Detecting bivariate outliers on the basis of normalizing transformations for non-Gaussian data

The statistical technique for detecting outliers in bivariate non-Gaussian data on the basis of normalizing transformations, prediction ellipse and a test statistic (TS) for the Mahalanobis squared distance (MSD), which has an approximate F distribution, is proposed. Application of the technique is considered for detecting outliers in two bivariate non-Gaussian data sets: the first, actual effort (hours) and size (adjusted function points) from 145 maintenance and development projects, the second, effort (hours) and mass (tonnes) of designed the section of the ship from 188 designs of sections

Detecting bivariate outliers on the basis of normalizing transformations for non-Gaussian data

The statistical technique for detecting outliers in bivariate non-Gaussian data on the basis of normalizing transformations, prediction ellipse and a test statistic (TS) for the Mahalanobis squared distance (MSD), which has an approximate F distribution, is proposed. Application of the technique is considered for detecting outliers in two bivariate non-Gaussian data sets: the first, actual effort (hours) and size (adjusted function points) from 145 maintenance and development projects, the second, effort (hours) and mass (tonnes) of designed the section of the ship from 188 designs of sections

Radial increment in European spruce (Picea abies) as indicator of sanitary condition of spruce forests in the Ukrainian Carpathians

In recent years, there has been an intense desiccation of spruce forests in the Ukrainian Carpathians, where European spruce is the main forest-forming species. Over the recent years, desiccation has spread to the spruce forest stands which grow in the Carpathians at the height of over 1,000 m above the sea level. This process causes large economic losses, significant deterioration of the condition and productivity of the forests in the Carpathians, decrease in the level of provision of ecosystemic services by forests, functions they perform, therefore leading to dangerous exogenic processes (floods, freshets, erosion, mudflows, landslides). To determine the interaction between the radial increment and sanitary condition of the spruce stands and substantiate the measures of the use of drying spruce forests, in the Vysokohirsky forestry reserve district of the Ukrainian Carpathians in anti-erosion forests, in hotbeds of desiccation of spruce in 2018, dendrochronological surveys were undertaken in two monitoring plots in forests in weak and severely weakened condition. We collected cores from the model trees, measured width of the annual rings, and developed individual dendrochronologies according to the absolute values of the radial increments and generalized dendrochronologies according to the absolute values of the radial increments and increment indices of the duration of 97 (1921–2017) and 81 years (1937–2017). We conducted single-factor dispersion analysis, calculated the indices of abnormality of the radial increments and correlation coefficient. The results revealed that the lowest increments occurred in the years 1965–1990 in the weakened stand and in 1997–2017 in the severely weakened stand. The relative indices of the forests ranged 83.8–114.6%. The cycles of increment lasted 7–9 years. Over the last few decades, favourable conditions for the growth of the trees took place in 1991–2010, unfavourable in 2011–2017, very unfavourable in 1981–1990. Synchronicity of annual radial increments in the spruces of two monitoring plots equaled 49 years. Correlation coefficient indicates that the type of the conditions of growth location has a significant effect on its variability in the process of trees’ life cycle. Average radial increment of the weakened stand of trees over the last 10 years decreased by 7.9%, while it declined by 54.9% in the severely weakened stand compared with the average increments of the tree stands for the surveyed periods, suggesting that the forests undergo different stages of succession: the weakened stand undergoes the stage of recovery after disturbance, severely weakened forest – stage of disturbance. The studies revealed the dependence of radial increment of spruce on the sanitary condition of the forests. The results of the studies may be used for the assessment of dynamic processes in forest ecosystems as a result of the impact of various factors and planning of the forestry measures

Constructing the nonlinear regression equations based on multivariate normalizing transformations

