IEEE - Aerospace and Electronic Systems - June 2022 - 9

Alos and Dahrouj
t is a vector of size h
ut;h
pj ¼ Dxt
hþ1
pj
hi
; ... ; Dxt
We use the differential values Dxt
pj
:
pj ¼ xt xt
1
pj
pj
j is the predicted class of the point ðxt
j ¼ class xt
pj 2 Zero; One
fg
(8)
of
each attribute pj to allow higher sensitivity for the occurrences
of faults, following the work of Eliahu [10]. The
output yt
is defined as
yt
pj Þ , which
(9)
where Zero is the Abnormal class, and One is the Normal
class. Accordingly, if the input vector ut;h
pj
Figure 2.
LSTM memory block with one cell (adapted from [7]).
it ¼ s Wxiut þWhiht
1 þWci ct
1 þ biðÞ (1Þ
ft ¼ s Wxfut þWhfht
1 þWcf ct
1 þ bf
(2Þ
ct ¼ ft ct
1 þ it tanh Wxcut þWhcht
1 þ bcðÞ (3Þ
ot ¼ s Wxout þWhoht
1 þWco ct þ boðÞ (4Þ
ht ¼ ot tanhctðÞ
(5Þ
where ut is the input signal at time step t, s is the sigmoid
activation function with a range of [0,1] [see (6)], tanh is
the hyperbolic tangent activation function with a range of
[-1,1] [see (7)], is the elementwise multiplication of
vectors, and W is the weight vector whose elements are
adjusted through the training phase [30]
s zðÞ ¼
tanhz
1
1 þ e
z
ðÞ ¼
ez e
z
ez þ e
z
:
(6Þ
(7Þ
Training the LSTM is accomplished using the backpropagation
through time (BPTT) technique, which is not
in the scope of this article. The reader is referred to [7] for
a full explanation of the BPTT technique. MLSTM considers
sliding windows, so input must be reshaped and preprocessed
before using LSTMs.
RESHAPINGINPUTFORLSTM
Let P ¼fpj :0 


IEEE - Aerospace and Electronic Systems - June 2022
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