Convolutional neural networks for modeling and forecasting nonlinear nonstationary processes

The object of research. The object of research is modeling and forecasting nonlinear nonstationary processes presented in the form of time-series data. Investigated problem. There are several popular approaches to solving the problems of adequate model constructing and forecasting nonlinear nonstationary processes, such as autoregressive models and recurrent neural networks. However, each of them has its advantages and drawbacks. Autoregressive models cannot deal with the nonlinear or combined influence of previous states or external factors. Recurrent neural networks are computationally expensive and cannot work with sequences of high length or frequency. The main scientific result. The model for forecasting nonlinear nonstationary processes presented in the form of the time series data was built using convolutional neural networks. The current study shows results in which convolutional networks are superior to recurrent ones in terms of both accuracy and complexity. It was possible to build a more accurate model with a much fewer number of parameters. It indicates that one-dimensional convolutional neural networks can be a quite reasonable choice for solving time series forecasting problems. The area of practical use of the research results. Forecasting dynamics of processes in economy, finances, ecology, healthcare, technical systems and other areas exhibiting the types of nonlinear nonstationary processes. Innovative technological product. Methodology of using convolutional neural networks for modeling and forecasting nonlinear nonstationary processes presented in the form of time-series data. Scope of the innovative technological product. Nonlinear nonstationary processes presented in the form of time-series data

FORECASTING GDP GROWTH RATE IN UKRAINE WITH ALTERNATIVE MODELS

The problem of constructing mathematical model for short-term fore-casting of GDP is considered. First, extended autoregression is constru-cted that takes two additional independent variables into consideration. The model resulted provides a possibility for generating short-term forecasts of GDP though not of high quality. Another model was constructed in the form of a Bayesian network. The model turned out to be better than the multiple regression, it provides quite good estimates for probabilities of GDP growth direction

Algorithm for simulating melting polar ice, Earth internal movement and volcano eruption with 3-dimensional inertia tensor

This paper reports the result of an investigation of a hypothesis that the melting polar ice of Earth flowing down to the equatorial region causes volcano eruptions. We assumed a cube inside the spherical body of Earth, formulated a 3-dimensional inertia tensor of the cube, and then simulated the redistribution of the mass that is to be caused by the movement of melted ice on the Earth’s surface. Such mass distribution changes the inertia tensor of the cube. Then, the cube’s rotation inside Earth was simulated by multiplying the Euler angle matrix by the inertia tensor. Then, changes in the energy intensity and the angular momentum of the cube were calculated as coefficients of Hamiltonian equations of motion, which are made of the inertia tensor and sine and cosine curves of the rotation angles. The calculations show that the melted ice increases Earth’s internal energy intensity and angular momentum, possibly increasing volcano eruptions

Empirical investigation on influence of moon’s gravitational-field to earth’s global temperature

This research examined a possibility of the Moon’s gravitational-wave that may influence Earth’s global temperature, with a mathematical method of empirical analysis with the data of the global temperature, global carbon dioxide, and the distance between Moon and Earth. We made the regression analysis of the global temperature over the factors of Moon’s gravitational field taken from the General Theory of Relativity and from the Newton’s gravity theory, with the data of the carbon-dioxide. The result shows that Newton’s gravitational field is related to Earth’s global temperature, while the influence of Moon’s gravitational wave is negligible. However, we also found a possibility that the gravitational wave could contribute to Moon’s gravitational-field upon the analysis of multicollinearity of two factors taken from Newton’s theory and the General Theory of Relativity

Analysis of moon’s gravitational-wave and earth’s global temperature: influence of timetrend and cyclic change of distance from moon

This research examined the influence of Moon’s gravitational-wave to Earth’s global warming process and the effects of time-trend and cyclic change of the distance between Moon and Earth. In the pervious research, we found that the Moon’s gravitational-wave could influence the process of the Earth’s global warming; and, we also found that Moon’s cyclic movement around Earth needed to be further investigated, because it gave a unique pattern of distribution in the data for the empirical analysis; while both global temperature and global carbon-dioxide increase almost linearly in the time-series. In this research we added dummy binary variables that simulate the trend of time and the cyclic changes. As a result we confirmed that the influence of Moon’s gravitational-wave is significant in the process of rising global temperature on Earth

Features of SAS Enterprise Guide for probabilistic modeling system, macroeconomic analysis and forecasting

This paper addresses to the problem of using SAS Enterprise Guide 6.1 as a means for building probabilistic models and as optimum method of modeling gross domestic product in terms of the economic crisis and social threats is proposed. Today in a complex socio-political and economic situation growing influence of external factors, presence of uncertainties and risks there exists a problem of anticipating potential threats in the humanitarian and social spheres and ways to overcome them aiming to provide food security and controllability of ecological situation. All these problems, as reported in the NATO program “Science for Peace and Security”, are of high priority for the countries that need to take into account threats to security, including Ukraine. That is why in the framework of the project NUKR. SFPP G4877 “Modeling and Mitigation of Social Disasters Caused by Catastrophes and Terrorism” the problems of scientific prediction of national economy for the period to 2030 as one of the measures preventing growth of social tension in the country are disclosed

Uncertainties in data processing, forecasting and decision making

Forecasting, dynamic planning, and current statistical data processing are defined as the process of estimating an enterprise’s current state on the market compared to other competing enterprises and determining further goals as well as sequences of actions and resources necessary for reaching the goals stated. In order to perform high-quality forecasting, it is proposed to identify and consider possible uncertainties associated with data and expert estimates. This is one of the system analysis principles to be hired for achieving high-quality final results. A review of some uncertainties is given, and an illustrative example showing improvement of the final result after considering possible stochastic uncertainty is provided

