Normal Distribution Law Research Articles

The state of rheological properties of blood in pregnant smokers with chronic nonspecific bronchial inflammation

Aim. To evaluate the effect of smoking on the blood rheology of pregnant smokers with chronic nonspecific bronchial inflammation. Materials and methods. The prospective study included 107 pregnant smoking patients and 136 non-smoking pregnant women who were observed in a polyclinic. The control group consisted of 42 non-smoking women without chronic diseases. The patients were examined according to the clinical guidelines for the treatment of chronic obstructive pulmonary disease. The speed and volume indicators of the function of external respiration, indicators of blood rheology were studied. The reliability of the results was assessed using the methods of parametric and nonparametric statistics. Before applying all statistical research methods, it was checked whether the sample obeys the Gaussian (normal) distribution law. A single-factor analysis of variance was used to determine whether there was a statistically significant difference between the averages of three or more independent groups. Results. Having refuted the null hypothesis about the absence of the effect of smoking on hemoglobin, using the Student's t-test method for dependent samples, it was established. Conclusion. The longer the period of tobacco use lasted, the more likely it was to develop changes in the viscosity qualities of blood, which undoubtedly affected the condition of patients and the fetus.

Modeling the Tourism Market Behavior Based on Discrete Equilibrium Models “Supply – Price – Demand”

Abstract The work is devoted to the modeling of the behavior of the tourism market in the conditions of a supply random lag, distributed according to normal and uniform distribution laws. The behavior of dependences on the tourist market of supply and demand on the price is considered. The modeling of the behavior of the tourism market was carried out using a market dynamic model in the plane of variables “supply – price – demand” taking into account the interests of different groups of consumers, primarily from the point of view of pricing. The delay between changes in supply and demand volumes is taken into account using a Cobweb model. To test this method, information was collected on family expenses when traveling abroad (outbound tourism, tourist vacations lasting 7-15 days) by surveying the employees of 38 travel organizations as of 2021. Three segments of the tourism market are identified: low ($2000 − 4000), medium ($4000 − 12000), and VIP-segment ($12,000 − 20,000). The analysis of the modeling results showed that the behavior of tourists of different segments can significantly influence the market dynamics. The use of a Cobweb model allowed for determining the level of stability of tourist behavior and assessing the possibility of consumer migration from one segment to another. Sensitivity to price changes and response to new offers from different segments can be different, which is important for determining pricing strategies, marketing, and the development of new tourism products.

Manifestation of the normal intensity distribution law (NIDL) in the rovibrational emission spectrum of hydroxyl radical

The latest experimental [Noll et al. Atmos. Chem. Phys. 20, 5269 (2020)] and theoretical [Brooke et al. J. Quant. Spectr. Rad. Transfer 168, 142 (2016)] data on the OH emission intensities are analysed with use of the NIDL. It is found that the calculated intensities of the Δ v > 6 transitions should not be trusted. The analysis of the OH data revealed that the NIDL theory is not applicable to the satellite bands. The effect of small reduced mass previously discovered in H 2 [Ushakov et al. J. Mol. Spectrosc. 399, 111863 (2024)], causing the NIDL straight-line slope to be larger than the one associated with the repulsive branch of the potential, is demonstrated in OH, and the same should be true of all the diatomic hydrides. We performed ab initio calculations of the OH repulsive branch and compared it with the one of Brooke et al. and the other due to Varandas and Voronin [Chem. Phys. 194, 91 (1995)]. We found that the ab initio PEF closely follows the Varandas-Voronin potential in the repulsive region important for calculating the overtone intensities [Medvedev, J. Chem. Phys. 137, 174307 (2012)].

The value of endocervical curettage during large loop excision of the transformation zone in combination with endocervical surgical margin in predicting persistent/recurrent dysplasia of the uterine cervix: a retrospective study

