Abstract A brief description of the wavelet analysis procedure is presented and an approach employing Daubechies’s wavelet functions developed。 Measured data are ana- lyzed by a FFT and wavelet method for a self-propelled, flexible model of the S175 container ship moving in waves。 The high frequency component of the recorded rigid body motions can be omitted without substantially affecting the main features of the data set。 The decom- position of the bending moment time history into low and high frequency components allows the time of im- pact occurrence and its amplitude to be easily detected。 Such quantities provide important information for the development of generic and realistic transient impact (e。g。 slamming, green water) force models for ships travelling in waves。81340

Keywords Wavelet analysis; flexible model test; wave load; non- linear。

Introduction

A ship in unrestricted service inevitably encounters severe sea states even when current improvements in weather routing systems are taken into account (ISSC VI。1, 2000)。 Non-linear effects on wave-induced loads, motions and structural responses are  often significant for a ship travelling in moderate and severe waves。 The slamming  loads and green water impact loads  are   im-

pulsive loads on local and global structures, inducing transient, high level, stresses on ship structures。 Spring/whipping responses of ocean going vessels are usually observed in moderate and severe sea states (Sto- rhaug et al, 2003)。 The green water problem is an ex- treme nonlinear wave-structure interaction in rough sea states。 Large value, impulsive green water impact loads are considered the cause of damage to ship structures, especially superstructure and ship equipment in the bow region (Stansberg and Karlsen, 2001; Faltinsen et al, 2002)。

Full-scale measurements and  model test investigations of slamming effects and green water impact on ship structures allow the determination of design loads and the verification of prediction methods of loads and re- sponses。 In a holistic analysis of ship structures it is important to identify the different types of hydrody- namic loads contributing to the total bending moment, (i。e。, ordinary wave loads and slamming force) in terms of magnitude, phase lag relative to the wave-induced peak and decay rate (Jensen and Mansour, 2003)。 The benefit of characterizing these contributions lies in es- timation of their relative importance with respect to different vessel operational conditions。 This allows predictions of possible dangerous situations and to de- sign, if necessary, structural modifications able to re- duce global ship elastic responses (Ciappi et al, 2003)。

Plastic materials enable an entirely elastic ship model to be manufactured allowing for reasonable satisfaction of the similitude principle。 In contrast to using a seg- mented model, the elastic model provides the means of measuring detailed structural response information over the whole hull of the ship, including bending    moment,

shearing force, torque at any cross section, etc。 (Wu et al, 2003)。 The purpose of the S175 flexible model ship tests carried out in CSSRC is to study wave-induced loads and motion responses of the ship in severe waves, focusing on the non-linearity of the loads with respect to wave height (Chen et al, 2001)。  The wavelet   analysis in the present study is based on data measured in these tests。

Basic formulae in wavelet analysis

Unlike Fourier transforms, wavelet transforms have an infinite set of possible basis functions。 For example, Harr’s simple wavelets and Daubechies wavelets (Niev- ergelt, 1999)。 The compactly supported wavelet family constructed of a scaling function  (x)  and N vanishing

moments satisfy the conditions

Wavelets  are  a  relatively  new  mathematical  tool    to