=Paper=
{{Paper
|id=Vol-2098/paper11
|storemode=property
|title=Optimization of Training in Weightlessness with
Respect to Personal Preferences
|pdfUrl=https://ceur-ws.org/Vol-2098/paper11.pdf
|volume=Vol-2098
|authors=Elena V. Fomina,Uliana A. Grushevskaya,Nataliya Yu. Lysova,Dmitry S. Shatov
}}
==Optimization of Training in Weightlessness with
Respect to Personal Preferences==
https://ceur-ws.org/Vol-2098/paper11.pdf
Optimization of Training in Weightlessness with
Respect to Personal Preferences
Elena V. Fomina1 , Uliana A. Grushevskaya2 , Nataliya Yu. Lysova1,3 , and
Dmitry S. Shatov2,3
1
Institute of Biomedical Problems, Russian Academy of Sciences, Moscow, Russia
2
Dostoevsky Omsk State University, Omsk, Russia
3
Sobolev Institute of Mathematics SB RAS, Omsk, Russia
cehbr@list.ru
Abstract. This paper contributes to the problem of life support in
weightlessness conditions during manned flight in space. We consider
an element of prospective autonomic decision support system aimed at
training control of cosmonauts on board. Using a regression model, we
consider one approach to training optimization with respect to personal
preferences of crew members. This approach aims at optimal choice of
treadmill mode of operation and the amount of axial load subject to
maintenance of the level of physical performance at the pre-flight level.
The results of tentative computations based on the experimental data
collected on board the International Space Station are reported and dis-
cussed.
Keywords: Physical exercise · Regression · Long space flight · Locomo-
tor training · Exercise
1 Introduction
The training process is a complex of activities that affect the athlete. In addition,
each athlete has individual psychological and physiological characteristics that
must be considered for proper management of training.
The essence of countermeasure effect in long duration space flight is pre-
vention of decrease of physical performance of cosmonauts. The main means of
countermeasure is locomotor training on treadmill in passive (leg-driven) and
active (motor-driven) mode of operation [1]. The load parameters can be set
and controlled by:
– duration
– heart rate
Copyright c by the paper’s authors. Copying permitted for private and academic purposes.
In: S. Belim et al. (eds.): OPTA-SCL 2018, Omsk, Russia, published at http://ceur-ws.org
Optimization of Training in Microgravity 135
– velocity of locomotion
– axial load (system of bungee cords creates a gravitational load during the
exercise)
– treadmill mode of operation (passive or active)
In long duration space flight, the control of physical condition of cosmonauts
is complicated by the remoteness of ground specialists. In such conditions, the
task of maintaining the physical form of the cosmonauts can be solved using
an on-board automated system that monitors the current state of each crew
member and is aimed at optimizing it. A control system of training process has
been developed and tested in Mars-500 experiment [3]. The system [3] consists
of the following subsystems: the collection and processing of information, the
organization of the measurements, the analysis of the measurements, and the
summarizing. The decisions of this system correspond to the coach’s actions
aimed at the implementation of a certain program of actions and the resolution of
emerging problems. The work reported in the present paper, aims at development
of an alternative approach to design of a decision support system based on
machine learning techniques which may be applied not only for training control
during autonomous space flights, but also for training on Earth.
2 Optimisation of Training with Respect to Physiological
Cost of Work
The analysis is based on data that describes the daily physical training of Russian
cosmonauts on board of the International Space Station, with respect to the
parameters of locomotor training, such as duration, velocity of locomotion, axial
load, treadmill mode of operation (passive or active), heart rate and so on.
The efficiency of physical training was determined in flight on the basis of
the test with stepwise increasing locomotor activity, which was carried out in
passive treadmill motion mode with an axial load not less than 60% of body
weight. The test consisted of the following five stages: 3 min of warm-up walk,
2 min of slow running, 2 min of running at moderate speed, 1 min of running
at maximum speed, and 3 min of cooling-down walk. In general, the duration of
the locomotor sample was 11 min, and its energy value was about 100 kcal.
This test is characterized by standardization of the sequence and duration of
each loading stage, allowing cosmonauts arbitrary choice of the intensity at each
of the work stages. The speed of treadmill motion, selected by the cosmonaut, is
an important informative indicator of his/her fitness level. This test is standard
in assessing the working ability in the Russian system of medical provision of
space flights.
To evaluate the effectiveness of applied training modes, we considered fast
running stage as the most indicative. The physiological cost of work is calculated
as the ratio of the heart rate to the product of the running speed and the change
in the axial load according to the following formula [1]:
HR
P hC = ,
V · AL
136 E. V. Fomina et al.
where
– P hC is the physiological cost of work
– HR is the heart rate
– V is the average speed
– AL is the axial load.
