An improved generalized flexibility matrix approach for structural damage detection

Figures & data

Figure 1. The size of the cross section of the hollow beam bridge.

Figure 2. The simplified plane beam.

Table 1. Damage cases in Example 1.

Damage case		Damaged element(s)	Damage extent
Case 1	Single damage	Element 4	15%
Case 2	Double damage	Element 4	15%
		Element 9	10%
Case 3	Triple damage	Element 4	15%
		Element 9	10%
		Element 16	20%
Case 4	Multiple damage	Elements 4, 20	15%
		Element 9	10%
		Element 16	20%

Figure 3. Calculated results for all damage cases in Table 1: (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4.

Figure 4. Mode shape curvatures for all damage cases in Table 1: (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4.

Figure 5. Calculated results for all damage cases in Table 1 with three level noises: (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4.

Figure 6. A three-span beam structure.

Table 2. Damage cases in Example 2.

Damage case		Damaged elements	Damage extent
Case 1	Double damage	Element 4	15%
		Element 6	20%
Case 2	Triple damage	Element 4	15%
		Element 6	20%
		Element 12	10%
Case 3	Multiple damage	Elements 4, 15	15%
		Element 6	20%
		Element 12	10%
Case 4	Multiple damage	Elements 4, 15	15%
		Elements 6, 18	20%
		Element 12	10%

Figure 7. Calculated results for four damage cases in Table 2: (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4.

Figure 8. Mode shape curvatures for all damage cases in Table 1: (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4.

Figure 9. Calculated results for four damage cases in Table 2 with three level noises: (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4.