*2.1. Assumption of Nondestructive Testing Based on Vibration Signal Analysis*

After damage to the structure of an equipment, the mass, stiffness and other characteristics of the equipment may all be changed. If all of these changes are considered, it is bound to increase the complexity of the research and analysis. Therefore, it is necessary to reasonably and concisely characterize the impact of damage on the structure. In engineering structures, common damages, such as cracks, have a great impact on local stiffness, while the change of local mass is usually minimal. Therefore, it can be assumed that the damage only leads to change in the local stiffness, and the change of local mass can be ignored. This assumption can be expressed as in Equation (1);

$$\begin{cases} \begin{array}{c} \mathbf{K}\_{\mathrm{D}} \neq \mathbf{K}\_{\mathrm{U}} \\ \mathbf{M}\_{\mathrm{D}} = \mathbf{M}\_{\mathrm{U}} \end{array} \end{cases} \tag{1}$$

where, **K**<sup>D</sup> and **M**<sup>D</sup> are the local stiffness matrix and mass matrix after damage; **K**<sup>U</sup> and **M**<sup>U</sup> are the local stiffness matrix and the mass matrix before damage. The assumptions described as Equation (1) are basically in line with current engineering practice [21–24], and this can greatly simplify the difficulty of the research. According to Equation (1), a factor of local damage in a structure can be further defined with Equation (2):

$$\mathbf{K}\_{\rm D} = (1 - \mathbf{D})\mathbf{K}\_{\rm U} \tag{2}$$

where, **D** is the factor matrix of local damage, and it ranges 0 ∼ 1, where 0 means no damage and 1 means complete destruction. Formula (2) describes the reduction of local stiffness caused by the damage, which is the basis for defining and simulating damage.

Based on the above assumptions, this paper has designed a nondestructive testing algorithm as follows.