BackgroundCervical cancer often originates from cervical cell dysplasia. Previous studies mainly focused on surgical margins and high-risk human papillomavirus persistence as factors predicting recurrence. New research highlights the significance of positive findings from endocervical curettage (ECC) during excision treatment. However, the combined influence of surgical margin and ECC status on dysplasia recurrence risk has not been investigated.MethodsIn this retrospective study, data from 404 women with high-grade squamous intraepithelial lesions (HSIL) who underwent large loop excision of the transformation zone (LLETZ) were analyzed. Records were obtained retrospectively from the hospital’s patient database including information about histopathological finding from ECC, endocervical margin status with orientation of residual disease after LLETZ, recurrent/persistent dysplasia after surgical treatment and need for repeated surgery (LLETZ or hysterectomy).ResultsPatients with cranial (= endocervical) R1-resection together with cells of HSIL in the ECC experienced re-surgery 17 times. With statistical normal distribution, this would have been expected to happen 5 times (p < 0.001). The Fisher’s exact test confirmed a statistically significant connection between the resection status together with the result of the ECC and the reoccurrence of dysplasia after surgery (p < 0,001). 40,6% of the patients with re-dysplasia after primary LLETZ had shown cranial R1-resection together with cells of HSIL in the ECC. Investigating the risk for a future abnormal Pap smear, patients with cranial R1-resection together with dysplastic cells in the ECC showed the greatest deviation of statistical normal distribution with SR = 2.6.ConclusionOur results demonstrate that the future risk of re-dysplasia, re-surgery, and abnormal Pap smear for patients after LLETZ due to HSIL is highest within patients who were diagnosed with cranial (endocervical) R1-resection and with cells of HSIL in the ECC in their primary LLETZ. Consequently, the identification of patients, who could benefit of intensified observation or required intervention could be improved.

Detection of uniformity and spatial correlation of subgrade compaction quality based on intelligent compaction technology

Intelligent compaction uniformity and spatial correlation detection of subgrade is an important part of intelligent compaction technology. In this paper, a subgrade compaction uniformity detection method is established based on the univariate statistical normal distribution 3σ criterion, and further a subgrade compaction quality spatial correlation detection method is established by the multivariate statistical spatial semi-variance function, and finally the established subgrade compaction uniformity and spatial correlation methods are verified by field tests. The subgrade compaction uniformity and spatial correlation are detected based on field tests. The results obtained in this paper show that the 3σ criterion based on normal distribution can be used for the detection of intelligent compaction uniformity of subgrade, and the field test results are verified by this method, and all the intelligent compaction uniformity of subgrade meets the requirements; considering the construction efficiency and the influence between rollers, it is recommended that the rolling speed should be in the interval range of 2–3 m/s, and the construction spacing of rollers is maintained at 10 m and above.

Reference Intervals of Mass Coefficients and Absolute Weights of Mini Pigs’ Organs

Introduction. Measurement of weights and calculation of mass coefficients of the laboratory animals’ internal organs are the integral stages of toxicological research. However, the absence of the correct intra-laboratory reference intervals corresponding to the normal values established for the animal population of a research laboratory could hinder the analysis of the mass coefficient changes in the experiment. For example, the data on weights and mass coefficients of mini pigs’ organs is being an issue due to its insufficient availability in the open sources. At the same time, in the literature there is a lot of such kind of data referring to the industrial pig breeds. Due to the wide use of the mini pigs in the pre-clinical research and because in the pig species taxonomy they are considered to be a weight category representing the pigs with reduced mass of the body with similar morphology of the organs and body systems, we have set an objective to determine and calculate the reference intervals of mass coefficients of internal organs relative to the mass of the body and brain, as well as the absolute weights of mini pigs’ internal organs and compare the results with the data on mini and industrial pig breeds in the literature sources.Materials and Methods. The data on 29 males and 29 females of the Vietnamese lop-bellied mini pig breed aged 6 months and older, who used to be in control groups of the various experiments held at JSC “SPA “House of Pharmacy” (Leningrad region) in the period from January 2018 to March 2024, was used to calculate the reference intervals. The statistical analysis was peRussian Federationormed using Microsoft Excel and Reference Value Advisor v2.1 software in compliance with the CLSI guidelines. Calculation of the reference intervals for all parameters was carried out by a robust method, the compliance with the normal distribution law was determined by Anderson–Darling test, in case of abnormal distribution of data, calculation of the reference interval was carried out with the Box–Cox transformation.Results. The data on the absolute weights of organs and their coefficients relative to the body and brain masses were presented in the form of the lower and upper reference limits and confidence intervals for each of the limit. The reference intervals of masses of organs across all parameters in males and females had similar limits, the most comparable values were found for the heart and brain parameters. The calculated interval of the heart absolute weight in males was 28.3–253 g, that of the brain was 46.5–93.7 g; in females these intervals were 42.9–279 g and 55.5–81.8 g respectively. Upon comparing the obtained data with the literature sources, it was found that the majority of the absolute weights of all measured mini pigs’ organs had fitted in the limits of the reference values, whereas the masses of the lungs and liver were at the lower limit or below the calculated intervals. The values of the absolute weights of most of the organs of the industrial pig breeds were higher than that of mini pigs, which was due to the difference in the body size and mass of the studied animal breeds. When comparing the mass coefficients of organs in relation to the body mass, it was found that the coefficients of most organs of the industrial breeds and mini pigs, on the contrary, were within the calculated reference intervals or slightly exceeded them.Discussion and conclusion. The calculated reference intervals of the mass coefficients of some organs in relation to the body mass, as well as the absolute weights of the spleen in mini pigs are comparable with the data available in literature for the industrial meat pig breeds. At the same time, the data available in the literature sources on the absolute weights of organs and their mass coefficients relative to the body mass of mini pigs, in most cases, have fitted into the calculated intervals. To increase the prognostic value of the obtained reference intervals, the analysis of a larger size sample is necessary.

