Relevant bibliographies by topics / Karhunen-Loeve expansion

Academic literature on the topic 'Karhunen-Loeve expansion'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Contents

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Karhunen-Loeve expansion.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Karhunen-Loeve expansion"

1

Paff, W. G., and G. Ahmadi. "On the Convergence of Karhunen-Loeve Series Expansion for a Brownian Particle." Journal of Applied Mechanics 60, no. 3 (September 1, 1993): 783–84. http://dx.doi.org/10.1115/1.2900876.

Full text
Abstract:
A linear Langevin equation for the velocity of a Brownian particle is considered. The equation of motion is solved and the Karhunen-Loeve expansion for the particle velocity is derived. The mean-square velocity as obtained by the truncated Karhunen-Loeve expansion is compared with the exact solution. It is shown, as the number of terms in the series increases, the result approaches that of the exact solution asymptotically.
APA, Harvard, Vancouver, ISO, and other styles
2

BABUŠKA, IVO, and KANG-MAN LIU. "ON SOLVING STOCHASTIC INITIAL-VALUE DIFFERENTIAL EQUATIONS." Mathematical Models and Methods in Applied Sciences 13, no. 05 (May 2003): 715–45. http://dx.doi.org/10.1142/s0218202503002696.

Full text
Abstract:
This paper addresses the issues involved in solving systems of linear ODE's with stochastic coefficients and loadings described by the Karhunen–Loeve expansion. The Karhunen–Loeve expansion is used to discretize random functions into a denumerable set of uncorrelated random variables, thus providing us for transforming this problem into an equivalent deterministic one. Perturbation error estimates and a priori error estimates between the exact solution and the finite element solution in the framework of Sobolev space are given. The method of successive approximations for finite element solutions is analyzed.
APA, Harvard, Vancouver, ISO, and other styles
3

Courmontagne, Ph. "A new formulation for the Karhunen–Loeve expansion." Signal Processing 79, no. 3 (December 1999): 235–49. http://dx.doi.org/10.1016/s0165-1684(99)00099-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Jaimez, Ramón Gutiérrez, and Mariano J. Valderrama Bonnet. "On the Karhunen-Loeve expansion for transformed processes." Trabajos de Estadistica 2, no. 2 (September 1987): 81–90. http://dx.doi.org/10.1007/bf02863594.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Li, Heng. "Conditional Simulation of Flow in Heterogeneous Porous Media with the Probabilistic Collocation Method." Communications in Computational Physics 16, no. 4 (October 2014): 1010–30. http://dx.doi.org/10.4208/cicp.090513.040414a.

Full text
Abstract:
AbstractA stochastic approach to conditional simulation of flow in randomly heterogeneous media is proposed with the combination of the Karhunen-Loeve expansion and the probabilistic collocation method (PCM). The conditional log hydraulic conductivity field is represented with the Karhunen-Loeve expansion, in terms of some deterministic functions and a set of independent Gaussian random variables. The propagation of uncertainty in the flow simulations is carried out through the PCM, which relies on the efficient polynomial chaos expansion used to represent the flow responses such as the hydraulic head. With the PCM, existing flow simulators can be employed for uncertainty quantification of flow in heterogeneous porous media when direct measurements of hydraulic conductivity are taken into consideration. With illustration of several numerical examples of groundwater flow, this study reveals that the proposed approach is able to accurately quantify uncertainty of the flow responses conditioning on hydraulic conductivity data, while the computational efforts are significantly reduced in comparison to the Monte Carlo simulations.
APA, Harvard, Vancouver, ISO, and other styles
6

Phoon, K. K., S. P. Huang, and S. T. Quek. "Simulation of second-order processes using Karhunen–Loeve expansion." Computers & Structures 80, no. 12 (May 2002): 1049–60. http://dx.doi.org/10.1016/s0045-7949(02)00064-0.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Hilai, Ran, and Jacob Rubinstein. "Recognition of rotated images by invariant Karhunen–Loeve expansion." Journal of the Optical Society of America A 11, no. 5 (May 1, 1994): 1610. http://dx.doi.org/10.1364/josaa.11.001610.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Smallwood, David. "Characterization and Simulation of Gunfire with Karhunen-Loeve Expansion." Journal of the IEST 47, no. 1 (September 14, 2004): 47–50. http://dx.doi.org/10.17764/jiet.47.1.3476326r02g27247.

