Prediction of joint opening-closing deformation is crucial to ensure the operation safety of immersed tube tunnels. This paper proposes a novel deformation prediction model based on the framework of "decomposition-prediction-integration", which combines the Sparrow Search Algorithm (SSA), Variational Modal Decomposition (VMD), Support Vector Regression (SVR) and Gated Recurrent Unit (GRU). First, the deformation sequence is decomposed into trend, period, and residual components by VMD. In this process, a innovative evaluation index () is proposed to guide the decomposition by combining the Root Mean Square Error () and the Sample Entropy (), while the VMD is hyper-parametrically optimized by SSA under the to improve the decomposition quality. Secondly, the trend component is fitted and predicted using the Least Squares Method; the SSA-SVR model is used to establish the nonlinear response relationship between the period component and the influence factor; the GRU model optimized by SSA is applied to excavate the temporal characteristics within the residual component, which in turn achieves the prediction of the residual component. Finally, the opening-closing deformation prediction results are obtained by integrating the prediction results of each component. The application results demonstrate that the proposed model is excellent in terms of reliability and applicability, with smaller prediction errors and higher accuracy than the other six models. It provides an innovative method for joint opening-closing deformation prediction.

中文翻译：

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基于SSA优化VMD、SVR和GRU的沉管隧道联合开闭变形联合预测模型

接头开合变形的预测对于保证沉管隧道的运营安全至关重要。本文提出了一种基于“分解-预测-集成”框架的新型变形预测模型，该模型结合了麻雀搜索算法（SSA）、变分模态分解（VMD）、支持向量回归（SVR）和门控循环单元（GRU） ）。首先，通过VMD将变形序列分解为趋势分量、周期分量和残余分量。在此过程中，创新性地提出了结合均方根误差（）和样本熵（）的评价指标（）来指导分解，同时通过SSA对VMD进行超参数优化，以提高分解质量。其次，利用最小二乘法对趋势分量进行拟合和预测；利用SSA-SVR模型建立周期分量与影响因子之间的非线性响应关系；利用SSA优化的GRU模型挖掘残差分量内的时间特征，进而实现残差分量的预测。最后综合各分量的预测结果得到开闭变形预测结果。应用结果表明，该模型具有优异的可靠性和适用性，与其他6个模型相比，预测误差更小，准确度更高。它为关节开闭变形预测提供了一种创新方法。