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In the paper we consider the inverse problem of evaluating kinetic parameters of the model of dehydriding of metal powder using experimental data. The «blind search» in the space of parameters revealed multiple physically reasonable solutions. The solutions were obtained using high–performance computational modeling based on BOINC–grid.

Correct modeling of complex dynamics of urban transportation flows requires the collection of large volumes of empirical data to specify types of the modes and their identification. At the same time, setting a large number of observation posts is expensive and technically not always feasible. All this results in insufficient factographic support for the traffic control systems as well as for urban planners with the obvious consequences for the quality of their decisions. As one of the means to provide large-scale data collection at least for the qualitative situation analysis, the wide-area video cameras are used in different situation centers. There they are analyzed by human operators who are responsible for observation and control. Some video cameras provided their videos for common access, which makes them a valuable resource for transportation studies. However, there are significant problems with getting qualitative data from such cameras, which relate to the theory and practice of image processing. This study is devoted to the practical application of certain mainstream neuro-networking technologies for the estimation of essential characteristics of actual transportation flows. The problems arising in processing these data are analyzed, and their solutions are suggested. The convolution neural networks are used for tracking, and the methods for obtaining basic parameters of transportation flows from these observations are studied. The simplified neural networks are used for the preparation of training sets for the deep learning neural network YOLOv4 which is later used for the estimation of speed and density of automobile flows.

An important role in the construction of mathematical models of dynamic systems is played by inverse problems, which in particular include the problem of parametric identification. Unlike classical models that operate with point values, interval models give upper and lower boundaries on the quantities under study. The paper considers an interpolation approach to solving interval problems of parametric identification of dynamic systems for the case when experimental data are represented by external interval estimates. The purpose of the proposed approach is to find such an interval estimate of the model parameters, in which the external interval estimate of the solution of the direct modeling problem would contain experimental data or minimize the deviation from them. The approach is based on the adaptive interpolation algorithm for modeling dynamic systems with interval uncertainties, which makes it possible to explicitly obtain the dependence of phase variables on system parameters. The task of minimizing the distance between the experimental data and the model solution in the space of interval boundaries of the model parameters is formulated. An expression for the gradient of the objectivet function is obtained. On a representative set of tasks, the effectiveness of the proposed approach is demonstrated.

Тhe new test-signals forming method for correlation identification of a nonlinear system based on Lee–Shetzen cross-correlation approach is developed and tested. Numerical Gauss–Newton algorithm is applied to correct autocorrelation functions of test signals. The achieved test-signals have length less than 40 000 points and allow to measure the 2nd order Wiener kernels with a linear resolution up to 32 points, the 3rd order Wiener kernels with a linear resolution up to 12 points and the 4th order Wiener kernels with a linear resolution up to 8 points.

We present results of a study aimed at identification of a controlled object’s channels based on postprocessing of measurements with development of a model of a multiple-input controlled object and subsequent active modelling experiment. The controlled object model is developed using approximation of its behavior by a neural network model using trends obtained during a passive experiment in the mode of normal operation. Recurrent neural network containing feedback elements allows to simulate behavior of dynamic objects; input and feedback time delays allow to simulate behavior of inertial objects with pure delay. The model was taught using examples of the object’s operation with a control system and is presented by a dynamic neural network and a model of a regulator with a known regulation function. The neural network model simulates the system’s behavior and is used to conduct active computing experiments. Neural network model allows to obtain the controlled object’s response to an exploratory stimulus, including a periodic one. The obtained complex frequency response is used to evaluate parameters of the object’s transfer system using the least squares method. We present an example of identification of a channel of the simulated control system. The simulated object has two input ports and one output port and varying transport delays in transfer channels. One of the input ports serves as a controlling stimulus, the second is a controlled perturbation. The controlled output value changes as a result of control stimulus produced by the regulator operating according to the proportional-integral regulation law based on deviation of the controlled value from the task. The obtained parameters of the object’s channels’ transfer functions are close to the parameters of the input simulated object. The obtained normalized error of the reaction for a single step-wise stimulus of the control system model developed based on identification of the simulated control system doesn’t exceed 0.08. The considered objects pertain to the class of technological processes with continuous production. Such objects are characteristic of chemical, metallurgic, mine-mill, pulp and paper, and other industries.

