chapter 5 cancellation of mecg signal in...
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CHAPTER 5
CANCELLATION OF MECG SIGNAL IN FECG
EXTRACTION
5.1 INTRODUCTION
The analysis of the fetal heart rate (FHR) has become a routine
procedure for the evaluation of the well-being of the fetus. Factors affecting
FHR are uterine contraction, baseline variability, hypoxia and oxygenation.
This method has many drawbacks such as position-sensitivity, signal drop out,
frequent confusion between maternal heart rate and FHR, failure in obese
patients (which in turn increases the rate of cesarean), and misinterpretation of
cardiotocogram traces and failure to act in time. The use of FECG for
monitoring the fetus overcomes all these limitations (Zarzoso et al 2001).
However, FECG is mixed with interferences. In this chapter a brief
introduction about fetal monitoring techniques, applications of FECG, and
various interferences in FECG are discussed. Experimental results of
interference (MECG) cancellation using BPN, CCN, ANFIS, and ANFIS-
FCM are also presented.
5.2 FETAL MONITORING TECHNIQUES
The most popular techniques available for noninvasive antepartum
fetal monitoring systems are fetal phonography, ultrasonography and
antepartum FECG.
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5.2.1 Phonography and Phonocardiography
Fetal phonography is the transcription of fetal sounds.
Phonocardiography specifically involves the transcription of fetal heart
sounds. Both cases are achieved by sensing fetal vibrations incident on the
maternal abdomen. The clinical results obtained using phonocardiography for
fetal monitoring are poor. The lack of success of phonographic monitoring
systems is attributed to inappropriate transducer design; typically the
transducers used for fetal heart monitoring are variants of those used for
adults. The resulting signal has a poor SNR. This requires heavy filtering,
which in turn leads to attenuation of potentially valuable signal information.
5.2.2 Ultrasonography
Fetal surveillance has relied heavily on ultrasound imaging since
the mid 1970s. Ultrasonic images are formed by the selective reflection of
acoustic energy in soft biological tissue. In medical imaging, ultrasound in the
frequency range of 2 to 20 MHz is coupled to the body by means of a piezo-
electric transducer.
The available systems for fetal monitoring are divided into those
providing one and two dimensional image data. The one dimensional system
employs a narrow ultrasound beam, which is used to illuminate specific fetal
structures. The resulting ultrasound reflections are detected and the motion of
the reflecting structure is quantified by using the Doppler principle. Doppler
ultrasound is routinely used to visualize the motion of fetal structures such as
heart valves. It is used as the basis for estimating heart rate. Portable (bedside)
Doppler ultrasound systems to monitor the FHR, e.g. the cardiotocograph, are
in common use. However there are objections to their routine use in long term
fetal monitoring. Firstly, there is some concern amongst clinicians on the
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safety to the fetus of prolonged exposure to ultrasound radiation. Secondly,
the naturally occurring fetal movements must be tracked by the ultrasound
beam. This requires close operator supervision because gross fetal movements
are often sporadic.
The two dimensional systems generate an array of ultrasound
beams. The beam array can be swept or scanned across the fetus and a two
dimensional image is formed using the detected ultrasound reflections. This is
referred as B-mode (brightness mode) ultrasonography. The systems
providing two dimensions of image data enable the routine characterization of
many physical fetal activities. However, their high capital and running costs
limits their use to short term monitoring in a clinical environment.
5.2.3 Fetal Electrocardiography
The FECG signal yields information about the condition of the
child during pregnancy. It is recorded non-invasively from the belly of the
pregnant woman. But it is mixed with noise like the MECG, respiration
baseline wander, power line interference etc. The low fetal SNR makes it
impossible to analyze the FECG. Attenuating the noise by classical filtering
techniques is not satisfactory due to an overlap in spectral content with the
FECG. The characteristics of each noise signal determine which signal
processing technique should be applied in order to achieve its removal.
5.3 APPLICATIONS OF FECG
FECG is used to determine several abnormalities of fetus such as
fetal asphyxia, congenital heart diseases (CHD), arrhythmias, etc. Fetal
asphyxia results from insufficient uterine blood flow and decreased maternal
arterial oxygen content. The diagnoses of asphyxia based on FHR gives an
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inaccurate result because there is no precise relationship that exists between
asphyxia and FHR. CHD refers to a problem with the heart's structure and
function due to abnormal heart development before birth. Cardiac arrhythmia
is a group of conditions in which the muscle contraction of the heart is
irregular or is faster or slower than normal. FECG is also used to diagnose
fetal position, twins and fetal well-being.
