A stochastic response surface approach for uncertainty propagation in ship maneuvering

Abstract

The uncertainty of various coefficients of 8 degrees of freedom (DoF) twin-propeller twin-rudder (TPTR) maneuvering mathematical model has been determined. A stochastic response surface method (SRSM) is developed for propagating these uncertainties to the full scale simulations of ship maneuvers. The proposed SRSM uses Hermite polynomial chaos (PC) expansion of standard random variables (SRVs) for analysis. Here SRVs are Gaussian variables. The SRSM approximates all model inputs and outputs as a function of SRVs and develops an approximate surrogate model for a specific output. The SRSM treats any deterministic model as a “black-box”. SRSM requires less computational time as compared to standard Monte Carlo Simulation (MCS) method. Full scale simulations of a TPTR model installed with gas turbine propulsion at a cruising speed of 30 knots have been carried out. There are 60 uncertain inputs and 14 uncertain outputs present in the model. A linear sensitivity study has been carried out to select a set of most sensitive inputs for each one of the different outputs. Only the sensitive inputs are considered for computing the output distribution. Asymmetric behavior and uncertainty in the characteristics of twin-propeller twin-rudder system are significant. Uncertainty for overshoot angle, advance, tactical diameter, propeller revolution and thrust, engine torque, rudder normal force and torque are presented.