Boundary element approach for identification of point forces of distributed parameter systems

Abstract

Abstract Recently the identification of an external force applied to distributed parameter systems has become increasingly important in relation to the analysis and control of geophysical and environmental phenomena. A boundary element approach is developed for identifying the external force applied to a number of points on the domain of a distributed parameter system, which is described by a non- homogeneous partial differential equation of parabolic (diffusion) type. Firstly, an integral equation corresponding to the given partial differential equation is derived. The solution of the integral equation at several reference points is computed by using the boundary element method, and then the locations and magnitudes of the external force are identified with the number of application points by minimizing the sum of the squares of relative errors. Numerical examples are presented to illustrate the usefulness of the proposed method.