基于机器学习的内孤立波波要素关系研究

内孤立波在海洋中的传播会携带能量和动量，不同振幅的内孤立波对海洋中的能量交换及海上工程等影响也不同，因此，研究内孤立波振幅与半波宽度、水深、分层条件、密度等水文特征参量之间的关系显得尤为重要。以往在研究中建立内孤立波振幅与它们之间的关系时，会受到不同理论有效适用范围的限制。本文借助实验室的水槽方法，设计了不同的水深、分层及密度条件下的内孤立波系列综合实验，发现内孤立波的振幅与半波宽度、水深、分层条件以及水体密度等参量之间并非简单线性关系。因此，利用机器学习的方法建立内孤立波振幅与上述参量之间的非线性关系，建立了支持向量机（SVM）和随机森林（RF）两种机器学习模型。将1 266组实验数据建立样本库，其中包含训练集970组，测试集296组，对模型进行参数调优，最终通过测试集验证，SVM模型的平均相对误差为17.3%，RF模型的平均相对误差为15.5%。该方法适用于多种不同的水文条件，有效解决先前理论存在的适用性问题。

Relationship between wave elements of internal solitary waves based on machine learning

The internal solitary waves that propagate in the ocean carry enormous energy and momentum. Internal solitary waves of varying amplitudes have a different impact on energy exchange and offshore engineering in the ocean. Therefore, it is essential to study the relationship between the amplitude of internal solitary waves, half-wave width, and hydrological characteristic parameters such as depth, stratification, and density. Previously, the relationship between the amplitude of an internal solitary wave and these parameters was constrained by multiple theories. In this paper, a series of comprehensive experiments under different depth, stratification, and density were designed using flume in the laboratory. The relationship between the amplitude of internal solitary waves, half-wave width, depth, stratification, and density is found to be nonlinear. Thus, the machine learning method can be used to establish a nonlinear relationship between the above parameters. We developed a sample database of 1 266 sets, including 970 training sets and 296 test sets using two models, support vector machine (SVM) and random forest (RF). The parameters of the model have been optimized. Finally, the average relative error of the SVM model is 17.3%, whereas that of the RF model is 15.5%. The results show that the machine learning method is effective and feasible. This method can be applied to various hydrological conditions, which effectively solve applicability issues in the previous theory.