E. Videcoq et D. Petit, Model reduction for the resolution of multidimensional inverse heat conduction problems, INT J HEAT, 44(10), 2001, pp. 1899-1911
For large linear heat conduction systems, it is proposed here to solve an i
nverse heat conduction problem (IHCP) that consists in the identification o
f several time-varying thermal solicitations from simulations of measured t
emperatures. For this inversion, instead of using a detailed model of large
size, this one is first transformed into a reduced model. The: latter is b
uilt with identified dominant eigenmodes of the system leading to a reduced
state representation that links the inputs (unknown solicitations) to the
outputs (simulated temperatures). The procedure is sequential and uses futu
re time steps. At first, a numerical 2D IHCP is provided: two time-varying
heat flux densities are estimated from various positions of two sensors. A
specific study on static and dynamic sensitivities is made. All example of
a 3D IHCP is also given. The method is particularly interesting in this las
t case where, at each time step, the resolution ufa system of order 9 (the
reduced model) takes the place of a system of order 1331 (the detailed mode
l). (C) 2001 Elsevier Science Ltd. All rights reserved.