Full text
Abstract:
Gunfire is used as an example to illustrate how the Karhunen-Loeve (K-L) expansion can be used to characterize and simulate nonstationary random events. This paper will develop a method to describe the nonstationary random process in terms of a K-L expansion. The gunfire record is broken up into a sequence of transient waveforms, each representing the response to the firing of a single round. First, the mean is estimated and subtracted from each waveform. The mean is an estimate of the deterministic part of the gunfire. The autocovariance matrix is estimated from the matrix of these single-round gunfire records. Each column is a realization of the firing of a single round. The gunfire is characterized with the K-L expansion of the autocovariance matrix. The gunfire is simulated by generating realizations of records of a single-round firing from the expansion and the mean waveform. The individual realizations are then assembled into a realization of a time history of many rounds firing. The method is straightforward and easy to implement, and produces a simulated record very much like the original measured gunfire record.
APA, Harvard, Vancouver, ISO, and other styles
9

Ai, Xiaohui. "Karhunen–Loeve expansion for the additive detrended Brownian motion." Communications in Statistics - Theory and Methods 46, no. 16 (August 2, 2016): 8210–16. http://dx.doi.org/10.1080/03610926.2016.1177079.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Lenz, Reiner, and Mats Österberg. "Computing the Karhunen-Loeve Expansion with a Parallel, Unsupervised Filter System." Neural Computation 4, no. 3 (May 1992): 382–92. http://dx.doi.org/10.1162/neco.1992.4.3.382.

Full text
Abstract:
We use the invariance principle and the principles of maximum information extraction and maximum signal concentration to design a parallel, linear filter system that learns the Karhunen-Loeve expansion of a process from examples. In this paper we prove that the learning rule based on these principles forces the system into stable states that are pure eigenfunctions of the input process.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Karhunen-Loeve expansion"

1

Scott, Karen Mary Louise. "Practical Analysis Tools for Structures Subjected to Flow-Induced and Non-Stationary Random Loads." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/38686.

Full text
Abstract:
There is a need to investigate and improve upon existing methods to predict response of sensors due to flow-induced vibrations in a pipe flow. The aim was to develop a tool which would enable an engineer to quickly evaluate the suitability of a particular design for a certain pipe flow application, without sacrificing fidelity. The primary methods, found in guides published by the American Society of Mechanical Engineers (ASME), of simple response prediction of sensors were found to be lacking in several key areas, which prompted development of the tool described herein. A particular limitation of the existing guidelines deals with complex stochastic stationary and non-stationary modeling and required much further study, therefore providing direction for the second portion of this body of work. A tool for response prediction of fluid-induced vibrations of sensors was developed which allowed for analysis of low aspect ratio sensors. Results from the tool were compared to experimental lift and drag data, recorded for a range of flow velocities. The model was found to perform well over the majority of the velocity range showing superiority in prediction of response as compared to ASME guidelines. The tool was then applied to a design problem given by an industrial partner, showing several of their designs to be inadequate for the proposed flow regime. This immediate identification of unsuitable designs no doubt saved significant time in the product development process. Work to investigate stochastic modeling in structural dynamics was undertaken to understand the reasons for the limitations found in fluid-structure interaction models. A particular weakness, non-stationary forcing, was found to be the most lacking in terms of use in the design stage of structures. A method was developed using the Karhunen Loeve expansion as its base to close the gap between prohibitively simple (stationary only) models and those which require too much computation time. Models were developed from SDOF through continuous systems and shown to perform well at each stage. Further work is needed in this area to bring this work full circle such that the lessons learned can improve design level turbulent response calculations.
Ph. D.
APA, Harvard, Vancouver, ISO, and other styles
2

Wang, Limin. "Karhunen-Loeve expansions and their applications." Thesis, London School of Economics and Political Science (University of London), 2008. http://etheses.lse.ac.uk/2950/.

