用集成动态模态分解法，实现高速双体船海况响应的高精度不确定性预测。
Data-driven uncertainty-aware seakeeping prediction of the Delft 372 catamaran using ensemble Hankel dynamic mode decomposition
- 通过时间延迟状态扩展构建无方程降阶模型，捕捉非线性与记忆效应。
- 频数派集成方法（FHDMDc）显著提升预测精度并提供可靠不确定性估计。
- 适用于船舶设计与航行支持，计算高效且结果逼近实测与仿真数据。
本研究提出并验证了一种基于集合的汉克尔动态模态分解带控制（HDMDc）方法，用于高速双体船Delft 372在海况5、傅汝德数Fr = 0.425条件下的不确定性海况响应预测。实验采集了1:33.3缩比模型在不规则波池中的波高、垂向运动、纵摇、甲板虚拟速度、桥楼加速度及总阻力的时间序列数据，并划分为训练、验证和测试集。HDMDc通过引入时滞状态与输入，构建无方程的线性降阶模型以捕获非线性与记忆效应。比较了贝叶斯（BHDMDc）与频率派（FHDMDc）两种集成策略：前者未优于确定性模型；后者在预测精度和不确定性估计方面表现更优。FHDMDc生成的运动概率密度函数与实验数据及URANS仿真高度一致，证明其在设计与运行支持中具备可靠性与计算效率。
原文摘要 · Abstract (English)
In this study, we present and validate an ensemble-based Hankel Dynamic Mode Decomposition with control (HDMDc) for uncertainty-aware seakeeping predictions of a high-speed catamaran, namely the Delft 372 model. Experimental measurements (time histories) of wave elevation at the longitudinal center of gravity, heave, pitch, notional flight-deck velocity, notional bridge acceleration, and total resistance were collected from irregular wave basin tests on a 1:33.3 scale replica of the Delft 372 model under sea state 5 conditions at Fr = 0.425, and organized into training, validation, and test sets. The HDMDc algorithm constructs an equation-free linear reduced-order model of the seakeeping vessel by augmenting states and inputs with their time-lagged copies to capture nonlinear and memory effects. Two ensembling strategies, namely Bayesian HDMDc (BHDMDc), which samples hyperparameters considered stochastic variables with prior distribution to produce posterior mean forecasts with confidence intervals, and Frequentist HDMDc (FHDMDc), which aggregates multiple model obtained over data subsets, are compared in providing seakeeping prediction and uncertainty quantification. The FHDMDc approach is found to improve the accuracy of the predictions compared to the deterministic counterpart, also providing robust uncertainty estimation; whereas the application of BHDMDc to the present test case is not found beneficial in comparison to the deterministic model. FHDMDc-derived probability density functions for the motions closely match both experimental data and URANS results, demonstrating reliable and computationally efficient seakeeping prediction for design and operational support.
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