The correlation analysis [2] revealed how the axial load value and the fraction
of the passive mode influence on the change in physiological cost. Thus, the
reverse dependence of the change in the physiological cost of work on the axial
load value and the fraction of the passive mode was shown. That is, in order to
maintain physical performance, a sufficient value of the axial load with which the
cosmonaut performs locomotor physical training and the fraction of the passive
mode play an important role, and when combined correctly, lead to minimal
changes in physiological cost during a space flight. In [2], a linear model based
on the multiple regression was constructed for prediction of physiological cost
on the basis of the axial load value and the fraction of the passive mode. The
adjusted coefficient of determination r2 , which shows the measure of the quality
of the regression model, turned out to be equal to 0.64. An analysis of this model
showed that the minimal change of physiological cost during the flight is achieved
by a sufficient axial load and sufficiently high percentage of the passive mode.
In our research, we formulated a hypothesis that the linear function is too
simplified for this problem and the regression analysis with quadratic functions
might be more appropriate.
Let us introduce the following notations:
P hC is the physiological cost before the flight.
PdhC is the predicted physiological cost in the flight session.
∆PdhC := P hC − Pd hC
The increment of physiological cost is represented as the quadratic form:
[
∆P hC(x, y) = b1 x + b2 y + b3 xy + b4 x2 + b5 y 2 + b6 (1)
Then we formulate a mathematical programming problem as follows:
[
∆P hC(x, y) → 0, (2)
where
bi ∈ R are the regression coefficients,
x ∈ [0, 1] is the axial load value, scaled to the [0,1] interval,
y ∈ [0, 1] is fraction of the passive treadmill mode of operation.
This problem involves only two variables, which allows solving the problem an-
alytically.
Optimization of Training in Microgravity 137
3 Evaluation and Preventing Overfitting
First, we define the machine learning problem using the notation introduced
earlier:
Sl = {s1 , s2 , ..., sl } is the dataset.
∆P hC : Sl → R+ is the target function.
AD = {g(s, b)|b ∈ D} is the predictive model, where
D ⊆ R6 is the parameter space,
x : Sl → [0, 1] is the first feature,
y : Sl → [0, 1] is the second feature,
g(s, b) = b1 x(s) + b2 y(s) + b3 x(s)y(s) + b4 x2 (s) + b5 y 2 (s) + b6 is the responce
function.
L(a, s) = (a(s)P − ∆P hC(s))2 is the loss function (square error), a ∈ AD , s ∈ Sl .
1
Q(a, S) = |S| L(a, s) is the empirical risk (MSE), a ∈ AD , S ⊆ Sl .
s∈S
µ(AD , S) = arg min Q(a, S) is the model that fitted on S using parameter
a∈AD
space D.
As will be shown later, using an entire parameter space of quadratic functions
leads to overfitting in our case. Therefore, we also used limited parameter spaces:
DQ : bi ∈ R
DL : bi = 0, i ∈ {3, 4, 5}
Dxy : bi = 0, i ∈ {4, 5}
D2 : b3 = 0
Dc : bi = 0, i ∈ {1, 2, 3, 4, 5}
We have four data sets, which we consider as four independent (but naturally
similar) tasks:
– fast run, first flight session
– average run, first flight session
– fast run, second flight session
– average run, second flight session
Each data set Sl consists of a very small number of samples (l < 20). This,
however, allows us to use leave-one-out cross-validation to estimate the gener-
alization error of each parameter space. Let us describe in detail the evaluation
procedure.
Thus, consider a fixed D. We can define coefficient of determination as fol-
lows:
Q(a, S)
r2 (a, S) = 1 − , S ⊆ Sl
Q(µ(ADc , S), S)
2
So, we want to find ∆P[hC = µ(AD , Sl ) and calculate rtrain = r2 (AD , Sl ). And
then, we can construct aLOO (cross-predict function) as follows:
∀s ∈ Sl : aLOO (s) = µ(AD , Sl \ {s})(s)
138 E. V. Fomina et al.
And finally, we can get r2 for cross-predicted values:
2
rLOO = r2 (aLOO , Sl )
2 2
We use rLOO (instead of an optimistic rtrain ) as an adequate quality measure
of the predictive model AD defined by the parameter space D.
4 Taking into Account Individual Preferences
Our experiments have shown that for each of the four data sets and for each
parameter space (except for the Dc ) there is a pair (x, y) for which
∆P[hC(x, y) = 0.
Therefore, we solved each of the following problems (separately from each
other):
x → min (3)
and
y → min (4)
considering that the following system of restrictions is fulfilled:
[
∆P hC(x, y) = 0 (5)
x ∈ [0, 1] (6)
y ∈ [0, 1] (7)
5 Computational Results
For each task and parameter space we built the model on the entire data set
and calculated the quality measures, including rank of the search space for each
2
task by rLOO (see Table 1).