5.4 MEASUREMENT OF FECG
The diagnostic tests of fetal well-being are categorized as invasive
and noninvasive. During delivery, accurate recordings can be made by placing
an electrode on the fetal scalp. However, as long as the membranes protecting
the child are not broken, one should look for noninvasive techniques. Further,
the use of noninvasive techniques enables the monitoring of well-being of
fetus from the early period of pregnancy onwards. The amplitude of FECG
increases during the first 25 weeks, mini towards the 32nd week and increases
again afterwards. Some of the problems that limit the extraction of FECG
using noninvasive technique are the presence of background noise leading to
poor SNR, no standard electrode positioning for optimizing acquisition, and
the shape of the signal that depends on the position of the electrodes and the
gestational age. Moreover, electrode output from the abdomen is hampered by
many artifacts. Therefore, it is required to remove these artifacts from FECG.
The types of artifacts are discussed in detail in section 5.5.
5.5 ARTIFACTS IN FECG SIGNAL
The artifacts in FECG signal are power line interference, electrode
contact noise, motion artifact, muscle contraction, baseline drift,
instrumentation noise generated by electronic devices, MECG, and EMG due
to uterus contraction and respiration.
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5.5.1 Power Line Interference
The cables carrying ECG signals from the examination room to the
monitoring equipment are susceptible to electromagnetic interference of
power line frequency. It consists of 50-60 Hz pick up and harmonics, which
are modeled as sinusoids. The amplitude varies up to 50 percent of the peak-
to-peak ECG amplitude. Many researchers have done work to cancel this
interference from the ECG signal. Specifically, adaptive noise cancellation
addresses this problem.
5.5.2 Electrode Contact Noise
It is a transient interference caused by loss of contact between the
electrode and the skin that effectively disconnects the measurement system
from the subject. The loss of contact can be permanent, or can be intermittent
as would be the case when a loose electrode is brought in and out of contact
with the skin as a result of movements and vibration. This switching action at
the measurement system input can result in large artifacts since the ECG
signal is usually capacitive coupled to the system. It can be modeled as
randomly occurring rapid baseline transition, which decays exponentially to
the baseline value and has a superimposed 50 Hz component.
5.5.3 Motion Artifact
Motion artifact is transient baseline changes caused by changes in
the electrode-skin impedance with electrode motion. As this impedance
changes, the ECG amplifier sees different source impedance, which forms a
voltage divider with the amplifier input impedance. Therefore, the amplifier
input voltage depends upon the source impedance, which changes as the
electrode position changes. The usual cause of motion artifact is assumed to
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be vibrations or movements of the patient. This type of interference represents
an abrupt shift in baseline due to movement of the patient while the ECG is
being recorded.
5.5.4 Electromyogram
The muscle contractions generate millivolt level potentials. EMG
noise has a frequency range of 1-5000 Hz. EMG is measured from within the
muscle or from the skin surface overlying the muscle. It has a spatial and
temporal interference pattern of the electrical activity of the activated motor
units located near the detection surfaces.
5.5.5 Baseline Drift
The baseline drift is low frequency interference in ECG signal
caused due to respiration. It is nothing but change in the d.c component of the
ECG signal. The drift of the base line with respiration is represented by a
sinusoidal component at the frequency of respiration (less than 0.5 Hz) added
to the ECG signal. The amplitude and the frequency of the sinusoidal
component are variables. The variations can be represented by amplitude
modulation of the ECG by the sinusoidal component added to the baseline.
5.5.6 Maternal Electrocardiogram
The main source of interference in FECG is MECG. It is a quasi-
periodic signal with a fundamental frequency of about 1 Hz. The fundamental
frequency of the FECG is about twice as that of MECG. The amplitude of
MECG is much higher (5 to 100 times) than that of the FECG. Hence, it is
difficult to recognize the FECG unless the MECG is cancelled. The main aim
of this work is therefore to eliminate the MECG.
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5.6 CANCELLATION OF MECG BY AIC
The mother and fetal hearts behave independently, which means
that both are uncorrelated. MECG is mainly recorded on the mother’s chest.