Contribution to Adjustment of Partial Safety Factors for RC Water Tank Design

Traditionally, the optimisation of civil engineering structures is conducted by a deterministic approach based on global safety factors recommended by the dimensioning codes, such as the Algerian seismic code (RPA) and the Eurocode (EN 1990). These factors are applied to take into account the uncertainties related to the most important parameters of the structure as well as the actions and their effects, and implicitly provide a target level of reliability. The use of these factors aims to introduce a sufficient margin of safety in order to increase the safety of the structure design and to reduce the role of uncertainties on the performance of the optimised structure. In this research, the authors propose to use the semi-probabilistic method in the limit state design of the top ring beam of a Reinforced Concrete (RC) water tank placed on the ground for assessing the partial safety factors of both loadings and materials strength. The reliability approach is first conducted using a computer code developed with Matlab© software based on the Monte Carlo simulation method and on the First Order Reliability Method (FORM). Two random variables are considered, i.e. the static live load and the concrete compressive strength, both modelled by normal distribution laws. In the second part of this work, partial safety factors are adjusted in order to achieve the target reliability in a range of performance of the civil engineering structure. This semi-probabilistic approach is applied to a case study of an RC tank of capacity 250 m3 in order to adjust safety factors so as to obtain a compatible probability of failure with the appropriate target value as a function of consequence class. The results of the study conclude that this semi-probabilistic method allows adjusting adequate partial safety factors according to target reliability.

ВЛИЯНИЕ ПОГРЕШНОСТЕЙ ИЗМЕРЕНИЯ КООРДИНАТ СУДНА НА КАЧЕСТВО ПРОЦЕССА УПРАВЛЕНИЯ

Autopilots are an integral part of modern ships. However, at present, many tasks are emerging, including the ones in the unmanned navigation field, requiring the use of new control algorithms and new means of monitoring navigation parameters. In particular, to solve such problems as keeping a vessel on a given trajectory, automating the ships’ divergence and similar tasks, it is necessary to have means of continuous monitoring of the ship’s location. For this purpose, receivers of global navigation satellite systems can be applied. To model control processes, it is necessary to know the distribution of positioning errors of modern devices. Some works show that over long time intervals (a day or more), positioning errors can be considered a random process with a Gaussian distribution. This paper presents the experimental study results of the distribution of positioning errors of a ship navigation receiver operating in the GPS and GLONASS systems, in a combined GPS/GLONASS mode, as well as in the indicated modes with differential corrections. The paper shows that at time intervals of seconds – minutes (characteristic of ship’s control systems), positioning errors of the navigation receiver cannot be represented by a random process with a Gaussian distribution law. The paper presents the results of a mathematical modelling of the process of holding a ship on a given trajectory using experimental values of positioning sensor errors. For the research, a mathematical model of an innovative ship with a wheel-propulsion steering complex is used. An algorithm is created that makes it possible to keep a vessel on a given trajectory with an accuracy acceptable for a practical use, commensurate with deviations determined by the design features of the ship’s hull and its propulsors.

