Ship dynamics mathematical models comparative analysis

The modern automatic ship control systems development, training simulators, ship operator assistance systems, as well as various onboard systems and complexes, requires the application of ship motion dynamics mathematical models. A comparative analysis of such models is presented in this study. Simplified models widely described in literature and developments were considered: the Nomoto model, second-order Nomoto model, first-order Nomoto model, Bech model, Norrbin model, and the model from the IEC-62065 standard. The mathematical models parameter identification was performed using optimization methods based on trial records of the tugboat Nikolay Semenchenko. The models accuracy is compared using the root mean square error (RMSE) for the ship’s yaw rate and coordinates. Objective – ship dynamics mathematical models comparative analysis. The review of native and foreign literature was conducted. Mathematical models of ship motion dynamics were implemented as software code, and model parameters were identified using optimization methods based on trial records. A comparative analysis of model accuracy revealed that the Nomoto model demonstrated the best results in terms of yaw rate RMSE, while the Bech model performed best in coordinate simulation accuracy. The results of the Bech, Nomoto, second-order Nomoto, and IEC-62065 models were similar (difference in yaw rate RMSE within 4.34%, coordinate RMSE within 9.1%). The IEC-62065 standard model is used for certifying automatic ship control systems. Therefore, the Bech, Nomoto, and second-order Nomoto models, which showed comparable results, can also be applied to developing automatic ship control systems. The first-order Nomoto and Norrbin models performed worse due to their lower dynamic order. The research results can be applied to developing mathematical models of ship motion dynamics and automatic ship motion control systems.