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估计海冰厚度函数的一种辨识方法

吕巍1,*  王伟萍1   

  1. 1.上海大学数学系, 上海 200444
  • 收稿日期:2017-09-18 出版日期:2018-12-15 发布日期:2018-12-15
  • 通讯作者: 吕巍 E-mail: lvwei@shu.edu.cn
  • 基金资助:

    国家自然科学基金(No. 11101262), 上海市重点学科资助项目(No. S30104), 上海高校一流学科(B类)资助项目

An identification method to estimate the thickness of sea ice

LV Wei1,*  WANG Weiping1   

  1. 1. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • Received:2017-09-18 Online:2018-12-15 Published:2018-12-15

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摘要：

提出一种采用海冰和海水温度观测数据来估计海冰厚度的辨识方法, 避免了因使用厚度数据所带来的种种局限性. 首先建立一个拟线性海冰-海水热力学系统, 得到了系统解的存在唯一性; 然后以该系统中描述海冰厚度函数的参数为辨识量, 以系统输出的温度和实际观测温度的偏差为目标泛函, 建立了以目标泛函为最小的参数辨识模型; 最后构造了以半隐式差分格式、遗传算法和Hooke-Jeeves算法相结合的数值算法, 得到了海冰厚度函数, 并对辨识量做了敏感性分析. 结果表明: 这种方法是有效可行的.

关键词: 参数辨识, 海冰厚度, 拟线性热力学系统, 数值算法, 敏感性分析

Abstract:

This study intended to provide an identification method to estimate the thickness of sea ice with the temperature of sea ice and sea water, which avoids the limitations of using thickness data directly. Firstly, a quasi-linear thermodynamic system with unknown thickness of sea ice is established, which proved the existence and uniqueness of its solution. Secondly, a parameter identification model is constructed which takes the thickness of sea ice as the identified variable, and takes the temperature deviation between the system output and practical observations as an objective function. Finally, a new algorithm, containing of the semi-implicit difference scheme, Genetic Algorithm and Hooke-Jeeves Algorithm, is established for  obtaining the thickness of sea ice. We proved our method is effective and feasible by analysing the sensitivity of identification variable.

Key words: parameter identification, thickness of sea ice, quasi-linear thermodynamic system, numerical algorithm, sensitivity analysis