**1. Introduction**

With the rapid development of modern industry, nondestructive testing (NDT) technology for machinery, architecture and other structures has been rapidly developed and widely applied. However, the emergence of new materials and technologies, as well as the harsh working conditions of high temperature, high pressure and high load, have put higher requirements on the development of nondestructive testing technologies [1,2]. The effective testing of materials and structural defects is crucial to ensure the safety of materials and the reliability of structures. In the early stage of defect, crack propagation is very likely to occur in the material components under cyclic loading, which may result in the local deformation and failure of materials, introducing a huge risk of the failure of the overall system structure [3–5]. Therefore, it is of great practical significance to use nondestructive testing technology to monitor the quality of engineering structures in the early stage without invasive sampling.

Currently, traditional nondestructive testing technologies such as ultrasonic methods, thermal wave-imaging methods, ray methods and acoustic emission methods are widely used in mechanical engineering and the construction industry [6–8]. However, there are some limitations in the quantitative detection and defect expression in these methods. With nondestructive testing using vibration signal wave, its vibration response can effectively excite the vibration waves of various modes in the components being tested, such as the longitudinal wave, transverse wave and surface wave [9,10]. The reference [11] took a three-layer rack structure with six layers of storage as an example, carried out the dynamic analysis on it under horizontal and vertical loads, and completed the verification

of force distribution and sag moment under test. By analyzing the interaction mechanism between the vibration wave and the structural material defects, the location and quantitative expression of the structural defects can be achieved. Compared to the traditional nondestructive testing technology, the nondestructive testing technology based on the vibration signal makes full use of the characteristics of wave and energy response. It has strong advantages in the detection and characterization of structural defects. In addition, due to its response in a wide frequency bandwidth, high sensitivity, and high spatial resolution, it has become one of the most important tools in the field of the structural defects of the material and nondestructive testing of damage [12–14].

In recent decades, researchers have done a lot of research on nondestructive testing technologies based on vibration signal analysis and obtained many meaningful research results. Cawley and Adams [15] found that the ratio of any two-order natural frequencies would change after the damage, which was only related to the damage location and had no relevance to the degree of damage when there was only single damage or multiple damage in the same degree in the structure, based on the assumption that the damage only caused changes in stiffness. Salawu [16] pointed out that different forms of damage might cause the same change of response frequency, especially in a situation of the damage of a symmetrical position in a symmetrical structure where the frequency index creates difficulty in distinguishing the damage. Yang et al. [17] proposed a method to add mass to solve the aforementioned issue. However, this method required the addition of known mass to the structure, which essentially changes the symmetric structure into asymmetric structure. Guan et al. [18] combined strain mode with wavelet transform and applied it to the damage identification of frame structures. Gu et al. [19] proposed a working strain mode identification technology under environmental excitation, and the corresponding damage-identification method. Pandey and Biawas [20] proposed a damage-identification method based on a modal flexibility matrix and studied the impact of damage on the flexibility matrix through numerical examples. The results showed that the damage location could be accurately determined by only using the first two order modes. However, the structure of the flexibility matrix was complex, which needs further improvement for engineering applications.

This paper presents a method for the detection of the local damage position in a structure and quantitative analysis based on vibration signal analysis. A novel algorithm of the nondestructive damage identification based on the unscented Kalman filter (UKF) was designed. This paper also expands a discussion about the disadvantages of the conventional application of the extended Kalman filter (EKF) in this field, which needs to spend high computational cost to calculate the Jacobi matrix. Compared to the EKF, the algorithm presented in this paper was able to substantially reduce the computing workload in the process of the structure damage identification, and significantly broaden the scope of application of nondestructive testing methods. The proposed method can also significantly improve the recognition efficiency and effectiveness in the engineering. At the same time, the method studied in this paper can effectively avoid: (1) the problem of low accuracy caused by the limitation of modal parameters in traditional damage-identification methods; and (2) the traditional method has a large amount of calculation work, which is not conducive to online loss identification. The effectiveness of the method was demonstrated in a computational application. The results show that the damage location identification, quantitative characterization and the anti-noise performance of UKF meets the requirements for practical engineering applications.
