Стохастическое моделирование каскадных сценариев возникновения и развития чрезвычайных ситуаций

Structural engineering makes a giant stride forward with this symposium. This book represents an international sym­ posium held in Stockholm honoring Prof. W. Weibull. It drew participants from 21 countries with a total of 55 invited papers. There were 7 scientific sessions. Most of our studies in school revolved about deterministic happenings. Random loading becomes more and more important when we equate events in our world with physical and mathematical reasoning. Probabilistic failure model and stochastic fatigue crack growth play important roles in the safety of nuclear structures, random loading due to wind turbulence, earthquake spectra, offshore structural design, and aircraft design. The initial paper summarizes Prof. Weibull's life and ac­ complishments including a mention of Weibull distribution used in fatigue studies. The initial session deals with extreme value theory (EVT). The first paper reviewed applications of extreme value theory to material behavior and indicates the importance of the accompanying statistical theory. The next paper generalizes Weibull distribution in matrix form. The following papers proclaim (a) extreme value theory as com­ patible to random field theory, (b) incomplete samples can be transformed to a mixed-exponential survival for a more com­ prehensive Weibull distribution, (c) EVT in endurance testing of ball and roller bearings, (d) use of the Slepian model identi­ fying the behavior of Gaussian noise near or between its zero crossing, (e) plastic movement of SDOF elastic plastic oscillator subjected to stationary Gaussian process excitation, and (/) generalized Hermitian polynomial used in the pertur­ bation method for nonlinear random vibrations. The final paper reports on Weibull distribution in large earthquake modelling. Session 2 reports on fatigue crack growth. Beginning with an analysis of stochastic equation models of crack growth, it continues with stochastic models of fatigue crack growth and propagation, prediction of crack growth under spectrum loading employing a cycle-by-cycle technique and fatigue life distribution in a random loading sense with interacting failures. The final paper considers a new approach to fatigue crack propagation under random loading and the use of Monte Carlo simulation in correlating micro fracture process and fatigue crack propagation. This session indicates that more experimental work is required in crack propagation to reach the same level as crack initiation. Session 3 comprises a total of 13 papers and dwells upon probabilistic failure models. The initial paper proposes a generalized probabilistic model for the fatigue life and reliability prediction of a structure containing noninteracting cracks and employs Poisson random sets. The next group of papers focuses upon (a) structural reliability treated as a single stochastic model, (Jb) fatigue life and reliability estimates of mineral pipe lines using probability theory, (c) Weibull-based equation employed in predicting the failure of a stressed brittle material, (d) a preliminary suggestion that specimens failed in proof tests may be used to estimate the parameters of the reliability function for the survivors, and (e) brittle material design using three parametric Weibull distributions. The next set of papers considers ring-in-ring tests on strength of cladded glass using the three-parameter Weibull distribution, prob­ abilistic analysis of plastic plates utilizing yield-line theory plus lower bound reliability analysis of plastic plates evaluated by inclusion-exc lusion theory. The final set of papers ques­ tions the possibility of flaws in the present probabilistic models for unidirectional fibrous composites, strength rela­ tions for cracks in unidirectiona l long fiber composites employing Weibull distribution and a stochastic approach in studying the fracture and fatigue of concrete. Session 4 delves into probabilistic fracture mechanics. The initial paper estimates the probable failure of PWR pressure vessels employing Weibull distribution and updates the wellknown Marshall A(a) and B(a) functions. The final set of papers covers probabilistic assessment of structures with weld defects, probability of fracture in main coolant pipes of PWR, and statistical modelling of shaft predictions (as measured by Charpy impact curve) in the reference temperature of pressure vessel welds. The authors suggested that U.S. Nuclear Regulatory Guide 1.99 be updated to remove excessive conservatism.

