340
Y. Shi et al.
In the light of the aforementioned analysis, the monitored arc acoustic signal could
be derived as:
S(t) = y(t) + D = s(t) + n(t) + D
(10.24)
where the DC bias is expressed as D; the pure arc sound signal is s(t); the DCremoval arc acoustic signal is represented by y(t); S(t) is the monitored signal; and
the ambient noise is expressed as n(t). The 50 Hz high-pass filter is used to eliminate
DC offset and power frequency interference.
Since the noise throughout the entire arc acoustic signal is stable, a pure arc
acoustic signal s(t) can be obtained by doing subtraction between the additive noise
n(t) and the original monitored signal S(t). Therefore, to denoise the arc sound signal,
the Spectral Noise Subtraction (SNS) method is brought in. Firstly, transferring both
sides of Eq. (10.24) through FFT:
Y (ω) = S(ω) + N (ω)
(10.25)
Then, the power spectrum of Eq. (10.25) can be derived as:
|Y (ω)|
2
= |S(ω)|
2
+ |N (ω)|
2
+ 2Re
S(ω)N (ω)
(10.26)
where because of the existence of the additive and stable noise s(t), Re
S(ω)N (ω)
is zero in one frame. Therefore, the amplitude of S(ω) can be derived as the following
equation:
|S(ω)| =
|Y (ω)|
2
− |N (ω)|
2
(10.27)
Nevertheless, from the point of mathematic, the consequence of |Y (ω)|
2
−|N (ω)|
2
is probably negative, by which a new noise called ’musical noise’ may be brought
in. The flow chart of the reformative spectral noise subtraction algorithm is shown
in Fig. 10.23 [35]. Figures 10.24 and 10.25 show the denoised arc sound signal. The
noise is suppressed, and the pure arc acoustic signal is maintained.
10.3.2.1 Statistical Characteristics in Time Domain
To avoid the interference of arc ignition and arc ending process, a piece of signal
(10 s) is selected during the stable welding process. The statistical characteristics
are detailed in Sect. 10.3.1.1. However, considering that an experienced welder can
weld perfectly by acoustic sensing, the logarithmic response of the ear should be
taken into account. The logarithmic energy (Le) is introduced to express the signal
energy.
Y. Shi et al.
In the light of the aforementioned analysis, the monitored arc acoustic signal could
be derived as:
S(t) = y(t) + D = s(t) + n(t) + D
(10.24)
where the DC bias is expressed as D; the pure arc sound signal is s(t); the DCremoval arc acoustic signal is represented by y(t); S(t) is the monitored signal; and
the ambient noise is expressed as n(t). The 50 Hz high-pass filter is used to eliminate
DC offset and power frequency interference.
Since the noise throughout the entire arc acoustic signal is stable, a pure arc
acoustic signal s(t) can be obtained by doing subtraction between the additive noise
n(t) and the original monitored signal S(t). Therefore, to denoise the arc sound signal,
the Spectral Noise Subtraction (SNS) method is brought in. Firstly, transferring both
sides of Eq. (10.24) through FFT:
Y (ω) = S(ω) + N (ω)
(10.25)
Then, the power spectrum of Eq. (10.25) can be derived as:
|Y (ω)|
2
= |S(ω)|
2
+ |N (ω)|
2
+ 2Re
S(ω)N (ω)
(10.26)
where because of the existence of the additive and stable noise s(t), Re
S(ω)N (ω)
is zero in one frame. Therefore, the amplitude of S(ω) can be derived as the following
equation:
|S(ω)| =
|Y (ω)|
2
− |N (ω)|
2
(10.27)
Nevertheless, from the point of mathematic, the consequence of |Y (ω)|
2
−|N (ω)|
2
is probably negative, by which a new noise called ’musical noise’ may be brought
in. The flow chart of the reformative spectral noise subtraction algorithm is shown
in Fig. 10.23 [35]. Figures 10.24 and 10.25 show the denoised arc sound signal. The
noise is suppressed, and the pure arc acoustic signal is maintained.
10.3.2.1 Statistical Characteristics in Time Domain
To avoid the interference of arc ignition and arc ending process, a piece of signal
(10 s) is selected during the stable welding process. The statistical characteristics
are detailed in Sect. 10.3.1.1. However, considering that an experienced welder can
weld perfectly by acoustic sensing, the logarithmic response of the ear should be
taken into account. The logarithmic energy (Le) is introduced to express the signal
energy.