to extend the model to fluvial flows requiring an appropriate boundary condition treatment. This treatment commonly relies on characteristics. However, in the frame of a two-layer model with five equations, those characteristics are not obvious to determine. This paper shows, how to extend numerically the common eigenstructure analysis to address the problem. Examples are presented and the boundary conditions treatment is illustrated on the particular case of a hydraulic jump over a mobile bed. Results of the numerical model including the adequate boundary conditions are favourably compared to experimental results.

Analyze the eigen-structure of DS-SS signals under narrow band interferences

In this paper, an approach of eigen-structure analysis for DS-SS (direct sequence spread spectrum) signals under NBI (narrow band interference) is proposed, which can estimate the PN (pseudo-noise) sequence blindly in lower SNR (signal-to-noise ratio) and SIR (signal-to-interference ratio) DS-SS signals. Of course, some parameters of DS-SS signals (such as period and chip interval of PN sequence) need to be known. First, the received signal is divided into continued nonoverlapping temporal vectors according to the period of PN sequence, and then we calculate and accumulate the correlation matrix of these vectors one by one. An operation of eigenvalue decomposition may be applied to the matrices; we can estimate the eigen-structure (which include the NBI eigen-waveforms and PN sequences) of received signals from the principal component eigenvectors blindly in the end. Based on the estimated NBI eigen-waveforms and PN sequences, the NBI can be rejected, and the DS-SS signals can be de-spreaded without the PN sequence too. Theoretic analysis and experimental results show that the approach is very effective. It can work well on the lower SNR and SIR ambient.