left bracket.
Bring the formula(9),(10) into the boundary
condition(11)~(14), you can get a set of equations on
,
,
,
,
,
,
,
, the coefficients of the
equation of vibration can be known.
3.2 Identification of simple supported
beam cracks by wavelet analysis
Span of simple supported beam is 800mm, Cross
section size is 20mm*40mm, it is known that there is
a crack at the left support 300mm, The depth of the
crack δ
respectively is 0.1、0.2、0.3、0.4、0.5、
0.6. Continuous wavelet transform from scale 1 to 25,
from this, we can get the maximum value of the
wavelet coefficients at the fracture section of each
scale, The modulus maximum of the wavelet
coefficients increases with the increase of the scale,
and is nonlinear. The Lipschitzα exponent can be
obtained by the logarithm of the modulus maximum
of the wavelet coefficients, and the Lipschitz α
exponent decreases with the increase of the depth of
the crack.(
Zhu, 2008) The crack singularities can be
obtained from the Lipschitzαexponent, the damage
degree of the crack beam can be judged.
4 SIMULATION CONTRAST OF FU
LIYE DE-NOISING AND
WAVELET DENOISING
The traditional way of Fourier denoising is to
transform the signal to Fourier transform first, then
low-pass filter, and finally reconstruct the (Shyu,
1996) of the signal after Fourier transform. This
method has very obvious shortcomings, the useful
signal is mainly concentrated in the low-frequency
part, the noise signal is mainly concentrated in the
high-frequency part, but also the useful signal is a
high frequency part, if using a simple low-pass filter,
high frequency part will be a useful signal with noise
signal to filter out, if using low pass filter in order to
save the narrow high-frequency part of the useful
signal, then the signal is filtered will still exist a lot of
noise signal, and the whole process is performed in
frequency domain, without time domain information.
Wavelet analysis can effectively combine the time
domain with the frequency domain(Zhang, 2008), In
the previous chapter, the wavelet threshold denoising
algorithm is introduced. To verify the superiority of
the wavelet denoising method, we select a segment of
Doppler signal, add white noise to it, then the Fourier
denoising and wavelet denoising are used
respectively,in this example, we use the MATLAB7.0
platform for simulation,use Sym8 wavelet
decompose three layers, wavelet coefficient threshold
quantization is quantified by heursure soft threshold.
Fig.1 Effect of Wavelet Denoising
Fig.2 Effect of Fourier Denoising
It can be seen from the diagram, compared to the
Fourier denoising method, it is ideal to obtain the
overall trend of the signal by the wavelet transform
de-noising method. Its basic idea is the function of the
bandpass filter based on the wavelet transform, The
signal is decomposed into different translation and
scaling wavelet or base functions and the wavelet
analysis has the window function is not the same,
with the local analysis ability is very good, can be
found that no other signal analysis methods of the
observed discontinuity and the breakpoint, thus
removing burr noise the.
5 CONCLUSIONS
In this paper, the method of ultrasonic sampling is
studied, and the theory of wavelet transform is used
as the main research method.,the damage degree of
the cracked simple supported beam is judged, and the
wavelet threshold de-noising of the sampled signal is
carried out. Through MATLAB simulation, the Fu
Liye denoising method and wavelet analysis
denoising method are compared. It shows that the
wavelet analysis has the advantage that Fu Liye can
not get rid of noise in bridge detection and denoising.
The research method has been applied to the design
of virtual wavelet de-noising instrument and the
design of ultrasonic nondestructive flaw detector. It