Full text
Abstract:
The Karhunen-Loeve Expansion (K-L expansion) is a bi-orthogonal stochastic process expansion. In the field of stochastic process, the Karhunen-Loeve expansion decomposes the process into a series of orthogonal functions with the random coefficients. The essential idea of the expansion is to solve the Fredholm integral equation, associated with the covariance kernel of the process, which defines a Reproducing Kernel Hilbert Space (RKHS). This either has an analytical solution or special numerical methods are needed. This thesis applies the Karhunen-Loeve expansion to some fields of statistics. The first two chapters review the theoretical background of the Karhunen-Loeve expansion and introduce the numerical methods, including the integral method and the expansion method, when the analytical solution to the expansion is unavailable. Chapter 3 applies the theory of the Karhunen-Loeve expansion to the field of the design experiment using a criteria called "maximum entropy sampling". Under such setting, a type of duality is set up between maximum entropy sampling and the D- optimal design of the classical optimal design. Chapter 4 uses the Karhunen-Loeve expansion to calculate the conditional mean and variance for a given set of observations, with application to prediction. Chapter 5 extends the theory of the Karhunen- Loeve expansion from the univariate setting to the multivariate setting: multivariate space, univariate time. Adaptations of numerical methods of Chapter 2 are also provided for the multivariate setting, with a full matrix development. Chapter 6 applies the numerical method developed in Chapter 5 to the emerging area of multivariate functional data analysis with a detailed example on a trivariate autoregressive process.
APA, Harvard, Vancouver, ISO, and other styles
3

Mulani, Sameer B. "Uncertainty Quantification in Dynamic Problems With Large Uncertainties." Diss., Virginia Tech, 2006. http://hdl.handle.net/10919/28617.

Full text
Abstract:
This dissertation investigates uncertainty quantification in dynamic problems. The Advanced Mean Value (AMV) method is used to calculate probabilistic sound power and the sensitivity of elastically supported panels with small uncertainty (coefficient of variation). Sound power calculations are done using Finite Element Method (FEM) and Boundary Element Method (BEM). The sensitivities of the sound power are calculated through direct differentiation of the FEM/BEM/AMV equations. The results are compared with Monte Carlo simulation (MCS). An improved method is developed using AMV, metamodel, and MCS. This new technique is applied to calculate sound power of a composite panel using FEM and Rayleigh Integral. The proposed methodology shows considerable improvement both in terms of accuracy and computational efficiency. In systems with large uncertainties, the above approach does not work. Two Spectral Stochastic Finite Element Method (SSFEM) algorithms are developed to solve stochastic eigenvalue problems using Polynomial chaos. Presently, the approaches are restricted to problems with real and distinct eigenvalues. In both the approaches, the system uncertainties are modeled by Wiener-Askey orthogonal polynomial functions. Galerkin projection is applied in the probability space to minimize the weighted residual of the error of the governing equation. First algorithm is based on inverse iteration method. A modification is suggested to calculate higher eigenvalues and eigenvectors. The above algorithm is applied to both discrete and continuous systems. In continuous systems, the uncertainties are modeled as Gaussian processes using Karhunen-Loeve (KL) expansion. Second algorithm is based on implicit polynomial iteration method. This algorithm is found to be more efficient when applied to discrete systems. However, the application of the algorithm to continuous systems results in ill-conditioned system matrices, which seriously limit its application. Lastly, an algorithm to find the basis random variables of KL expansion for non-Gaussian processes, is developed. The basis random variables are obtained via nonlinear transformation of marginal cumulative distribution function using standard deviation. Results are obtained for three known skewed distributions, Log-Normal, Beta, and Exponential. In all the cases, it is found that the proposed algorithm matches very well with the known solutions and can be applied to solve non-Gaussian process using SSFEM.
Ph. D.
APA, Harvard, Vancouver, ISO, and other styles
4

Rau, Christian, and rau@maths anu edu au. "Curve Estimation and Signal Discrimination in Spatial Problems." The Australian National University. School of Mathematical Sciences, 2003. http://thesis.anu.edu.au./public/adt-ANU20031215.163519.

