The inverse solution using this inexact measurement as the simulated temperature measurements is shown in Figure 11.
By using this 1 % error, the resultant average error of the inverse solution is about 2.29 %. In order to show the estimated inverse solutions more clearly, we plot Figure 12 which is the estimated σ2(R,θ,t) obtained from Figures 10 and 11 at time t = 5 and 16, respectively,
From above numerical test cases for the present transient inverse geometry problem it is concluded that the advantages of using the CGM in estimating unknown boundary configurations are: (i) very accurate inverse solutions can be recasted when increasing the measurement errors and (ii) the number of sensor can be reduced without appreciably affecting to accuracy of the accurate inverse solutions.
VII. CONCLUSIONS
The Conjugate Gradient Method (CGM) along with the Boundary Element Method (BEM) was successfully applied for the solution of the inverse geometry problem in estimating the shape of frost growth by utilizing temperature readings. Several test cases involving different number of sensors and measurement errors were considered. The results show that the accuracy of inverse solutions obtained by CGM remain acceptable as the measurement errors are increased and the number of sensor are reduced.
ACKNOWLEDGMENT
This work was supported in part through the National Science Council, R. O. C., Grant number, NSC-87-2212-E-006-107.
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Figure 1. The system under consideration.
Figure 2. The graphical analysis of CGM from n to (n+1) iterations.
Figure 3. The exact shape of frost growth in numerical test case 1.