The effect of FECG on MECG is negligible due to the large distance between
the small fetal heart and the mother’s chest electrodes, also the magnitude of
FECG is less compared to that of MECG. But, when FECG is measured at the
abdomen of the mother, MECG is a significant interference. The problem in
hand deals with the suppression of MECG component in FECG. The block
diagram of AIC for FECG extraction is shown in Figure 5.1.
Figure 5.1 Block diagram of AIC for FECG extraction
In Figure 5.1, the signal measured from mother’s abdomen )(ky is
inevitably noisy due to the mother’s heartbeat signal )(kn , which is measured
clearly via sensor at the thoracic region. However, )(kn does not appear
directly in )(ky . Instead, it travels through the nonlinear passage (mother’s
ECG recorded from Mother’s Abdomen
FECG
ECG recorded from mother’s chest as the reference Signal
Adaptation Techniques
MECG Nonlinear passage
Estimated interferen
-
+
Estimated FECG Measured
signal
Σ Σ
)(ˆ kd
)(kx +
)(kd
)(kn
+
)(ky 0)(),(
)()()(ˆ)()()(ˆ
keaskxkekx
kdkdkxkx
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body) and appears as delayed and distorted version of )(kn called as
interference i.e. )(kd . A clean version of the noise signal (MECG) that is
independent of the required FECG signal is considered in order to estimate
the interference. It acts as a reference signal for the adaptation. As long as
)(kx is not correlated with )(kn , )(ky can be used as the desired output for
training. In this report BPN, CCN, ANFIS and ANFIS-FCM are used as the
adaptation techniques to estimate the MECG interference in the measured
signal )(ky . When the estimated interference is very close to the actual
interference in )(ky , these two get cancelled and the required FECG signal is
obtained as the output. The implementation phases for AIC in real biosignals
are given in the form of a flowchart in Figure 5.2.
Figure 5.2 Flowchart for implementation of AIC in real biosignals
In FECG extraction, proposed techniques take the MECG as the
reference signal and the measured signal (abdominal signal), )(ky as the target
Delayed noise signal
Noise Signal
Adaptation Techniques
Estimated interference
Estimated required signal
Σ
- +
Measured signal
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signal and try to estimate the MECG present in the measured signal. Once the
designated epoch is reached or the goal (minimum value of )(ˆ kx ) is reached
(whichever is earlier), it stops training and gives the estimated
interference )(ˆ kd . Then FECG is extracted by simply subtracting )(ˆ kd
from )(ky . The flowchart for finding the noise in the estimated signal is shown
in Figure 5.3. The noise is obtained by passing the estimated signal (FECG)
through a Butterworth filter. The cut off frequency is selected based on the
frequency component of the estimated signal.
Figure 5.3 Flowchart for finding the noise in the estimated signal
The signals recorded at a sampling frequency of 500 Hz for about
5 seconds from 8 electrodes located on a pregnant woman’s body
(5 electrodes on the abdomen and 3 electrodes on the chest) are considered to
extract the FECG. These signals are taken from the website mentioned by
Jafari et al (2005).
Butterworth Filter
Σ
-
+
Noise
Estimated Signal obtained from AIC
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The real cutaneous electrode recordings for a duration of 2 seconds
(1000 samples) are plotted in Figures 5.4 and 5.5. Figure 5.4 shows the
abdominal signals recorded in 5 locations. They have both MECG and FECG
along with some high frequency noise. Figure 5.5 shows the signals recorded
in the mother’s thoracic region (MECG). Due to the longer distance between
the thorax electrodes and the fetal heart, no FECG heartbeat component can
be perceived in Figure 5.5. The abdominal signal, abd1 and thoracic signal
(MECG), thr3 are used in this work for AIC as these signals posses rich
information.
Figure 5.4 Abdominal signals from different electrode positions
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Figure 5.5 MECG signals recorded at the thorax region of a pregnant
woman
5.7 IMPLEMENTATION OF ADAPTATION TECHNIQUES
FOR AIC
The implementation of proposed adaptation techniques is explained
in this section.
5.7.1 Implementation of BPN
The software used for the implementation of BPN is MATLAB.
The steps used are:
1. Specifying the inputs and targets to the BPN.
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2. Giving the minimum and maximum values of the input
ranges.
3. Specifying the number of layers and the number of units in
each layer.
