The Parametric Optimization of Voltage Multiplier

The evolutionary model of voltage multiplier parametric optimization which includes 5 diodes and 5 capacitors is reviewed. It executes the transformation of alternating into constant voltage using a five times larger amplitude. The valve work is modelled according to the scheme of an ideal key. The original mathematical model of voltage multiplier which includes additional logical variables is deducted. It aссepts binary meanings 0 and 1, where 0 corresponds to closed valve status and 1 corresponds to open. In order to receive such a model, it is necessary to indicate the amount of open and closed valve combinations. Then for each of them, it is necessary to write the system of differential equations. Comparing them with each other the single differential equation system with additional logical variables is written as a generalization. The evolutional model is used in order to select the capacitor volume meaning. The goal function forecasts two conditions: maximum meaning of output voltage 1 kV and its minimal fluctuations in the stable regime.

IDENTIFYING DEVELOPMENT PRIORITIES OF UNDERGROUND INFRASTRUCTURE IN METROPOLISES USING SYSTEM METHODOLOGY

Purpose: Determining construction priorities of underground transport infrastructure objects by evaluating morphological models of car tunnels considering the impact on the ecological and technogenic safety of urbanized territories. Methodology: modified morphological analysis of geological environment, urbanized territories and transport infrastructure of sites in a metropolis, expert estimation method. Findings: a morphological model was tested as a tool set for determining construction priorities of underground transport infrastructure objects; inter-related morphological tables for geological environment and structural-functional factors of urbanized territories in a tunnel area were constructed; an estimation of models regarding development of underground infrastructure was conducted using the planned car tunnels in Kyiv as an example; the impact of tunnels on reducing the ecological and technogenic risks of urbanized space was justified, and the priority construction object was chosen according to these criteria. Originality: for the first time the reduction of ecological and technogenic risks of urbanized space was chosen as a goal function in morphological models for the development of underground transport infrastructure in metropolises; the systemic characteristics of urban territories were obtained that describe the favorability of the geological environment and structural-functional factors for car tunnel construction in center metropolis areas; an impact ratio was proposed for synthesizing morphological analysis results and determining the priorities of underground transport infrastructure objects by influence on the ecological and technogenic risks. Practical implications: the created methodology and tool set for determining priorities of underground object construction at the pre-project stage, the opportunity to consider the ecological and technogenic risks of urban space development by consecutive construction of underground transport infrastructure objects and identifying an order for this sequence.

A pessimistic bilevel stochastic problem for elastic shape optimization

We consider pessimistic bilevel stochastic programs in which the follower maximizes over a fixed compact convex set a strictly convex quadratic function, whose Hessian depends on the leader’s decision. This results in a random upper level outcome which is evaluated by a convex risk measure. Under assumptions including real analyticity of the lower-level goal function, we prove the existence of optimal solutions. We discuss an alternate model, where the leader hedges against optimal lower-level solutions, and show that solvability can be guaranteed under weaker conditions in both, a deterministic and a stochastic setting. The approach is applied to a mechanical shape optimization problem in which the leader decides on an optimal material distribution to minimize a tracking-type cost functional, whereas the follower chooses forces from an admissible set to maximize a compliance objective. The material distribution is considered to be stochastically perturbed in the actual construction phase. Computational results illustrate the bilevel optimization concept and demonstrate the interplay of follower and leader in shape design and testing.

Credibilistic fuzzy clustering based on evolutionary method of crazy cats

The problem of fuzzy clustering of large datasets that are sent for processing in both batch and online modes, based on a credibilistic approach, is considered. To find the global extremum of the credibilistic fuzzy clustering goal function, the modification of the swarm algorithm of crazy cats swarms was introduced, that combined the advantages of evolutionary algorithms and a global random search. It is shown that different search modes are generated by a unified mathematical procedure, some cases of which are known algorithms for both local and global optimizations. The proposed approach is easy to implement and is characterized by the high speed and reliability in problems of multi-extreme fuzzy clustering.

