Statistical Mathematical Modeling Research Articles

Основні показники вогнестійкості сосни звичайної в умовах Лівобережного Лісостепу

Метою дослідження є визначення основних морфометричних показників вогнестійкості дерев сосни звичайної в умовах свіжого субору Лівобережного Лісостепу та їхніх вікових змін. На відміну від пожежостійкості, вогнестійкість визначає ступінь потенційної спроможності дерева зберігати свою життєдіяльність на індивідуальному рівні після пірогенних пошкоджень. Виявлено, що верхня межа розташування грубої кори найбільше залежить від діаметра (r = 0,97) та віку дерев (Ff = 83,2, Fst = 1,8). Визначено, що товщина кори на всіх висотах заміру зазвичай є більшою в дерев із більшою висотою верхньої межі розташування грубої кори, в зоні переходу грубої кори в тонку вона становить 0,1–0,9 мм. Товщина кори в окоренковій частині дерев сосни звичайної в 10–15 разів перевищує товщину кори в тріщинах, де вона становить 1,5–5,8 мм, тому під час низових пожеж є ризик локального ураження камбію вздовж тріщин. Враховуючи отримані результати, було розроблено статистично-математичну модель, за якою можна оцінювати висоту верхньої межі розташування грубої кори дерев у сосняках.

Analysis and Prediction of the Machining Force Depending on the Parameters of Trochoidal Milling of Hardened Steel

Current demands on quality are the engine of searching for new progressive materials which should ensure enough durability in real conditions. Due to their mechanical properties, however, they cannot be applied to conventional machining methods. In respect to productivity, one of the methods is the finding of such machining technologies which allow achieving an acceptable lifetime of cutting tools with an acceptable quality of a machined surface. One of the mentioned technologies is trochoidal milling. Based on our previous research, where the effect of changing cutting conditions (cutting speed, feed per tooth, depth of cut) on tool lifetime was analysed, next, we continued with research on the influences of trochoid parameters on total machining force (step and engagement angle) as parameters adjustable in the CAM (computer-aided machining) system. The main contribution of this research was to create a mathematical-statistical model for the prediction of cutting force. This model allows setting up the trochoid parameters to optimize force load and potentially extend the lifetime of the cutting tool.

General Tendencies of the Behaviour of Vegetables Developed in a Soil Contaminated with Heavy Metals

The paper presents experimental results obtained in the study of heavy metals transfer from soil to vegetables. The experiments for which the raw and statistically processed data are presented in this paper are preliminary experiments within an extensive research program of plant behaviour in soils contaminated with heavy metals. These experiments underlie the development of primary statistical mathematical models that are also presented in the paper. These experiments will also form the basis for far more consistent experiments that follow plants throughout the life cycle. The statistical mathematical models presented in this paper facilitate extracting important conclusions about how plants accumulate heavy metals as well as about the accumulation rate behaviour during experiments. Both experiments and mathematical models will form the basis of complex experiments and dynamic mathematical models in the next stage of research.

Uncertainty analysis of key factors affecting fracture height based on box-behnken method

Hydraulic fracturing technology was one of the main technologies to achieve efficient development of unconventional oil and gas resources. Longitudinal propagation of hydraulic fracture was one of the main factors affecting the reservoir stimulation. At present, there was still a lack of qualitative analysis for the problem of hydraulic fracture penetration. Based on the linear elastic fracture mechanics, the fluid-solid coupling mechanical behavior of reservoir was simulated by plane strain three-dimensional model. The longitudinal initiation and extension process of hydraulic fracture was simulated and analyzed. The effect of in-situ stress and physical parameters on fracture height was studied. At the same time, the key parameters for controlling fracture height were screened through hurricane analysis and Box-Behnken test design. Based on the response surface analysis method, a mathematical statistical model with good fit with the actual calculation results was established to predict the statistical significance of the key parameters controlling the fracture height. According to the designed fracture height, the combination of parameters corresponding to the fracture height was calculated by using the mathematical statistical model prediction. The results showed that the stress difference and elastic modulus difference between the mudstone and the conglomerate layer were the key factors to control the fracture height. The overlying mudstone layer with high in-situ stress and low elastic modulus can reduce the fracture height and effectively restrict the fracture penetration. This study had theoretical significance for understanding the mechanism of hydraulic fracturing.