Prykhodko, N. V. Constructing the nonlinear regression equations based on multivariate normalizing transformations / N. V. Prykhodko, S. B. Prykhodko // Вісн. ХНУ ім. В. Н. Каразіна. Сер. Математичне моделювання. Інформаційні технології. Автоматизовані системи управління. – Харків, 2018. – Вип. 39. – С. 61–68.В статті розглядаються методи побудови рівнянь, довірчих інтервалів та інтервалів передбачення нелінійних регресій на основі багатовимірних нормалізуючих перетворень для негаусовських даних. У якості прикладу побудовано нелінійне регресійне рівняння для оцінювання розміру програмного забезпечення інформаційних систем з відкритим кодом на PHP із застосуванням багатовимірного нормалізуючого перетворення Джонсона для сімейства SB. Це рівняння отримано за вибіркою чотиривимірних негаусовських даних: фактичний розмір програмного забезпечення у тисячах рядків коду, загальна кількість класів, загальна кількість зв'язків та середня кількість атрибутів на клас у концептуальній моделі даних з 32 інформаційних систем, розроблених з використанням мови програмування PHP. Попередньо зазначені дані були перевірені на наявність викидів із використанням квадрату відстані Махаланобиса (Mahalanobis): для рівня значимості, що дорівнює 0,005, викиди відсутні. Гіпотезу про багатовимірну нормальність було перевірено за критерієм квадрату відстані Махаланобиса. Побудоване нелінійне рівняння у порівнянні з іншими регресійними рівняннями (як лінійними, так і нелінійними, які отримані за допомогою одновимірних нормалізуючих перетворень Джонсона та десяткового логарифму) має більший множинний коефіцієнт детермінації і менше значення середньої величини відносної похибки. Продемонстровано, що погана нормалізація багатовимірних негаусовських даних за допомогою одновимірних перетворень або її відсутність призводить до збільшення ширини довірчих інтервалів та інтервалів передбачення як нелінійної так і лінійної регресії для більшої кількості рядків даних у порівнянні з багатовимірним нормалізуючим перетворенням.In the paper we consider the techniques to construct the equations, confidence and prediction intervals of nonlinear regressions on the basis of multivariate normalizing transformations for non-Gaussian data. We demonstrate that the poor normalization of multivariate non-Gaussian data using the univariate transformations leads to an expansion of the confidence and prediction intervals of non-linear regression for a larger number of data rows compared to the multivariate normalizing transformation

Method to extrapolate the stress-rupture curves of high-temperature materials

Наведено метод прогнозування тривалої міцності матеріалів, виходячи з концепції базових діаграм. Запропоновано прості співвідношення, що зв’язують розрахункову довговічність і відповідне їй діюче напруження, визначене по базовій діаграмі. Ефективність методу проілюстровано при розрахунках довговічності сталей SUS 316-HP (18Cr-12Ni-Mo) і JIS SCMV 4NT (2,25Cr-1Mo) для досить широких діапазонів діючих напружень і температур. Показано перевагу даного підходу відповідно найпоширеніших параметричних методів Ларсона-Міллера, Орра-Шербі-Дорна, Менсона-Саккопа, Труніна й ін.The method to predict the stress-rupture strength of materials using 3000–7000 h test data and the master-curve concept is presented. Simple formulas relating the theoretical lifetime and the corresponding stress determined from the master curve are proposed. To determine accurately the difference between the true stress and the stress found from the master curve, an approximating function of β based on available test data is used. The quantity β is the cotangent of the angle between the ordinate axis and a segment of the stress-rupture curve plotted on log–log scale. The parameters of the approximating function can be assumed to be either invariant to the test temperature or determined from the difference between the experimental and calculated values for each isotherm. The assumption of invariance is equivalent to the hypothesis that the family of stress-rupture curves can be reduced to a unified curve. The latter approach results in a better agreement between calculated and experimental data. In some cases, however, the assumption that the parameters of the approximating function are constant allows obtaining reliable results with accuracy sufficient for practical purposes. The method is capable of extrapolating the lifetime to values that are more than in 30 times greater than the available experimental data. The efficiency of the method is illustrated by calculating the lifetime of steels SUS316-HP (18Cr–12Ni–Mo) and JIS SCMV 4NT (2.25Cr–1Mo) for quite wide ranges of stress and temperature. The linear dependence of the mismatch function on β is used as the approximating function. Using a function rather than a set of constant parameters, as in the master curve method, always results in a better agreement between calculated and experimental data when extrapolating stress-rupture curves. It is shown that the method has advantages over the master-curve approach and popular parameters such as Larson-Miller, Orr-Sherby-Dorn, Manson-Succop, Conrad’s, Korchynsky-Clauss, and Trunin’s. The parameters of the linear models are calculated using multifactor linear regression