Full text
Abstract:
In many instances arising prominently, but not exclusively, in imaging problems, it is important to condense the salient information so as to obtain a low-dimensional approximant of the data. This thesis is concerned with two basic situations which call for such a dimension reduction. The first of these is the statistical recovery of smooth edges in regression and density surfaces. The edges are understood to be contiguous curves, although they are allowed to meander almost arbitrarily through the plane, and may even split at a finite number of points to yield an edge graph. A novel locally-parametric nonparametric method is proposed which enjoys the benefit of being relatively easy to implement via a `tracking' approach. These topics are discussed in Chapters 2 and 3, with pertaining background material being given in the Appendix. In Chapter 4 we construct concomitant confidence bands for this estimator, which have asymptotically correct coverage probability. The construction can be likened to only a few existing approaches, and may thus be considered as our main contribution. ¶ Chapter 5 discusses numerical issues pertaining to the edge and confidence band estimators of Chapters 2-4. Connections are drawn to popular topics which originated in the fields of computer vision and signal processing, and which surround edge detection. These connections are exploited so as to obtain greater robustness of the likelihood estimator, such as with the presence of sharp corners. ¶ Chapter 6 addresses a dimension reduction problem for spatial data where the ultimate objective of the analysis is the discrimination of these data into one of a few pre-specified groups. In the dimension reduction step, an instrumental role is played by the recently developed methodology of functional data analysis. Relatively standar non-linear image processing techniques, as well as wavelet shrinkage, are used prior to this step. A case study for remotely-sensed navigation radar data exemplifies the methodology of Chapter 6.
APA, Harvard, Vancouver, ISO, and other styles
5

Tempone, Olariaga Raul. "Numerical Complexity Analysis of Weak Approximation of Stochastic Differential Equations." Doctoral thesis, KTH, Numerisk analys och datalogi, NADA, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3413.

Full text
Abstract:
The thesis consists of four papers on numerical complexityanalysis of weak approximation of ordinary and partialstochastic differential equations, including illustrativenumerical examples. Here by numerical complexity we mean thecomputational work needed by a numerical method to solve aproblem with a given accuracy. This notion offers a way tounderstand the efficiency of different numerical methods. The first paper develops new expansions of the weakcomputational error for Itˆo stochastic differentialequations using Malliavin calculus. These expansions have acomputable leading order term in a posteriori form, and arebased on stochastic flows and discrete dual backward problems.Beside this, these expansions lead to efficient and accuratecomputation of error estimates and give the basis for adaptivealgorithms with either deterministic or stochastic time steps.The second paper proves convergence rates of adaptivealgorithms for Itˆo stochastic differential equations. Twoalgorithms based either on stochastic or deterministic timesteps are studied. The analysis of their numerical complexitycombines the error expansions from the first paper and anextension of the convergence results for adaptive algorithmsapproximating deterministic ordinary differential equations.Both adaptive algorithms are proven to stop with an optimalnumber of time steps up to a problem independent factor definedin the algorithm. The third paper extends the techniques to theframework of Itˆo stochastic differential equations ininfinite dimensional spaces, arising in the Heath Jarrow Mortonterm structure model for financial applications in bondmarkets. Error expansions are derived to identify differenterror contributions arising from time and maturitydiscretization, as well as the classical statistical error dueto finite sampling. The last paper studies the approximation of linear ellipticstochastic partial differential equations, describing andanalyzing two numerical methods. The first method generates iidMonte Carlo approximations of the solution by sampling thecoefficients of the equation and using a standard Galerkinfinite elements variational formulation. The second method isbased on a finite dimensional Karhunen- Lo`eve approximation ofthe stochastic coefficients, turning the original stochasticproblem into a high dimensional deterministic parametricelliptic problem. Then, adeterministic Galerkin finite elementmethod, of either h or p version, approximates the stochasticpartial differential equation. The paper concludes by comparingthe numerical complexity of the Monte Carlo method with theparametric finite element method, suggesting intuitiveconditions for an optimal selection of these methods. 2000Mathematics Subject Classification. Primary 65C05, 60H10,60H35, 65C30, 65C20; Secondary 91B28, 91B70.
QC 20100825
APA, Harvard, Vancouver, ISO, and other styles
6

