In this work, experiment design for marine vessels is explored. A dictionary-based approach is used, i.e., a systematic way of choosing the most informative combination of independent experiments out of a predefined set of candidates. This idea is quite general but is here tailored to an instrumental variable (IV) estimator with zero-mean instruments. This type of estimator is well-suited to deal with parameter estimation for second-order modulus models, which is a class of models often used to describe motion of marine vessels. The method is evaluated using both simulated and real data, the latter from a small model ship as well as from a full-scale vessel. Further, a standard motion-planning problem is modified to account for the prior-made choice of information-optimal sub-experiments, which makes it possible to obtain a plan for the complete experiment in the form of a feasible trajectory.

This work deals with a class of nonlinear regression models called second-order modulus models. It is shown that the possibility of obtaining consistent parameter estimators for these models depends on how process disturbances enter the system. Two scenarios where consistency can be achieved for instrumental variable estimators despite non-additive system disturbances are demonstrated, both in theory and by simulation examples. Copyright (C) 2020 The Authors.

As marine vessels are becoming increasingly automated, having accurate simulation models available is turning into an absolute necessity. This holds both for the facilitation of development and for achieving satisfactory model-based control. Such models can be obtained through system identification, and in this thesis, particular emphasis is given to experiment design and parameter estimation, which constitute two central steps in the system identification process. The analysis is carried out for a special class of nonlinear regression models called second-order modulus models, which is a type of model that is often used for describing nonlinear hydrodynamic effects in greybox identification of ships.

First, it is demonstrated that the accuracy of an instrumental variable (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. Further, it is shown that the possibility of obtaining consistent parameter estimators for models of this type depends on how the process disturbances enter the system and on the amount of prior knowledge that is available about the disturbances’ probability distributions. In cases where the first-order moments are known, the aforementioned approach gives consistent estimators even when disturbances enter the system before the nonlinearity. To obtain consistent estimators in cases where the first-order moments are unknown, a framework for estimating auxiliary nuisance parameters that depend on the disturbances’ first and second-order moments is suggested. This can be done by describing the process disturbances as stationary stochastic processes in an inertial frame and utilizing the fact that their effect on a vessel depends on the vessel’s attitude.

After this, the attention is more clearly focused on experiment design, and a systematic approach for choosing the most informative combination of independent sub-experiments out of a predefined set of candidates is proposed. Further, a technique to account for an upcoming subtraction of the instruments’ mean during the experiment design is suggested, and the consequences of various ways of having the mean subtracted are explored. Additionally, it is shown how the dictionary-based method for finding an excitation signal can be combined with a motion-planning framework to obtain a trajectory that is both informative and spatially feasible.

The suggested methods are evaluated in experimental work and show promising results on both simulated and real data, the latter from a full-scale marine vessel as well as a small-scale model ship.