4. Mentioning the activation functions for each layer.
TANSIG is a hyperbolic tangent sigmoid transfer
function which is used as the activation function for the
hidden layer to calculate a layer's output from its net
input
PURELIN is a linear transfer function which is used as
the activation function for the output layer
5. Creating a feed forward back propagation network model by
using the command called NEWFF.
6. Simulating the network for plotting the network output.
7. Specifying the training parameters like
learning rate
momentum
performance goal
number of epochs etc.
8. Training the network using the training function called
TRAINLM.
9. Giving the conditions to stop training the network
The maximum number of EPOCHS (repetitions) is
reached or
The maximum amount of TIME has been exceeded or
Performance has been minimized to the GOAL or
The performance gradient falls below MINGRAD.
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5.7.2 Implementation of CCN
The software used for the implementation of CCN is same as that
of BPN. The CCN procedure includes the following steps.
1. Specifying the inputs and targets to the CCN.
2. Giving the minimum and maximum values of the input
range
3. Mentioning the number of neurons randomly in different
layers
4. Forming a rough architecture with the randomly specified
neurons using NEWCF.
5. Refining the architecture by finding the covariance between
the input and the rough architecture output.
6. Obtaining the final architecture by including the maximum
covariance unit.
7. Remaining steps are same as that of BPN.
5.7.3 Implementation of ANFIS
The basic steps used in the computation of ANFIS are given below:
1. Specifying the inputs and targets
2. Generating an initial Sugeno type FIS system using the
MATLAB command GENFIS1. It goes over the data in a
crude way and finds a good starting system.
3. Giving the parameters like number of iterations (epochs),
tolerance error etc for learning.
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4. Leaning process starts using the command ANFIS and stops
when goal is achieved or the epoch is completed, whichever
is earlier.
5. The EVALFIS command is used to determine the output of
the FIS system for given input.
5.7.4 Implementation of ANFIS-FCM
ANFIS-FCM uses the implementation steps similar to that of
ANFIS except the data clustering operation. The steps for ANFIS-FCM
include:
1. Initializing the membership matrix with random values
between 0 and 1
2. Calculating the fuzzy cluster centers
3. Computing the cost function (or objection function)
4. Stopping the training if either it is below a certain tolerance
value or its improvement over previous iteration is below a
certain threshold.
5. Compute a new membership matrix
5.8 EXPERIMENTAL RESULTS
Experiments are carried out to cancel the MECG in FECG using
different AI techniques. The techniques along with their results are discussed
in this section.
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5.8.1 Results with BPN
The BPN used for MECG cancellation consists of an input layer
with two neurons, hidden layer with 35 neurons and an output layer with
single neuron. Its structure is shown in Figure 5.6 (a), where
IW {1, 1} = Initial weights connecting the layer inputs to the
hidden layer,
LW {2, 1} = Layer weights connecting the output of hidden layer
to the inputs of output layer
b {1} = Layer 1 bias values
b {2} = Layer 2 bias values.
Figure 5.6(b) shows the flow diagram from the input to the output
of the network, where p {1} represents the input layer, a{1} is the hidden
layer, a{2} is the output layer and y{1}is the output. Figure 5.6(c) gives the
details between p {1} and a{1}. The details of weights between p{1} and
a{1} are shown in Figure 5.6(d). It shows only 5 neurons weight out of 35
neurons in the hidden layer for simplicity. The connections between the
hidden and output layer are shown in Figure 5.6(e). The weights between
a{1} and a{2} are shown in Figure 5.6(f).
(a) BPN structure with single input layer, single hidden layer and an
output layer
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(b) Flow diagram from the input to the output of the network
(c) Connection between the input layer and the hidden layer
(d) Weights between the input layer and the hidden layer
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(e) Connection between the hidden layer and the output layer
(f) Weights between the hidden layer and the output layer
Figure 5.6 BPN structure for FECG extraction
The parameters used for training BPN are epochs = 10, learning
rate = 0.5, parameter goal set =0.65, minimum time to train in
seconds = infinity and momentum =0.9. The performance criteria used in
BPN is Mean Square Error. The training result is shown in Figure 5.7 which
gives the relationship between the epochs and the MSE.
