Identification and Stochastic Optimizing the UAV Motion Control in Turbulent Atmosphere

In a class of diffusion Markov processes, we formulate a problem of identification of nonlinear stochastic dynamic systems with random parameters, multiplicative and additive noises, control functions, and the state vector at a final time moment. For such systems, the identifiability conditions are being studied, and necessary conditions are formulated in terms of the general theory of extreme problems. The developed engineering methods for identification and optimizing nonlinear stochastic systems are presented as well as their application for unmanned aerial vehicles under wind disturbances caused by atmospheric turbulence, namely, for optimizing the autopilot parameters during a rotary maneuver of an unmanned aerial vehicle in translational motion, taking into account the identification of its angular velocities.

Explicit Stable Finite Difference Methods for Diffusion-Reaction Type Equations

By the iteration of the theta-formula and treating the neighbors explicitly such as the unconditionally positive finite difference (UPFD) methods, we construct a new 2-stage explicit algorithm to solve partial differential equations containing a diffusion term and two reaction terms. One of the reaction terms is linear, which may describe heat convection, the other one is proportional to the fourth power of the variable, which can represent radiation. We analytically prove, for the linear case, that the order of accuracy of the method is two, and that it is unconditionally stable. We verify the method by reproducing an analytical solution with high accuracy. Then large systems with random parameters and discontinuous initial conditions are used to demonstrate that the new method is competitive against several other solvers, even if the nonlinear term is extremely large. Finally, we show that the new method can be adapted to the advection–diffusion-reaction term as well.

THEORETICAL ANALYSIS OF EXISTING CONCEPTS TO EVALUATE THE NON-FAILURE OF RC STRUCTURES IN OPERATION

The article presents a theoretical analysis of existing concepts to evaluate the non-failure of RC structures in operation. To perform the analysis, the authors considered a number of scientific works of both Ukrainian and foreign researchers. The main focus was on works in which the model of the stochastic nature of the RC structure operation included random parameters of acting loads, as well as the reserve of its bearing capacity and serviceability (geometric dimensions of cross sections of constructive members, strength and deformation characteristics of materials, etc.). Among others, according to the authors, important problems in terms of analysis of a single work were the volume of statistical selection of random parameters, their number and impact on the study result, as well as rationality of the adopted method of calculating the probability of failure (or non-failure work) of RC structure in operation. Based on the processing of a number of scientific works, the authors highlight the relevance, advantages and disadvantages of the concepts of non-failure assessment proposed there, as well as the formulate the conclusions and recommendations for further experimental and theoretical research in this area.

AN APPROXIMATE METHOD TO PRESENT THE BUCKLING STRENGTH OF A GRILLAGE IN A PROBABILISTIC FORM

An approximate method for calculation in probabilistic terms of the buckling strength of a grillage under unidirectional in-plane compression is proposed. The geometric properties of longitudinals and transverses and the mechanical properties (yield stress and modulus of elasticity) of the material they are built from are treated as random parameters that may change over ship’s service life. The cumulative distribution function of the grillage’s critical buckling strength is calculated by using an analytical formula for multitude sets of input parameters while all of them having the same level of certainty. The assumption is that the critical buckling strength has the same (or very similar) level of certainty as that of the input parameters. The accuracy of the proposed approximate method is relatively high (the maximal error is around 2%). It is recommended for use when specialized computer programs for application of Monte Carlo simulation method are not available. The method does not require a complicated specialized computer program and can be run on EXCEL computer program.

Novel anomalous diffusion phenomena of underdamped Langevin equation with random parameters

The diffusion behavior of particles moving in complex heterogeneous environment is a very topical issue. We characterize particle's trajectory via an underdamped Langevin system driven by a Gaussian white noise with a time dependent diffusivity of velocity, together with a random relaxation timescale $\tau$ to parameterize the effect of complex medium. We mainly concern how the random parameter $\tau$ influences the diffusion behavior and ergodic property of this Langevin system. Besides, the comparison between the fixed and random initial velocity $v_0$ is conducted to show the effect of different initial ensembles. The heavy-tailed distribution of $\tau$ with finite mean is found to suppress the decay rate of the velocity correlation function and promote the diffusion behavior, playing a competition role to the time dependent diffusivity. More interestingly, a random $v_0$ with a specific distribution depending on random $\tau$ also enhances the diffusion. Both the random parameters $\tau$ and $v_0$ influence the dynamics of the Langevin system in an non-obvious way, which cannot be ignored even they has finite moments.