OPTIMIZATION ALGORITHM OF RESOURCE ALLOCATION IN ORDER TO EXAMINE THE ECONOMIC EFFECTS OF LINEAR PROGRAMMING MODEL RESPONSE

The concept of examining decisions using abstract research constructions as virtual aids enables the design of the management platform and the creation of the behavior of the future state of the system. Checking the effects of decisions in a real system through an appropriate mathematical-logical apparatus certainly affects the reduction of randomness and spontaneity of management. The symbolic connection of the input that produces the combined input action and the output that manifests the reaction expressed by the degree of sensitivity and enables the translation of the imaginary expression of reality into the operative mathematical language. The commitment to this type of model is based on the fact of almost standardized procedures in terms of choosing the priority of including certain forms of resources, which makes it representative in terms of achieving the goal function defined by the criterion of optimality. In this sense, we can talk about a whole range of optimization problems with mutually inconsistent tactical goals and thus the need for their refined balance, and one of such challenges is the focus of attention of a specific research project. The mathematical model represents a formalized description of the action of physical contents, and we use it to support the decision-making process when the complexity of reality allows that. Accordingly, to express the regularity of functioning, a deterministic model of linear programming in the form of a set of relations describing the input-output effect of influential factors used in this paper. With a tolerant simplification of reality, the perception of the model, based on the coincidence with the structure of the original, actually shows an approximation that means analogous behavior demonstrated on the quantitative model or its derivative - the optimization model. This thesis supports the fact that the corresponding relationship between the model and the original allows the examination of the behavior of the observed hypothetical system, and the analysis of the sensitivity map of the variable, in the form of a goal function, becomes a source of modeling information. Also, the system is not influenced by a high rate of change that would mean expanding from deterministic to stochastic modeling, but all methodological resources are mobilized so that the model concept would not become a theoretical misconception that would lead to quasi-decision making. The author’s analytical thinking and logic try to give a chance to the imagination, which connects creativity and physical resources that indicates several alternatives, which contain future parameters. In this way, the authors use the model as an increment of knowledge to connect the a priori management reserve of their accuracy with the reality of hypothetical data within a rational approach.

Mathematical model implementation in conditions of uncertainty and possible risks

The article presents the theoretical and methodological principles for forecasting and mathematical modeling of possible risks in technological and biotechnological systems. The authors investigated in details the possible approach to the calculation of the goal function and its parameters. Considerable attention is paid to substantiating the correctness of boundary value problems and Cauchy problems. In mechanics, engineering, and biology, Cauchy problems and boundary value problems of differential equations are used to model physical processes. It is important that differential equations have a single physically sound solution. The authors of this article investigate the specific features of boundary value problems and Cauchy problems with boundary conditions in a two-point medium, and determine the conditions for the correctness of such problems in the spaces of power growth functions. The theory of pseudo-differential operators in the space of generalized functions was used to prove the correctness of boundary value problems. The application of the obtained results will make it possible to guarantee the correctness of mathematical models built in conditions of uncertainty and possible risks. As an example of a computational mathematical model that describes the state of the studied object of non-standard shape, the authors considered the boundary value problem of the system of differential equations of thermal conductivity for the embryo under the action of a laser beam. For such a boundary value problem, it is impossible to guarantee the existence and uniqueness of the solution of the system of differential equations. To be sure of the existence of a single solution, it is necessary either not to take into account the three-layer structure of the microbiological object, or to determine the conditions for the correctness of the boundary value problem. Applying the results obtained by the authors, the correctness of the boundary value problem of systems of differential equations of thermal conductivity for the embryo is proved taking into account the three-layer structure of the microbiological object. This makes it possible to increase the accuracy and speed of its implementation on the computer. Key words: forecasting, risk, correctness, boundary value problems, conditions of uncertainty

Statement and solution the problem of designing of water-tight bulkheads web frames for large container vessels by using DNV-GL rules requirements and optimization techniques