Lin, Tzu-Chi, and 林子期. "Data-Driven Smooth TestsBased on Karhunen-Loeve Expansion." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/28978306000835558545.

Full text
Abstract:
碩士
國立臺灣大學
經濟學研究所
97
New data-driven smooth tests are proposed in this thesis. The new tests are proposed to eschew the downward weighting problem of the traditional omnibus tests, and the new tests are constructed based on the components of Karhunen-Lo′eve expansion of limiting process. As examples, we construct tests for the null hypothesis of stationarity, coefficient stability, symmetric dynamics of quantile autoregressive model, and bivariate independence. Simulation results show that, new tests have moderate size control and nice power performance for a wide range of alternatives. In contrast to traditional omnibus tests, new tests are more robust to complex models and perform well under high-frequency alternatives.
APA, Harvard, Vancouver, ISO, and other styles
7

徐明志. "Karhunen-Loeve Expansion with Time-Frequency Analysis Technique for Signal Recognition." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/43889568165214202468.

Full text
Abstract:
碩士
國立海洋大學
電機工程學系
90
The time-frequency distribution(TFD) can accurately transform signals into two-dimensional time-frequency domain. It has extensive application in the nonstationary fields of sonar, seismology and underwater acoustic. Most of the current high resolution time-frequency methods are based on the structure of the Cohen time-frequency distribution. However, since the time-frequency distribution has the bilinear property which will produce the cross terms factor treated it as the noise. It is important to sharp the signal and reduce the cross term efficiently. In this thesis, we compare the signal resolution of different kind kernel function, and try to find a way to promote the ability of time-frequency resolution. The received signal will be analyzed with time-frequency analyzed first, and the eign vector of analysis signal will be extracted by Karhunen-Loeve expansion. The eign vector will be compared with database. The probability of recognition can reach 80 percent at SNR=10 dB.
APA, Harvard, Vancouver, ISO, and other styles
8

Zhang, Mengqiu. "Experimental guided spherical harmonics based head-related transfer function modeling." Phd thesis, 2012. http://hdl.handle.net/1885/9796.

Full text
Abstract:
In this thesis we investigate the experimental guided spherical harmonics based Head-Related Transfer Function (HRTF) modeling where HRTFs are parameterized as frequency and source location. We focus on efficiently representing the HRTF variations in sufficient detail by mathematical modeling and the experimental measurements. The goal of this work is towards an optimal functional HRTF modeling taking into account the demands of decreasing the computational cost and alleviating the HRTF interpolation and/or extrapolation in the headphone based binaural systems. To represent HRTF by models, we firstly consider the high variability of HRTFs among individuals caused by the differentiation of the scattering effects of the individual bodies on the sound waves. We conduct a series of statistical analyses on an experimental HRTF database of human subjects to reveal the correlation between the physical features of human beings, especially pinna, head, and torso, and the corresponding HRTFs. The strategy enables us to identify a minimal set of physical features which strongly influence the HRTFs in a direct physical way. We next consider the continuity of the HRTF representation in both spatial and frequency domain. We define a functional HRTF model class in which the HRTF spatial representation has been justified to be well approximated by a finite number of spherical harmonics while HRTF frequency representation remains the focus of this thesis. In order to seek an efficient representation for HRTF frequency portion, we derive a metric that is able to numerically evaluate the efficiency of different complete orthonormal bases. We show that the complex exponentials form the most efficient basis. Given the identified basis, we then provide a solution to determine the dimensionality of the representation. To represent HRTF by measurements, we firstly consider the required angular resolution and the most suitable sampling scheme taking into account the two dimensional angular direction and the wide audio frequency range. We review the spherical harmonic analysis of the HRTF from which the least required number of spatial samples for HRTF measurement is derived. Considering how the HRTF data should be sampled on the sphere, we propose a list of requirements for the determination of the HRTF measurement grid. In addition to explaining how to measure the HRTF over sphere according to the identified scheme, we propose a fast spherical harmonic transform algorithm. We next consider the feasible experimental setup for a non-anechoic situation, that is, the measurements can be made when there is some reverberation. We emphasize on the design of the test signal and the post-processing to extract HRTFs.
APA, Harvard, Vancouver, ISO, and other styles
9

