Estimation of Nonlinear Greybox Models for Marine Applications

Sammanfattning: As marine vessels are becoming increasingly autonomous, having accurate simulation models available is turning into an absolute necessity. This holds both for facilitation of development and for achieving satisfactory model-based control. When accurate ship models are sought, it is necessary to account for nonlinear hydrodynamic effects and to deal with environmental disturbances in a correct way. In this thesis, parameter estimators for nonlinear regression models where the regressors are second-order modulus functions are analyzed. This model class is referred to as second-order modulus models and is often used for greybox identification of marine vessels. The primary focus in the thesis is to find consistent estimators and for this an instrumental variable (IV) method is used.First, it is demonstrated that the accuracy of an IV estimator can be improved by conducting experiments where the input signal has a static offset of sufficient amplitude and the instruments are forced to have zero mean. This two-step procedure is shown to give consistent estimators for second-order modulus models in cases where an off-the-shelf applied IV method does not, in particular when measurement uncertainty is taken into account.Moreover, it is shown that the possibility of obtaining consistent parameter estimators for models of this type depends on how process disturbances enter the system and on the amount of prior knowledge about the disturbances’ probability distributions that is available. In cases where the first-order moments are known, the aforementioned approach gives consistent estimators even when disturbances enter the system before the nonlinearity. In order to obtain consistent estimators in cases where the first-order moments are unknown, a framework for estimating the first and second-order moments alongside the model parameters is suggested. The idea is to describe the environmental disturbances as stationary stochastic processes in an inertial frame and to utilize the fact that their effect on a vessel depends on the vessel’s attitude. It is consequently possible to infer information about the environmental disturbances by over time measuring the orientation of a vessel they are affecting. Furthermore, in cases where the process disturbances are of more general character it is shown that supplementary disturbance measurements can be used for achieving consistency.Different scenarios where consistency can be achieved for instrumental variable estimators of second-order modulus models are demonstrated, both in theory and by simulation examples. Finally, estimation results obtained using data from a full-scale marine vessel are presented.