Modelling of the creep processes and the stress-rupture strength of materials

Запропоновано модель для опису одновимірних неізотермічних процесів деформування, що враховує пошкодженість при повзучості для широких діапазонів напруження і температури. Уточнено області застосування параметричних методів для прогнозування тривалої міцності матеріалів. Подано методику для конкретизації запропонованих рівнянь стану та показано їх ефективність при описуванні повзучості матеріалів.A model for describing one-dimensional nonisothermal deformation processes that considers the damage under creep for a wide range of stress and temperature is proposed. The influence of the stress state and temperature on the creep rate variation is taken into account by means of a scalar function of damage level, with all three specific portions of the creep curve being described. The Lemaitre and Plumtree model is used as an evolutionary relationship, considering that its parameters are stress- and temperature-dependent. Based on the relationships described by the stress-rupture curves, the procedure is proposed for specifying the parameters of the evolutionary equation. The application areas of the known parametric methods for predicting the stress-rupture strength of materials are specified based on the experimental investigations. It is shown that these methods allow extrapolating the creep-rupture life to the values that exceed the available experimental data by no more than a factor of 10 with accuracy sufficient for engineering purposes. To extend the prediction capabilities to 300 thousand hours or more on the basis of the test results of limited duration, a modified base diagram method is proposed. A linear dependence is proposed to approximate the residual function in terms of the base diagram method. In the case, where it is impossible to reduce the stress-rupture curves to a common curve, the residual function parameters are determined from the experimental data for one isotherm. In this case, its parameters are the functions of temperature. The advantages of this approach over the Larson–Miller, Orr–Sherby–Dorn, Manson–Succop, Trunin and other parameters are shown during the extrapolation of stress-rupture strength to long lifetimes. To describe the dependence of the creep strain rate on the stress, creep strain, damage level function and temperature, the relationship of the strain-hardening theory is used with the corresponding change of the stress value for the effective stress defined by Kachanov. The procedure is proposed for specifying the constitutive equations in terms of the strain distribution in creep and the stress-rupture curves. The obtained values of the parameters calculated at the fixed stress and temperature values are approximated using the smoothing-surface approximation. The efficiency of describing the creep processes is shown in the strain calculations for alloy 19Cr-18Co-4Mo-3Ti-3Al-B and steels 12Cr-18Ni-Mo, 21Cr-32Ni-Ti-Al. Good agreement is shown between the predicted and experimentally obtained data for quite wide ranges of working stress and temperature

Murals as an element of the tourist image of the city of Odesa

The article discusses in detail the latest objects of tourist display of the city of Odessa - murals. These works of art increase the aesthetic appeal of the city's districts, promote cultural heritage and promote the development of tourism in the area, and ultimately, together with other recreational and tourism facilities, influence the formation of the tourist image of the city. Thus, the development and development of excursions with the involvement of a kind of urban art – murals, will contribute to the restoration of tourist activities in the city in peacetime

Resorts as multifunctional recreation and tourism centers

The article deals with the functioning of modern resorts as multifunctional recreation and tourism centers. Today, maintaining a healthy lifestyle has become a trend all over the world. As a result, traditional resort establishments are being modernized and provide the latest innovative wellness and spa services. Ukraine has a rich recreational potential to support existing and develop new resorts that can offer a variety of wellness treatments and leisure activities for various market segments

Formation of the sea passenger transportation market and cruise tourism industry

The article is devoted to the emergence, development and current state of sea passenger transportation. The main stages of development of sea passenger transportation, characteristics of vehicles, difficulties that arose during the operation of passenger vessels are presented. The factors that contributed to the development and industry of sea cruises are analyzed. The issues of gradual transformation of sea cruises into tourist entertainment of mass tourism are considered

Information technologies, geoinformation systems and cartographic support in the system of professional training of tourism experts and geographers

The article is devoted to the problems of using information technologies, Geographic Information Systems and cartographic materials in the tourism sector, both in the educational process and directly in the work of tourist enterprises. Emphasis is placed on specialized software products for solving the management problems of tourist enterprises. The article describes the functional features of maps, GIS products, and Internet resources used for cartographic support of tourist and recreational activities