Figure 5.7 Training results of BPN
Trai
ning
, Goa
l
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The results of AIC using BPN are shown in Figure 5.8. Only 350
samples of data are shown in this Figure for clarity purpose. In Figure 5.8 (a)
is the abdominal signal (which contains both MECG and FECG), (b) is
MECG alone (c) is the estimated thoracic signal determined by BPN, (d) is
the estimated FECG after cancellation and (e) is the noise present in the
estimated FECG after AIC.
Figure 5.8 Results with BPN (a) Abdominal signal (b) MECG
(c) Estimated MECG in Abdominal signal (d) Estimated
FECG (e) Noise after AIC
In this work, a Butterworth filter of order 5 and normalized
frequency of 0.7 is considered. Arrow in Figure 5.8 (d) shows the presence of
MECG in estimated FECG even after AIC. Based on this signal, it is difficult
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to differentiate the FECG component from the MECG. It is, hence, observed
that the cancellation of MECG is not perfect when BPN is used.
5.8.2 Results with CCN
Another AI technique namely CCN is used for AIC. The structure
of CCN for FECG extraction is same as that of BPN except the way in which
the weights are adjusted. The results of AIC with CCN are shown in Figure
5.9. They give all the information which are same as in Figure 5.8. In Figure
5.9 (d), arrow indicates the presence MECG component which is less than
that in the BPN method. But, significant noise is present between 50 and 100
samples
Figure 5.9 Results with CCN (a) Abdominal signal (b) MECG
(c) Estimated MECG in Abdominal signal (d) Estimated
FECG (e) Noise after AIC
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5.8.3 Results with ANFIS
Matlab version 7.5 is used for software implementation of ANFIS.
Since no idea is available about the initial membership functions, the
command called genfis1 is used to examine the training data set and generate
a single output Sugeno type FIS that is used as the starting point for ANFIS
training. Fuzzy model with 2 inputs and one output generated by this
command is shown in Figure 5.10, where delayed thoracic and thoracic
represent the inputs to the fuzzy model. Each input contains 3 MFs. Infismat
represents the system name and has 9 fuzzy rules. Estimated thoracic
represents the system output. Since the Sugeno type FIS is used in this
application, defuzzification is not required at the output.
Figure 5.10 Fuzzy model generated by GENFIS
After generating the fuzzy model, ANFIS requires a good number
of epochs, training pair, and MFs for training. The function used for training
is anfis, and generalized bell shape MF (gbellmf) is used for ANFIS training.
The structure of ANFIS used for the extraction of FECG is shown in Figure
5.11. Two nodes are present in the input layer and the inputs are MECG and
the delayed MECG. Fuzzification is done by layer 1 (inputmf) which allocates
3 MFs to each input. Totally 9 rules are used in layer 2 (rule). Normalization
layer (layer 3) is not included in this architecture. Layer 4 is the
defuzzification layer (outmf). Layer 5 performs summation operation. After
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training, the estimated MECG is obtained using the command evalfis. The
results obtained through ANFIS are shown in Figure 5.12.
Figure 5.11 ANFIS structure
Figure 5.12 Results of AIC in FECG with ANFIS (a) Abdominal signal
(b) MECG (c) Estimated MECG in Abdominal signal
(d) Estimated FECG (e) Noise after AIC
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It may be observed that the magnitude of noise that is present
between 50 and 100 samples in Figure 5.12 (d) is very much less than that in
Figure 5.9 (d). By comparing the Figures 5.8 (d), 5.9 (d) and 5.12 (d), it is
inferred that ANFIS gives better cancellation of MECG without degrading the
FECG. Three more cases are considered to demonstrate the power of ANFIS
in FECG extraction. Figure 5.13 (a) shows a case in which the measured
signal contains 3 non-overlapping FECG beats and 2 MECG beats.
Figure 5.13 (b) shows the output of ANFIS which is the estimated MECG
present in the abdominal signal and Figure 5.13 (c) shows the estimated
FECG.
Figure 5.13 ANFIS output (a) Abdominal signal with non-overlapping
FECG beats and MECG beats (b) Estimated MECG
(c) Estimated FECG
Figure 5.14 (a) shows the second case where the abdominal signal
consists of partially overlapping FECG beats and MECG beats.
Figures 5.14 (b) and (c) show the MECG and estimated MECG in abdominal
signal respectively. Figure 5.14 (d) shows the estimated FECG.
