# A Kriging Model Based Finite Element Model Updating Method for Damage Detection
## 1 Introduction  
Damage can occur in civil, mechanical and aerospace structures after long service or under extreme environmental events. Once accumulated to a certain extent, damage can lead to structure failure, resulting in significant loss of life and property [1]. Therefore, how to use effective damage identification methods to monitor and evaluate damage has been a popular topic in engineering. As a global damage detection methodology, finite element (FE) model updating has been widely studied and applied in recent decades [2; 3; 4]. The basic idea of it is that an FE model and the actual structure often have some deviations, and the reliability of the FE model can be improved by modifying the physical parameters of the FE model and making the response predicted by the modified FE model as close as possible to the actual structural response. The methodology was originally used as a major means of correcting a theoretical model before structural analysis and optimization, to ensure accuracy and validity of the constructed FE model. Its application in the field of damage identification is mainly to modify the parameters of the FE models through the measured response data of the initial and damaged structures, respectively. Then, the position and extent of the damage are assessed by comparing the difference between the parameters of the elements or substructures of the two updated FE models. It is a method to locate and quantify damage simultaneously. In the early research, the sensitivity based model updating method has achieved great success [5]. The principle of this method is discussed in detail by [PERSON], et al. [6] and the three most common dynamic responses used in this method are frequency, mode shape and frequency response function. Among them, the frequency and mode shape are widely studied to solve engineering problems,where usually only some degrees of freedom are measured [7]. The mode shape is mainly used as a supplement to the frequency to deal with the case of more updating parameters than with the number of measured frequencies [8; 9]. The frequency response function itself can provide enough response information and has been used in many studies of model updating [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21], but it also places high demand on the testing environment, which, to some extent, limits its application. One of the main limitations of model updating methods in engineering applications is the computational efficiency. In theory, the denser the finite element mesh is, the more accurate the prediction of the structural response is--a dense FE mesh improves the reliability of the model updating results. However, a very fine finite element mesh will result in a considerable increase in the computational time of a single theoretical model response. If the model updating procedure requires a considerable number of iterations to converge, the required computation time will be long and even become unacceptable. In this context, the surrogate model (also called the response surface method), as a quick alternative to computer experiments (FE analysis), has attracted the attention of many researchers. The core idea of the surrogate model is to replace the FE analysis model by simulating a much simplified model for the relationship between the parameters and the response. After confirming the accuracy of the surrogate model, the response of the theoretical model is calculated directly through this model in the iterative process to achieve the purpose of quick solution. At present, the surrogate model based global optimization has been extended to nonlinear optimization problems [22]. There have been many applications of surrogate models in place of the finite element models. [PERSON] and [PERSON] [23], and [PERSON] and [PERSON] [24; 25] use the response surface method for model correction and damage identification. The polynomial of a particular order is used to fit the relationship between the parameters and the responses.