Coupled Nonlinear Barge Motions, Part I: Deterministic Models Development, Identification and Calibration

This paper focuses on the development of optimal deterministic, nonlinearly coupled barge motion models, identification of their system parameters, and calibration of their prediction capability using experimental results. The ultimate objective is to develop accurate yet sufficiently low degree-of-freedom stochastic models suitable for efficient probabilistic stability and reliability analyses of US Naval barges for preliminary design and operation guideline development (see Part II). First a three-degree-of-freedom (3DOF) fully coupled roll-heave-sway model, which features realistic and practical high-degree polynomial approximations of rigid body motion relations, hydrostatic and hydrodynamic force-moment specifically suitable for barges, is examined. The hydrostatic force-moment relationship includes effects of the barge’s sharp edge and combined roll-heave states, and the hydrodynamic terms are in a “Morison” type quadratic form. System parameters of the 3DOF model are identified using physical model test results from several regular wave cases. The predictive capability of the model is then calibrated using results from a random wave test case. Recognizing the negligible sway influence on coupled roll and heave motions and overall barge stability, and in an attempt to reduce anticipated stochastic computational efforts in stability analysis, a two-degree-of-freedom (2DOF) roll-heave model is derived by uncoupling sway from the roll-heave governing equations of motion. Time domain simulations are conducted using the 3DOF roll-heave-sway and the 2DOF roll-heave models for regular and random wave cases to validate the model assumptions and to assess their (numerical) prediction capabilities.