Comparing generic and vectorial nonlinear manoeuvring models and parameter estimation using optimal truncated least square support vector machine

An optimal truncated least square support vector machine (LS-SVM) is proposed for the parameter estimation of nonlinear manoeuvring models based on captive manoeuvring tests. Two classical nonlinear manoeuvring models, generic and vectorial models, are briefly introduced, and the prime system of SNAME is chosen as the normalization forms for the hydrodynamic coefficients. The optimal truncated LS-SVM is introduced. It is a robust method for parameter estimation by neglecting the small singular values, which contribute negligibly to the solutions and increase the parameter uncertainty. The parameter with a large uncertainty is sensitive to the noise in the data and have a poor generalization performance. The classical LS-SVM and optimal truncated LS-SVM are used to estimate the parameters, and the effectiveness of optimal truncated LS-SVM is validated. The parameter uncertainty for both nonlinear manoeuvring models is discussed. The generalization performance of the obtained numerical models is further tested against the validation set, which is completely left untouched in the training. The R2 goodness-of-fit criterion is used to demonstrate the accuracy of the obtained models. This work was performed within the Strategic Research Plan of the Centre for Marine Technology and Ocean Engineering (CENTEC), which is financed by Portuguese Foundation for Science and Technology (Fundação para a Ciência e Tecnologia-FCT) under contract UID/Multi/00134/2013 - LISBOA-01-0145-FEDER-007629. This work was partly supported by the Research Council of Norway through the Centres of Excellence funding scheme, Project number 223254 - AMOS. The PMM data was provided by SINTEF Ocean and were collected in the course of the Knowledge-building Project for the Industry ``Sea Trials and Model Tests for Validation of Shiphandling Simulation Models'' [59], supported by the Research Council of Norway.