Simultaneous identification of the external input and parameters of diffusion type distributed parameter systems

Abstract

A simultaneous identification method is proposed for an unknown diffusion constant and an unknown external input of a distributed parameter system governed by a non-homogeneous partial differential equation of parabolic (diffusion) type. The mathematical formulation of the identification problem is presented using the weighted residual expression and the boundary element partition, both of which are fundamental to the boundary element method. The unknowns of the distributed parameter systems are identified from the noisy or noise-free state observations taken at the points on the boundary by minimizing a certain criterion function based on the above mathematical formulation. Numerical examples illustrate the usefulness of the proposed identification method.

Simultaneous identification of multi-irregular interfacial boundary configurations in non-homogeneous body using surface displacement measurements

“…where N 1 is the number of nodes on the outer boundary of 1 , N 2 is the number of nodes on the outer boundary of 2 , N 3 is the number of nodes on the outer boundary of 3 , N 4 is the number of nodes on interfacial boundary À 1,2 I and N 5 is the number of nodes on interfacial boundary À 2,3 I . Equation 13is rearranged by passing all unknowns to a vector X on the left-hand side.…”

“…Inverse application of the boundary elements method (BEM) to identify internal flaws, cavities, cracks and inclusions inside solid bodies dates back to late 1980s. 1–7 Similar methodology has also been used in the cases of shape estimation problems, to estimate the shape of cavities and inclusions inside solid bodies. 8–17…”

“…Inverse application of the boundary elements method (BEM) to identify internal flaws, cavities, cracks and inclusions inside solid bodies dates back to late 1980s. [1][2][3][4][5][6][7] Similar methodology has also been used in the cases of shape estimation problems, to estimate the shape of cavities and inclusions inside solid bodies. [8][9][10][11][12][13][14][15][16][17] Identification of one irregular interface boundary between two homogenous, isotropic bodies was first reported by Huang and Chao.…”

Inclusion Identification by Inverse Application of Boundary Element Method, Genetic Algorithm and Conjugate Gradient Method

“…Among these are (1) what effect will the inevitable errors in experimental measurements have on the ability to estimate the sought parameters and (2) what is the influence of the inclusion size on the estimation process?…”

“…Estimation of the shape of an inclusion in two-dimensional region using impedance measured at the domain surface [1] , estimation of the diffusion constant of a homogeneous body as well as unknown internal heat sources utilizing surface temperature measurements [2] , estimation of the optimal sizes and locations of coolant flow passages for a userspecified steady distribution of surface temperatures and fluxes [3] , investigation of a spatially regularized solution of inverse elasticity problem using the BEM [4] , estimation of thermal and mechanical properties along with location and size of a circular inclusion [5] , nondestructive detection of cavities by an inverse elastostatics BEM [6] , damage detection and assessment of structures from static responses [7] , estimation of the geometric and material properties of an inclusion using BEM and implementation of regularization function [8] , Local optimization techniques in inverse elasticity problems using BEM [9] , estimation of geometric shape of an irregular boundary between a numbers of solid elastic bodies using surface temperatures [10] , are among some of the investigations done in this field.…”