Graybox Modelling of Ships Using Indirect Input Measurements

Abstract: A ship's roll dynamics is very sensitive to changes in the loading conditions and a worst-case scenario is that the ship will capsize. Actually, the mass and center of mass are two of the most influential parameters in most mechanical systems. However, it is difficult to uniquely estimate these parameters for a ship under normal operational conditions without special experiments or equipment.Instead of focusing on a sensor-rich environment where all possible signals on a ship can be measured and a complete model of the ship can be estimated, this thesis presents an approach where a model of a subsystem of the ship's dynamics is estimated using only a limited set of sensors. More specifically, the roll dynamics is studied and it is assumed that only motion measurements from an inertial measurement unit (IMU) together with measurements of the rudder angle are available. Hence, direct measurements of the true inputs to the subsystem are not available, but the measurements indirectly contain information about the inputs and these indirect input measurements can be used as a substitute.To understand the properties of the proposed method, it is applied to an approximate model of the ship's roll dynamics. The analyses show that only a subset of the unknown parameters can be estimated simultaneously and that the estimation problem is similar to closed-loop system identification.A multi-stage method that uses several datasets is introduced to circumvent the restrictions shown in the identifiability analysis. An iterative closed-loop instrumental variable approach is used to estimate subsets of the parameters in each step. The approach is verified on experimental data with good results.It is shown that a well-established and more complete ship model can be used to derive a generalization of the approximate model, with more input measurements and a few extra parameters. The generalized model has the same basic properties as the approximate model. The added complexity is due to the ship's interaction with water. Because of this extra complexity, an iterative joint closed-loop instrumental variable approach based on a graybox formulation and using multiple datasets simultaneously is introduced to estimate the parameters.Finally, experiments with a scale ship model are described. The joint identification method is applied to the collected data and gives promising results.