一种高效高精度小样本的流固耦合代理模型
A HIGHLY EFFICIENT AND ACCURATE SURROGATE MODEL FOR FLUID-STRUCTURE INTERACTION WITH LIMITED DATA
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摘要: 针对传统流固耦合数值模拟计算效率低、建模成本高的技术瓶颈, 本文使用了一种基于本征正交分解(Proper Orthogonal Decomposition, 简称POD)与高斯过程回归(Gaussian Process, 简称GP)的数据驱动降阶模型(Reduced Order Model, 简称ROM)实现了流固耦合问题的代理仿真. 本文通过融合无网格粒子法对流固耦合问题的仿真结果, 构建了高保真流场数据集, 重点实现了高维流场特征提取与多物理场耦合响应预测两大关键问题, 建立了流固耦合ROM. 该模型基于POD方法建立流场本征模态空间, 实现数百万维流场数据的低维特征表达(维度约简率可达99.8%), 并结合GP非参数化建模框架, 在仅数十个训练样本的条件下即实现了高精度预测. 数值实验表明: 在内插情况, 模型对流场的平均预测误差在2%左右; 当参数外推范围达5%时, 最大相对误差仍保持在4.7%以内; 即便在参数外推20%的严苛工况下, 模型仍能保持定性可靠. 效率测试表明: 本ROM的计算耗时仅为传统SPH方法的10%左右. 该方法可成功应用于(1)不同密度比工况下的结构沉没过程动力学预测, 其流固耦合核心特征捕捉误差在5%左右; (2)水下运动体尾迹场重构, 表面波高预测与仿真结果的平均误差约为2%. 研究成果为海洋流固耦合问题的分析提供了高效计算工具.Abstract: To address the computational inefficiency and high modeling costs of conventional fluid-structure interaction (FSI) simulations, this study proposes a data-driven reduced-order model (ROM) integrating Proper Orthogonal Decomposition (POD) with Gaussian Process (GP) regression. By leveraging high-fidelity simulation datasets from meshfree particle methods, the proposed framework resolves two critical challenges: high-dimensional flow field feature extraction and multi-physics coupled response prediction. The POD-based methodology establishes an intrinsic modal space that achieves 99.8% dimensionality reduction for million-dimensional flow field data. Combined with the non-parametric GP modeling architecture, the ROM achieves highly accurate predictions using only dozens of training samples. Numerical experiments demonstrate that the model attains a mean prediction error of approximately 2% for flow field variables in interpolation scenarios. Under parameter extrapolation conditions, the maximum relative error remains below 4.7% within 5% extrapolation ranges and maintains qualitative reliability even at 20% extrapolation levels. Computational efficiency tests reveal that the ROM requires only 10% of the time consumed by conventional SPH methods. Practical applications confirm the model's effectiveness: (1) For structural sinking dynamics under varying density ratios, the prediction error for key FSI features remains around 5%; (2) In reconstructing wake fields of underwater moving bodies, the average error in surface wave height prediction reaches 2% compared with full-order simulations. This work provides an efficient computational framework for analyzing marine FSI problems, with potential extensions to complex hydrodynamic scenarios requiring rapid multi-parametric evaluations.