Identification of Distributed Parameter Systems Using Finite Differences

A method is presented to identify partial differential equations and associated boundary conditions of a distributed parameter system. The method is applicable to linear, nonlinear, and time-varying systems. The technique requires that the form of the differential equation and boundary conditions be known up to a set of constant parameters. Finite differences are used to approximate derivatives. Identification is carried out by using normal operating data. The accuracy of the identification depends upon the approximation errors and measurement noise. Methods for decreasing approximation errors are presented.