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.

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 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.

I takt med att marina farkoster blir mer autonoma ökar behovet av noggranna matematiska farkostmodeller. Modellerna behövs både för att förenkla utvecklingen av nya farkoster och för att kunna styra farkosterna autonomt med önskad precision. För att erhålla allmängiltiga modeller behöver olinjära hydrodynamiska effekter samt systemstörningar, främst orsakade av vind- och vattenströmmar, tas i beaktning. I det här arbetet undersöks metoder för att skatta okända storheter i modeller för marina farkoster givet observerad data. Undersökningen gäller en speciell typ av olinjära modeller som ofta används för att beskriva marina farkoster. Huvudfokus i arbetet är att erhålla konsistens, vilket betyder att de skattade storheterna ska anta rätt värden när mängden observerad data ökar. För det används en redan etablerad statistisk metod som baseras på instrumentvariabler.

Det visas först att noggrannheten i modellskattningsmetoden kan förbättras om datainsamlingsexperimenten utförs på ett sätt så att farkosten har signifikant nollskild hastighet och instrumentvariablernas medelvärde dras bort. Den här tvåstegslösningen påvisas vara fördelaktig vid skattning av parametrar i den ovan nämnda modelltypen, framför allt då mätosäkerhet tas i beaktning.

Vidare så visas det att möjligheten att erhålla konsistenta skattningsmetoder beror på hur mycket kännedom om systemstörningarna som finns tillgänglig på förhand. I fallet då de huvudsakliga hastigheterna på vind- och vattenströmmar är kända, räcker den tidigare nämnda tvåstegsmetoden bra. För att även kunna hantera det mer generella fallet föreslås en metod för att skatta de huvudsakliga hastigheterna och de okända modellparametrarna parallellt. Denna idé baserar sig på att beskriva störningarna som stationära i ett globalt koordinatsystem och att anta att deras effekt på en farkost beror på hur farkosten är orienterad. Genom att över tid mäta och samla in data som beskriver en farkosts kurs, kan man således dra slutsatser om de störningar som farkosten påverkas av. Utöver detta visas det att utnyttjande av vindmätningar kan ge konsistens i fallet med störningar av mer generell karaktär.

Olika scenarion där konsistens kan uppnås visas både i teori och med simuleringsexempel. Slutligen visas också modellskattningsresultat som erhållits med data insamlad från ett fullskaligt fartyg.