METHOD FOR GENERATING A DATA SET FOR TRAINING A NEURAL NETWORK IN A TRANSPORT CONVEYOR MODEL

The object of research is a stochastic input flow of material coming in the input of a conveyor-type transport system. Subject of research is the development of a method for generating values of the stochastic input material flow of transport conveyor to form a training data set for neural network models of the transport conveyor. The goal of the research is to develop a method for generating random values to construct implementations of the input material flow of a transport conveyor that have specified statistical characteristics calculated based on the results of previously performed experimental measurements. The article proposes a method for generating a data set for training a neural network for a model of a branched, extended transport conveyor. A method has been developed for constructing implementations of the stochastic input flow of material of a transport conveyor. Dimensionless parameters are introduced to determine similarity criteria for input material flows. The stochastic input material flow is presented as a series expansion in coordinate functions. To form statistical characteristics, a material flow implementation based on the results of experimental measurements is used. As a zero approximation for expansion coefficients, that are random variables, the normal distribution law of a random variable is used. Conclusion. It is shown that with an increase in the time interval for the implementation of the input material flow, the correlation function of the generated implementation steadily tends to the theoretically determined correlation function. The length of the time interval for the generated implementation of the input material flow was estimated.

ДОСЛІДЖЕННЯ ОСОБЛИВОСТЕЙ ОБРОБЛЕННЯ СИГНАЛІВ ДИНАМІЧНИХ ЦІЛЕЙ В БОРТОВИХ РУХОМИХ ІМПУЛЬСНИХ РАДІОЛОКАТОРАХ

The characteristic features of coherent (quasi-coherent) and incoherent accumulation and detection of signals received from the radio air (reflected from a passive dynamic target) are considered, which are an additive mixture of a useful component and a possible "noise-like" interference with the added "own" noise of the receiving path in airborne mobile pulse radars air base. It is assumed that the random components of the input signal are adequately described by a normal (or close to it) distribution law, and the signal (during the accumulation interval) is harmonic, the period of which is uniquely related to the Doppler frequency shift in the received signal. Necessary and sufficient conditions for coherent (quasi-coherent) and incoherent effective signal accumulation are formulated, analytical and graphical dependencies are given for determining the output ratio "signal /(noise+interference)" at different multiplicities of coherent and incoherent accumulation in both time and spectral domains. A mathematical model based on the system modeling package "System View" was developed and investigated, which demonstrates, by means of adequate simulation and statistical averaging, the peculiarities and quantitative differences of the results of coherent and incoherent accumulations at various, in particular low, but practically significant, input ratios "signal /( noise+interference)", as well as from the multiplicity of accumulation, that is, the number of received signals during the permissible interval of accumulation.

Pore structure characteristics of coral reef limestone: a combined polarizing microscope and CT scanning study

Coral reef limestone is a special class of geological medium formed through long-term deposition following the death of reef-building coral groups. Because it retains the skeletal structure of marine organisms during its formation, its pore structure is hyper-developed and complex. Deciphering the pore structure of the coral reef limestone is important because it is closely related to its macroscopic physical and mechanical properties. This study conducted a comprehensive analysis of the pore structure features of two types of coral reef limestone collected from the construction site of a nuclear power station located in the South China Sea using a combination of polarizing microscopy and CT scanning technologies. The fractal dimension of the pore structure of the treated reef limestone image was calculated, and the pore structure characteristics were statistically analyzed by considering several parameters including porosity, pore size, pore equivalent radius, shape factor, etc. In addition, the directional feature of the pore structure was explored. The results show that the improved watershed segmentation algorithm can accurately segment the pore structure of reef limestone images; both coral reef limestone specimens are loose of high porosity; the fractal dimension of pore structure lay between 1.58∼1.75, indicative of a high self-similarity; the pore size of the two coral reef limestone specimens is quite different, and the distribution of equivalent pore radius conforms to the normal distribution law; the pore structure of the two samples had obvious directionality, which can be quantified using a directional tensor. This study sheds light on future investigations linking the microscopic structure and macroscopic properties of coral reef limestones.

