Recommendations for regularization in the inverse estimation of ice-induced propeller moments for ice-going vessels

Abstract To date, the insufficient quantification of ice-induced propeller moments leads to uncertainty and over-design of ship propulsion systems. Recent developments document the use of lumped mass models and inverse solutions of the external ice-induced propeller moments from indirect measurements on the propulsion shaft. However, these inverse solutions suffer from instability. This article studies various regularization methods which are required in the inverse solution process to insure the stability of the solution. The study focuses on the success rates of the regularization methods. Specifically, the success rate of the automatic selection of a regularization parameter within the inverse solution algorithm was evaluated. Full-scale measurements of the shaft-line of an ice-going vessel were used as inputs for the regularization of the inverse problem. It was found that the Tikhonov regularization method was the most reliable for the analysed case studies. Furthermore, the solution times for the regularization methods were considered. The limitations of the lumped mass inverse model used with the regularization methods are presented and discussed, suggesting that the model is not ideally suited for the application.