**4. Conclusions**

This paper presents a vibration signal analysis method based on UKF. A simulation was conducted to analyze the interaction process between the vibration and the frame structure defects. A nondestructive damage-detection algorithm based on UKF was designed in this paper. Taking the beam structure unit widely used in production as an example, the damage-identification effect of the UKF method under known excitation and unknown excitation was investigated, and the damage location and quantitative evaluation of the damage degree of the frame structure using the proposed algorithm were realized. The results show that the research method in this paper has obvious advantages in damage location and quantitative performance. Compared with the traditional Kalman filter method, the biggest advantage of the UKF method is that it does not need to calculate the Jacobi matrix, and the calculation amount is equivalent to that of EKF, but its accuracy is obviously higher than that of EKF. Thus, the calculation workload in the process of the damage identification of the frame structure is greatly reduced and the application is much simpler. In the field of structural material damage identification, the method shows a better universality. The proposed method also significantly increases the efficiency and effectiveness, as well as the damage location accuracy of damage identification in current engineering applications. The analysis of the response signal in the structure under additional noise shows that the nondestructive testing method presented in this paper can still give reliable damage-identification results under the condition of interference, showing a characteristic of strong anti-interference and high robustness. In the follow-up study, we will comprehensively analyze the material and beam structure characteristics, and use the finite element method to study the deformation, principal stress, tensile stress and shear stress of the beam element, so as to improve the practical application effect of the identification algorithm.

**Author Contributions:** Conceptualization, X.L.; data curation, D.S. and Z.Y.; investigation, X.L.; theoretical analysis, X.L.; formal analysis, X.L., D.S. and Z.Y.; writing—original draft, X.L.; writing—review and editing, X.L, D.S.; supervision, Z.Y.; project administration, X.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the National Natural Science Foundation of China (Grant Nos. 51105066), the Natural Science Foundation of Liaoning Province, China (Grant Nos. 2019-MS-119).

**Conflicts of Interest:** The authors declare no conflict of interest.
