IEEE Computational Intelligence Magazine - November 2020 - 48
signal TR is not beneficial. However, the prediction results have
been boosted when the TR signal was smoothed.
The same procedure has been followed to train RNNs to
predict the CC signal corresponding to Tamil Nadu. The results
of the trained RNN on the test set is presented in Figure 15.
The same effect of smoothing the TR signal is evident in Figure 15(a). The second and third modes of the CC signal are not
as accurate as those of Maharashtra. The reason is that we conformed to the same architecture which was developed initially
for Maharashtra. In the following we discuss this in more details.
We first look into the mean absolute percentage error
(MAPE) corresponding to predictions for both cases, in order
to compare the precision of the two different forecast problems
with one another. The MAPE is calculated as
MAPE = mean e 100 #
pt - yt
o (12)
yt
where p t and y t represent respectively the predicted and
observed values of the time series. The MAPEs for Maharashtra
and Tamil Nadu are 6.23% and 7.77%, respectively.
As explained in Section III-B, the decomposed IMFs with
similar center frequencies are used to train separate RNNs.
Here we further work out the phase of each decomposed IMF
corresponding to the CC, T, and H signals for both states using
Gabor's complex analytical signal X a (t) [33] which is defined as
where X(t) and Xt (t) are respectively the original signal and its
Hilbert transform. One can obtain the instantaneous phase of
each band IMF as follows,
= tan -1 e
Xt (t)
o.(14)
X (t)
Figure 16 shows the obtained unwrapped phase of the IMFs
corresponding to the aforementioned signals for both states
(cf. unwrap() in Matlab). From Figures 16(a) and 16(b), the
phase of the IMFs corresponding to the CC, H, and T signals
of Maharashtra are more synchronised compared to those of
0.1
1,000
0.08
Transmission Rate
Confirmed Cases
z (t)
1,200
800
600
400
0.06
0.04
0.02
200
0
X a (t) = X (t) + jXt (t), (13)
0
10
20
30
40
50
60
70
0
80
0
10
20
30
Day
(a)
40
50
60
70
80
60
70
80
Day
(b)
45
90
40
70
Humidity (%)
Temperature (°C)
80
35
30
60
50
40
30
20
25
0
10
20
30
40
50
60
70
80
10
0
Day
(c)
FIGURE 17 Signals (a) CC; (b) TR; (c) T; and (d) H corresponding to the state Gujarat.
48
IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2020
10
20
30
40
50
Day
(d)
90
IEEE Computational Intelligence Magazine - November 2020
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