**1. Introduction**

Simulation models of the ship propulsion system play an increasingly important role, for instance in controller design [1,2] and condition monitoring [3]. The drawback of using simulation models, however, is that the required parameters are often unknown or very uncertain. Therefore, building a simulation model and determination or estimation of its parameters can be a time-consuming task, which often requires significant experience (see for recent examples [4–6]). After building and verifying the model, its validity can sometimes be quantified, at least for a specific domain of applications [7]. Periodic re-validation is not commonly reported, while it is known that many of the physical parameters that play a role in the performance of the ship propulsion plant are time-variant. Examples of time-variant factors are fouling of the hull and propeller, turbocharger contamination, and so on.

A comprehensive description of identification techniques is given by Ljung [8]. Since the 1990s artificial neural network techniques have been widely used to identify electric motor parameters [9–11] as well as linear and nonlinear least-squares algorithms [12,13].

**Citation:** Vrijdag, A.; Martelli, M. Parameter Identification of a Model Scale Ship Drive Train. *J. Mar. Sci. Eng.* **2021**, *9*, 268. https://doi.org/ 10.3390/jmse9030268

Academic Editor: Kostas A. Belibassakis

Received: 19 January 2021 Accepted: 22 February 2021 Published: 2 March 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Despite the abundant literature on identification techniques, publication of their application to determine marine propulsion plant parameters is not widespread. A noteworthy exception is the research effort that has been put into the identification of parameters of a dynamic thruster performance model for remotely operated underwater vehicles, which attempts to capture the dynamic response of propeller thrust and torque to the applied electric motor torque [14–25]. The following observations are made regarding these papers:


Data-driven modeling approaches such as those reported by Coraddu et.al. [26] might offer benefit in the sense that by making use of large amounts of historical data in combination with advanced algorithms, a "superfit" model can be generated. Drawbacks of using such a black box approach are the amount of required data, the time over which the data are to be collected, and the lack of insight on the physical behavior of the underlying system.

Although the data-driven approaches based on huge datasets will, without doubt, play an important role in the future, in this paper multiple identification techniques are proposed to obtain the propulsion system parameters, based on short (but informationrich) controlled performance tests, and are tested on model scale. The potential benefit of application of these approaches on full scale is that they can be used to, in a relatively short time span (possibly in real time), quantify system performance during sea acceptance trials, after periodic maintenance or following a system upgrade. Comparison of this fingerprint with sister ships or with previous fingerprints could potentially be used to understand the state of decay of components giving a significant contribution to a condition-based approach to ship maintenance operations [27].

To demonstrate the idea, a model scale ship available at Delft University of Technology (DUT) and Genoa University (UNIGE) is used. First, the non-linear system model of its propulsion plant including electric DC-motor, gearbox, and propeller is derived and subsequently linearized. Both models contain the same unknown parameters. Note that this paper focuses on bollard pull conditions, although the ideas can be extended to free sailing conditions as well.

Subsequently, multiple identification methods are explained and applied, making use of data collected during various types of experiments. The resulting parameter sets are implemented in the non-linear and linear simulation models, and their behavior is validated in both time and frequency domains.

At the end of the paper, a possible path is given for the development of full-scale ship propulsion "fingerprinting" techniques through system performance tests. Such a path includes simulation-based research and both model-scale and full-scale experimental research.
