Information Technology Reference
In-Depth Information
•
q
3
→
The right foot is in stance phase and the left foot is in stance phase (double
limb support but different of
q
1
because the feet position).
•
→
q
4
The right foot is in swing phase and the left foot is in stance phase (left
limb single support).
Input Vector (
U
)
As we have explained, we only use two of the three available accelerations, which
are
a
x
and
a
y
. Therefore, the set of input variables is:
U
. Each of these
input variables will have only three associated linguistic labels because, as we will
show in the experimental results, they are enough to achieve a good accuracy keep-
ing a high interpretability of the model.
=
{
a
x
,
a
y
}
The linguistic labels for each linguistic
variable are:
,where
S
,
M
and
B
are linguistic
terms representing small, medium, and big, respectively.
As an initial step, we normalized the signals. First, we subtracted the average
making them to be centered on zero. Then, we rescaled them in the range given by
their standard deviations. This allowed us to perform the analysis at the scale that
gives us more information about the signal changes.
{
S
a
x
,
M
a
x
,
B
a
x
}
and
{
S
a
y
,
M
a
y
,
B
a
y
}
Transition Function (
f
)
As showed in Section 11.2.2, the only thing required to determine the structure of
the FRBS is the definition of which transitions are allowed and which are not. This
is easily represented by means of a state diagram. Fig. 11.3 shows the proposed state
diagram of the FFSM for the human gait cycle. This state diagram is very simple
because the accelerations produced during the human gait are quasi-periodic, i.e.,
they are repeated with approximately similar values and periods. Moreover, all the
states are correlative, i.e., they always follow the same activation order. Therefore,
it is rather easy to define the allowed transitions and the forbidden ones.
From the state diagram represented in Fig. 11.3 it can be recognized that there
are 8 fuzzy rules in total in the system, 4 rules to remain in each state and other 4 to
change between states. In contrast to machine learning techniques, we derived the
rules from the designer's perceptions about the human gait acceleration signals. We
chose
q
1
as the initial state, i.e.,
S
0
=(
. The FFSM is able to synchronize
without the need of doing previous segmentation of the signal when the conditions
of
q
1
are fulfilled. We defined the conditions of amplitude to remain in a state or to
change between states by combining the information obtained from the sensors and
the available expert knowledge about the human gait. We applied self-correlation
analysis to the vertical acceleration to obtain an approximation of the signal period
T
. In agreement with our knowledge about the typical human gait cycle, we as-
signed to each state a duration according to its percentage of the period
T
. Fig. 11.2
shows a generic example of the linguistic labels
T
st ay
and
T
change
used to define the
temporal constraints.
1
,
0
,
0
,
0
)
