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中文摘要：
为建立考虑船舶横摇的船舶4自由度响应型数学模型,首先采用类比建模的方法建立船舶横摇响应型数学模型,并首次提出了船舶横摇指数的概念;然后利用多元回归分析软件SPSS17.0及偏最小二乘法对8条船舶数据进行分析,得到横摇指数的最优回归公式;最后,联立Nomoto模型和船舶横摇响应型数学模型得到船舶4自由度响应型数学模型.该模型结构简单,较传统的船舶水动力数学模型更为简捷方便,且基本满足精度要求.
英文摘要：
In order to build a 4 degrees responding mathematical model for ships, the paper establishes a responding mathematical model for ship roll by analog modeling method , and puts forward the concept of the indexes of roiling for the first time. Then, the regression equations of are obtained by doing SPSS muhinomial regression and Partia least-squares regression （PLS） of 8 ships. Finally, a 4 degrees responding mathematical model for ships is got by combining Nomoto model and the responding mathematical model for ship roll. Comparing with the traditional ship hydrody- namic mathematical model, the proposed model is simple and easy to analyze, which can basically meet accuracy require- ments.
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