Ultrasound examination of material properties is a precision method for determining their elastic and strength properties in connection with the small wavelength formed in the material after impact of a laser beam. In this paper, the wave processes arising during these measurements are considered in detail. It is shown that full-wave numerical modeling allows us to study in detail the types of waves, topological characteristics of their profile, speed of arrival of waves at various points, identification the types of waves whose measurements are most optimal for examining a sample made of a specific material of a particular shape, and to develop measurement procedures.

To carry out full-wave modeling, a grid-characteristic method on structured grids was used in this work and a hyperbolic system of equations that describes the propagation of elastic waves in the material of the thin plate under consideration on a specific example of a ratio of thickness to width of 1:10 was solved.

To simulate an elastic front that arose in the plate due to a laser beam, a model of the corresponding initial conditions was proposed. A comparison of the wave effects that arise during its use in the case of a point source and with the data of physical experiments on the propagation of laser ultrasound in metal plates was made.

A study was made on the basis of which the characteristic topological features of the wave processes under consideration were identified and revealed. The main types of elastic waves arising due to a laser beam are investigated, the possibility of their use for studying the properties of materials is analyzed. A method based on the analysis of multiple waves is proposed. The proposed method for studying the properties of a plate with the help of multiple waves on synthetic data was tested, and it showed good results.

It should be noted that most of the studies of multiple waves are aimed at developing methods for their suppression. Multiple waves are not used to process the results of ultrasound studies due to the complexity of their detection in the recorded data of a physical experiment.

Due to the use of full wave modeling and analysis of spatial dynamic wave processes, multiple waves are considered in detail in this work and it is proposed to divide materials into three classes, which allows using multiple waves to obtain information about the material of the plate.

The main results of the work are the developed problem statements for the numerical simulation of the study of plates of a finite thickness by laser ultrasound; the revealed features of the wave phenomena arising in plates of a finite thickness; the developed method for studying the properties of the plate on the basis of multiple waves; the developed classification of materials.

The results of the studies presented in this paper may be of interest not only for developments in the field of ultrasonic non-destructive testing, but also in the field of seismic exploration of the earth's interior, since the proposed approach can be extended to more complex cases of heterogeneous media and applied in geophysics.

An algorithm is proposed to identify parameters of a 2D vortex structure used on information about the flow velocity at a finite (small) set of reference points. The approach is based on using a set of point vortices as a model system and minimizing a functional that compares the model and known sets of velocity vectors in the space of model parameters. For numerical implementation, the method of gradient descent with step size control, approximation of derivatives by finite differences, and the analytical expression of the velocity field induced by the point vortex model are used. An experimental analysis of the operation of the algorithm on test flows is carried out: one and a system of several point vortices, a Rankine vortex, and a Lamb dipole. According to the velocity fields of test flows, the velocity vectors utilized for identification were arranged in a randomly distributed set of reference points (from 3 to 200 pieces). Using the computations, it was determined that: the algorithm converges to the minimum from a wide range of initial approximations; the algorithm converges in all cases when the reference points are located in areas where the streamlines of the test and model systems are topologically equivalent; if the streamlines of the systems are not topologically equivalent, then the percentage of successful calculations decreases, but convergence can also take place; when the method converges, the coordinates of the vortices of the model system are close to the centers of the vortices of the test configurations, and in many cases, the values of their circulations also; con-vergence depends more on location than on the number of vectors used for identification. The results of the study allow us to recommend the proposed algorithm for identifying 2D vortex structures whose streamlines are topologically close to systems of point vortices.