Overlapping of cooking behavior in high-rise residential buildings

The design of a centralized cooking-fume exhaust system for high-rise residential buildings lacks the parameters related to cooking behavior, such as the coincidence factors. This study surveyed 12-, 14-, and 25-floor residential units by using a thermometer to obtain the continuous temperature profiles for study cooking behavior. Python was used to identify the breaks of temperature gradient, and continuous temperature profiles were transformed into a group of step signals consisting of only “0” and “1” while interfering fluctuations were eliminated and turning points were determined. The hourly overlapping rate of the residential unit after data processing is highly similar. The abstraction of cooking behavior is a mathematical statistical model that obeys normal distribution. A typical cooking behavior model based on normal distribution was established using the main cooking periods, kurtosis, and skewness values, the modeling step length, the peak value of the coincidence factors, and the time corresponding to the peak. Using different correction coefficients to correct the peak value of the coincidence factors can extend the application scope of the model to buildings of any height. In addition, the coincidence factor of 50% can be used as a design parameter for the flue cross section and fan selection parameters. Thus, the selected fan, which is fully loaded during cooking periods and has low load during non-cooking periods, has significant energy saving potential.

Formalized Computer-Aided Handwriting Psychology: Validation and Integration into Psychological Assessment.

In contrast to traditional researches that involve a manual, non-quantitative, and subjective way of performing handwriting analysis, in the current research, a special computer-aided method of revised handwriting analysis is used. It includes the detection of personality traits via manual quantitative registration of handwriting signs and their automated quantitative evaluation. This method is based on a mathematical–statistical model that integrates multiple international publications on the evaluation of handwriting signs. The first aim is the validation of the revised method against the 16 Personality Factor Questionnaire Revised (16PF-R), which is performed as a self-report personality test by test persons and was developed and researched empirically by Raymond B. Cattell et al. A second aim is the development of an integrated model for assessment including handwriting analysis: when both methods come to the same result on a certain scale, then the construct can be accepted with higher reliability; in contrast, when results are contradictory, they should be regarded as a limitation of each method and raise awareness in the researchers, as these contradictions are a precious source of additional information regarding the complexity, ambiguity, and context specificity of personality traits.

Review of restoration processes for damaged social infrastructures in Japan and building a performance indicator for designing disaster mitigation policy

Japan has experienced many large-scale natural disasters such as earthquakes, typhoons accompanied by heavy rain and landslides, and tornadoes. Based on the data of damage caused by four recent major earthquakes in Japan (the Hanshin-Awaji, Niigata-Chubu, Great East Japan, and Kumamoto earthquakes), we investigate the restoration processes of public utilities for major social infrastructure including electricity, gas, water, and communication lines by comparing the differences regarding the speed and trends. The results of various statistical data analyses and mathematical modelling analyses are used to make policy suggestions. In addition, we attempt to build performance indicators (PIs) for water supply businesses to measure the robustness of the water supply network system. Using actual data related to the water supply in Japan, we illustrate the numerical results for the PIs, which can be used to design natural disaster mitigation policies.

Mathematical Modeling of Roughness Changing of Hard Metal Coatings Obtained by Contactless Electrospark Deposition

Results of the roughness studies of multicomponent hard metal layers on X12 tool steel (210Cr12/1.8–2.2% C, 12%Cr) obtained by contactless local electrospark deposition using two types hard metal electrodes (WC–TaC–Co–Al2O3 and WC–(Ti, Ta, Nb)C–Co–Al2O3) are presented here. Dense, smooth, and uniform coatings with a good repeatability of properties have been obtained. The minimal and maximal values of thickness δ, of the roughness parameter Ra, and of micro hardness HV of obtained coatings are changed by altering the stratification regimes in borders: δ = 3–12 μm, Ra = 0.8–2.2 μm and HV = 8.5–18 GPa, respectively. The influence of the process parameters and the electrode composition on the roughness of the layers obtained have been studied. Mathematical-statistical models and equations describing the roughness of the coatings have been created and worked out. They enable obtaining of coatings with a predetermined roughness by controlling regime parameters. Specific ways of obtaining coatings with reduced roughness at the maximum possible thickness, as well as recommendations for their appropriate application, have also been proposed and justified. Based on the obtained regression equations and graphical dependencies, it is possible to optimize properties of the coatings and the conditions of their deposition in order to obtain maximum tribo-effect and increased performance properties of the coated surfaces for different cases of exploitation.

