Table 1: Process monitoring classiﬁed based on monitoring
variable. (R. Teti and Dornfeld, 2010).
relatively higher signal to noise (S/N) ratio and im
proved frequency response for high frequencies (Lee
and Dornfeld, 1998). However, in applications that
involve low material removal rate (MRR), magnitude
of elastic waves produced by toolworkpiece interac
tion is much lower compared to processes like turn
ing, milling, drilling etc. In such cases, other sensing
systems must be relied upon to give meaningful in
formation regarding the process (e.g. Vibration sen
sor). Table 1 gives a summary of past literature on
types of sensing system and signal processing used,
classiﬁed based on monitoring aspect. An exhaustive
review on process monitoring including the types of
sensors used and signal processing methods is given
in (R. Teti and Dornfeld, 2010). In our experiments
we have employed a triaxial accelerometer to capture
vibration data.
2.2 Frequency Domain Analysis
Signal processing techniques can be broadly classi
ﬁed as time domain and frequency domain. Sev
eral researches have used both techniques in appli
cations involving tool wear/breakage detection and
indirect surface integrity detection. For instance, in
(T. I. ElWardany and Elbestawi, 1996), kurtosis(time
domain) and frequency domain analysis is used suc
cessfully to understand tool properties in a drilling
process. In time domain analysis, statistical meth
ods are used to distinguish persisting patterns/trends.
This includes skewness, kurtosis, corelation coefﬁ
cient etc.In frequency domain analysis, captured sig
nal is analyzed in the frequency domain and changes
to individual frequency components are often indica
tive of the changes in process variables.
Frequency domain analysis also helps to visualize the
effect of noise ﬁltering and various other window
ing and ﬁltering techniques. As the sampling fre
quencies in this experiment falls in the range of 40
51.2 kHz, performing time domain analysis proved to
be challenging due to the size of data captured and
hence frequency domain analysis was effective to un
derstand process characteristics. Signal power also
contains pertinent information regarding the source of
signal generation. Conventionally, fast fourier trans
form (FFT) can be used to determine power spec
trum. In stochastic processes, performing FFT will
not be useful to reduce the noise embedded in the sig
nal, hence some averaging needs to be performed to
increase the S/N ratio. Welch’s power spectrum esti
mate essentially calculates power spectrum using FFT
coupled with averaging. This helps to minimise the
signal power caused by random variations. FFT do
not account in for discontinuities between successive
periods as the data captured is assumed to be of a sin
gle period of a periodically repeating waveform and
this phenomenon is referred to as spectal leakage. Ap
plying Welch’s estimate method also helps to reduce
spectral leakage and reduces the effect caused by un
desired frequencies.
Welch’s method to compute PSD is performed by di
viding the time series data into segments that are suc
cessive and averaging the periodograms of each seg
ments or frames. Consider x
m
(n) to be the input signal
where m = 0,1,..,K − 1,K = total number of frames
and n = 0,1,..,M − 1, periodogram of m th frame is
given by,
Px
m
,M(k) = 1/M 
N−1
∑
n=0
x
m
(n)e
−2πnk/N

2
(1)
then Welch’s power spectrum estimate is computed
as,
S
W
x
(w
k
) = 1/K
K−1
∑
m=0
Px
m
,M(k) (2)
Upon analyzing the power readings of certain fre
quency components, it was noted that the changes
observed was corresponding to the completed num
ber of passes. Analysing frequency component of
the vibration signal is imperative to ﬁnshing processes
as the fundamental frequency and its harmonics con
tain coherent information which can be atributed to
spindle behavior and also the ﬁnshing of the compo
nent. Shop ﬂoor operators require systems that are
less sophisticated and adopting a frequency domain
analysis method gives that ﬂexbility as opposed to
other machine learning algorithms or statistical meth
ods. Welch’s estimate method is preferred as an eas
ier method to implement in such cases as it gives a
more visual means of interpretation. However, ma
chine learning algorithms provide more stability in
applications involving predictive maintenance.
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