The use of the Karhunen-Loève decomposition for the modeling of distributed parameter systems

Abstract

The Karhunen-Loève decomposition is used to obtain low-dimensional dynamic models of distributed parameter systems. The Karhunen-Loève decomposition is a technique of obtaining empirical eigenfunctions from experimental or numerical data of a system. These empirical eigenfunctions are optimal in the sense that the degree of freedom of the lumped parameter system is minimum when obtained from a distributed parameter system by means of a Galerkin procedure employing these empirical eigenfunctions as a basis set. This technique can easily treat nonlinear distributed parameter systems defined on irregular domains to yield lumped parameter systems with a small degree of freedom, which could not be lumped by means of conventional techniques such as traditional Galerkin methods or orthogonal collocation methods. The result of the present paper can be used in the control or parameter estimation of nonlinear distributed parameter systems defined on irregular domains, which are the cases with many practical engineering systems.