A Statistical Modelling Approach for Guiding the Optimum Surgical Intervention of Breast Cancer

Breast cancer is most common tumour diagnosis for women worldwide. Over the last almost 40 years widespread adoption of mammographic screening has established Breast Conserving Surgery (BCS) followed by irradiation as the most practised treatment of choice. However, in absence of tools to determine the optimal quantum of tissue to be excised the debate continues for achieving a balance between the effectiveness of surgical intervention and the later stage personalisation of treatment, and so, a wide variation in practice is a common phenomenon globally. We attempt to introduce a definite measure that determines efficacy of BCS while protecting aesthetic value of life for Women affected with breast cancer.
 74 mammography examinations and the surgical interventions of those women underwent for the management of breast cancer were used to compute the coefficient of lesion. In first step the lesion and the mammary gland proper are measured applying geometry. In the second step volume of tissue mass to be removed was calculated taking into account the measures from the 1st step and we present the coefficient of lesion mathematically. We empirically illustrated our methodological approach for determining the tissue mass to be excised.
 Conventionally, it is assumed that if the volume of tissues to be removed does not exceed 25% of the volume of the mammary gland, a Breast Conserving Surgery, is performed, however, our empirical illustration demonstrated that the established decision making parameter is not tenable for determining the extent / type of surgery undertaken.
 We have developed a coefficient aligned with the stage of the carcinoma and founded the base for developing a statistical (mathematical) model. Application of such a model accommodating tumour biology and patient characteristics shall not only provide intraoperative real time information to surgeons but also predict the prognosis of optimal surgical intervention of breast cancer.
 The next step is to develop a model using the data of the mammographic examination and the coefficient of breast lesion as covariates for determining the potentially effective volumes of surgical intervention needed, and plan reconstructive measures considering the effect of time on such intervention.

A Real-time Algorithm for Regional Crowd Counting Based on Survival Analysis Theory

This paper proposes a real-time algorithm for regional crowd counting based on survival analysis theory. Our algorithm can accurately calculate regional people flow in real time over a long period, which considers tourists’ stopping time as a type of survival time, and discretizes its continuous distribution probability as a proportion of stopping people in a monitoring region. Compared to other crowd counting methods, our algorithm calculates regional population in real time using a mathematical statistical model, which greatly reduces the dependence on hardware devices. Experiments in two real scenarios verify that the average accuracy of our algorithm is over 91% in comparison with 60% of sensing devices.

Kiwifruit flesh firmness determination by a NIR sensitive device and image multivariate data analyses

A prototype based on a NIR sensitive camera and a Xenon lamp was set up and used to capture 8 bit gray scale (from 0 = black to 255 = white) image of the radiation that passes through the fruit. The count of the pixels with different gray tone was used to build statistical-mathematical models to correlate and predict the kiwifruit flesh firmness. One hundred sixteen fruits conveniently stored to obtain firmness within a range of penetrometric force from 0.8 N to 87 N, were submitted to the optical measurements. Simple regression between the gray tone having the maximum number of pixels and the firmness showed an exponential correlation with R2 values of 0.717. On the contrary, the tone uniformity (maximum number of pixels with the same gray tone) resulted linearly correlated with hardness (R2 = 0.687). PLS algorithm allowed prediction of the flesh firmness with R2 of 0.777 (RMSE = 13 N). Artificial neural networks produced similar results. Although the current technique does not fully satisfies the need of an accurate selection, it could be considered for on-line applications by improving performances (e.g. acting on lamp spectral emissions and camera detection) and with easy mechanical modifications of the sorting lines.

Surface Control of the Frequency of Stratospheric Sudden Warming Events

AbstractThe frequency of stratospheric sudden warming events (SSWs) is an important characteristic of the coupled stratosphere–troposphere system. However, many modern climate models are unable to reproduce the observed SSW frequency. A previous study suggested that one of the reasons could be the momentum damping at the surface. The goal of the present study is to understand what determines the climatological SSW frequency and how the surface damping comes into play. To this end, we conduct a parameter sweep with an idealized model, using a wide range of values for the surface damping. It is found that the SSW frequency is a strong and nonlinear function of the surface damping. Various tropospheric and stratospheric factors are identified to link the surface damping to the SSW frequency. The factors include the magnitude of the surface winds, the meridional and vertical wind shear, the synoptic eddy activity in the troposphere, the transient wave activity flux at the lower stratosphere, and the strength of the stratospheric polar vortex. Mathematical–statistical modeling, informed by the parameter sweep, is used to quantify how the different factors relate to each other. This successfully reproduces the complex variations of the SSW frequency with the surface damping seen in the parameter sweep. The results may help in explaining some of the difficulties that climate models have in simulating the observed SSW frequency.

