analyze time series data, but in many respects, wavelets are a synthesis of older ideas producing new elegant mathematical results  and efficient computational  algo-

rithms (Percival and Walden, 2000)。 In particular, a wavelet analysis, presents time and frequency localiza- tion of measured data, and is a suitable numerical tool to approximate data with sharp discontinuities or sharp variations。 An interesting application of wavelets was presented by Newland (1993) to analyze the vibration records of a two-degree-of-freedom system, in which one response is a stationary random process to white noise excitation and the other a non-stationary  response

 (2x  k)(2x  j)dx  0, for k  j and  j, k  I。



where M1,  M2 are integer constants。

The family of Daubechies wavelets (Daubechies, 1992) is used in the present study。 The scaling function (or father function, basic building block)  (x)  for x<M1=0

or x>M2=2N-1 is a compactly supported function, and determined by the recursive relation

2N1

to an impulsive excitation。 Patsias et al (2002 a, b)  used

image  sequences  and  wavelets  to  extract  natural fre-

quencies, modal damping and mode shapes in a struc- tural dynamics study。 Kwon et al (2001) analyzed the ringing phenomenon of a vertical circular cylinder in breaking waves by using continuous Morlet wavelet transforms (Percival and Walden, 2000)。 They   showed

In this two-scale dilation equation, the value of the scaling function (x) is evaluated by the weighted  sum

of the Daubechies scaling filters hk , if the initial values of (x) at integer points are known, where

that high frequency components (ringing) were gener- ated at the onset of the breaking wave impact in the time

for  all  dyadic  numbers。 The

domain, which is hardly detectable if one relies on tra- ditional spectral analysis。

In this paper, a brief description of a wavelet analysis

wavelet function (or mother function) is estimated by the weighted sum of the wavelet filters  gk , which is    a

function of the conjugation of  h1k  denoted by  h1k   , if

procedure  is  presented  adopting  Daubechies   wavelet

functions (Daubechies, 1992)。 The measured data of a self-propelled, flexible model of the S175 container ship travelling in severe regular waves is analyzed by a  Fou-

the initial values of That is,

(x) at integer points are   known。

rier analysis method and the proposed wavelet   method。

 

Non-linear heave and pitch motions, vertical accelera- tions, vertical bending moment data on several trans- verse sections of the ship are presented using the differ- ent  methods。  The  numerical  results  show  that   Dau-

The filters  hk  satisfy the general relation,

bechies wavelet function series reconstructs  the   meas-

ured data in the time domain precisely, and decomposes

time history records at several different frequency   lev-

els。 By using a filtering technique in the wavelet analy- sis, the high frequency component of the recorded rigid body motion signals can be omitted without substan- tially affecting the main features of the data set。 This high frequency content is induced by local flexible    re-

and their values for the Daubechies wavelets family  are