Multidimensional Factors To Measure Quality In Education Institutions

This study aims to assess satisfaction with the quality of education in educational institutions in Algeria and to determine the factors that significantly influence it. The study was based on a survey of inspectors representing the primary control body for educational institutions in Algeria. The questionnaire contained questions based on which the inspectors assessed the quality of education in 1,101 schools (representative sample). A three-point Likert scale was used to evaluate inspectors’ agreement with the statements included in the questionnaire. The questionnaire consists of 7 factors that characterize the quality of the professional development of pedagogical workers, the educational program, textbooks, the educational process, the conditions of school education, the evaluation process, and the effectiveness of the teacher’s work. Correspondence of the data to the normal law of distribution was confirmed with the help of SENWEKS (asymmetry coefficient/skewness coefficient) and KIRTOSIS (variation coefficient or excess) indicators. The reliability of the research tools and the possibility of relying on the questionnaire data were confirmed using Cronbach’s alpha coefficient and validity – using the overall internal consistency coefficient. The internal consistency reliability of the questionnaire was confirmed using Pearson’s linear correlation coefficients between the factors and the total score of the questionnaire. The study proved that the factors of the quality of education, with the highest level of satisfaction expressed by the respondents, were the quality of educational programs (inspectors have a favourable opinion about the educational content, considering it relevant and well structured) and textbooks (inspectors appreciate the clarity and richness of the content of the textbook, emphasizing its essential role in student learning), while they were the least satisfied with the quality of learning conditions (inspectors point to a lack of educational resources, inadequate infrastructure and a large number of students in the classroom). One-sample Student’s t-test (one-sample T-Student Test) was used to identify the factors that have the most significant impact on measuring the quality of education in educational institutions in Algeria. The most important factors were the effectiveness of the teachers, the quality of the curriculum and the quality of the textbooks. The research emphasizes the importance of continuous learning and adequate support for teachers.

АНАЛИЗ ВЗАИМОСВЯЗИ НИКОТИНОВОЙ ЗАВИСИМОСТИ И ПАССИВНОГО КУРЕНИЯ СО СТЕПЕНЬЮ ТЯЖЕСТИ ХРОНИЧЕСКОЙ ОБСТРУКТИВНОЙ БОЛЕЗНИ ЛЕГКИХ У КУРЯЩИХ ЖЕНЩИН РЕПРОДУКТИВНОГО ВОЗРАСТА

Introduction. We studied the nicotine addiction stage and secondhand smoke interrelationships with the chronic obstructive pulmonary disease severity in smokers of reproductive age. Aim of the study was to research in the nicotine addiction and secondhand smoke impact upon the development of chronic obstructive pulmonary disease severity in smoking women of reproductive age. Materials and Methods. Using the questionnaire methodology developed, the nicotine addiction stage was analyzed in reproductive women with and without secondhand smoke (based on questionnaire survey outcomes). There were 107 smoking female patients of reproductive age divided into two groups: Those with secondhand smoke and those without it. Observational group consisted of 42 non-smoking women without any chronic diseases. Chronic obstructive pulmonary disease was diagnosed based on the clinical recommendations of the Russian Respiratory Society (2021). The data obtained during the study were analyzed followed by the comparison of the outcomes between the groups of smoking patients with secondhand and non-secondhand smoking, against the observational group. The outcomes led us to determine whether there is a statistically significant relationship between secondhand smoke and nicotine addiction stage in the development of chronic obstructive pulmonary disease. The reliability of the outcomes was assessed using the methods of parametric and nonparametric statistics. Before using all statistical research methods, we checked whether the sampling complied with the Gaussian (normal) distribution law. Variables that did not obey the normal distribution law or those with the uncertain distribution law were analyzed using a nonparametric statistical method, i. e., Pearson criterion. Results and Discussion. Average age of the smoking patients is 26.5 years. Average index of smokers was 6.59 pack-years. The smokers’ index exceeded the middle of the indicator contributing to the chronic obstructive pulmonary disease development (10 pack – years), which is typical for a young age and their smoking experience. It was found that the nicotine addiction stage correlates with the chronic obstructive pulmonary disease severity with a statistically significant reliability. Conclusions. Secondhand smoke in addition to active smoking, reduces the temporal characteristics of chronic obstructive pulmonary disease severity.