Mayo, Talea Lashea. "Data assimilation for parameter estimation in coastal ocean hydrodynamics modeling." Thesis, 2013. http://hdl.handle.net/2152/23316.

Full text
Abstract:
Coastal ocean models are used for a vast array of applications. These applications include modeling tidal and coastal flows, waves, and extreme events, such as tsunamis and hurricane storm surges. Tidal and coastal flows are the primary application of this work as they play a critical role in many practical research areas such as contaminant transport, navigation through intracoastal waterways, development of coastal structures (e.g. bridges, docks, and breakwaters), commercial fishing, and planning and execution of military operations in marine environments, in addition to recreational aquatic activities. Coastal ocean models are used to determine tidal amplitudes, time intervals between low and high tide, and the extent of the ebb and flow of tidal waters, often at specific locations of interest. However, modeling tidal flows can be quite complex, as factors such as the configuration of the coastline, water depth, ocean floor topography, and hydrographic and meteorological impacts can have significant effects and must all be considered. Water levels and currents in the coastal ocean can be modeled by solv- ing the shallow water equations. The shallow water equations contain many parameters, and the accurate estimation of both tides and storm surge is dependent on the accuracy of their specification. Of particular importance are the parameters used to define the bottom stress in the domain of interest [50]. These parameters are often heterogeneous across the seabed of the domain. Their values cannot be measured directly and relevant data can be expensive and difficult to obtain. The parameter values must often be inferred and the estimates are often inaccurate, or contain a high degree of uncertainty [28]. In addition, as is the case with many numerical models, coastal ocean models have various other sources of uncertainty, including the approximate physics, numerical discretization, and uncertain boundary and initial conditions. Quantifying and reducing these uncertainties is critical to providing more reliable and robust storm surge predictions. It is also important to reduce the resulting error in the forecast of the model state as much as possible. The accuracy of coastal ocean models can be improved using data assimilation methods. In general, statistical data assimilation methods are used to estimate the state of a model given both the original model output and observed data. A major advantage of statistical data assimilation methods is that they can often be implemented non-intrusively, making them relatively straightforward to implement. They also provide estimates of the uncertainty in the predicted model state. Unfortunately, with the exception of the estimation of initial conditions, they do not contribute to the information contained in the model. The model error that results from uncertain parameters is reduced, but information about the parameters in particular remains unknown. Thus, the other commonly used approach to reducing model error is parameter estimation. Historically, model parameters such as the bottom stress terms have been estimated using variational methods. Variational methods formulate a cost functional that penalizes the difference between the modeled and observed state, and then minimize this functional over the unknown parameters. Though variational methods are an effective approach to solving inverse problems, they can be computationally intensive and difficult to code as they generally require the development of an adjoint model. They also are not formulated to estimate parameters in real time, e.g. as a hurricane approaches landfall. The goal of this research is to estimate parameters defining the bottom stress terms using statistical data assimilation methods. In this work, we use a novel approach to estimate the bottom stress terms in the shallow water equations, which we solve numerically using the Advanced Circulation (ADCIRC) model. In this model, a modified form of the 2-D shallow water equations is discretized in space by a continuous Galerkin finite element method, and in time by finite differencing. We use the Manning’s n formulation to represent the bottom stress terms in the model, and estimate various fields of Manning’s n coefficients by assimilating synthetic water elevation data using a square root Kalman filter. We estimate three types of fields defined on both an idealized inlet and a more realistic spatial domain. For the first field, a Manning’s n coefficient is given a constant value over the entire domain. For the second, we let the Manning’s n coefficient take two distinct values, letting one define the bottom stress in the deeper water of the domain and the other define the bottom stress in the shallower region. And finally, because bottom stress terms are generally spatially varying parameters, we consider the third field as a realization of a stochastic process. We represent a realization of the process using a Karhunen-Lo`ve expansion, and then seek to estimate the coefficients of the expansion. We perform several observation system simulation experiments, and find that we are able to accurately estimate the bottom stress terms in most of our test cases. Additionally, we are able to improve forecasts of the model state in every instance. The results of this study show that statistical data assimilation is a promising approach to parameter estimation.
text
APA, Harvard, Vancouver, ISO, and other styles
10

