and Computational Methods

#### 539.3+519.86 Multiscale modeling of elastic-plastic composites with an allowance for fault probability

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2016-2-323

The purpose of this article is to propose a model of deformation of elastic-plastic composite materials with periodic structures with an allowance for fault probability of the composite phases. The model is based on a variant of the deformation theory of plasticity with the active loading. To simulate the effective characteristics of elastic-plastic composites, we applied the method of asymptotic homogenization of periodic structures. For numerical solution of linearized problems on the periodicity cell we offered the finite elements method using SMCM software medium developed at the Scientific-Educational Center of Supercomputer Engineering Modeling and Program Software Development of the Bauman Moscow State Technical University. We provide the research with the examples of numerical computations for dispersion-reinforced metal composites (aluminum matrix filled with SiC particles). Finally, we present the results of numerical modeling of deformation processes, damage accumulation and metal-composite destruction.

Dimitrienko Y., Gubareva E., Sborschikov S. Multiscale modeling of elastic-plastic composites with an allowance for fault probability. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 3-23

#### 536.24 Parametric identification of a mathematical model of heat exchange process for thin-walled curved shells of turbomachines

**Andrianov I. K. (Komsomolsk-na-Amure State Technical University), Grinkrug M. S. (Komsomolsk-na-Amure State Technical University)**

doi: 10.18698/2309-3684-2016-2-2438

The paper considers a mathematical model of the heat exchange process occurring in the thin-walled curved shells of turbomachines. We propose an algorithm for calculating the thermal state on the boundary surfaces of the shell and of the coating according to the desired thermal condition. We present the calculation results of the temperature distribution in the given temperature field for the most terminally loaded shell surface caused by the heat effect.

Andrianov I., Grinkrug M. Parametric identification of a mathematical model of heat exchange process for thin-walled curved shells of turbomachines. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 24-38

#### 629.762 Aircraft motion parameters recovery from the data of their discrete registration. Part 2. Methods using regularization

**Plyusnin A. V. (Bauman Moscow State Technical University/JSC MIC NPO Mashinostroyenia)**

doi: 10.18698/2309-3684-2016-2-3954

The article examines methods of aircraft motion parameters recovery from the data of their low resolution recordings in the gas-dynamic ejection experimental test.

Plyusnin A. Aircraft motion parameters recovery from the data of their discrete registration. Part 2. Methods using regularization. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 39-54

#### 531.36:521.1 Modeling of a space station dynamics in vicinity of an asteroid

**Rodnikov A. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2016-2-5568

We suggest classification for dynamical problems of a space station motion near a precessing small planet. This classification is based on three signs. These signs are the model of the asteroid gravitational potential, the method of holding the space station near the small planet, the type of dynamical problem. Within the offered classification we review the results received earlier. In particular, we construct sets of the space station equilibria or stationary orbits if the asteroid gravitational potential is composed by potentials of two real or conjugate complex point masses on real or imaginary distance and if the station coast along the leier or it moves freely. (In our case the leier is a tether with ends fixed in the asteroid poles). Moreover, we establish some facts of stability for the found orbits and equilibria and note some integrable cases of the motion equations along the leier

Rodnikov A. Modeling of a space station dynamics in vicinity of an asteroid. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 55-68

#### 519.8 Stochastic models of the two unit duel fight

**Chuev V. U. (Bauman Moscow State Technical University), Dubogray I. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2016-2-6984

On the basis of the theory of continuous Markov processes we developed models of the two unit duel fight. We obtained computing formulas for calculating the basic fight indicators. Moreover, we found that the pre-emptive strike of one of the units participating in the fight has a significant impact on the fight outcome of the units which are similar in forces. The strike has a negligible impact, if one of the units has a significant advantage. The findings of the research show that the use of model with constant effective firing rates can lead to significant errors in the evaluation of its results. Finally, we found that the pre-emptive strike, coupled with a high degree of effective firing rate growth, can sometimes compensate for more than the double initial superiority of the opponent. We show the possibility of using approximations of the effective firing rate of the fighting units by the different functions of the fight time.

Chuev V., Dubogray I. Stochastic models of the two unit duel fight. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 69-84

#### 519.237.07 Factorial modeling using neural network

**Chauvigny V. A. (Sobolev Institute of Mathematics, Omsk branch, Siberian Branch of the Russian Academy of Sciences), Goltiapin V. V. (Sobolev Institute of Mathematics, Omsk branch, Siberian Branch of the Russian Academy of Sciences)**

doi: 10.18698/2309-3684-2016-2-85103

The paper deals with the factorial modeling of the initial stage arterial hypertension. The modeling was carried out by the factorization method based on the neural network and the back propagation of error algorithm. This factorization method is an alternative to the classical factor analysis. We implemented an algorithm for constructing the factorial structure based on the neural network in software. This method has been improved for the factor rotation and obtaining an interpretable solution. The hypertension factorial structure obtained by this factorization method is in accordance with the results of the factorial modeling by other methods.

Chauvigny V., Goltiapin V. Factorial modeling using neural network. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 85-103

#### 519.862.6 Analytical dependences between the determination coefficients and the ratio of error variances of the test items in Deming regression model

**Bazilevsky M. P. (Irkutsk State Transport University)**

doi: 10.18698/2309-3684-2016-2-104116

The article deals with the problem of building regression models, in which all variables have stochastic nature. To solve it, we propose to use the determination coefficient. We obtain analytical dependencies of the determination coefficients from the ratio of error variances of the test items. We set the optimization problem, assuming the maximization of the determination coefficients sum for each Deming regression equation. We give a model example of the numerical processing of Deming regression with its parameters and sign errors which are known.

Bazilevsky M. Analytical dependences between the determination coefficients and the ratio of error variances of the test items in Deming regression model. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 104-116