usually determined by a spectral factorization method (Daubechies, 1992)。

Similar to a discrete Fourier transform method, the discrete wavelet transform requires an extension of   the

sponses arising at the point of installation of the meas- uring  devices。    By  decomposing  the  vertical bending

data series S0, S1, …, S

2n 1

with a constant interval step

moment time history into low  frequency  and  high  fre-

into  a periodic  data set  of

2n1 entries, i。e。 S0, S1,   …,

quency components, impact occurrence is easily de- tected, and impact characteristics (i。e。 maximum value, duration, decay behaviour, etc) exhibited by the fluid- structure interaction system and transient force deter- mined。 This information can be used in the    generation

S ,S   , 。。。, S 。   To achieve a small edge   effect

2   1     2 2 1

due to this extension, a mirror extension or cubic spline extension method is usually adopted (Nievergelt, 1999)。

Once the family of wavelets is chosen and the data    se-

of empirical formulae to describe  transient impact forces acting on ships travelling in severe waves。

ries S0, S1,…, S

2  1

, with a constant interval step,    are

extended into a periodic data set of 2n+1, the signals  can

be expressed approximately by the scaling function

~ 2n11

are localized both in frequency (by compression in    the

form ofx   ) and in space (by shifting a distance of N-

Wavelet decomposition works in a similar manner to   a

Due  to  the  periodic  property  of  the  extended  signal

windowed Fourier transform, where the window is sim-

series, the series of coefficients  a0 , a1, 。。。,a n11

are also

ply  a  wave  base  that  is  compactly  supported  within

x

a periodic data set。 Substituting Eq。 3 into Eq。 5, we find that the signal expression is replaced by an equiva- lent combination of  2n  slower level scaling     functions

( x  j) and   of   2n   slower   level   wavelet  functions

(       N 1 j) [N 1, N] 。  However,  an advantage

2m

of wavelet transforms over the windowed Fourier trans- form is that the windows vary between the different frequency  levels  (Daubechies,  1992)。     From  Eq。   7,

~changes in the function  f (x) at each frequency level are

( x  j) , in the form2

determined by the values of  c nm

A larger value of  c j

at a higher level n-m  implies

signal discontinuities or transient oscillations at the location。

Extreme wave load test of a flexible ship model

ABS702  material  was   used  to   build   a  3。6m    self-

propelled  flexible  model  of  the  S175  container ship。

The thickness of plastic plate for the hull is 2mm, and

for bulkhead, keel and deck  girder  4mm。   Twenty-one