Dutta, Parikshit. "New Algorithms for Uncertainty Quantification and Nonlinear Estimation of Stochastic Dynamical Systems." Thesis, 2011. http://hdl.handle.net/1969.1/ETD-TAMU-2011-08-9951.

Full text
Abstract:
Recently there has been growing interest to characterize and reduce uncertainty in stochastic dynamical systems. This drive arises out of need to manage uncertainty in complex, high dimensional physical systems. Traditional techniques of uncertainty quantification (UQ) use local linearization of dynamics and assumes Gaussian probability evolution. But several difficulties arise when these UQ models are applied to real world problems, which, generally are nonlinear in nature. Hence, to improve performance, robust algorithms, which can work efficiently in a nonlinear non-Gaussian setting are desired. The main focus of this dissertation is to develop UQ algorithms for nonlinear systems, where uncertainty evolves in a non-Gaussian manner. The algorithms developed are then applied to state estimation of real-world systems. The first part of the dissertation focuses on using polynomial chaos (PC) for uncertainty propagation, and then achieving the estimation task by the use of higher order moment updates and Bayes rule. The second part mainly deals with Frobenius-Perron (FP) operator theory, how it can be used to propagate uncertainty in dynamical systems, and then using it to estimate states by the use of Bayesian update. Finally, a method to represent the process noise in a stochastic dynamical system using a nite term Karhunen-Loeve (KL) expansion is proposed. The uncertainty in the resulting approximated system is propagated using FP operator. The performance of the PC based estimation algorithms were compared with extended Kalman filter (EKF) and unscented Kalman filter (UKF), and the FP operator based techniques were compared with particle filters, when applied to a duffing oscillator system and hypersonic reentry of a vehicle in the atmosphere of Mars. It was found that the accuracy of the PC based estimators is higher than EKF or UKF and the FP operator based estimators were computationally superior to the particle filtering algorithms.
APA, Harvard, Vancouver, ISO, and other styles

Books on the topic "Karhunen-Loeve expansion"

1

Benesty, Jacob, Jingdong Chen, and Yiteng Huang. Speech Enhancement in the Karhunen-Loeve Expansion Domain. Springer International Publishing AG, 2011.

Find full text
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Karhunen-Loeve expansion"

1

Levy, Bernard C. "Karhunen Loeve Expansion of Gaussian Processes." In Principles of Signal Detection and Parameter Estimation, 1–47. Boston, MA: Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-76544-0_7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Huang, S. P., K. K. Phoon, and S. T. Quek. "Karhunen-Loeve Expansion for Simulation of Non-Stationary Gaussian Processes Using the Wavelet-Galerkin Approach." In Computational Mechanics–New Frontiers for the New Millennium, 59–64. Elsevier, 2001. http://dx.doi.org/10.1016/b978-0-08-043981-5.50014-6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Grenander, Ulf, and Michael I. Miller. "Second Order and Gaussian Fields." In Pattern Theory. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198505709.003.0010.

