3.3.2. Conditions of Damage on Column 2

When column 2 is damaged, the proposed algorithm is also used to identify *k*<sup>1</sup> ∼ *k*3, α and β. The recognition results are compared with that in Figure 5, as shown in Figure 6.

It can be seen from Figure 6 that: (1) among the stiffness parameters, only *k*<sup>1</sup> decreased considerably compared with that in the nondestructive condition. It was about 4.11 <sup>×</sup> 105 N/m without damage, while about 2.53 <sup>×</sup> 105 N/m after the damage, with a decrease rate of 38.4%. According to Table 1, when the stiffness of Column 2 decreases by 64.9% under Condition 2, the theoretical reduction of *k*<sup>1</sup> between the first layer and second layer should be 47%. There is a small difference between the identification by UKF and theoretical values, and this does not affect the location of damage. (2) The mass damping coefficient α does not have significant change, but the stiffness damping coefficient β changes significantly after the damage. This phenomenon was caused by the stiffness change of the frame structure which is reasonable. In conclusion, the damage-identification method based on UKF has achieved good performance, which can not only locate the damage position effectively, but also give an accurate damage degree estimation.

**Figure 6.** Identification of the frame's structural parameters in the case of damage on Column 2: (**a**) recognition results of *k*1, (**b**) recognition results of *k*2, (**c**) recognition results of *k*3, (**d**) recognition results of α and (**e**) recognition results of β.
