Ch. Huang et al., SHAPE IDENTIFICATION PROBLEM IN ESTIMATING GEOMETRY OF MULTIPLE CAVITIES, Journal of thermophysics and heat transfer, 12(2), 1998, pp. 270-277
A shape identification problem (or an inverse geometry heat conduction
problem) is solved to detect the unknown shape of multiple cavities b
y using the steepest descent method (SDM). One of the advantages of us
ing the SDM lies in that it easily can handle problems having a large
number of unknown parameters. The boundary element method is used to c
alculate the direct as well as the sensitivity and adjoint problems be
cause of its characteristic of easily handling the problem considered
here. Results obtained by using the SDM to solve the inverse problems
are verified based on the numerical experiments. One concludes that th
e SDM is applied successfully in estimating the arbitrary shape of cav
ities, and the rate of convergence is also very fast. Moreover, the ac
curacy of the inverse solutions depends on the positions of the sensor
s. When the sensors are arranged closer to the cavities, the estimated
results are more accurate. Finally, the effects of the measurement er
rors on the inverse solutions are discussed.