Nonlinear Model Evaluation Via System Identification of a Moored Structural System

Complex nonlinear and chaotic responses have been observed and demonstrated in various compliant ocean systems characterized by nonlinear mooring restoring force and coupled fluid-structure interaction exciting force. The design of these systems, with inherent high degree of nonlinear dynamics, presents a challenge to the engineer. An experimental mooring system exhibiting nonlinear behavior due to geometric nonlinearity of mooring line angles and the complexity of hydrodynamic excitations is chosen for the study. Three alternative multiple-input/single-output models, nonlinearstructure linearly-damped (NSLD) model, nonlinear-structure coupled hydrodynamically-damped (NSCHD) model, and nonlinearstructure nonlinearly-damped (NSND) model distinguished by the different inputs and outputs used are derived and Reverse MultipleInput/Single-Output technique are examined. With the input wave and output system response data known, based on multiple input/single-output linear analysis of reverse dynamic system, the methodology identifies the linear and nonlinear system properties. A detailed study has been conducted on the different reverse dynamic models to identify the most suitable physical representative model for the ocean mooring system considered. INTRODUCTION The highly nonlinear responses of compliant ocean structures characterized by a large-geometry restoring force and a coupled fluid-structure interaction excitation are of great interest to ocean engineers and naval architects. An understanding of the nonlinear responses including coexisting periodic (primary, subharmonic and superharmonic resonance) and aperiodic (quasi-periodic and chaotic) phenomena is essential to ensure sound engineering design and safe operation of these structures. To analyze these nonlinear phenomena, deterministic analysis theories and numerical prediction techniques have been developed for single-point mooring systems (Gottlieb et al 1992), ships (Bishop and Virgin 1988), and multi-point mooring systems (Bernitsas and Chung 1990, Gottlieb and Yim 1993). Stochastic extensions of these analysis techniques have also been developed by Lin and Yim (1996, 1997) to provide guidelines for interpreting field and experimental observations where randomness cannot be neglected. To calibrate the prediction capability of these techniques, a number of experiments have been conducted (Thompson and Stewart 1987, Isaacson and Phadke 1994, Lin and Yim 1998). In order to compare analytical predictions to experimental results, the system parameters employed in the analytical techniques need to be identified. Because the system is nonlinear, conventional system identification techniques based on linear system theory (Bendat and Piersol 1993) are not applicable. A Reverse Multiple-Input/SingleOutput (R-MI/SO) technique has been developed to determine amplitude and frequency dependent properties of various nonlinear systems, including the Duffing and Van der Pol types, subjected to broadband excitation inputs (Bendat et al 1992). Numerically simulated random excitations were used to verify the technique. For ocean engineering applications of the MI/SO methods, both Direct and Reverse methods have been applied to identify nonlinear system response properties of a naval frigate and a barge using measured field data (Bendat 1998). In demonstrating the applicability of the techniques, since the hydrodynamic force on the moving body excited by the waves was not directly measured, linear equivalent wave input was used as an approximation. An experiment has been performed at the O. H. Hinsdale Wave Laboratory at Oregon State University (OSU) on a multi-point moored submerged sphere subject to wave excitations (Yim et al 1993). In this study, the wave input and the system responses measured during the test are employed for parameter identification. Three mathematical models -nonlinear-structure linearly-damped (NSLD) model, nonlinear-structure coupled hydrodynamicallydamped (NSCHD) model, and nonlinear-structure nonlinearlydamped (NSND) model -are derived to depict the physics of the fluid-structure interaction of the SDOF, symmetric spherical mooring system submerged in ocean waves. A detailed study is conducted on the different reverse dynamic models to arrive at the most physically representative model for the ocean mooring system considered.