ABSTRACT

Sampling method is an effective tool for building approximated models, which can improve the efficiency of hull form optimisation. A dynamic sampling method (DSM) is introduced herein to improve the accuracy and efficiency of the approximated model by considering the influences of sample quality measures in both input and output parameter spaces. The DSM uses leave-one-out to obtain an estimate of the cross-validation errors, which are maximised to determine the sample points in the design space. The variation is used for the calculation of continuous and multimodal regions. The proposed method is compared, using both numerical examples and hull form optimisation, with traditional sampling methods from the literature. The stem profile’s optimisation for KCS based on DSM and static sampling method is performed. And the optimised hull form with less ship resistance is obtained. The comparison results show that DSM performs better than the static sampling method.

Abbreviations: AM: approximated models; ACE: accumulative error; AMDSM: approximated models based on dynamic sampling method; AMUD: approximated models based on uniform design; CAMM: continuous and multimodal; CF: covariance function; CFD: computational fluid dynamics; CV: cross validation; CVV: cross validation variance; DSM: dynamic sampling method; eLOO: leave-one-out error; LOO: leave-one-out; LHS: Latin Hypercube Sampling; MAPE: mean absolute predictive error; MCS: Monte Carlo Sampling; NN: neural network; RAAE: relative average absolute error; RMSE: root mean square error; SM: sampling methods; SP: sample points; SSM: static sampling method; TS: test samples; UDL: uniform design; VF: variation function.

摘要

采样方法是建立近似模型的有效工具，可以提高船体形式优化的效率。本文介绍了一种动态采样方法（DSM），通过考虑输入和输出参数空间中样本质量度量的影响来提高近似模型的准确性和效率。DSM使用留一法获得交叉验证误差的估计值，该估计值将被最大化以确定设计空间中的采样点。该变化用于连续和多峰区域的计算。使用数值示例和船体形式优化，将所提出的方法与文献中的传统采样方法进行了比较。基于DSM和静态采样方法对KCS进行了茎轮廓的优化。并获得了抗舰船阻力较小的优化船体形式。比较结果表明，DSM的性能优于静态采样方法。

缩写： AM：近似模型；ACE：累积误差；AMDSM：基于动态采样方法的近似模型；AMUD：基于统一设计的近似模型；CAMM：连续和多模式；CF：协方差函数；CFD：计算流体动力学；简历：交叉验证；CVV：交叉验证方差；DSM：动态采样方法；eLOO：一劳永逸的错误；LOO：一劳永逸；LHS：拉丁文Hypercube抽样；MAPE：平均绝对预测误差；MCS：蒙特卡洛抽样；NN：神经网络；RAAE：相对平均绝对误差；RMSE：均方根误差；SM：抽样方法；SP：采样点；SSM：静态采样方法；TS：测试样品；UDL：统一设计；VF：变化函数。