# Dynamic Response Analysis of Overpass Ramp Based on Grey System Theory Model
## 1 Introduction
Actual traffic conditions were simulated using the traffic micro-simulation method, and vehicle forces and masses were applied to the finite element model of the bridge using the equivalent nodal force method. An operational modal analysis (OMA) was conducted in the time domain, and modal parameters were extracted using the stochastic subspace identification method. Finally, the study achieved a satisfactory accuracy in estimating modal scaling factors while avoiding the practical difficulties encountered by the traditional mass change method in real-world applications. Grey theory effectively uncovers and summarizes internal laws and makes predictions when data and information are scarce and uncertain factors exist. The existing prediction methods for bridge deflection mainly include grey theory, neural networks, and Kalman filtering. Among them, grey theory has received widespread attention due to its simple principles and ease of implementation. Based on grey system theory, [PERSON] et al. [14] addressed the mismatch between traditional parameter estimation methods and accuracy validation criteria for the GM(1, 1) model in previous construction control applications. He transformed the parameter estimation problem under the criterion of minimizing the average relative error into a linear programming problem, implemented through Python programming. Consequently, a new theoretical model was obtained for deflection predictions. Using a bridge numbered 1 in Shaanxi Province as the engineering background, [PERSON] predicted the deflection values of the beam ends after concrete pouring and prestressing tension. Based on the relevant principles of grey system theory, [PERSON] et al. [15] and his colleagues conducted a modeling analysis using the GM(1, 1) model with mathematical-statistical methods, relying on a bridge currently in operation as the engineering backdrop. They compared and analyzed the model results with the measured data and conducted relevant tests. The results indicated that all of the GM(1, 1) model indicators met the first-level accuracy requirements. Based on grey model theory, [PERSON] [16] established a grey GM(1, 1) model to predict the changes in deflection during bridge construction and compared the predictions with actual measured values. The conclusions indicated that the grey prediction model can effectively predict the changes in deflection during construction, providing a reference for the next construction phase. [PERSON] et al. [17] applied grey system theory to establish a GM(1, 1) model using the numerical simulation results and field-measured results of deflection and stress under different working conditions during the actual construction process of a continuous rigid frame bridge as the original differential sequence. Using Matlab as the calculation tool, they developed a corresponding computational program to predict the changes in deflection and stress during cantilever construction. The results showed that the predictions agreed with the actual field test results. The above information mainly discusses load testing for straight bridges, but there are a few research projects on load testing for interchanges, including ramp bridges. The grey prediction model only requires a small amount of data--typically, only four data points are needed for the modeling and prediction--making it particularly suitable for situations where historical data are scarce or difficult to obtain. This model boasts a high prediction accuracy and simple computation and can be integrated with other prediction models (such as neural networks). This study proposes a safety prediction method for interchanges based on grey prediction and conducts experimental research on a modal analysis, displacement, and strain. According to the requirements in the specifications [18], the monitoring sections were determined, and the measuring points were reasonably arranged. The loading test scheme is introduced in detail.