Эмпирический анализ активной зоны ядерного реактора ЧАЕС за 5 секунд до взрыва

У дослідженні використоно методологію емпіричного аналізу для вивчення перехідних процесів активної зони ядерного реактора за кілька секунд до вибуху під час аварії на Чорнобильській АЕС. Параметри вибрано з опублікованих робіт [1]. Сценарієм цього аналізу передбачено зниження швидкості потоку основного циркуляційного насоса та побудовано регресивні моделі для вивчення цього сценарію. Розглянуто результати застосованої моделі і зроблено висновки про зменшення витрат головного циркуляційного насоса та реактивності протягом останніх кількох секунд до вибуху.This study uses the methodology of empirical analysis for analyzing the transient mode of the nuclear reactor core, a few second before the explosion at the time of the Chernobyl accident. The parameters were selected from the published articles [1]. A scenario was assumed for this analysis, such as the reduction of the flow rate of the Main Circulation Pump, and regression models were constructed to examine this scenario. The results of the models application were examined, and conclusions were made regarding the reduction of the flow rate of the Main Circulation Pump and the reactivity during the last few seconds to the explosion.В исследовании использована методология эмпирического анализа для изучения переходных процессов активной зоны ядерного реактора за несколько секунд до взрыва во время аварии на Чернобыльской АЭС. Параметры выбраны из опубликованных работ [1]. Сценарием этого анализа предположено снижение скорости потока основного циркуляционного насоса и построены регрессионные модели для изучения этого сценария. Рассмотрены результаты примененной модели и сделаны выводы об уменьшении расходов главного циркуляционного насоса и реактивности в течение последних нескольких секунд до взрыва

Анализ взрыва ядерного реактора Чернобыльской АЭС в апреле 1986 г. при помощи тензорных уравнений

Проаналізовано процес вибуху активної зони ядерного реактора на Чорнобильській атомній електростанції у квітні 1986 р. за допомогою тензорних рівнянь, які демонструють рух вектора в тривимірних координатах кривої часу, потоку води та пустоти. Рівняння показують, що цей вектор рухається вздовж геодезичної прямої у координатах кривої, яка описується фундаментальним тензором (gµν), символом Крістофеля (Γαµνσ) і тензором Річчі (Rµν), де µ, ν, σ, α — індекси, які позначають координати. Розв’язання тензорних рівнянь показує, що геодезична пряма вектора має сингулярну точку, яка описує точку обертання активної зони ядерного реактора від нормального функціонування до вибуху.This research analyzes the process of the explosion of the reactor core of Chernobyl nuclear plant in April 1986, using the tensor equations. These tensor equations show a movement of a vector in the three dimensional curvature coordinates of time, water flow, and void. The equations shows that this vector moves along the geodesic in the curvature coordinates, which is described by fundamental tensor (gµν), Christoffel symbol (Γαµνσ) and Ricci tensor (Rµν), where µ, ν, σ, α are suffixes that indicate the coordinates. The solution of the tensor equations shows that the geodesic of the vector has a singular point, which describes a turning point of the reactor core from the normal operation to the explosion, which we reported in our previous articles [1, 2].Проанализирован процесс взрыва активной зоны ядерного реактора на Чернобыльской атомной электростанции в апреле 1986 г. при помощи тензорных уравнений, которые демонстрируют движение вектора в трехмерных координатах кривой времени, потока воды и пустоты. Уравнения показывают, что этот вектор движется вдоль геодезической прямой в координатах кривой, которая описывается фундаментальным тензором (gµν), символом Кристоффеля (Γαµνσ) и тензором Риччи (Rµν), где µ, ν, σ, α — индексы, обозначающие координаты. Решение тензорных уравнений показывает, что геодезическая прямая вектора имеет сингулярную точку, которая описывает точку вращения активной зоны ядерного реактора от нормального функционирования до взрыва

Анализ ядра атомного реактора Чернобыльськой атомной станции за 5 секунд до взрыва в трехмерном сферическом пространстве

Проаналізовано потік води та пустоти (бульбашкові включення) ядра атомного реактора Чорнобильської атомної станції за 5 секунд до вибуху з використанням математичної моделі у тривимірній сферичній системі координат. Для вирішення задачі цей феномен розглянуто за аналогією із законом всесвітнього тяжіння та проаналізовано з використанням методу Шварцшільда. Розраховано радіус сферичного простору води та пустот, що вказує на граничне значення, за якого ядро реактора втратило здатність контролювати потужність. Виконано аналіз за регресійним методом за допомогою експоненціальної моделі і підтверджено вплив пустот та води на потужність реактора.This research analyzed the water flow and bubble (void) of nuclear reactor core of Chernobyl Power Plant, for 5 seconds before the explosion, using a mathematical model of two-dimensional spherical coordinates. To solve the problem, we considered this phenomenon as an analogy of Newtonian gravity theory, which had been solved in Schwarzchild Solution. As a result, the calculated radius of the spherical space of water and bubble indicated the maximum limit, at which the reactor core lost the control of reactor power. And, then, a regression analysis, with exponential model, confirmed the influence of bubble and water to the reactor’s power.Проанализированы поток воды и пустоты (пузырьковые включения) ядра атомного реактора Чернобыльской атомной станции за 5 секунд до взрыва с использованием математической модели в трехмерной сферической системе координат. Для решения проблемы этот феномен рассмотрен по аналогии с законом всемирного тяготения и проанализирован с использованием метода Шварцшильда. Рассчитан радиус сферического пространства воды и пустот, указывающий на максимальный предел, при котором ядро реактора утратило способность контролировать мощность. Выполнен анализ регрессионным методом с помощью экспоненциальной модели и подтверждено влияние пустот и воды на мощность реактора