Vol 26, No 3 (2022)

A constructive method is proposed for solving a spatiotemporal control problem in systems with distributed parabolic parameters under the conditions of the given accuracy of uniform approximation of the final state of a plant to the required spatial distribution of the controlled variable. The developed approach is based on the previously designed alternance method for constructing the parameterizable programmed control algorithms, which extended the results of the theory of nonlinear Chebyshev approximations to a wide range of optimization problems and uses the fundamental laws of the subject area. It is shown that in linear quadratic problem optimization the equations of optimal controllers with autonomous modal controls in the open domain of their definition and taking into account restrictions on the nature of the spatial distribution of the control actions specified by the conditions of technical implementation are reduced to linear feedback algorithms for the measured state of the plant with nonstationary transmission coefficients and the given dependence on the spatial arguments of the controlled value. The results obtained are extended to the problem of searching for time-invariant spatially distributed controls, considered as the desired design solutions for a plant.

We propose a numerical method for predicting the individual deformation characteristics of structural elements by a “leader” product. The basis of this method is generalized one-parameter models. These models relate the integral characteristics of the stress state to the integral characteristics of the deformation state in the “generalized load – generalized displacement” coordinates. The scope of the method is structural elements of the same type, which are under identical conditions of external loading and are characterized by a large spread of deformation characteristics (generalized displacement). It is assumed that the operation of one structural element (prototype) begins some time earlier than the others. A hypothesis on the similarity of all realizations reduced to a single origin by a time shift in the “generalized displacement – time” coordinates is introduced. Using statistical information on the initial sections of “lagging” structural elements and the sample prototype, the statistical characteristics of the similarity parameter of the operated structural element are determined in relation to the “leader” product, and then its deformation characteristics are predicted.

In the paper, we investigate friction units and structural elements (rods, threaded connections) under creep conditions. Based on statistical correlation analysis of the experimental information, a verification of the similarity hypothesis usabilty for all implementations of the structural elements studied is carried out. The method was illustrated by an example of predicting the wear of the friction units of the front landing gear of the aircraft depending on the number of take-off and landing cycles. The method was also illustrated with an example of how to calculate the elongation of rods made of a polyvinylchloride compound under uniaxial loading and axial displacement of the screwing area of a threaded joint under creep conditions.

The experimental data for the generalized displacement of specific implementations are shown to not exceed the calculated limits of the confidence interval for mathematical expectation for all structural elements considered in prediction time intervals of one to four “basic” intervals, within which estimates of random parameters for specific structural elements were determined.

Within the framework of the Euler equations, the possibility of achieving extreme pressure values at the inner point of a stationary flow of a nonviscous gas is considered. The flow can be non-barotropic. The well-known (G.B. Sizykh, 2018) subsonic principle of maximum pressure (SPMP) cannot be applied in transonic and supersonic flow regions. Under the conditions of the classical principle of maximum pressure by C. Truesdell (1953), there is no restriction on the values of local Mach numbers, but it has a number of features that do not allow it to be used to verify numerical calculations in the same way as it can be done when using SPMP in subsonic regions. A previously unknown principle of maximum pressure is discovered: a function of derivative flow parameters is found, which must have a certain sign (different for minimum and for maximum pressure) at the point where the pressure reaches a strict or nonstrict local extremum. This principle of maximum pressure is called “general” (GPMP) because its conditions do not include barotropicity, restrictions on the values of local Mach numbers, and the assumption that the gas obeys the Mendeleev–Clapeyron equation. One of the consequences of GPMP is the conclusion that the requirement of barotropicity can be excluded from the conditions of Truesdell's principle of maximum pressure. It is proposed to use GPMP to verify numerical calculations of the ideal gas flow behind a detached shock wave formed in a supersonic flow around bodies and to verify numerical calculations of a viscous gas flow around bodies in regions remote from sources of vorticity, where the effect of viscosity can be neglected.

In an inverse extremal problem for a combinatorial scheme with a given value of the objective function of the form of a certain extreme value of its characteristic, a probabilistic model is developed that ensures that this value is obtained in its outcomes. Two types of such characteristics are considered, relating to each of the schemes or to a set of outcomes.

The pre-asymptotic analysis of such a model is carried out by the author's enumerative method. It is based on the construction of an iterative random process with iterations of successive stages of a numbered non-repetitive enumeration and the formation of outcomes of the scheme. The iterative development of the process is represented by a probabilistic graph.

The study of the outcomes of the scheme according to the model in the enumerative method is carried out in the following areas: visual numbering of the outcomes of the scheme, finding their number, establishing a one-to-one correspondence between the types and numbers of outcomes of the scheme, obtaining their probabilistic distribution (controlled by a random process of listing the outcomes of the scheme), and modeling them with this distribution.

Along with the direct study of circuits in these areas, algorithms are proposed to obtain results for them by partially recalculating them from the results of a similar analysis of more general, previously studied circuits without restrictions or with less restrictions on the values of the characteristics under consideration.