Поперечные переборки крупнотоннажных контейнерных судов представляют собой сложные конструкции, при проектировании которых обычно используется методология проверочного расчета на основе метода конечных элементов (МКЭ). Для создания конечно-элементной модели необходимо знать размеры всех элементов конструкций, входящих в состав переборки. Поэтому такой подход к проектированию является итерационным, что обуславливает высокую трудоемкость процесса проектирования. На ранних стадиях проектирования размеры конструкций поперечных переборок контейнеровоза могут быть быстро и достаточно точно оценены на основе аппарата нелинейного программирования, относительно простой модели составной (конструктивно-ортотропной) пластины и нормативных требований Правил классификационных обществ. Такой подход применяется в Российской практике при проектировании двойных конструкций типа двойное дно или понтон плавучего дока. В статье предложено решение задачи проектирования рамного набора поперечной переборки крупнотоннажного контейнеровоза на нагрузки от контейнеров, действующие на переборку при качке судна. Конструкция переборки приводится к условной модели «коффердамного» типа. Затем используется методика приведения составной «конструктивно-ортотропной» пластины к изотропной пластине с несколько иным соотношением сторон, но с такими же параметрами изгиба. Это позволяет применить существующие табличные данные для определения расчетных изгибающих моментов и перерезывающих сил, которые после аппроксимации представляются в виде полиномов – аналитических зависимостей. Показана постановка оптимизационно-поисковой задачи математического программирования. Целевая функция – характеристика массы рамного набора. Ограничения задачи формируются на основе нормативных требований DNV-GL и математических зависимостей модели составной пластины. Для решения задачи используется инструмент MS Excel «Поиск решения» Представлены результаты тестового проектного расчета применительно к конструкции крупнотоннажного контейнеровоз с контейнерной вместимостью 18 тыс. TEU. Сопоставление результатов проектирования с оригинальными расчетами фирмы – проектанта показали удовлетворительное соответствие. The transverse bulkheads of the large container vessels are complex structures that are commonly designed using the finite element method (FEM) verification methodology. To create a finite element model, it is necessary to know the dimensions of all structural elements of the bulkhead. Therefore, this approach to design is iterative, which leads to a high complexity of the design process. At the early stages of design, the dimensions of the structures of the transverse bulkheads of a container vessel can be quickly and accurately estimated based on the nonlinear programming technique, a relatively simple model of a composite (structural-orthotropic) plate, and the regulatory requirements of the Rules of Classification Societies. This approach is used in practice in Russia when designing double structures such as a double bottom or pontoon of a floating dock. The article proposes a solution to the problem of the transverse bulkhead web frames designing in application to a large-tonnage container vessel for loads of containers acting on the bulkhead when the vessel is moving on the waves. The bulkhead structure is reduced to the conditional "cofferdam" type model. The technique is used to reduce a composite "structurally-orthotropic" plate to an isotropic one with a slightly different aspect ratio, but with the same bending parameters. This allows applying the existing tabular data to determine the design bending moments and shear forces, which, after approximation, are represented as polynomial analytical dependencies. The statement the optimization-search problem of mathematical programming is shown. The goal function is the characteristic of the bulkhead's webs mass. The constraints of the problem are formed on the DNV-GL regulatory requirements and mathematical relationships of the composite plate model. MS Excel tool "Solver" is used to solve the problem. The results of a test calculation are presented as applied to a large-capacity container ship with container capacity of 18000 TEU. Comparison of the design results with the original calculations of the designer’s company showed satisfactory agreement.

The Array Optimization of Vertical Axis Wind Turbine Based on a New Asymmetric Wake Model

With the increasing demand for wind energy, the vertical axis wind turbine (VAWT) is attracting more and more attention. In order to design the VAWT array for better performance, the VAWT wake model needs to reflect the wake characteristics well. Based on the asymmetric wake characteristic, a new VAWT wake model is proposed in this paper, which is a combination of two semi Gaussian functions with different deviations, and can be called the “double semi Gaussian functions wake model”. The model is simple and has only four parameters (mean, amplitude, left deviation and right deviation). Compared with the traditional Gaussian and Top-hat model, this model can better reflect the asymmetric characteristic of the VAWT wake. In particular, it can describe the behavior of wake merging in the case of counter-rotating twin turbines. Based on this wake model, the velocity field of VAWT array can be reproduced accurately. The goal function is mainly based on the performance of a basic array unit, and it can ensure the rapidity of the optimization process. The optimal arrangements under two different criteria are analyzed. Moreover, the truncation ratio is introduced to ensure that the downstream turbine works at the rated condition, and the optimal arrangements under different truncation ratios are analyzed. In this paper, the proposed wake model provides a good choice for the preliminary design of the VAWT array, and some relevant suggestions on the array arrangement have been put forward.

Mathematical modeling and research of optimal cutting of cardboard packaging

A mathematical model describing the goal function is suggested. Its arguments are the geometric parameters of a particular type of cardboard packaging. The goal function is studied to the extreme to determine their optimal values at the lowest cardboard consumption. The optimal geometric parameters for prismatic packages of a given volume have been found. The unification of components of this prismatic packaging is performed. The dependence of the packaging material area on the values of geometric parameters of a specific prismatic package is numerically analyzed.

Smart SDN Management of Fog Services to Optimize QoS and Energy

The short latency required by IoT devices that need to access specific services have led to the development of Fog architectures that can serve as a useful intermediary between IoT systems and the Cloud. However, the massive numbers of IoT devices that are being deployed raise concerns about the power consumption of such systems as the number of IoT devices and Fog servers increase. Thus, in this paper, we describe a software-defined network (SDN)-based control scheme for client–server interaction that constantly measures ongoing client–server response times and estimates network power consumption, in order to select connection paths that minimize a composite goal function, including both QoS and power consumption. The approach using reinforcement learning with neural networks has been implemented in a test-bed and is detailed in this paper. Experiments are presented that show the effectiveness of our proposed system in the presence of a time-varying workload of client-to-service requests, resulting in a reduction of power consumption of approximately 15% for an average response time increase of under 2%.