Structural damage detection using improved particle swarm optimization

This work was done in Sun Yat-sen University.

Figures & data

Table 1. Parameter values for DPSO.

Structure	M	a	b	ε	δ	c3
Beam	15	0.3	0.5	10^−4	10^−6	0.1
Truss
Plate	15	0.1	0.9	10^−4	10^−6	0.1

Figure 1. A simply supported beam and its cross section.

Figure 2. Damage detection results of beam case 1 without noise.

Figure 3. Damage detection results of beam case 1 with noise.

Table 2. Identified values of damaged elements and relative errors of different structures with noise.

Case	Element number	GA	PSO	DG	DI
Beam case 1	1	0.513 (2.6%)*	0.384 (23.1%)	0.489 (2.1%)	0.489 (2.0%)
	9	0.871 (0.4%)	0.878 (0.4%)	0.873 (0.3%)	0.873 (0.3%)
Beam case 2	2	0.0800 (2.2%)	0.0187 (9.0%)	0.115 (1.7%)	0.113 (1.5%)
	9	0.0675 (3.6%)	0.137 (4.1%)	0.144 (4.9%)	0.142 (4.6%)
	16	0.091 (6.6%)	0.115 (3.9%)	0.184 (3.7%)	0.181 (3.4%)
Truss	2	0.288 (1.7%)	0.109 (27.2%)	0.296 (0.6%)	0.297 (0.3%)
	10	0.320 (13.4%)	0.173 (37.8%)	0.401 (0.2%)	0.402 (0.3%)
	17	0.144 (7.0%)	0.0716 (16.0%)	0.180 (2.4%)	0.179 (2.7%)
	18	0.244 (0.8%)	0.0902 (21.3%)	0.240 (1.3%)	0.233 (2.2%)
	23	0.369 (2.9%)	0.276 (11.4%)	0.373 (3.6%)	0.369 (3.0%)
	28	0.209 (2.8%)	0.201 (3.8%)	0.230 (0.05%)	0.234 (0.5%)

* a (b%) denotes identified result (relative error).

Figure 4. Evolutionary processes of fitness values of beam case 1 without noise.

Figure 5. Damage detection results of beam case 2 without noise.

Figure 6. Damage detection results of beam case 2 with noise.

Figure 7. Evolutionary processes of damaged elements of beam case 2 without noise.

Figure 8. Evolutionary processes of fitness values of beam case 2 without noise.

Figure 9. A 31-bar truss structure.

Figure 10. Damage identification of the truss without noise.

Figure 11. Damage identification of the truss case with noise.

Figure 12. Evolutionary processes of DG-PSO without noise.

Figure 13. Evolutionary process of DI-PSO without noise.

Figure 14. Evolutionary processes of fitness values from DG-PSO and DI-PSO.

Figure 15. Sketch of a four-edge simply supported plate ((1), (2), …, (63) denote node number of the FEM; 1, 2, … , 48 denote element number) (Dimensions not scaled).

Figure 16. Damage detection results of DPSO in plate.

Figure 17. Evolutionary process of damage indices in plate case.