Full text
Abstract:
This chapter studies second order and Gaussian fields on the background spaces which are the continuum limits of the finite graphs. For this random processes in Hilbert spaces are examined. Orthogonal expansions such as Karhunen–Loeve are examined, with spectral representations of the processes established. Gaussian processes induced by differential operators representing physical processes in the world are studied.
APA, Harvard, Vancouver, ISO, and other styles
4

Balossino, Nello, and Davide Cavagnino. "Approximation of bidimensional karhunen loeve expansions by means of monodimensional karhunen loeve expansions, applied to image compression." In Proceedings IWISP '96, 205–8. Elsevier, 1996. http://dx.doi.org/10.1016/b978-044482587-2/50045-8.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Karhunen-Loeve expansion"

1

Mulani, Sameer, Rakesh Kapania, and Robert Walters. "Karhunen-Loeve Expansion of Non-Gaussian Random Process." In 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-1943.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

So, W. S., and A. O. Steinhardt. "Adaptive subspace nulling based on Karhunen-Loeve expansion." In [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing. IEEE, 1992. http://dx.doi.org/10.1109/icassp.1992.226228.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Sun, G., C. W. Thomas, J. Liebman, D. Stilli, and E. Macchi. "BSPM spatial data reduction by normalized Karhunen-Loeve expansion." In Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, 1988. http://dx.doi.org/10.1109/iembs.1988.94437.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Kozek, W. "Optimally Karhunen-Loeve-like STFT expansion of nonstationary processes." In Proceedings of ICASSP '93. IEEE, 1993. http://dx.doi.org/10.1109/icassp.1993.319686.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Chang, Ming-Xian, and Ren-Shian Chen. "The Karhunen-Loeve Expansion of 1D and 2D OFDM Channel Responses." In 2011 IEEE Vehicular Technology Conference (VTC Fall). IEEE, 2011. http://dx.doi.org/10.1109/vetecf.2011.6093037.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

QU, YANYUN, NANNING ZHENG, and CUIHUA LI. "USING WAVELET TRANSFORM TO ESTIMATE THE EIGENFUNCTIONS OF KARHUNEN-LOEVE EXPANSION." In Proceedings of the International Computer Congress 2004. World Scientific Publishing Company, 2004. http://dx.doi.org/10.1142/9789812702654_0005.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Wang, Zhiqian, Raghunath K. Rao, Dibyendu Nandy, Jezekiel Ben-Arie, and Nebosja Jojic. "Generalized feature detection using the Karhunen-Loeve transform and expansion matching." In Visual Communications and Image Processing '96, edited by Rashid Ansari and Mark J. T. Smith. SPIE, 1996. http://dx.doi.org/10.1117/12.233257.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Balasubramanian, M., S. S. Iyengar, P. Wolenski, J. Reynaud, and R. W. Beuerman. "Adaptive noise filtering of white-light confocal microscope images using Karhunen-Loeve expansion." In Optics & Photonics 2005, edited by Andrew G. Tescher. SPIE, 2005. http://dx.doi.org/10.1117/12.615252.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Páta, Petr. "Properties of Karhunen-Loeve Expansion of astronomical images in comparison with other integral transforms." In The fifth huntsville gamma-ray burst symposium. AIP, 2000. http://dx.doi.org/10.1063/1.1361660.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Vladimirov, Igor G., Ian R. Petersen, and Matthew R. James. "A Quantum Karhunen-Loeve Expansion and Quadratic-Exponential Functionals for Linear Quantum Stochastic Systems∗." In 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE, 2019. http://dx.doi.org/10.1109/cdc40024.2019.9029437.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Reports on the topic "Karhunen-Loeve expansion"

1

Aadithya, Karthik, Eric Keiter, and Ting Mei. The Karhunen Loeve Expansion. Office of Scientific and Technical Information (OSTI), March 2019. http://dx.doi.org/10.2172/1761975.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Chen, Yi, Dongbin Xiu, John Davis Jakeman, and Claude Gittelson. Dimension reduction for PDE using local Karhunen Loeve expansions. Office of Scientific and Technical Information (OSTI), September 2015. http://dx.doi.org/10.2172/1221524.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Karhunen-Loeve expansion' for particular source types:
Journal articles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography