# Model Updating Using Frequency Response Functions Based on Sherman-Morrison Formula
## 1 Introduction  
Finite element model with high accuracy plays an important role in structural dynamics design, which is the premise of dynamic response prediction, vibration control, and structural optimization [1; 2; 3]. Due to the idealization hypothesis of structural simplification, the errors of structural parameters, and the errors of finite element (FE) discretization, the FE models may not accurately reflect the dynamics performance of the structures [4; 5; 6]. With the rapid development of numerical simulation in engineering applications, model updating methods gradually revealed its importance, which makes the dynamic characteristics of the theoretical model as consistent as possible with the actual structure. As a bond between FE models and actual structures, model updating has become a powerful tool and which has been paid extensive attention [7; 8]. Many types of approaches have been developed for a variety of problems. [PERSON] et al. [9] proposed a method based on particle swarm optimization to update the FE model by using sequence niche technology, which greatly improved the reliability of finding the global minimum; [PERSON] et al. [10] proposed a new probabilistic FE model updating method based on hierarchical Bayesian modeling for identification of structural parametersunder varying environmental conditions. Taking the strain mode as the target response, [PERSON] and [PERSON] et al. [11] constructed the target function to be updated by using the strain mode frequency and modal confidence errors, the parameters were updated by using the Genetic Algorithm. Aiming at the model updating of the nonlinear structure, [PERSON] and [PERSON] et al. [12] took the instantaneous characteristics, including instantaneous frequency and instantaneous amplitude, as the objective function of the nonlinear model updating, and used the annealing global optimization method to obtain the optimal value of the nonlinear parameters. [PERSON] et al. [13] proposed a model updating method that separated the non-linear characteristics of subsystem from the parameter uncertainties to establishing a representative linear mathematical model and applied it to a structural dynamics verification problem which developed by Sandia National Laboratory. The above methods focus on the recent hot spots to carry out research, frequency response function (FRF)'s based model updating is an alternative method with some advantages, FRFs can adequately reflect the dynamic characteristics of a structure, using which as the feature will get rid of modal identification. Model updating based on FRFs avoids the error caused by modal fitting, and match of the predicted modal shapes with the measured data are not necessary, so it is suitable for structural updating with relatively dense modal distribution. [PERSON] et al. [14; 15] proposed a new structural damage detection method based on FRFs data and natural frequencies, adopted pseudo-linear sensitivity equation to accurately identify the location and severity of damage; [PERSON] et al. [16; 17] proposed an estimation method for structure mass and stiffness considering damping effect and using the FRF data for FE model updating; [PERSON] et al. [18] proposed a FE model updating method that can identify and update the damping matrix of the system, and studied the updating capability of different damping levels through three different experimental beam structures; [PERSON] et al. [19] proposed an iterative method combining model updating method with model reduction technology, effectively improved the efficiency of the updating; [PERSON] et al. [20] successfully updated the stiffness, mass and damping parameters between the analytical and the experimental FRFs through the laboratory test of the four-story shear frame structure; [PERSON] et al. [21; 22] conducted the model updating of local nonlinear structure based on the initial FE model of the structure and the primary harmonic response data obtained from low amplitude and high amplitude excitation.