Karhunen-Loeve Representation of Periodic Second-Order Autoregressive Processes

نویسندگان

  • Didier Lucor
  • Chau-Hsing Su
  • George E. Karniadakis
چکیده

In dynamic data driven applications modeling accurately the uncertainty of various inputs is a key step of the process. In this paper, we first review the basics of the Karhunen-Loève decomposition as a means for representing stochastic inputs. Then, we derive explicit expressions of one-dimensional covariance kernels associated with periodic spatial second-order autoregressive processes. We also construct numerically those kernels by employing the Karhunen-Loève expansion and making use of Fourier representation in order to solve efficiently the associated eigenvalue problem. Convergence and accuracy of the numerical procedure are checked by comparing the covariance kernels obtained from the Karhunen-Loève expansions against theoretical solutions.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Comparison between Karhunen–Loeve and wavelet expansions for simulation of Gaussian processes

The series representation consisting of eigenfunctions as the orthogonal basis is called the Karhunen–Loeve expansion. This paper demonstrates that the determination of eigensolutions using a wavelet-Galerkin scheme for Karhunen–Loeve expansion is computationally equivalent to using wavelet directly for stochastic expansion and simulating the correlated random coefficients using eigen decomposi...

متن کامل

Karhunen–Loeve expansions for the detrended Brownian motion

The detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the subspace spanned by linear functions. Karhunen–Loeve expansion for the process is obtained, together with the explicit formula for the Laplace transform of the squared L 2 norm. Distribution identities are established in connection with the second order Brownian bridge dev...

متن کامل

Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes

A random process can be represented as a series expansion involving a complete set of deterministic functions with corresponding random coe<cients. Karhunen–Loeve (K–L) series expansion is based on the eigen-decomposition of the covariance function. Its applicability as a simulation tool for both stationary and non-stationary Gaussian random processes is examined numerically in this paper. The ...

متن کامل

استفاده از تبدیل karhunen-Loeve در پردازش داده ها ی لرزه ای سه بعدی

رکوردهای حاصل از برداشت لرزه ای بازتابی معمولا دارای نوفه های لرزه ای همدوستی1هستند که توسط چشمه انرژی لرزه ای تولید می شوند. امواج هوا2 و امواج سطحی3 از جمله این نوفه ها می باشند.حذف نوفه های لرزه ای همدوس از رکوردهای لرزه ای بازتابی بعنوان یکی از مراحل مهم پردازش بشمار می آید. در مطالعات لرزه نگاری سه بعدی که در مقیاس پروژه های مهندسی برداشت می شوند (engineering Scale 3-D Seismic Surveys) ...

متن کامل

Model Reduction, Centering, and the Karhunen-Loeve Expansion

We propose a new computationally efficient modeling method that captures existing translation symmetry in a system. To obtain a low order approximate system of ODEs prior to performing Karhunen Loeve expansion we process the available data set using a “centering” procedure. This approach has been shown to be efficient in nonlinear scalar wave equations.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004