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
2N1
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 h1k denoted by h1k , 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 极端波浪载荷实验船模的小波分析英文文献和中文翻译(2):http://www.youerw.com/fanyi/lunwen_94996.html