Eigenanalysis Method Research Articles

Rotating Stall Inception Prediction Using an Eigenvalue-Based Global Instability Analysis Method

The accurate prediction of rotating stall inception is critical for determining the stable operating regime of a compressor. Among the two widely accepted pathways to stall, namely, modal and spike, the former is plausibly believed to originate from a global linear instability, and experiments have partially confirmed it. As for the latter, recent computational and experimental findings have shown it to exhibit itself as a rapidly amplified flow perturbation. However, rigorous analysis has yet to be performed to prove that this is due to global linear instability. In this work, an eigenanalysis approach is used to investigate the rotating stall inception of a transonic annular cascade. Steady analyses were performed to compute the performance characteristics at a given rotational speed. A numerical stall boundary was first estimated based on the residual convergence behavior of the steady solver. Eigenanalyses were then performed for flow solutions at a few near-stall points to determine their global linear stability. Once the relevant unstable modes were identified according to the signs of real parts of eigenvalues, they were examined in detail to understand the flow destabilizing mechanism. Furthermore, time-accurate unsteady simulations were performed to verify the obtained eigenvalues and eigenvectors. The eigenanalysis results reveal that at the rotating stall inception condition, multiple unstable modes appear almost simultaneously with a leading mode that grows most rapidly. In addition, it was found that the unstable modes are continuous in their nodal diameters, and are members of a particular family of modes typical of a dynamic system with cyclic symmetries. This is the first time such an interesting structure of the unstable modes is found numerically, which to some extent explains the rich and complex results constantly observed from experiments but have never been consistently explained. The verified eigenanalysis method can be used to predict the onset of a rotating stall with a CPU time cost orders of magnitude lower than time-accurate simulations, thus making compressor stall onset prediction based on the global linear instability approach feasible in engineering practice.

Excitation Flexibility of On-Antenna Power Combining

In this letter, a design methodology is proposed for on-antenna power combining with flexible input power ratios. Designing multi-feed antennas with direct power combining requires weighted driving signals to match the field distribution at the resonant mode of the antenna, imposing serious restrictions on their implementation. To overcome this drawback, we proposed a method to relax the excitation criterion by altering the impedance matching conditions of the multi-feed antenna, giving the RF designers a degree of freedom. First, an eigenanalysis method is employed to extract the active impedance values for each port of the antenna. Then, according to a preferred input power distribution, proper impedance matching is built based on the active impedance values. The resulting multi-feed antenna resembles the single-feed antenna in terms of the radiation performance with desired driving signals. A series of four-feed slot antennas were fabricated to validate the proposed method. Simulation and measurement results show that under different excitation scenarios the radiation performance of the antenna remains intact, demonstrating the flexibility for on-antenna power combining.

Influence of Inverter Controller Parameters on the Small-signal Stability of LCC-HVDC System Based on a Practical Project

Unreasonable control parameters of the Line Commutated Converter based High Voltage Direct Current (LCC-HVDC) system may induce small-signal instability. This paper studies the impact of inverter controller parameters on steady response of the LCC-HVDC system under weak AC grid condition. Firstly, according to a practical project, the small-signal model of LCC-HVDC system is established based on the switching function. Then, the eigen-analysis method is adopted to study the impact of the controller parameters on the inverter side on the oscillation mode and damping characteristics of the LCC system, and the correctness of results is verified by PSCAD/EMTDC simulation. The conclusion shows that reasonable controller parameters can improve the stability margin of the system.

Unraveling the combined actions of a Holling type III predator–prey model incorporating Allee response and memory effects

In this article, we have studied a memory dependent prey–predator model with logistic type prey growth subject to the Allee effect and Holling type-III functional response. To include the memory effect, we have used here a fractional order system. The model contains at most four equilibrium points among which one is trivial, two are axial, and the last one is interior. Here we have studied behavior of these four equilibrium points using eigen analysis method. Our investigation shows that the trivial equilibrium point is stable for strong Allee effect, and unstable for weak Allee effect. Between the two axial equilibrium points, one is stable under certain condition but the other is always unstable. This unstable equilibrium point exists only for strong Allee case. The interior equilibrium point arises when the axial equilibrium point is unstable. Stability condition of this interior equilibrium point depends on the parametric relationship. The schematic diagram divides the a-p plane into five sub-regions in both the cases of memory dependent and memory less system. The number and nature of the equilibrium points in different sub-regions are different. Finally, we have drawn the bifurcation diagrams considering all the equilibrium points in different sub-regions and the results are concluded at the end.

Pitch Stability Analysis for Mechanical-Hydraulic-Structural-Fluid Coupling System of High-Lift Hoist Vertical Shiplift

Pitch stability of the high-lift wire rope hoist vertical shiplift under dynamic hydraulic levelling has always been an issue of concern. It not only affects working efficiency but also brings significant challenges to operational safety. A new mechanical-hydraulic-structural-fluid (MHSF) coupling dynamics model and a developed semi-analytical method are presented for stable property analysis. The models of the hydraulic levelling subsystem, shallow water sloshing subsystem, the main hoist mechanical subsystem, and the shiplift chamber structure subsystem are built using a closed-loop transfer function, multi-modal theory, and an second-type Lagrangian equation, respectively. Then, a core twenty-one order state matrix of the MHSF coupling system is established using the state-space method. Subsequently, the Lyapunov motion stability theory and Eigen-analysis method are used in combination to judge the pitch stability and analyse the characteristics of the subsystems. Taking four typical high-lift hoist vertical shiplifts as examples, the rationality of the proposed model and method is validated. The results indicate that although the pitch stability safety factor under hydraulic dynamic levelling is reduced by about 15 % to 44 % with respect to hydraulic static levelling, hydraulic dynamic levelling still can meet stability requirements. Furthermore, for the designed 200 m level hoist vertical shiplift, the preliminary design parameters can ensure the pitch stability safety factor under dynamic hydraulic levelling of not less than 1.1. The element most prone to instability is the shallow water sloshing subsystem; increasing the synchronous shaft stiffness or the water boundary layer damping ratio can effectively enhance the pitch stability.

Analysis of Mode Interaction in Ultra-low Frequency Oscillation Based on Trajectory Eigenvalue

Complex phenomena such as prolongedly undamped ultra-low frequency oscillation (ULFO) and eigenmode re-excitation are observed in the simulations of hydroelectric power systems. Emphases are put on nonlinearities and mode interactions, which cannot be analyzed by traditional eigen-analysis methods. In order to investigate the mechanism of the evolvement of the nonlinear dynamic process in ULFO, this paper proposes a method to analyze the mode interactions quantificationally. First, a disturbed trajectory is decoupled into a set of time-varying components. Second, transfer matrices of eigenmodes are extracted along the trajectory. Third, consecutive sequences of eigenvalues and trajectories of components are formed by a proposed technique. Based on the decoupled components and transfer matrices, the mechanisms of mode interactions and inheritance relationships between eigenmodes are analyzed. The causes and developments of the above complex phenomena are revealed by the proposed method in a test two-machine system. Meanwhile, the accuracy of the eigenmode matching technique is verified in the New England system.

Robust generalized sidelobe canceller based on eigenanalysis and a MaxSINR beamformer

A robust generalized sidelobe canceller is proposed to combat direction of arrival (DOA) mismatches. To estimate the interference-plus-noise (IPN) statistics characteristics, conventional signal of interest (SOI) extraction methods usually collect a large number of segments where only the IPN signal is active. To avoid that collection procedure, we redesign the blocking matrix structure using an eigenanalysis method to reconstruct the IPN covariance matrix from the samples. Additionally, a modified eigenanalysis reconstruction method based on the rank-one matrix assumption is proposed to achieve a higher reconstruction accuracy. The blocking matrix is obtained by incorporating the effective reconstruction into the maximum signal-to-interferenceplus- noise ratio (MaxSINR) beamformer. It can minimize the influence of signal leakage and maximize the IPN power for further noise and interference suppression. Numerical results show that the two proposed methods achieve considerable improvements in terms of the output waveform SINR and correlation coefficients with the desired signal in the presence of a DOA mismatch and a limited number of snapshots. Compared to the first proposed method, the modified one can reduce the signal distortion even further.