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Figure 5.15 (a) shows the third case (same as Figure 5.12) in which the
abdominal signal has full overlap between the first FECG and the MECG
beats. This represents the extreme case where the FECG is completely
masked by the MECG component to the extent that the FECG beat is no
longer visually distinguishable. The three arrows in Figure 5.15 (a) indicate
the location of FECG signal in the abdominal signal. The three arrows in
Figure 5.15 (c) indicate the location of the estimated FECG signal. Figure
5.15 (c) shows that the ANFIS technique is successful in extracting the FECG
signal in this case also. However, the extracted FECG in the overlapping
region is slightly distorted compared to the FECG in other locations.
Figure 5.14 ANFIS output (a) Abdominal signal containing partially
overlapping FECG beat and two MECG beats (b) MECG
(c) Estimated MECG (d) Estimated FECG
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The 2 second signals are divided into different frames in order to
explain the effectiveness of the proposed technique for the extraction of
FECG. Practically, if the signals are divided into many frames, then there is a
possibility of losing some important data. It also increases the processing time.
But ANFIS can process the entire data without frames which in turn decreases
the processing time. In order to find out the SNR of the estimated FECG
signal Butterworth filter is used to separate the amount of noise present in the
estimated FECG.
Figure 5.15 ANFIS output (a) Abdominal signal containing full overlap
between the first FECG beat and the MECG (b) Estimated
MECG (c) Estimated FECG
Results with ANFIS-FCM
Though ANFIS yields better performance than BPN and CCN, the
use of Fuzzy C– Means clustering method is also investigated to explore the
possibility of reducing mean square value of the estimated FECG signal and
convergence time and increasing SNR.
(a)
(b)
(c)
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In this application of ANFIS-FCM, the ANFIS structure is chosen
as explained in section 5.8.3. Four clusters are considered in order to cluster
the input data. Based on the cluster centroid and the nature of the signal
characteristics, the number of samples in each cluster varies. It is shown in
Figure 5.16. Cluster diagram varies from time to time depending on the
selection of the centroid. Clustering takes the advantage of less data searching,
fast convergence time and less mean square value of the estimated FECG.
The results of AIC using ANFIS-FCM are presented in Figure 5.17. Centroid
values obtained for 2 inputs and a target data are given below.
Delayed Thoracic signal = [-186.5163 31.9500 -25.7755 613.6460]
Thoracic Signal = [-177.2455 32.9020 -25.7821 623.2298]
Target = [12.3848 -2.1505 0.5948 -39.6686]
Figure 5.16 Four clusters of ANFIS-FCM
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Figure 5.17 ANFIS-FCM output (a) Abdominal signal (b) MECG
(c) Estimated MECG in Abdominal signal (d) Estimated
FECG (e) Noise after AIC
If the Figures 5.15(c) and 5.17(d) are compared, visually it is
difficult to make any difference. But the quantitative comparison in terms of
performance criteria shown in Table 5.1 clearly indicates the improved
performance of ANFIS-FCM over ANFIS.
5.9 PERFORMANCE COMPARISON
In order to make a comparative study of the four AI techniques
used for the cancellation of MECG in the abdominal signal, three
performance criteria namely mean square value of the estimated FECG signal,
SNR and convergence time are computed in each case as discussed in
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section 4.6. The parameters used for the comparison are MF=3, Epochs=10,
SS=0.5 and samples =350. The computed values are presented in Table 5.1.
Table 5.1 Performance comparison of AI techniques in FECG
Sl.No. Technique Mean Square value
of the estimated FECG SNR (dB)
Convergence Time(s)
1 BPN 28.3577 9.2233 1.9530
2 CCN 15.0883 8.3267 1.4220
3 ANFIS 12.2366 25.1788 1.0920
4 ANFIS -FCM 11.6366 37.2695 0.6410
From Table 5.1, it is concluded that ANFIS- FCM produces least
Mean Square value of the estimated FECG and convergence time and highest
SNR among the four techniques. The effects of varying parameters like
epochs, step size, membership function on the performance are discussed in
the following section.
5.10 EFFECT OF VARYING TRAINING PARAMETERS IN
ANFIS
In order to choose the optimum values for the important training
parameters like epochs, step size, and membership function, it is necessary to
study the effect of variation on the parameters.
