Key Takeaways & Executive Findings
- •• The proposed RIME-VMD-BiLSTM surrogate model achieves rapid and accurate prediction of nonlinear seismic responses in vehicle-track-bridge systems, outperforming standard LSTM and BiLSTM models. • Integration of VMD and RIME optimization significantly enhances prediction accuracy and robustness, demonstrating excellent transferability across varying conditions. • Vehicle speed, bridge damping, and seismic intensity notably affect the seismic response, but have minimal impact on the surrogate model's predictive performance. • The model provides a computationally efficient alternative to traditional finite element methods, enabling rapid seismic damage assessment and vehicle safety analysis for high-speed railway bridges.
Abstract
This paper proposed a RIME-VMD-BiLSTM surrogate model to rapidly and precisely predict the seismic response of a nonlinear vehicle-track-bridge (VTB) system. The surrogate model employs the RIME algorithm to optimize the variational mode decomposition (VMD) parameters (k and α) and the architecture and hyperparameter of the bidirectional long- and short-term memory network (BiLSTM). After comparing different combinations and optimization algorithms, the surrogate model was trained and used to analyze a typical 9-span 32-m high-speed railway simply supported bridge system. A series of numerical examples considering the vehicle speed, bridge damping, seismic intensity, and training strategy on the prediction effect of the surrogate model were conducted on the extended OpenSees platform. The results show that the BiLSTM model performed better than the LSTM model, whereas the prediction effects of the single-LSTM and BiLSTM models were relatively poor. With the introduction of the VMD and RIME optimization techniques, the prediction effect of the proposed RIME-VMD-BiLSTM model was excellent. The abovementioned factors had a significant influence on the seismic response of a VTB system but little impact on the prediction effect of the surrogate model. The proposed surrogate model exhibits notable transferability and robustness for predicting the VTB’s nonlinear seismic response.
1. Introduction
China lies at the junction of the circum-Pacific and Eurasian seismic belts, featuring frequent and widely dispersed seismic activities. This inevitably affects high-speed trains running on bridges during and after earthquakes [1]. The current development focus of China’s high-speed railway (HSR) is gradually shifting from large-scale construction to operation and maintenance. Bridges, as vital transportation components of railway systems, play a pivotal role in ensuring the safety of a country’s socioeconomic development [2]. Therefore, it is imperative to develop rapid and precise seismic response prediction techniques to facilitate structural seismic damage assessment and vehicle safety analysis, thereby enabling the expeditious implementation of rescue operations and the mitigation of immeasurable loss of life and property.
Currently, the prevailing research approach for the prediction of the seismic response of vehicle-track-bridge (VTB) systems is based on massive finite element calculations [3, 4]. However, the finite element method requires repeated dynamic response analyses and even remodeling when involving seismic damage prediction, bridge susceptibility assessment, reliability, and nonlinear model correction. These efforts usually take hours or even days and consume a large amount of computing resources. The low computational efficiency of this method presents a significant challenge in meeting the demands of rapid assessment. Consequently, it is urgent to develop efficient and accurate simulation strategies.
In recent years, the rapid development of a surrogate model has prompted many scholars to combine it with the finite element technique to establish an approximate mapping relationship between the response and loading action [5, 6]. This reduces the computational cost of the structural analysis and partially solves the issue of computational inefficiency. Many surrogate models exist, such as response surface methodology [7] and support vector machine [8]. However, these surrogate models typically only simulate linear or weak nonlinear dynamic behaviours. It is difficult to accurately simulate the dynamic behaviour of complex nonlinear systems, such as the VTB system, particularly during an earthquake.
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LIU Han-yun, WANG Zi-yi, HAN Yan, ZHOU Na-ya, MAO Jian-feng, JIANG Li-zhong (2025). RIME-VMD-BiLSTM: A surrogate model for seismic response prediction of nonlinear vehicle-track-bridge system. Journal of Central South University. https://doi.org/10.1007/s11771-025-6079-z
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Frequently Asked Questions
What is the RIME-VMD-BiLSTM surrogate model?
It is a machine learning-based surrogate model that combines the RIME optimization algorithm, variational mode decomposition (VMD), and bidirectional long short-term memory (BiLSTM) networks to rapidly and accurately predict the seismic response of nonlinear vehicle-track-bridge systems.
How does the RIME-VMD-BiLSTM model improve prediction accuracy?
The RIME algorithm optimizes VMD parameters and BiLSTM architecture, while VMD decomposes the seismic response into intrinsic mode functions, enhancing the model's ability to capture complex nonlinear dynamics, leading to superior prediction performance compared to standard LSTM and BiLSTM models.
What are the key findings of the study?
The proposed model outperforms single LSTM and BiLSTM models, and the integration of VMD and RIME optimization significantly improves prediction accuracy. Factors like vehicle speed and seismic intensity affect the seismic response but have minimal impact on the surrogate model's predictive performance, demonstrating its robustness and transferability.
What is the significance of this research for high-speed railway engineering?
The surrogate model offers a computationally efficient alternative to traditional finite element methods, enabling rapid seismic damage assessment and vehicle safety analysis for high-speed railway bridges, which is crucial for timely rescue operations and mitigation of losses during earthquakes.
Where was the study published and who are the authors?
The study was published in the Journal of Central South University, 2025, Volume 32, Issue 10, pages 4073-4091. The authors are LIU Han-yun, WANG Zi-yi, HAN Yan, ZHOU Na-ya, MAO Jian-feng, and JIANG Li-zhong.
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