基于线性模型的帆船性能影响因素分析

Analysis of Influencing Factors of Sailing Ship Performance Based on Linear Model

摘要: 本研究利用代尔夫特船舶流体力学实验室的帆船数据，利用线性模型量化了各变量与帆船单位重量排水的剩余阻力之间的关系，并基于该数据提出了帆船设计的优化方案。首先，本文探究了帆船数据集中各变量间的相关关系，发现帆船的单位重量排水剩余阻力与各变量间存在较强的对数线性关系。当对帆船的单位重量剩余阻力以2为底取对数后发现，取对数后的单位重量排水剩余阻力与各变量间存在一定的线性关系，但与各可控因素之间的线性关系均不显著。其次，本文探究了各可控因素与弗劳德数之间的交互作用对帆船单位重量排水剩余阻力的影响。将交互作用引入后，各自变量间产生了较强的共线性，于是分别用岭回归和Lasso拟合数据，发现Lasso在此数据上表现出了较好的效果。其拟合的取对数数据的回归均方为0.220，原始数据的回归均方为4.64。且其结果中，取对数后数据的回归残差可以均匀地分布在某个范围内。最后，根据得到的对数线性模型可知，在弗劳德数一定的情况下，各指标中梁宽吃水量比对帆船的单位重量排水剩余阻力影响最大，其次是船长排水量比，最后是浮心纵坐标。故在实际生产中，设计者更应该关注帆船的船长排水量比。

Abstract: In this study, the relationship between the variables and the residual resistance of the vessel per unit weight is quantified by linear model using the sailing data from the Laboratory of Ship Fluid Mechanics in Delft, and based on the data, an optimization scheme of sailing design is proposed. First of all, this paper explores the correlation between variables in the sailing data set, and finds that there is a strong log-linear relationship between the residual resistance per unit weight of sailing boat and each variable. When the logarithm of the residual resistance per unit weight of a sailing boat is taken as base 2, it is found that there is a certain linear relationship between the residual resistance per unit weight after logarithm and various variables, but the linear relationship between the residual resistance per unit weight and various controllable factors is not significant. Secondly, this paper explores the interaction between the controllable factors and Froude number on the residual resistance of the vessel per unit weight. After the interaction was introduced, a strong collinearity was generated between the variables. Therefore, ridge regression and Lasso were used to fit the data respectively, and it was found that Lasso showed a better effect on the data. The fitting regression mean square of logarithmic data is 0.220, and that of original data is 4.64. In the results, the regression residuals of logarithmic data can be evenly distributed in a certain range. Finally, according to the obtained log-linear model, under the condition of constant Froude number, the ratio of beam width to draft of each index has the greatest influence on the residual resistance of the vessel per unit weight, followed by the ratio of captain displacement, and finally the ordinate of center of buoyancy. Therefore, in the actual production, designers should pay more attention to the skipper displacement ratio.