Response surface modeling for lab-scale column bioleaching of low-grade uranium ore using a new isolated strain of Acidithiobacillus Ferridurans

The microbial-assisted dissolution of minerals from low-grade ore resources has been recently developed into interesting processes to recover valuable metals, because of limitation in high- grade ore resources.In the present study, lab-scale column bioleaching of low-grade uranium ore by a new isolated strain of chemolithotrophic Acidithiobacillus Ferridurans, SBU-SH2 KY497231, which is isolated from a sulfur hot spring in Ardabil, NW of Iran, is investigated. Influence of bioleaching parameters is evaluated by setting up continues column experiments and using uranium samples provided from Sghand uranium mine, Yazd, central Iran. Furthermore, response surface methodology is used for statistical optimization of uranium recovery rate and its compliance with empirical results is examined. The statistical results show maximum 95.5% uranium extraction is obtained during 26 days at pH = 2.5, the temperature of 35 °C, at particle size of 4.64 mm, aeration and irrigation rate 0.78 ml/cm2/min and 1.03 ml/cm2/min respectively which are confirmed by experimental results.Analysis of experimental data by a statistical mathematical model indicates the most key factors on column uranium bioleaching are aeration and irrigation rate respectively. Maximum uranium recovery from leaching of control solution without bacterial cells is 11.33% which shows the isolated bacterium has a considerable influence on uranium recovery. In comparison to the other research reporters of column uranium bioleaching, the new strain of Acidithiobacillus Ferridurans, SBU-SH2, KY497231, indicates its salient features.

Application of probability distributions mixture of safety indicator in risk assessment problems

The main indicator of quality functioning of the aircraft pilotage system is flight safety. Thereby, in accordance with acceptable risk concept, demands with safety indicators are being determined in probability form and circumferential acceptable risk values could be very small order of magnitude 10−6–10−8. Such demands for the precision characteristics of vertical echeloning and automatic landing of civil aircrafts are valid during flights in all weather conditions. At certification of aircrafts these demands should be confirmed. Thereto, the only possible way of demand confirmation with such small risks is statistical mathematical modeling in the wast range of disturbing factors. Mathematical modeling is inseparable part of aircraft piloting system development and it is accepted as legitimate at corresponding verification, which enables the guarantee for adequate aircraft movement modeling. The most complete information about aircraft movement probability characteristics is contained within laws of their probability distributions. In classical mathematical statistics papers there is no investigations of very small and very big probabilities. Therefore for solving the safety problems, connected with needs for investigation “tail” (last) distribution parts, necessary to develop a new methods. One of them is presented into this paper. For problems of statistical modeling of aircraft movement in the wast range of disturbing factors the typical appearance of “breach”—distribution law alteration of analyzed parameters. The cause of the “breach” is realization of unlikely extreme values of disturbed random factors and their mixtures at large quantities of modeling, which reconduct corresponding systems in areas of nonlinearity. It is mentioned that the effect of “breach” is characteristical not only for problems of aircraft piloting but also for the wast range of problems in different practice applied areas—ecology, quality management (Six Sigma methodology) and other.

Importance of inpatient hypoglycaemia: impact, prediction and prevention.

Hypoglycaemia is a key barrier to achieving euglycaemic control in people who are hospitalized. Inpatient hypoglycaemia has been linked to adverse clinical outcomes, including mortality and longer stay in hospital. A number of studies have applied mathematical tools and statistical models to predict inpatient hypoglycaemia and identify factors that may result in hypoglycaemic events. Several different approaches have been tested to prevent inpatient hypoglycaemia. These can be categorized as human intervention, computerized methods or application of medical devices. In this review we provide an overview of the epidemiology of inpatient hypoglycaemia and its impact on patients and hospitals. We also discuss the existing methodology used to predict inpatient hypoglycaemia and the limited number of trials performed to prevent inpatient hypoglycaemia. The review highlights the urgent need for evidence-based methods to reduce inpatient hypoglycaemia.

Analysis and comparison of some criteria of checking the probability distribution deviation from the normal distribution law

A number of criteria of sample data concordance with the normal probability distribution law has been classified, and some recommendations for using these criteria in practice of engineering statistical analysis have been given. An original approach to testing the considered criteria has been proposed, which is based on the logics of building significance criteria, which allowed placlacing the criteria in the order of preference, when the standard normal distribution is taken for reference. This approach has been tested earlier in assessing adequacy of statistical mathematical models and assessing the degree of statistical similarity, when the information about performance quality of complex technical systems is combined, which was obtained in the process of experimental development. However, applying this approach to the problems of comparing criteria of measurement data concordance with the normal probabilities distribution law required additional research caused by lack of programs and tables of percentage points normality criteria statistics. The article presents the results of using of the interval estimation and experimental-statistical method of Taguchi for solving the problem.

