This paper contributes to the problem of life support in weightlessness conditions during manned ight 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- ight level. The results of tentative computations based on the experimental data collected on board the International Space Station are reported and discussed.
The training process is a complex of activities that a ect 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 e ect in long duration space ight is
prevention 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 [
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 { 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 ight, 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 [
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 e ciency of physical training was determined in ight 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 ve 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 tness level. This test is standard in assessing the working ability in the Russian system of medical provision of space ights.
To evaluate the e ectiveness 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 [
P hC =
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 [
In our research, we formulated a hypothesis that the linear function is too simpli ed 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 ight.
P dhC is the predicted physiological cost in the ight session.
P dhC := P hC P dhC
The increment of physiological cost is represented as the quadratic form:
P [hC(x; y) = b1x + b2y + b3xy + b4x2 + b5y2 + b6 Then we formulate a mathematical programming problem as follows:
P [hC(x; y) ! 0;
where
bi 2 R are the regression coe cients,
x 2 [0; 1] is the axial load value, scaled to the [
Evaluation and Preventing Over tting First, we de ne the machine learning problem using the notation introduced earlier:
space D.
Sl = fs1; s2; :::; slg is the dataset.
P hC : Sl ! R+ is the target function.
AD = fg(s; b)jb 2 Dg is the predictive model, where D R6 is the parameter space, x : Sl ! [0; 1] is the rst feature, y : Sl ! [0; 1] is the second feature, g(s; b) = b1x(s) + b2y(s) + b3x(s)y(s) + b4x2(s) + b5y2(s) + b6 is the responce function.
L(a; s) = (a(s) P hC(s))2 is the loss function (square error), a 2 AD, s 2 Sl. Q(a; S) = jS1j sP2S L(a; s) is the empirical risk (MSE), a 2 AD, S Sl. (AD; S) = arg min Q(a; S) is the model that tted on S using parameter a2AD
As will be shown later, using an entire parameter space of quadratic functions leads to over tting in our case. Therefore, we also used limited parameter spaces: DQ : bi 2 R DL : bi = 0; i 2 f3; 4; 5g Dxy : bi = 0; i 2 f4; 5g D2 : b3 = 0 Dc : bi = 0; i 2 f1; 2; 3; 4; 5g { fast run, rst ight session { average run, rst ight session { fast run, second ight session { average run, second ight session
We have four data sets, which we consider as four independent (but naturally similar) tasks:
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 generalization error of each parameter space. Let us describe in detail the evaluation procedure.
Thus, consider a xed D. We can de ne coe cient of determination as follows: r2(a; S) = 1 ; S
Sl
Q(a; S)
Q( (ADc ; S); S) So, we want to nd P [hC = (AD; Sl) and calculate rt2rain = r2(AD; Sl). And then, we can construct aLOO (cross-predict function) as follows: 8s 2 Sl : aLOO(s) = (AD; Sl n fsg)(s) and considering that the following system of restrictions is ful lled:
And nally, we can get r2 for cross-predicted values: rLOO = r2(aLOO; Sl) 2 We use rL2OO (instead of an optimistic rtrain) as an adequate quality measure 2 of the predictive model AD de ned 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 y ! min P [hC(x; y) = 0 x 2 [0; 1] y 2 [0; 1] (3) (4) (5) (6) (7) 5
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 di erent 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 coe cient of the model. This metric is designed to re ect 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
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 over tting. The most adequate and robust results are obtained using the linear regression model and its extension 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 scienti c researches of the SB RAS I.3., project 0314-2018-0001. The authors thank A.V. Eremeev for his help in problem formulation.