Multiband Simulations of Multistream Polarimetric Microwave Radiances Over Aspherical Hydrometeors

AbstractA numerical precision assessment and simulation results of the Unified Microwave Radiative Transfer (UMRT) model incorporating aspherical frozen hydrometeors based on the NASA Goddard Space Flight Center (NASA/GSFC) OpenSSP database are presented. It is shown that UMRT maintains unconditional numerical stability and computational efficiency for absorbing and scattering clouds. UMRT requires symmetry of the transition matrix for the discretized planar‐stratified radiative transfer equation to realize numerically stable and accurate matrix operations as required by the discrete ordinate eigenanalysis method. UMRT has heretofore been restricted to spherical polydispersive hydrometeors. In this study, the necessary block‐diagonal structure of the full Stokes matrix for randomly oriented OpenSSP aspherical hydrometeors is shown to be maintained, albeit with small asymmetric deviations, which introduce small asymmetric components into the transition matrix that are negligible for most remote sensing applications. An upper bound of the brightness temperature error calculated by neglecting the asymmetric components of the transition matrix under even extreme atmospheric conditions is shown to be small. Hence, the OpenSSP hydrometeor database can be reliably used within the UMRT model. Block‐diagonal Stokes matrix elements along with other single‐scattering hydrometeor parameters were subsequently used in radiative simulations of multistream dual‐polarization radiances for a simulated hurricane event to demonstrate the inherent numerical stability and utility of the enhanced UMRT model. An intercomparison of computed upwelling radiances for a multiphase distribution of aspherical OpenSSP hydrometeors versus a mass‐equivalent Mie hydrometeor polydispersion for key sensing frequencies from 10 to 874 GHz shows the considerable impact of complex (vs. simple spherical) hydrometeors on predicted microwave radiances.

Establishment of a 4650-year-long eigenvalue chronology based on tree-ring cores from Qilian junipers (Juniperus przewalskii Kom.) in Western China

This paper describes a tree-ring width chronology that spans the past 4650 years, established using the recently developed eigenanalysis technique. The aim is to show whether this eigenanalysis method enables the extraction of long-term tree-growth variations that are due to climatic changes, from a large dataset comprising 1263 tree-ring width records sampled from the highlands of Western China. In order to exclude the so-called growth rate/life span association effect, tree-ring width records were sorted into six subsets, based on the life spans of the trees sampled: 200–400, 400–600, 600–800, 800–1000, 1000–1500 years old, and trees older than 1500 years. Some partial chronologies were created, by pairing the set of all tree samples (living, dead, archaeological remains) with the living trees belonging to each subset. We computed the contours of tree-growth variations (on both 100-year and longer time scales) for each subset, ending with six pairs of these partial subset chronologies. Two sums of all these partial chronologies thus yielded a record of precipitation variations over a period ranging from 2627 BCE up to 2012 CE. It was found that this record shows a high degree of similarity to the existing chronology produced using the regional curve standardization (RCS) method applied to the same dataset, indicating that the eigenvalue chronology is capable of faithfully extracting long-term climatic variations. This also confirms that the first eigenvector represents the growth pattern that is characteristic of each biologically unique tree as well as the micro-environment of each tree stand. The variations observed over the last millennium seem to be connected to a cycle of solar activity with a period of ∼200 years. However, a clear lack of correspondence between solar activity and tree growth prior to 1000 CE indicates that the recent consistency may be coincidental. We believe that the eigenanalysis technique is readily applicable to other kinds of tree-ring datasets from different parts of the world.

Efficient Eigen-Analysis for Large Delayed Cyber-Physical Power System Using Explicit Infinitesimal Generator Discretization