Advances in thermal level measurement techniques using mathematical models, statistical models and decision support systems in blast furnace

The estimation of thermal level in blast furnace is of utmost importance, because the processes occurring inside the blast furnace are complex in nature and any drift in thermal level could lead to abnormal furnace state. The present review is made to understand the methods for estimating thermal level in blast furnace, and the drift in estimation of the thermal level. The thermal level estimation is divided into 3 categories, viz. mathematical models, statistical models and decision support systems. The mathematical models are based on the first principle of thermodynamics and give an estimate of the thermal level in blast furnace. On the other hand, the statistical models are mainly the data-based approach that uses the historical data to predict the instability in blast furnace. Lastly, the decision support systems are the prescriptive models that give the recommendations for making the necessary corrections in the process parameters to avoid occurrence of abnormality in blast furnace. Further, the drifts in estimation of thermal level by these techniques are identified and recommendations are made to improve the accuracy of thermal level estimation. The recommendations to control thermal level in blast furnace are provided which when applied in the industrial blast furnace, can avoid the occurrence of catastrophic condition.

АНАЛІЗ ПІДХОДІВ ЩОДО СТВОРЕННЯ МАТЕМАТИЧНОЇ МОДЕЛІ ДЛЯ ЗАДАЧ МОНІТОРИНГУ ПРИРОДНО-ТЕХНОГЕННИХ СИСТЕМ НА ОСНОВІ ВИЗНАЧЕННЯ ІМОВІРНОСТІ ПОСТУПОВИХ ВІДМОВ

The approaches for creating a mathematical model for monitoring natural and technogenic systems (PTS) and emergency situations (ES) based on the probability of gradual failures are outlined. The monitoring of the NAS and ES provides for comprehensive monitoring of changes in the natural and anthropogenic environment and its components. The complexity of this process is determined mainly by the complexity of the diagnostics of the monitoring objects and the precise measurement of a large number of indicators that determine the conditions and factors of the state of the NAS, environmental pollution, etc. The practical solution of this problem is possible on the basis of the use of modern mathematical and geo-information methods of modeling that provide a comprehensive reflection of heterogeneous and multi-linked processes of formation and development of emergency situations of different origins, which can not be achieved with the use of traditional technologies. To describe the functioning of monitoring systems, it is worth building a mathematical model of the research object. The most complete state of the object of the study is characterized by its mathematical functional and statistical model. However, a more complete description of the static and dynamic state of the monitoring object is a probabilistic description of the state of objects with the help of distribution laws of the probabilities of the parameters of the input influences elements, output parameters and vector-operators. Since the probabilities of sudden bounces are determined by known formulas of the reliability theory, the main attention is drawn to the determination of the probability of the gradual failures occurrence.It is established that three mathematical models may be applied to determine the probability of gradual failures (a mathematical model based on the integration of differential equations; a mathematical model based on the Monte Carlo method; a mathematical model based on the quasilinear disturbances method). The results show, that the proposed method of research may use to simulate various scenarios of flooding in the territories of the Chernihiv region.

Constructing Gibbs Measure in a Rigorous Way

Equilibrium statistical mechanics studies mathematical models for physical systems with many particles interacting with an external force and with one another. In this paper we describe an interaction model that generalizes several of these models in one model. An infinite model is constructed as the limiting case of finite interaction models, that is as a thermodynamic limit. The key point in constructing a thermodynamic limit is a proof of existence of the limiting probability measure (Gibbs measure). Traditional proofs use DLR formalism and are quite complicated. Here we explain a more transparent and more constructive proof for the case of high temperatures. The paper provides a detailed, step-by-step rigorous construction of a statistical model and corresponding proofs. The paper also includes a version of the central limit theorem for a random field transformed by a renormalization group, in a special case of the interaction model.

Development of seasonal solar radiation estimation models for Dokuz Eylul University campus area for controller of a two-axis solar tracker

In urban locations, it is generally hard to find enough spaces for solar power plants. However, micro-energy generation systems like solar trackers can be located even in crowded cities and becoming a significant technology in solar energy systems. In this study, the measured global solar radiation data for the research area, Tinaztepe/Izmir (38°22'15.3"N 27°12'28.5"E), were logged, then analysed using statistical methods and seasonal daily global solar radiation mathematical models of Tinaztepe/Izmir were developed. The results of these mathematical models give more precise daily average solar radiation value for Tinaztepe/Izmir than previous Izmir global solar radiation models.