Effects of physical correlations on long-distance GPS positioning and zenith tropospheric delay estimates

Researchers can incorporate uncertainties in computational fluid dynamics (CFD) that go beyond the inaccuracies caused by numerical discretization thanks to stochastic simulations. This study confirms the validity of current stochastic modeling tools by providing examples of stochastic simulations in conjunction with numerical solutions for incompressible flows. A numerical technique for solving deterministic and stochastic models is developed in this work. Our approach employs the Euler‐Maruyama method for stochastic modeling, representing a stochastic version of the third‐order explicit‐implicit scheme. For the deterministic model, the scheme is third‐order accurate. The consistency and stability of the constructed scheme are provided in the mean square sense. The scheme is the predictor–corrector type that is built on two time levels. Moreover, a mathematical model of the Casson nanofluid flow with variable thermal conductivity is given with the effect of the chemical reaction. The appropriate transformations are used to condense the set of partial differential equations (PDEs) down to one that is dimensionless. The scheme is applied for the deterministic and stochastic models of dimensionless flow problems. The velocity profile's deterministic and stochastic behavior are shown using contour plots. Results show that growing values of the thermal mixed convection parameter enhance the velocity profile. This article presents the progress made in stochastic computational fluid dynamics (SCFD) and highlights the energy‐related aspects of our discoveries. Our computational approach and stochastic modeling techniques provide new insights into the energy properties of Casson nanofluid flow, specifically regarding the variability of thermal conductivity and chemical processes. Our objective is to clarify the complex interaction of these factors on energy dynamics. This article presents a contemporary summary of the latest SCFD advancements. Additionally, it highlights potential directions for future research and unresolved issues that require attention from the members of the field of computational mathematics.

A stochastic bivariate ecology model for competing species

The game task of confrontation of the attacked hardware-redundant dynamic system with an attacking enemy operating in conditions of incomplete information about the behavior of the attacked enemy in a conflict was posed and solved numerically and analytically. The attacking party aspires to increase the intensity of failures of the components of the attacked system due to its attack resources, up to its total failure. The attacked party, due to the corresponding strategy of redistribution of the reserve units of the hardware-redundant dynamic system between the failed main units at the appropriate instants of time, strives to maximize the probability of a failure-free operation of the attacked system by the end of the confrontation (game) with the attacking enemy. Behavior of the system under attack in the process of a conflict is approximated by the Markov process, while the number of the operable states is equal to the number of the failed functional units, not exceeding the number of the standby units. As a function of the board in the considered game the probability of a failure-free operation of the attacked system is used by the time the game ends. The solution to the game is the vector of the system setup moments after the corresponding failures of the functional units and a set of the reservation vectors corresponding to the instantaneous settings of the attacked system, which maximize the probability of a system failure during a conflict. The differential game model is reduced to a multi-step matrix model with the given probabilities of the states of the attacking enemy. Numerical algorithms for calculation of the reservation vector for the attacked system are presented, which maximize the probability of its trouble-free operation by the end of the game and for solving of the game problem in a form convenient for its implementation on a personal computer.

A stochastic model of fatigue crack growth in heterogeneous material

3D stochastic reservoir modelling is an emerging new technology for the oil and gas industry and is increasingly used by oil and gas companies as a tool to support major business decisions in field development planning, and the acquisition and management of petroleum assets. However, the potential benefit that 3D stochastic reservoir modelling can offer is still overlooked by many asset teams. Conventional methods are often still applied for field development planning and reserve estimation, where over-simplified geological models are used and reservoir uncertainties are substantially under-estimated. This is one reason why the oil and gas industry does not have a good track record in estimating reserves and field development planning. 3D stochastic reservoir modelling methods that incorporate the structural-stratigraphic framework, facies and petrophyscial properties can ensure that the reservoir models fully describe reservoir heterogeneity. This in turn lays a sound foundation for field development planning. The 3D stochastic reservoir modelling methods also quantify and reduce uncertainties in various aspects of the reservoir. This allows a field development plan to be more robust yet flexible enough to take the advantage of upside reserve potential and to be economically sound if the downside case occurs. Based on quantification of uncertainties, optimal well positions and well paths can be designed to maximise oil and gas recovery.

In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations contain a Markov term, a memory term and a term suggestive of stochastic noise. Within this framework we express standard model reduction methods such as averaging and homogenization which eliminate the memory term. We further discuss ways to deal with the memory term and how the type of noise depends on the underlying deterministic chaotic system. Secondly, we review current approaches in stochastic data-driven models. We discuss how the drift and diffusion coefficients of models in the form of stochastic differential equations can be estimated from observational data. We pay attention to situations where the data stems from multi scale systems, a relevant topic in the context of data from the climate system. Furthermore, we discuss the use of discrete stochastic processes (Markov chains) for e.g. stochastic subgrid-scale modeling and other topics in climate science.

