An iterative filter for solution of the inverse heat-conduction problem

Comparative application of CGM and Wiener filtering techniques for the estimation of heat flux distribution

“…However, because the experimental temperature data are inevitably affected by uncertainties, the stopping criterion can be defined by adopting the approach called the discrepancy principle, originally formulated by Morozov [39] and later on implemented for filtering technique and applied by many authors [5,40,41]. According to this principle, the inverse problem solution is regarded to be sufficiently accurate when the difference between the estimated and measured temperatures is close to the standard deviation of the measurements.…”

State Estimation Problems in Heat Transfer

“…International Journal for Uncertainty Quantification ∂T ∂y = 0 at y = and y = L, for t > 0 (19) T = T 0 for t = 0, at 0 < x < L and 0 < y < L (20) where C and k are the volumetric heat capacity and thermal conductivity of the plate material, respectively, h is the heat transfer coefficient at the surface of the plate, L and e are the width and thickness of the plate, respectively, and g(x, y, t) is the sought volumetric heat source term. We assume that transient temperature measurements are available at several positions (x, y) at the plate surface.…”

“…In this paper, we present the application of the Kalman filter and of two different algorithms of the Particle filter, namely the sampling importance resampling and auxiliary sampling importance resampling [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], to state estimation problems in heat transfer [19][20][21][22][23][24][25][26][27][28][29][30]. Before focusing on the applications of interest, the state estimation problem is defined and the Kalman and particle filters are described.…”

Hybrid modeling of direct and inverse problems of heat conduction

“…This information (even though inaccurate, nevertheless relatively reliable) can be obtained by modeling on analog devices (HCS based on AP), and the temperatures in zones directly affecting the identification of the boundary conditions will be refined by the digital processor. When the problem is thus stated, the matrices and vectors contained in the falter are of much lower order, and this ~so obviates the stringent requirements that the memory and the speed of the digital computer have to fulfill; the use of the iteration modification of the filter [ 16] makes it possible substantially to increase the accuracy of the solution. NOTATION T, temperature; X, thermal conductivity; c, specific heat; p, density; t, time; x, y, z, Cartesian coordinates; q, heat flux; ~, heat-transfer coefficient; a, thermal diffusivity; R, electrical resistance.…”