IEEE Computational Intelligence Magazine - February 2022 - 110

training and validation subsets and the
remaining 20% for the testing subset.
Then, the previously selected 80% is
divided into 80% for the training subset
and the remaining 20% for the validation
subset. The properties of the datasets are
summarized in Table I.
Finally, the MTS streams are divided
into subsequences through the use of
sliding windows. The window size is set
to 200 time steps (days) and the slide to
5 time steps (days).
2) Parameter Settings
In order to perform any experiments, it
is necessary to define the parameters of
the two GAs included in the proposed
framework. Recall that each of the GAs
is applied twice: once with the initial
dataset that comprises only one window
for each disk (One-window dataset), and
one that is built after the double round
labeling of the windows (Labeled-window
dataset).
For the first GA, a usual scheme in
GAs is followed (see Section II-C1). Specifically,
the probabilities of the crossover
and the mutation are 0.95 and 0.75,
respectively. Each mutation type (addition,
alteration and removal) has the same
probability of occurrence. Additionally,
the population size and the maximum
number of generations are set at 20. Each
individual is trained by the Adam stochastic
optimizer [35] using the cross entropy
as a loss function and a maximum of 45
epochs which may be interrupted if the
classifier does not improve during 3
epochs. Depending on the dataset to
which the method is applied, based on
preliminary experiments, different batch
sizes and learning rates are used:
❏ For the One-window dataset, the
batch size is set to 60 and the learning
rate is initialized to 0.01, decreased to
0.001 during the 36 to 43 epochs and
decreased again to 0.0001 during the
last two epochs.
TABLE I Properties of benchmark datasets.
DATASET
Dataset 1
Dataset 2
Dataset 3
64%/ %/ %16 20
5%
3%
1%
❏ The Labeled-window dataset is larger
and more complex than the previous
one. Therefore, the batch size is set to
128 and the learning rate is initialized to
0.01, decreased to 0.001 during the 6 to
30 epochs, decreased again to 0.0001
during the 31 to 43 epochs, and for the
last two epochs it is set to 0.0001.
Regarding the definition of the individuals,
the number of LSTM and CNN
blocks is limited to a maximum of 3 (for
each type) and to a maximum of 2 for the
pooling blocks. In addition, for the convolutional
blocks, the number of layers is
restricted to values between 1 and 8, the
available choices for the output size are
32, 64, 128, 256 or 512 and the kernel
size can be 1, 3 or 5 based on the settings
used for CNNs in other state-of-the-art
works. For the LSTM blocks, the number
of layers is restricted to values between 1
and 4 and the output size can take the
following values: 64, 128 or 256. All these
restrictions are applied to limit the computational
resources.
For the second GA, the same schema
as for the first one is followed. The
parameters for the GA are the same,
except for the population size, which is
50 individuals instead of 20.
3) Experiments to Compare the
Proposed Approach with Other
Methods
The objective of the experimentation is
to validate the proposed method. To this
end, the results obtained in the original
dataset, Dataset 1 (see Table I), are compared
with those obtained in other
related works.
In general, the approaches used in the
literature are very different in nature, in the
type of data they require, in the evaluation
metrics they apply, etc. In this sense, carrying
out a fair comparison is not always
possible [4], [13]. Taking this into account,
relevant and recent works that have also
addressed the problem as a binary classifiTRAIN/VALID/TEST
IMBALANCE RATE CORRECT DISKS FAILED DISKS
5748
5748
5748
333
177
58
cation problem and are sufficiently
detailed to be replicated are selected. The
methods chosen for comparison are those
described below:
❏ In [17], each daily vector of SMART
measurements is considered an
instance of the classification problem.
Nine raw SMART features highly
correlated to failure events are selected.
Then, they define the lead-time as a
hyper-parameter to optimize and all
the observations inside this lead-time
are labeled as failed samples. In order
to reduce the impact of the class
imbalance, they propose using the
SMOTE oversampling technique.
Finally, logistic regression, SVM, random
forest (RF) and gradient boosted
tree (GBT) classifiers are applied. They
obtain the best results with a lead-time
of 20 observations (days) together with
the SVM with the selected features
and without using the SMOTE, and
with the RF and the GBT with all the
features and without using SMOTE.
These three approaches are applied to
the previously described dataset.
❏ In [16], each daily vector of SMART
measurements is considered an instance
of the classification problem. As in the
previous approach, the lead time is preset,
but in this case, sliding windows and
a majority voting strategy are implemented
for classification. They apply
RF, feed-forward neural networks and
the k-means clustering algorithm for
failure prediction. The best results are
achieved with the RF classifier with
7-observations (days) lead-time and
with windows of 3 observations for the
majority voting strategy.
❏ In [22], the measurements of the
SMART attributes over time are considered
a MTS. To address the problem
of failure prediction they follow this
process: first, they find the subset of
SMART attributes indicative of disk
replacements by identifying those
dimensions of the MTS that have significant
change points. After that, they
compute a compact representation of
the selected dimensions of the fulllength
MTS stream using exponential
smoothing. Each selected dimension of
the MTS is compacted into a single
110 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2022
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