For each parameter space we calculated average rank and number of different
signatures among the constructed models (see Table 3). By the signature of the
model, we have in mind the Boolean vector, determined by the sign of each co-
efficient of the model. This metric is designed to reflect some kind of consistency
between models that are found in a given parameter space.
Finally, we solved the optimization problems (see Table 2).
Results indicate that the ”semi-quadratic” predictive model ADxy is the most
reasonable among those considered, and also competes well with the linear one.
6 Conclusion
A new approach to training optimization with respect to personal preferences of
crew members is evaluated. It is shown that given the sample of small size, usage
of the quadratic regression model leads to an overfitting. The most adequate and
robust results are obtained using the linear regression model and its extension
Optimization of Training in Microgravity 139
Table 1. Models and metrics
2 2
Speed Session D rtrain rLOO b1 b2 b3 b4 b5 b6 rank
Avg 1 DL 0.72 0.59 -372.70 -126.59 0.00 0.00 0.00 355.70 1
Avg 1 Dxy 0.74 0.57 -509.56 -349.72 415.50 0.00 0.00 431.58 2
Avg 1 D2 0.72 0.52 58.96 -119.61 0.00 -379.08 -6.75 235.83 3
Avg 1 DQ 0.77 0.48 -486.89 -751.65 861.07 -129.60 153.76 482.03 4
Avg 1 Dc 0.00 -0.14 0.00 0.00 0.00 0.00 0.00 96.81 5
Avg 2 Dxy 0.76 0.62 -530.64 -473.02 712.82 0.00 0.00 421.98 1
Avg 2 D2 0.77 0.56 709.57 140.24 0.00 -904.92 -218.71 -8.26 2
Avg 2 DL 0.67 0.51 -300.96 -90.18 0.00 0.00 0.00 294.34 3
Avg 2 DQ 0.79 0.44 382.44 -179.33 427.01 -729.45 -133.18 129.36 4
Avg 2 Dc 0.00 -0.14 0.00 0.00 0.00 0.00 0.00 88.11 5
Fast 1 DL 0.34 0.10 -257.43 -118.19 0.00 0.00 0.00 291.86 1
Fast 1 Dxy 0.35 -0.03 -407.63 -363.09 456.03 0.00 0.00 375.15 2
Fast 1 Dc 0.00 -0.14 0.00 0.00 0.00 0.00 0.00 102.21 3
Fast 1 DQ 0.38 -0.22 -316.50 -800.72 944.08 -200.36 165.92 411.84 4
Fast 1 D2 0.35 -0.37 281.97 -107.75 0.00 -473.89 -10.06 141.90 5
Fast 2 DQ 0.79 0.52 -919.54 -1016.85 1349.81 134.87 186.81 634.46 1
Fast 2 Dxy 0.75 0.45 -645.08 -577.88 902.74 0.00 0.00 498.38 2
Fast 2 DL 0.65 0.37 -364.25 -95.28 0.00 0.00 0.00 342.10 3
Fast 2 D2 0.66 0.15 3.47 -23.57 0.00 -325.27 -67.00 232.19 4
Fast 2 Dc 0.00 -0.14 0.00 0.00 0.00 0.00 0.00 98.85 5
Table 2. Preferences optimisation
Speed Session D x → min y x y → min
Avg 1 DL 0.615 1.000 0.954 0.000
Avg 1 Dxy 0.847 0.000 0.847 0.000
Avg 1 D2 0.621 1.000 0.870 0.000
Avg 1 DQ 0.000 0.759 0.814 0.000
Avg 2 Dxy 0.000 0.892 0.795 0.000
Avg 2 D2 0.000 0.066 0.012 0.000
Avg 2 D2 0.000 0.576 0.772 0.000
Avg 2 DL 0.678 1.000 0.978 0.000
Avg 2 DQ 0.000 0.520 0.758 0.000
Fast 1 DL 0.675 1.000 1.000 0.291
Fast 1 Dxy 0.350 1.000 0.920 0.000
Fast 1 DQ 0.000 0.585 0.847 0.000
Fast 1 D2 0.671 1.000 0.920 0.000
Fast 2 DQ 0.000 0.719 0.779 0.000
Fast 2 Dxy 0.000 0.862 0.773 0.000
Fast 2 DL 0.678 1.000 0.939 0.000
Fast 2 D2 0.665 1.000 0.850 0.000
140 E. V. Fomina et al.
Table 3. parameter spaces ranking
D Avg rank Signatures
Dxy 1.75 1
DL 2 1
DQ 3.25 3
D2 3.5 3
Dc 4.5 1
that takes into account the combined impact of both factors, the axial load and
the percentage of passive treadmill mode.
Acknowledgement. The work was supported by the program of fundamental
scientific researches of the SB RAS I.3., project 0314-2018-0001. The authors
thank A.V. Eremeev for his help in problem formulation.
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