НОВІ МАТЕМАТИЧНІ МОДЕЛІ ПОВЗДОВЖНІХ ГІДРОДИНАМІЧНИХ СИЛ НА КОРПУСІ СУДНА

Abstract

Development of modern ship's automatic steering systems, navigation simulators, research of ship maneuvers stipulates the necessity of adequate mathematical models of the ship propulsion complex. The main components of the non-inertial forces of the ship propulsion complex are the hydrodynamic forces on the hull. Therefore, the improvement of mathematical models of these forces refers to important scientific and practical problems. This paper proposes a general approach to the construction of mathematical models of hydrodynamic forces on the hull. The approach is based on a multivariate quasilinear regression analysis, considering the values of the multiple correlation coefficient, the significance of the model, and the significance of each explanatory factor (regressor). In particular, the Fisher's criterion was used to test the significance of the models, and the statistical significance of each regressor was checked with the help of the Student's criterion. In addition, the standard error of each regressor was investigated. We also checked the absence of multicollinearity of the obtained models. The inadequacy of many existing mathematical models of hydrodynamic derivatives of longitudinal hydrodynamic forces on the hull is shown. In particular, it was found that one-factor correlation analysis cannot provide the construction of adequate models with high significance for all hydrodynamic derivatives. It has also been proven that applying only the AIC minimum criterion (Akaike Information Criterion) cannot ensure that all the regression analysis criteria are met. New adequate models of hydrodynamic derivatives have been constructed for longitudinal hydrodynamic forces on the hull with a high level of correlation, high indicators of significance of the models as a whole and of each regressor separately. The models are built for the whole range of variation of the block coefficient: (0.5; 0.9) and separately for the two ranges: (0.5; 0.7) and (0.7; 0.9). As regressors, we used the relations of the basic geometric parameters of the vessel, such as length, breadth on the current waterline, draught and the value of the block coefficient.