Time delays significantly compromise the performance of wide-area measurement and control system and thus may jeopardize the stability of cyber-physical power systems (CPPS). A delayed CPPS (DCPPS) has a transcendental characteristic equation, leading to an infinite number of eigenvalues basically unsolvable by traditional eigen-analysis methods. In this paper, an explicit infinitesimal generator discretization (EIGD) approach is presented to tackle the traditionally intractable problem. First, the delayed differential equation of DCPPS is transformed to an ordinary differential equation by using an operator called infinitesimal generator. The operator is then optimally discretized, resulting in a highly structured, sparse and explicit approximant matrix. By exploiting the sparsity of the matrix and that of system matrices, the rightmost eigenvalues of the original DCPPS can be accurately computed. The contributions of the EIGD approach lie in the following: 1) it forms a theoretical foundation for accurately obtaining the critical eigenvalues of a CPPS with multiple delays; 2) it constructs a highly structured approximant matrix that enables efficient eigen-analysis of a large DCPPS by making full use of sparsity techniques; and 3) it integrates the shift-invert transformation, Arnoldi algorithm, Newton correction and eigen-sensitivity to form a computational framework for the analysis of large DCPPS. The accuracy, efficiency and scalability of EIGD have been extensively studied and thoroughly validated on the two-area four-machine test system and a practical large transmission grid.

Eigenanalysis of SNP data with an identity by descent interpretation

Principal component analysis (PCA) is widely used in genome-wide association studies (GWAS), and the principal component axes often represent perpendicular gradients in geographic space. The explanation of PCA results is of major interest for geneticists to understand fundamental demographic parameters. Here, we provide an interpretation of PCA based on relatedness measures, which are described by the probability that sets of genes are identical-by-descent (IBD). An approximately linear transformation between ancestral proportions (AP) of individuals with multiple ancestries and their projections onto the principal components is found.In addition, a new method of eigenanalysis “EIGMIX” is proposed to estimate individual ancestries. EIGMIX is a method of moments with computational efficiency suitable for millions of SNP data, and it is not subject to the assumption of linkage equilibrium. With the assumptions of multiple ancestries and their surrogate ancestral samples, EIGMIX is able to infer ancestral proportions (APs) of individuals. The methods were applied to the SNP data from the HapMap Phase 3 project and the Human Genome Diversity Panel. The APs of individuals inferred by EIGMIX are consistent with the findings of the program ADMIXTURE.In conclusion, EIGMIX can be used to detect population structure and estimate genome-wide ancestral proportions with a relatively high accuracy.

Field intensity factors around inclusion corners in 0–3 and 1–3 composites subjected to thermo-mechanical loads

A super inclusion corner apex element for polygonal inclusions in 0–3 and 1–3 composites is developed by using numerical stress and displacement field solutions based on an ad hoc finite element eigenanalysis method. Singular stresses near the apex of inclusion corner under thermo-mechanical loads can be obtained by using a super inclusion corner apex element in conjunction with hybrid-stress elements. The validity and the applicability of this technique are established by comparing the present numerical results with the existing solutions and the conventional finite element solutions. As examples of applications, a square array of square inclusions in 0–3 composites and a rectangular array of rectangular inclusions in 1–3 composites are considered. All numerical examples show that the present numerical method yields satisfactory solutions with fewer elements and is applicable to complex problems such as multiple singular points or fields in composite materials.

Investigation of Order of Singularity in 3D Two-phase Transversely Isotropic Piezoelectric Dissimilar Joints by Eigen Analysis Method

The distribution of stress singularity field near the vertex of two-phase material components is very important to maintain the reliability of intelligent materials. Piezoelectric material, due to its characteristic direct-converse piezoelectric effect, has naturally received considerable attentions. In this paper, stress singularity at a vertex in transversely isotropic piezoelectric dissimilar material joints is analyzed. Eigen analysis based on FEM is used for stress singularity field analysis of piezoelectric dissimilar material joints. The Eigen equation is used for calculating the order of stress singularity, and the angular function of elastic displacement, electric potential, stress and electric displacement. Stress and electric displacement fields demonstrate that the value near the free edge of the joint is larger than that at the inner portion. From the numerical result, it is suggested that delamination of the interface may occur at the interface edge of the dissimilar piezoelectric material joints due to the higher stress concentration at the free edge.