Dynamic game theoretic models of the corporative innovative development are investigated. The proposed models are based on concordance of private and public interests of agents. It is supposed that the structure of interests of each agent includes both private (personal interests) and public (interests of the whole company connected with its innovative development first) components. The agents allocate their personal resources between these two directions. The system dynamics is described by a difference (not differential) equation. The proposed model of innovative development is studied by simulation and the method of enumeration of the domains of feasible controls with a constant step. The main contribution of the paper consists in comparative analysis of efficiency of the methods of hierarchical control (compulsion or impulsion) for information structures of Stackelberg or Germeier (four structures) by means of the indices of system compatibility. The proposed model is a universal one and can be used for a scientifically grounded support of the programs of innovative development of any economic firm. The features of a specific company are considered in the process of model identification (a determination of the specific classes of model functions and numerical values of its parameters) which forms a separate complex problem and requires an analysis of the statistical data and expert estimations. The following assumptions about information rules of the hierarchical game are accepted: all players use open-loop strategies; the leader chooses and reports to the followers some values of administrative (compulsion) or economic (impulsion) control variables which can be only functions of time (Stackelberg games) or depend also on the followers’ controls (Germeier games); given the leader’s strategies all followers simultaneously and independently choose their strategies that gives a Nash equilibrium in the followers’ game. For a finite number of iterations the proposed algorithm of simulation modeling allows to build an approximate solution of the model or to conclude that it doesn’t exist. A reliability and efficiency of the proposed algorithm follow from the properties of the scenario method and the method of a direct ordered enumeration with a constant step. Some comprehensive conclusions about the comparative efficiency of methods of hierarchical control of innovations are received.

The paper presents a mathematical model that describes the process of obtaining biogas from livestock waste. This model describes the processes occurring in a biogas plant for mesophilic and thermophilic media, as well as for continuous and periodic modes of substrate inflow. The values of the coefficients of this model found earlier for the periodic mode, obtained by solving the problem of model identification from experimental data using a genetic algorithm, are given.

For the model of methanogenesis, an optimal control problem is formulated in the form of a Lagrange problem, whose criterial functionality is the output of biogas over a certain period of time. The controlling parameter of the task is the rate of substrate entry into the biogas plant. An algorithm for solving this problem is proposed, based on the numerical implementation of the Pontryagin maximum principle. In this case, a hybrid genetic algorithm with an additional search in the vicinity of the best solution using the method of conjugate gradients was used as an optimization method. This numerical method for solving an optimal control problem is universal and applicable to a wide class of mathematical models.

In the course of the study, various modes of submission of the substrate to the digesters, temperature environments and types of raw materials were analyzed. It is shown that the rate of biogas production in the continuous feed mode is 1.4–1.9 times higher in the mesophilic medium (1.9–3.2 in the thermophilic medium) than in the periodic mode over the period of complete fermentation, which is associated with a higher feed rate of the substrate and a greater concentration of nutrients in the substrate. However, the yield of biogas during the period of complete fermentation with a periodic mode is twice as high as the output over the period of a complete change of the substrate in the methane tank at a continuous mode, which means incomplete processing of the substrate in the second case. The rate of biogas formation for a thermophilic medium in continuous mode and the optimal rate of supply of raw materials is three times higher than for a mesophilic medium. Comparison of biogas output for various types of raw materials shows that the highest biogas output is observed for waste poultry farms, the least — for cattle farms waste, which is associated with the nutrient content in a unit of substrate of each type.

This paper formulates and solves a practical problem of data recovery regarding the distribution of languages on regional level in context of China. The necessity of this recovery is related to the problem of the determination of the linguistic diversity indices, which, in turn, are used to analyze empirically and to predict sources of social and economic development as well as to indicate potential conflicts at regional level. We use Ethnologue database and China census as the initial data sources. For every language spoken in China, the data contains (a) an estimate of China residents who claim this language to be their mother tongue, and (b) indicators of the presence of such residents in China provinces. For each pair language/province, we aim to estimate the number of the province inhabitants that claim the language to be their mother tongue. This base problem is reduced to solving an undetermined system of algebraic equations. Given additional restriction that Ethnologue database introduces data collected at different time moments because of gaps in Ethnologue language surveys and accompanying data collection expenses, we relate those data to a single time moment, that turns the initial task to an ’ill-posed’ system of algebraic equations with imprecisely determined right hand side. Therefore, we are looking for an approximate solution characterized by a minimal discrepancy of the system. Since some languages are much less distributed than the others, we minimize the weighted discrepancy, introducing weights that are inverse to the right hand side elements of the equations. This definition of discrepancy allows to recover the required variables. More than 92% of the recovered variables are robust to probabilistic modelling procedure for potential errors in initial data.