Identification of thermal conductivity and the shape of an inclusion using the boundary elements method and the particle swarm optimization algorithm

Figures & data

Figure 1. Plane inhomogeneous body.

Figure 2. Geometric parameters and problem modelling.

Figure 3. gbest (left) and lbest sociometric pattern.

Figure 4. Plane inhomogeneous body with boundary conditions.

Figure 5. Sample of the fitness function values and percent error as function of iteration.

Table 1. Comparison of the fitness function and the actual error function.

Number of measurements	1 Node	2 Nodes	6 Nodes
f(x)	3.6 × 10^− 17	8.9 × 10^− 13	2.7 × 10^− 10
% Error	56.14%	25.43%	12.03%

Figure 6. Elliptic inclusion identification with centre point (0.5 , 0.5).

Figure 7. Elliptic inclusion identification with centre point (0.65, 0.8).

Figure 8. Pear shaped inclusion identification with centre point (0.5 , 0.5).

Figure 9. Pear shaped inclusion identification with centre point (0.65, 0.8).

Table 2. Influence of inclusion size on the estimation.

Case No.	A	B	% Area	% Error
1	6	25	23.40	18.14
2	9	36	17.46	12.03
3	16	49	11.22	11.22
4	25	64	7.86	13.41
5	36	81	4.84	15.37

Table 3. The influence experimental errors on the estimation process.

Percent error (%)	Average % error	Minimum % error	Maximum % error
1	13.74	12.18	15.67
2	15.53	11.96	18.28
3	18.10	12.18	24.18
4	19.21	16.11	22.63
5	23.26	15.85	29.91