Analytical estimation of natural frequencies and mode shapes of a beam having two cracks

Abstract In this paper, an analytical estimation based on the Rayleigh's method is extended for a beam having one or two cracks to find natural frequencies and mode shapes in order to overcome weakness of solving eigenvalue problem. Weakness of solving eigenvalue problem to obtain exact natural frequencies and mode shapes is that, an algebraic equation must be solved numerically and then coefficients of trigonometric and hyperbolic terms in mode shapes will be found using matrices obtained from compatibility conditions at each point of cracks and boundary conditions. So this method does not show effects of crack size and location in the explicit form. The advantage of analytical estimation based on the Rayleigh's method over the eigen analysis method is that, the Rayleigh method obtains explicit expression for both natural frequencies and mode shapes in which effect of parameters such as crack size and location on natural frequencies and mode shapes can be investigated analytically. In the analytical estimation method, mode shapes of cracked beam are constructed by adding a polynomial function which shows effect of cracks, to mode shape of undamaged beam. The coefficients of the polynomial function are obtained by using boundary conditions and compatibility equations at the point of cracks. However in this paper it is shown that the accuracy of this estimation decreases when crack depth increases. Therefore, this paper also investigates on the upper limit of crack depth in which natural frequencies have error less than 5% and mode shapes have error less than 7% obtained by analytical estimation in compare to the exact solution. In the literature, it is shown that, analytical estimation based on the Rayleigh's method can predict only the first natural frequency of a simply supported cracked beam with sufficient accuracy, but no more investigation reported for finding the reliable range of crack depth natural mode shapes or higher natural frequencies. So, in this study, upper limit of crack depth has been found for both cases of beam with one or two cracks for first three natural frequencies and mode shapes.

A Unified Microwave Radiative Transfer Model for General Planar Stratified Media: Slab Formulation

A unified microwave radiative transfer (UMRT) model is presented for computing the thermal radiation emitted from any geophysical medium composed of planar layers of either densely or tenuously distributed moderately sized spherical scatterers. UMRT employs the discrete-ordinate eigenanalysis (DOE) method with layer adding to solve the differential radiative transfer equation for such multilayer structures. UMRT inherits the symmetrization and analytical diagonalization and factorization techniques of symmetric and positive definite matrices from the discrete-ordinate tangent linear radiative transfer (DOTLRT) model presented by Voronovich These techniques ensure accuracy, numerical stability, and rapid computation for all matrix operations required for DOE along with a fast Jacobian calculation for radiance assimilation purposes. UMRT extends the applicability of DOTLRT by including both the Mie theory and the dense media radiative transfer (DMRT) theory. Other nontrivial extensions within UMRT are the following: 1) The vertical and horizontal radiation intensities are coupled within each layer by applying the reduced Mie or DMRT phase matrices, and 2) the physical temperature profile of a layer is allowed to be linear in height. The symmetry properties of both the reduced Mie and DMRT phase matrices are proved, and the associated scattering and absorption coefficients are compared and discussed. The UMRT slab formulation is validated by imposing energy conservation, and the numerical results for some nominal cases are produced and discussed.

An effective numerical analysis of singular stress fields in dissimilar material wedges under thermo-mechanical loads

A super wedge apex element for dissimilar material wedges is developed by using numerical stress and displacement field solutions with an ad hoc finite element eigenanalysis method. Singular stresses near the apex of an arbitrary dissimilar material wedge under thermo-mechanical loads can be obtained by using a super wedge apex element in conjunction with hybrid-stress elements. The validity and applicability of this technique is established by comparing the obtained results with existing asymptotic solutions. All numerical examples show that the present numerical method yields satisfactory solutions with fewer elements and is applicable to complex problems such as multiple singular points or fields.

Power density spectrum for the identification of residence time distribution signals

One of the most important applications of radioisotopes in industry is the residence time distribution (RTD) measurement. RTD can be used for optimizing the design of industrial systems and determining their malfunctions. The RTD signal may be subject to different sorts of noise. This leads to errors in the RTD calculations, and hence leads to wrong analysis in the determination of system malfunctions. This paper presents a proposed approach for RTD signal identification based on power density spectrum (PDS). The cepstral features are extracted from the signal or/and its PDS. The PDS is estimated using nonparametric, parametric, and eigen-analysis methods. The identification results are analyzed and compared for different estimation methods in order to select the best PDS estimation method for RTD signal identification. Neural networks are used for training and testing in the proposed approach. The proposed approach is tested using RTD signals obtained from the measurements carried out with radiotracer technique. The experimental results show that the proposed approach with features extracted from the PDS of the RTD signals calculated using eigen-analysis methods is the most robust and reliable in RTD signal identification.

