# Simulation-Based Model-Updating Method for Linear Dynamic Structural Systems
###### Abstract  
The dynamic characteristics of buildings and their behavior under various dynamic loads play a crucial role in civil engineering applications, particularly for earthquake-resistant structural design. Employing a precise mathematical model of the structural system makes it possible to accurately predict the actual structural performance under dynamic loads, such as winds and earthquakes. Given this perspective, finite element model-updating approaches in structural systems have gained significant attention in recent decades. This paper proposes a simulation-based model-updating technique that utilizes measured free vibration responses to the correct structural parameters of multi-degree-of-freedom systems. A five-degree-of-freedom building model is subjected to shaking table tests to demonstrate the effectiveness of the proposed method. The experimental data for this method consists of the dynamic behavior of the system under the seismic excitation of the El Centro 1940 earthquake and the results of the free vibration tests. The MATLAB/Simulink parameter estimation tool is employed to establish a correlation between the analytical model and the measured dynamic response from the building model. Compared to the measured structural responses, the updated analytical model, which incorporates the proposed simulation-based model-updating technique, demonstrates high accuracy in predicting the responses through effective corrections of stiffness and damping coefficients. model update; parameter estimation method; MATLAB/Simulink; structural dynamics; free vibration response +
Footnote †: journal: Applied  
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experimental measurements. [PERSON] et al. [4] proposed a novel method for identifying structural damping using experimental modal analysis data. [PERSON] et al. [5] presented a probabilistic model-updating technique to address uncertainties in measured eigenvectors and eigenfrequencies. The matrix mixing method has taken place in the literature as an alternative technique utilized in model updating [6]. This method combines experimental modal data with analytical ones by inverting mass and stiffness matrices. The error matrix method, proposed by [PERSON] and [PERSON] [7], is another model-updating technique that involves estimating the error in mass and stiffness matrices. These model-updating techniques are called direct methods and offer advantages such as lower processing time and no convergence problems. However, these computationally efficient methods raise questions about the validity of the updated system matrices. In the 1990s, iterative methods, including eigenvalue solutions and frequency response functions (FRFs), started to be utilized in model-updating studies [8]. By utilizing FRF data instead of modal data in the model-updating approach, errors that could arise from the modal analysis phase are eliminated. [PERSON] and [PERSON] [9] investigated a method to update the damping matrices of a simple three-degree-of-freedom lumped parameter system using measured FRFs. [PERSON] and [PERSON] [10] introduced an iterative FRF method, in which the difference between the measured and analytical data is expressed as a linear function of the parameters to be updated. [PERSON] and [PERSON] [11] conducted a study on an automated parameter selection procedure, addressing the challenge of choosing an appropriate set of updating parameters. The effectiveness of the proposed method is demonstrated through a simulated case study and its application to an actual engineering structure. [PERSON] and [PERSON] [12] introduced an FRF-based model-updating method that utilizes an extreme learning machine model to establish the relationship between correcting parameters and structural responses. [PERSON] and [PERSON] [13] proposed an FE model-updating technique that utilizes the Taguchi method to optimize the difference between measured and analytical vibration data. [PERSON] et al.