Calibration of the Dynamic Model of the Concrete Bridge Railway by Genetic Programing Algorithm

In the present study, the results of two numerical finite element models prepared for the dynamic behavior of a concrete bridge in the rail transport network have been modified using the GP algorithm compared to the field data. In this research, taking into account the logical error for the data obtained from the two numerical models and field survey, in addition to modifying the results of models in the field of frequency, acceleration and displacement, the assumed values in the analyses in the error range should be corrected. The results of the GP algorithm showed the success of the algorithm in reducing errors between numerical and field results; so that the errors are limited in the range of %. The bridge studied in this paper is the Arroyo Bracea Bridge in Spain that is made of concrete beams and slabs. This is a bridge with two 15.25 m spans and a 45-degree angle with I-shaped beams crossing two railways. This bridge is modeled with two finite element methods and then is measured via a field survey to evaluate the results of the both models. Then, the difference between the results of the two numerical models and field survey is reduced by proposing the GP algorithm. This bridge is modeled by SAP2000 using orthotropic plate, isotropic plate and beams model. In both models, 6 degrees of freedom are considered for each point, and the interaction between the train and the bridge is neglected. The values of mass, modulus of elasticity, cross-sectional specifications, and degree of stiffness of the support are determined for each model. Accuracy of dynamic parameters was obtained from the studied bridge and experimental samplings are conducted from two finite element models. In addition to surveying the dynamic specifications of the soil around the bridge, in this study, the natural frequency of the bridge is obtained with analysis of modals and values of acceleration and displacement in traffic load conditions by installing the piezoelectric accelerometers at 11 points of the bridge. In this study, the soil characteristics around the bridge were also examined. First, by explaining the basics of the GP algorithm, the algorithm prepared in this article was introduced. The data on cross-sectional values, modulus of elasticity, and mass were selected as effective parameters from the initial data of the models and were randomly recorded along with field data in the error range of 1000. For having data with the same level, the values of parameters were normally distributed. Then, by implementing the algorithm proposed for the initial data of each model, a mathematical equation was presented per field data. These equations, in addition to reducing the error of the results of the model, also modify the initial data by providing correction coefficients. The proposed algorithm reduces the error data by 20.31% for acceleration on the part of the bridge deck.  Given the importance of dynamic behavior of the bridges in high-speed or heavy-load lines, the high accuracy of the results of the analyses related to this behavior is very important. However, the use of GP algorithm for calibration in analysis of bridge dynamic behavior is very restricted and there is still a possibility of development and improvement. One of the achievements of this paper is that it can be used in similar issues by providing mathematical equations, modifying initial parameters with correction coefficients, and significant reduction in error values. For further research, it is also suggested to investigate the matching factor in specific vectors in the modal analysis via this method. Determining the optimal values of the proposed algorithm parameters using the other methods and sensitivity analysis of GP algorithm compared to the changes in parameters are among the other proper suggestions for subsequent research.