PMD Design for High-Speed WDM Backbone Network Systems Based on Field PMD Measurements

We propose a polarization mode dispersion (PMD) design for high-speed wavelength-division multiplexing (WDM) backbone network systems based on field PMD measurements on installed optical fibers for long-term commercial use. Implementing a high-speed network system on an installed fiber requires measuring PMD, because the PMD characteristics of most installed fibers are unknown. For enhanced practicality, we must be able to precisely evaluate PMD characteristics precisely with just one measurement. To understand the statistical properties of measured PMD values, we use the Jones Matrix Eigenanalysis (JME) method to conduct long-term (12 months) PMD measurements on installed fibers. We statistically analyze the measurement results and confirm that the measured values match the theory that considers the accuracy of the measurement instrument. This enables a PMD design of desired outage probability based on PMD measurements of installed fibers. We also carry out a 43-Gb/s return-to-zero differential quadrature phase shift keying (RZ-DQPSK) signal transmission with high PMD fibers in order to confirm the effectiveness of our PMD design. The PMD values of the in-line amplifier transmission line are settled so as to meet the worst value of the design. We confirm that 43-Gb/s RZ-DQPSK signals are stably transmitted at the design value.

A restricted selection index method based on eigenanalysis

Selection indices, used in animal and plant breeding to select the best individuals for the next breeding cycle, are based on phenotypic observations of traits recorded in candidate individuals. The restrictive selection index (RSI) facilitates maximizing the genetic progress of some characters, while leaving others unchanged. Recently a selection index (SI) was proposed based on the eigen analysis method (ESIM), in which the first eigenvector (from the largest eigenvalue) is used as the SI criterion, and its elements determine the proportion of the trait that contributes to the SI. However, the current ESIM, which has two main limitations, is based on the assumption that the vector of coefficients of the index is equal to the genotypic variance-covariance matrix among the traits multiplied by the vector of economic weights, and does not allow one to restrict the number of traits. In this study, we develop a more general ESIM that has two main features, namely, it makes no assumption concerning the coefficients of the index and it can be generalized to a restrictive ESIM (RESIM). We use two datasets to illustrate the theoretical results and practical use of ESIM and RESIM, and to compare them with standard unrestrictive and restrictive selection indices. The main advantages of RESIM over traditional unrestrictive and restrictive SIs are that its statistical sampling properties are known; its selection responses are equal to or greater than those estimated from the traditional restrictive SI; and it does not require economic weights and thus can be used in practical applications when all or some of the traits need to be improved simultaneously (traditional SIs cannot improve several traits simultaneously if economic weights are not available). Finally, we prove that the coefficients of the traditional RSI belong to the space generated by the eigenvectors of RESIM.

Exploring Co-Occurence Between Speech and Body Movement for Audio-Guided Video Localization

This paper presents a bottom-up approach that combines audio and video to simultaneously locate individual speakers in the video (2D source localization) and segment their speech (speaker diarization), in meetings recorded by a single stationary camera and a single microphone. The novelty lies in using motion information from the entire body rather than just the face to perform these tasks, which permits processing nonfrontal views, unlike previous work. Since body movements do not exhibit instantaneous signal-level synchrony with speech, the approach targets long term co-occurrences between audio and video subspaces. First, temporal clustering of the audio produces a large number of intermediate clusters, each containing speech from only a single speaker. Then, spatial clustering is performed in the video frames of each cluster by a novel eigen-analysis method to find the region of dominant motion. This region is associated with the speech assuming that a speaker exhibits more movement than the listeners. Thus, partial diarization and localization is obtained from the intermediate clusters. Speech from an intermediate cluster is modeled by a mixture of Gaussians and the speaker's location is represented by an eigen-blob model. In the ensuing iterative clustering stage, the diarization and localization results are progressively refined by merging the closest pair of clusters and updating the models until a stop criterion is met. Ideally, each final cluster contains all the speech from a single speaker and the corresponding eigen-blob model localizes the speaker in the image. Experiments conducted on 21 h of real data indicate that the proposed localization approach leads to a relative improvement of 40% over mutual information-based localization and that speaker diarization improves by 16% by incorporating visual information. The proposed approach does not require training and does not rely on a priori hand/face/person detection.