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5.10.1 Effect of Varying Epochs
The number of epochs is varied from 10 to 50 in steps of 10 and the
performance criteria are computed for each value epoch. The results of
variation of epochs are presented in Table 5.2.
Table 5.2 Comparison of performance criteria by varying the epochs
Sl.No Epochs Mean Square value
of the estimated FECG SNR(dB)
Convergence Time (s)
1 10 12.0253 23.8848 0.375
2 20 12.0194 24.2073 0.641
3 30 11.9651 24.3714 0.86
4 40 11.9651 24.3714 1.125
5 50 11.9651 24.3714 1.359
It is observed from Table 5.2 that when the number of epochs
increases, its effect on Mean Square value of the estimated FECG and SNR is
very less, but it increases the convergence time. Hence epoch 10 is selected
by a default for ANFIS training.
5.10.2 Effect of Varying Step Size
The step size in ANFIS training is varied from 0.2 to 0.7 in steps of
0.1. The computed values of performance criteria for different step sizes are
given in Table 5.3.
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Table 5.3 Comparison of performance criteria by varying the step size
Sl.No Step size Mean Square value
of the estimated FECG
SNR
(dB)
Convergence Time (s)
1 0.2 12.0224 24.1441 0.375
2 0.3 11.9936 24.294 0.391
3 0.4 11.996 24.3761 0.375
4 0.5 12.0253 23.8848 0.375
5 0.6 11.7968 25.021 0.375
6 0.7 11.8065 24.5793 0.375
Average 0.45 11.9401 24.38321667 0.377666667
It is noted from Table 5.3 that variation in SS produces random
variation in Mean Square value of the estimated FECG, SNR and
convergence time. Hence, an average SS value of 0.5 is used for training.
5.10.3 Effect of Varying the Number of MF
The number of MF used in ANFIS training is varied form 2 to 6 in
steps of one. The performance criteria are calculated for each MF and are
shown in Table 5.4.
It is inferred from Table 5.4 that when the MF increases, Mean
Square value of the estimated FECG decreases which in turn increases the
SNR. However, it also increases the convergence time. Hence, an MF value 3
is chosen as a compromise between the Mean Square value of the estimated
FECG and the convergence time.
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Table 5.4 Comparison of performance criteria by varying the number
of MF
Sl.No MF Mean Square value
of the estimated FECG Convergence Time (s)
1 2 12.3277 0.219
2 3 12.0253 0.406
3 4 11.6519 0.797
4 5 11.2837 1.657
5 6 10.6925 3.141
5.10.4 Choice of the Type of MF
Five different types of MF (Gaussian two sided, Trapezoidal,
Gaussian Single sided, Triangular, Gbell) are tried for ANFIS training. The
variation of performance criteria for these types is given in Table 5.5. When
the type of MF is changed, there is no significant variation in Mean Square
value of the estimated FECG and convergence time. Since Gbell has a
property of smoothness and also yields less Mean Square value of the
estimated FECG, it is used to generate the fuzzy model. The shape of the MF
changes during the process of ANFIS training. The shape of the MF before
and after training is shown in Figure 5.18. The x axis in Figure 5.18
represents the amplitude range of the input and the y axis gives the
membership value. During training, ANFIS varies the MF parameters to map
the reference inputs with the target.
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Table 5.5 Choice of the type of MF on the performance criteria
Sl.No MF Type Mean Square value
of the estimated FECG Convergence
Time (s)
1 Gaussian 2 sided 12.4183 0.469
2 Trapezoidal 12.386 0.391
3 Gaussian 12.2173 0.39
4 Triangular 12.1181 0.36
5 Gbell 12.0253 0.375
Figure 5.18 MF before and after training
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The ANFIS-FCM technique uses the same training parameters as
that of ANFIS. Hence, separate study of variation in performance criteria for
changes in training parameters is not required.
5.11 CONCLUSION
The motivation for monitoring the fetus during pregnancy is to
recognize pathologic conditions, typically asphyxia, with sufficient warning
to enable intervention by the clinician before irreversible changes set in.
However, the monitoring techniques in current practice have serious
shortcomings. The noise free FECG is required to overcome these limitations.
Measurement of FECG is affected with many artifacts. The major artifact
called MECG is cancelled from the FECG using four AI techniques.
Performance comparison of these techniques has been made in terms of Mean
Square value of the estimated FECG, SNR, and convergence time.