ВЕРОЯТНОСТЬ ФОРМИРОВАНИЯ НИКОТИНОВОЙ ЗАВИСИМОСТИ У КУРЯЩИХ ПАЦИЕНТОК С ХРОНИЧЕСКОЙ ОБСТРУКТИВНОЙ БОЛЕЗНЬЮ ЛЕГКИХ С УЧЕТОМ СТАЖА КУРЕНИЯ И КОЛИЧЕСТВА ВЫКУРИВАЕМЫХ СИГАРЕТ

Introduction. This paper presents the results of assessing the likelihood of developing nicotine addiction, depending on smoking history and on the number of cigarettes smoked per day by women of fertile age. The aim is to establish the prognostic probability of nicotine addiction development in smokers, depending on smoking history and on the number of cigarettes smoked. Materiаls and Methods. The prospective study included 107 smoking female patients with chronic obstructive pulmonary disease and nicotine addiction of different stages (hereinafter referred to as nicotine addiction). The patients were divided into 2 groups, depending on their secondhand smoke: 53 smoking patients with and 54 smoking patients without secondhand smoke. The observational group consisted of 42 non-smoking women without any chronic diseases. Chronic obstructive pulmonary disease was diagnosed based on the clinical recommendations of the Russian Respiratory Society (2021). Reliability of the outcomes was assessed using the methods of parametric and nonparametric statistics. Prior to the application of all statistical research methods, we checked whether our sam- pling complied with the Gaussian (normal) distribution law. The distribution law was described using the Kolmogorov- Smirnov and Lilliefors normality criteria, and a single-sample Shapiro-Wilco normality test. Nonlinear links of binary features with quantitative or qualitative features were evaluated using logistic regression. Logistic regression analysis made it possible to create a statistical model for predicting the probability of an event based on available data. Results and Discussion. With an average smoking activity of 14 cigarettes per day, the onset of nicotine addiction in the first group (a combination of active and secondhand smoke) began with the smoking experience of 12 years, reaching the maximum probability with the experience of 15 years. In the second group, nicotine addiction appeared and reached its maximum (100 %) four years later than in the first group. With an increase in the number of cigarettes up to 16 per day, an identical pattern was observed within the course of earlier nicotine addiction. Conclusions. Secondhand smoke, in addition to active smoking, increases the nicotine load with the development of more pronounced prerequisites for the pathogenetic processes of chronic obstructive pulmonary disease development.

Оценка параметров по засоренным выборкам

Parametric estimates based on contaminated samples are considered in the paper. The paper provides an over-view of algorithms for estimating the mean and the variance for a one-dimensional sample, as well as estimating the mean vector and the covariance matrix for a multidimensional sample. The paper uses the Minimal Covariance Determinant (MCD) algorithm adapted for one-dimensional sample and the MCD algorithm for multidimensional sample. The parameters are estimated on a subsample, the size of which is determined by a given confidence probability. Examples for samples with different levels of contamination are considered. In both examples, the sample was a union of two subsamples. The first subsample, the main one, was generated by normal distribution laws. The second subsample, auxiliary, was generated by different distribution laws. The examples demonstrate the dependence of the estimation accuracy on the confidence level and contamination. The figures illustrate the operation of the MCD algorithm. The main idea of the paper is to show the robustness of the MCD algorithm.

On the Wave‐Normal Distribution of Lightning‐Generated Whistlers and Their Propagation Modes

AbstractObservations from Van Allen Probes are analyzed to obtain the statistical wave normal distribution of lightning‐generated whistlers (LGWs). An automatic algorithm is developed to identify burst mode waveform data with LGW signals and analyze the wave polarization information for these LGW signals. The spatial distribution of the LGW occurrence and the probabilities of different propagation types demonstrate that most LGWs can be observed in the low L‐shell region (L &lt; 3), where the dominant propagation type is oblique outward. Parallel propagation dominates in the high L‐shell region, but the LGW occurrence is very small. Additionally, a small group of oblique but inwardly propagating LGWs are observed at low altitudes (&lt;0.2RE). A ray tracing simulation is performed not only to confirm predominant oblique and outward wave vectors in the vast region of the plasmasphere but also to verify the existence of these inward propagating LGW signals at low altitudes near the topside ionosphere.

