Modeling for IMU-based Online Estimation of a Ship's Mass and Center of Mass

Abstract

A ship's roll dynamics is very sensitive to changes in the loading conditions and a worst-case scenario is the loss of stability. This paper proposes an approach for online estimation of a ship's mass and center of mass. 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, a minimal approach is adopted. A model of the roll dynamics is derived from a well-established model in literature and it is assumed that only motion measurements from an inertial measurement unit together with measurements of the rudder angle are available. Furthermore, identifiability properties and disturbance characteristics of the model are presented. Due to the properties of the model, the parameters are estimated with an iterative instrumental variable approach to mitigate the influence of the disturbances and it uses multiple datasets simultaneously to overcome identifiability issues. Finally, a simulation study is presented to investigate the sensitivity to the initial conditions and it is shown that there is a low sensitivity for the desired parameters.

Online Estimation of Ship's Mass and Center of Mass Using Inertial Measurements

“…The parameter k should be thought of as representing the physical restoring properties of the ship, for instance, being dependent on factors such as the hull shape, while the term M gz g + mgz m represents the influence by the mass and its location on the restoring properties. For a thorough derivation of the model, see Linder et al (2015) or Linder (2014).…”

“…The issue is thatv is unknown but an alternative model can be formed by eliminatingv. The key to this elimination is the known relation between the measured tangential acceleration a s defined in (7), the acceleration a y and the signalv (Linder et al, 2015). The acceleration a y of the ship in the Earth-fixed xy-plane has two parts, firstly a contribution from the sway motion and secondly due to the angular velocity about the yaw axis.…”

“…Note that the starting times t i , i = n, c, l are used to emphasize that these datasets are not collected at the same time. For more details, see Linder et al (2015) or Linder (2014). …”

“…A simplified model of the roll dynamics was used and it was assumed that only motion data from an inertial measurement unit (IMU) together with the rudder angle were available. In Linder et al (2015), an extended model was derived from well-established results in literature to also consider the strong couplings in ships.…”

“…This paper presents an experimental study of online estimation of a ship's mass and center of mass using the recently proposed approach derived in Linder et al (2015) with data recorded from a scale ship operated in a basin. The data was collected under moderate sea conditions in free run experiments where the scale model was controlled manually using a joystick.…”