Model Reduction via the Karhunen - Loeve Expansion Part II : Some Elementary Examples

Model Reduction via the

In Part II of this paper we present some elementary examples of distributed parameter system model reduction using the techniques described in Part I. In particular, we focus on using the Karhunen-Loeve expansion and Galerkin's method to formulated reduced order models for a heat diiusion system and temperature eld dynamics in a Rapid Thermal Chemical Vapor Deposition reactor. Simulation result...

Model Reduction via the Karhunen-Loeve Expansion Part I: An Exposition

In formulating mathematical models for dynamical systems, obtaining a high degree of qualitative correctness (i.e. predictive capability) may not be the only objective. The model must be useful for its intended application, and models of reduced complexity are attractive in many cases. In Part I of this paper we provide an exposition of some techniques that are useful in finding models of reduc...

Model Reduction via the Karhunen-Loeve Expansion: An Exposition

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.

Stochastic analysis of saturated–unsaturated flow in heterogeneous media by combining Karhunen-Loeve expansion and perturbation method

In this study, a stochastic model for transient saturated–unsaturated flow is developed based on the Karhunen-Loeve expansion of the input random soil properties combined with a perturbation method. The log-transformed saturated hydraulic conductivity f ðxÞ and the soil pore size distribution parameter aðxÞ are assumed to be normal random functions with known covariances. We decompose f ðxÞ and...