Features of calculating the strength of gantry and ship cranes gear units in the probabilistic aspect

The performed study is the result of collecting statistical data on failures of port transshipment and floating cranes. It is found that many accidents of components and parts of crane mechanisms can be associated with an erroneous determination of design loads. In order to increase the strength reliability, numerous field tests were carried out in river and sea ports under various modes of transshipment for different types of cargo. Tests have shown that operational loads are random in nature, and their laws of distribution over time of individual crane mechanisms can be approximated by truncated normal Gauss laws, accounting for which at the stage of new design developments, as shown by the practice of performing strength fatigue calculations, is not possible. In the article, in order to use the obtained laws at the design stage, it is proposed to replace the representation of operational loads with initial moments that are common to the entire crane mechanism, and transfer individual characteristics consideration such as stress concentration coefficients, fatigue curve parameters, operating time or test base, to subsequent stages of machine components development. For practical testing of the operational loads representation by the normal Gauss laws, a critical analysis of their initial moments, which makes it possible to identify inconsistencies in the representations of variable loads proposed for strength calculation, is given. For the corrected truncated normal load distribution law, the initial moments, the value of the order of which corresponds to the formulas structure used in calculating fatigue resistance at variable load amplitudes (in particular, under alternating loading modes), are determined. The presentation of corrected normal distribution laws with initial moments complements the normative documents used in practice when performing strength calculations under variable loading conditions, significantly simplifies calculations and makes it possible to take it into account at the stage of new design developments in accordance with the formulas established in the current normative documents.

Python Software Tool for Diagnostics of the Global Navigation Satellite System Station (PS-NETM)–Reviewing the New Global Navigation Satellite System Time Series Analysis Tool

The time series of GNSS coordinates contain signals caused by the age-related movement of tectonic plates, the deformation of the Earth’s surface, as well as errors at different time scales from sub-daily tidal deformation to the long-term deformation of the surface load. Depending on the nature of the signal, specific approaches are used for both the visual interpretation and pre-processing of time series and their statistical analysis. However, none of the present software analyzes the nature of the residual errors but assumes their random nature and obedience to the classical normal distribution. One of the methods for analyzing the time series of coordinates with residual, unaccounted-for systematic errors is the non-classical error theory of measurements. The result of this work is a developed software solution for analyzing the time series of GNSS coordinates to test their normality, or in other words, to test whether a particular GNSS station is subject to the influence of small, unaccounted-for errors. Conclusions: After testing our software on four reference stations in Europe, we concluded that none of the chosen stations followed the normal law of distribution; thus, it is vital to perform such tests before conducting any experiments on the time series from reference stations.

An approach to automating the daily performance indicators monitoring of a transport company

The article compares the results of applying some statistical criteria to detect suspicious values (gross outliers) in the daily performance indicators of one of the transport companies in the Russian Federation. The criteria applicable to data samples with a normal distribution law are considered. In this connection, a preliminary test of the hypothesis about the correspondence of the distribution of controlled quantities to this law was carried out. It is shown that identifying gross outliers in the values of the indicators under consideration requires the simultaneous application of several statistical criteria.

DETERMINING STRUCTURAL RELIABILITY CONSIDERING THE ASYMMETRY OF DISTRIBUTION LAWS

Abstract. In the calculations of structural reliability, it is mainly considered that the laws of distribution of random values of resistance and load effect obey the normal law (Gauss’s law). This law is convenient to use and the most widespread. Therefore, it has found wide application in reliability theory for solving most problems. The law of distribution is symmetric, that is, random variables are distributed symmetrically relative to its center (mathematical expectation). But, as experimental studies show, both the material resistence and the load effect on the structure in most cases are subject to asymmetric laws. The asymmetry of the material resistance can be neglected in most practical cases, but failure to take into account the asymmetry of the load effect can lead to significant errors in determining structural reliability. The authors chose two laws with different degrees of positive asymmetry to approximate the load distribution, namely gamma and lognormal laws. The normal (symmetric) law was used for the resistence distribution law. The results of reliability calculations that take into account different load distribution laws are presented in the form of a table and a graph. The graph shows the dependence of structural reliability on the reliability index for symmetric (PN) and asymmetric (PNG, PNL) laws. All calculations were performed using the Mathcad complex, which allows calculating values with sufficient accuracy. The issue of how to choose the distribution law for the load effect obviously depends on the operation mode of a particular bridge and should be based on appropriate statistical studies. The purpose of this paper is to show the need for taking into account the law of asymmetry in order to determine the structural reliability. Eurocode norms also require to take into account the asymmetry of distribution laws. Keywords: structural reliability, normal distribution law, safety factor, asymmetric distribution laws, reliability index.