Simultaneous Estimation of Location and Timewise-Varying Strength of a Plane Heat Source

Abstract

An inverse analysis utilizing the conjugate gradient method of minimization and the adjoint equation is used to estimate unknown location and timewise-varying strength of a plane heat source placed inside a plate with insulated boundaries. No prior information is used for the functional form of timewise variation of the source strength. Transient temperature recordings computed at the boundaries of the region, modified by adding random errors, served as the simulated experimental data for the inverse analysis. In order to examine the accuracy of the estimation under most strict conditions, timewise variation of the source strength is chosen in the form of rectangular, triangular, and sinusoidal functions. An implicit finite difference scheme is used to solve the resulting inverse problem with a CRAY Y-MP supercomputer.