From 1972 to 1974, I was working on a PhD thesis entitled Multiple Server Queues with Service Time Depending on Waiting Time.The method of analysis was the embedded Markov chain technique, described i

A novel approach to stochastic operator modeling for multiple target search tasks Is introduced. Unlike the large majority of experiments in literature the focus Is on modeling and prediction of the sequence of detected and identified targets, rather than the prediction of time consumption. We investigate the prediction accuracy of three stochastic operator models: (1) a classic Markov Chain of first order, (2) a factorial Hidden Markov Model, and (3) a Variable-Length Markov Chain, The parameters are estimated with the help of empirically acquired traces from search experiments with 37 experienced operators. Five search scenarios with a varying number of targets were studied. Moreover, the prediction accuracy of two deterministic, but semantic models are Investigated: (4) a nearest-neighbor estimator and (5) a nearest-neighbor estimator with perfect procedural memory. Both semantic models do not rely on the empirical data, but Integrate task-specific a-priori knowledge. The results show a significantly highest prediction accuracy of the nearest-neighbor estimator with perfect memory, while the memoryless estimator has the lowest accuracy. These findings are Independent of the number of targets and Indicate the remarkable ability of the operator to memorize already attended targets. The Variable-Length Markov Chain has the significantly highest prediction accuracy among the stochastic models. Finally, a regression formula of the prediction accuracy depending on the number of targets is derived.

Comparison of deterministic and stochastic SIS and SIR models in discrete time

Methods and models for decision-making on the allocation of resources that are sufficiently important area of modern science are developed in this chapter. Need to take account of probability factors requires the development of stochastic models, and the desire of the decision to reduce the damage caused by the deterioration of the environment requires the development of methods of correction the original plan, and, therefore, leads to multistage models and methods of their optimization. The complex of mathematical methods and decision making models of distribution of resources in conditions of incomplete information on the base of using combined target functionals built by the classical principles of choice, such as egalitarianism and utilitarianism are used for analysis and modeling of right distribution of production and investment resources by the region/industry development in order to forecast the situation of managing risks of distribution resources within changing of social-economic sphere of considered projects.

The article is devoted to the question of regional digitalization and telecommunication development of Ukraine. The conceptual basis of telecommunication development (TCD) assessment by system analysis methods is provided. The status classification model of the region according to the TCD level was investigated.The forecasting models of the TCD level of the region are developed by Markov chain with discrete status. The regional features have been studied. The homogeneous groups of TCD regions have been formed. Visual analysis of the obtained clustering trees by hierarchical methods allowed to conclude about a stable and high-quality division into three clusters. There are clusters of the high, medium and low level of telecommunication. The dynamics of regional clusters moving is estimated. There is set of regions that have never changed their position all the time. Thus, Volyn region was included in the cluster of regions with the medium TCD level. Kharkiv region was included in the high level TCD cluster. The most regions were characterized by a change in level. We get the opportunity at the next stage of the study to estimate the frequency of transitions of regional systems from state to state and to determine the matrices of transition probabilities for each year separately. The forecast of TCD level has been made by stochastic modeling methods, the probabilities of regions falling into different states in 2021 have been estimated. The status of systems with low TCD are likely to be in the high-level group of regions with a probability of slightly more than 2 %. for two years. The probability that the system with medium level of development for two years will remain in the same group is 61,7%. The probability that the status will worsen is 13,8 %, and that will improve – 24,5 %. The probability that the region is stayed in the same group the next two years is 69.5 %. The probability that the high level TCD region is moved to the medium level cluster of regions is 27,6 %, and probability to the low level TCD is 2,9 %.

In this paper, a stochastic modelling method is used to study the reliability evaluation problem of fault-tolerant control systems (FTCSs). The faults in the system are described by a Markov chain, while the fault detection and isolation (FDI) and system operation for reliability evaluation are described by two semi-Markov chains. The semi-Markov description of FDI removes the restrictive memoryless assumption in Markov models and provides a general model for cyclic FDI schemes. Furthermore, a reliability index and evaluation method are presented for FTCSs. This index reflects the control performance and hard deadline and can be used as a quantitative reliability measure for FTCSs.

Reliability evaluation of Fault Tolerant Control Systems with a semi-Markov FDI model