S. K. Bhattacharyya e-mail: skbh@iitm.ac.in R. Panneer Selvam Department of Ocean Engineering, Indian Institute of Technology, Madras, India Parameter Identification of a Large Floating Body in Random Ocean Waves by Reverse MISO Method Dynamics of a large moored floating body in ocean waves involves frequency dependent added mass and radiation damping as well as the linear and nonlinear mooring line characteristics. Usually, the added mass and radiation damping matrices can be esti- mated either by potential theory-based calculations or by experiments. The nonlinear mooring line properties are usually quantified by experimental methods. In this paper, we attempt to use a nonlinear system identification approach, specifically the Reverse Mul- tiple Inputs-Single Output (R-MISO) method, to a single-degree-of-freedom system with linear and cubic nonlinear stiffnesses. The system mass is split into a frequency indepen- dent and a frequency dependent component and its damping is frequency dependent. This can serve as a model of a moored floating system with a dominant motion associated with the nonlinear stiffness. The wave diffraction force, the excitation to the system, is assumed known. This can either be calculated or obtained from experiments. For numerical illus- tration, the case of floating semi-ellipsoid is adopted with dominant sway motion. The motion as well as the loading are simulated with and without noise assuming PM spec- trum and these results have been analyzed by the R-MISO method, yielding the frequency dependent added mass and radiation damping, linear as well as the nonlinear stiffness coefficients quite satisfactorily. @DOI: 10.1115/1.1493201# Keywords: Added Mass, Damping, Nonlinear, Noise, System Identification, Random Wave, R-MISO, Wave Spectrum Introduction The response of a system to an excitation depends on the pa- rameters embedded in the equation of motion. Methods to esti- mate these parameters form the major concern of System Identi- fication ~SI!. Estimation of the parameters of the equation of motion is also referred to as parameter identification. SI can be based upon time or frequency domain approaches. In this paper, a relatively new frequency domain nonlinear SI method, specifi- cally, the Reverse Multiple Input-Single Output ~R-MISO! method @1,2#, has been adopted for the problem of a large moored floating body under random wave loading based upon a linear spectral description. The SI problem consists of predicting the frequency dependent added mass and radiation damping of the floating body as a Single-Degree-Of-Freedom ~SDOF! system as well as the linear and nonlinear stiffnesses of the system provided by the mooring lines. Cubic nonlinearity is assumed for modeling the mooring line stiffness. The linear stiffness can be partially due to the hydrostatic restoring force of a floating body and partially due to the mooring line. However, in the SDOF system consid- ered, the hydrostatic stiffness is absent, the degree of freedom being sway. The definition of degrees of freedom of a floating body is shown in Fig. 1 and the schematic diagram of a moored floating body with direction of motion considered for parameter identification in this paper is shown in Fig. 2. The excitation and the response time series are utilized in the SI analysis, and these data have been simulated with and without noise in the numerical example and the R-MISO method applied to these data. The R-MISO method is a generalized non-iterative frequency domain method in which conditioned spectral density functions of the input and output are used and the roles of the input and output are reversed to form a MISO model. It is robust, computationally light, and requires no starting estimates. It has found application in a variety of nonlinear systems, namely, Duffing, Van der Pol, Mathieu, and dead-band systems @3#. It has been used for identi- fication of parameters in nonlinear integro-differential equations of motion @4#. R-MISO SI algorithm based on the conditioned spectral density functions is well established @5#. Ocean engineering applications of SI are relatively few. Kalman filtering algorithms have been used in the identification of hydro- dynamic coefficients associated with the Morison’s equation @6#. Extended Kalman filtering algorithms have been developed and applied to identify linear and nonlinear hydrodynamic coefficients in the mathematical models of ship maneuvering from ship trial data @7#. SI technique based on NARMAX routines has been used to establish the possibility of a simple extension to the Morison’s equation, which can improve wave force prediction @8,9#. Similar investigations were also carried out to determine wave force mechanisms on a vertical cylinder in random waves using nonlin- ear frequency domain analysis procedure, which is similar to MISO methods @10#. R-MISO method in SDOF systems under random ocean waves has been focus of some recent investigations @11–13#, wherein the determination of the drag and inertia coefficients embedded in the Morison’s equation formed the objective. System Identification System Identification involves deducing the parameters of a system, whose governing equation of motion is known, from the excitation and response time history. In this paper, we are con- cerned with the nonlinear equation of motion of a SDOF system given by @ m1a ~ v !# x ¨ 1c ~ v ! x ˙ 1kx 1Kx 3 5 f (1) Contributed by the OOAE Division of THE AMERICAN SOCIETY OF MECHANI- CAL ENGINEERS for publication in the ASME JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received by the ASME OOAE Division, June 2001; final revision, February 2002. Associate Editor: S. Calisal. Journal of Offshore Mechanics and Arctic Engineering MAY 2003, Vol. 125 Õ 81 Copyright © 2003 by ASME Downloaded From: http://asmedigitalcollection.asme.org/ on 04/23/2015 Terms of Use: http://asme.org/terms