# A Kriging Model Based Finite Element Model Updating Method for Damage Detection
## 1 Introduction
The least-squares method is used to determine the coefficients of the polynomial based on reasonable initial sampling [23; 24; 25; 26; 27] (using D-optimal design or central composite design). A small number of sampling points can be effectively used to predict the response of the structure under different parameters. In addition, [PERSON] and [PERSON] [28] used the moving least-squares method to solve the coefficients of the response surface polynomial in order to increase the influence of the sampling points near the prediction point on its prediction value. [PERSON] and [PERSON] [29] combined the response surface method with differential evolution algorithm for effective parameter identification. [PERSON] et al. [30] compared the effects of constructing response surfaces using different radial basis functions to update a large span cable-stayed bridge. Furthermore, as a special response surface construction method similar to the Gaussian basis function [31], the Kriging model has received more and more attention in recent years [32], [PERSON], et al. [33] used the Kriging model to establish the relationship between the positional parameters of two beams and the frequency of the whole structure, for fast interval model updating to define the uncertain range of the parameters. [PERSON] et al. [34] proposed a 2-level model updating method based on Kriging predictor for large complex structures. [PERSON], [PERSON] and [PERSON] [17] introduced the Kriging model into an acceleration frequency response function-based model updating method, which is performed successfully on a honeycomb sandwich beam. [PERSON] and [PERSON] [35] proposed a sequential surrogate modeling method. On the basis of a certain amount of initial sampling points, this method constructs response surfaces for different responses respectively through a specific adding point criterion. Most of the methods mentioned above have chosen the frequency as the output response of the surrogate model. This is mainly because the response surface of a frequency has a relatively gentle shape with respect to different system parameters. Particularly when a polynomial is used as the mathematical construct of a surrogate model, the frequency is not sensitive to the cross terms of the polynomial. So an accurate response surface can be built from a small number of sample points. On the other hand, the frequency response function (FRF) can provide more structural vibration information than the frequency and its use as response in surrogate modeling is worth investigating, which has rarely been attempted. Therefore, in this paper, a Kriging model with good simulation effect of nonlinear response surface is constructed to establish the relationship between the updating parameters and the residual of the Frequency Domain Assurance Criterion (FDAC) value, and a model updating method is used on the Kriging model for damage identification. The efficient global optimization (EGO) algorithm is introduced to realize fast convergence of the updating procedure. The proposed method is applied to a simulated example of a cantilever beam with three weakened elements and a laboratory three-story frame structure to verify its effectiveness.