Probability Distribution Law Research Articles

Reliability Analysis of Normal, Lognormal, and Weibull Distributions on Mechanical Behavior of Wood Scrimber

Reliability analysis of mechanical strength could be used for evaluation of wood scrimber properties in this study. Normal, lognormal, and Weibull distributions were used to determine and selected the optimal model for wood scrimber for the first time. The results of reliability analysis indicated that the bending and tensile strength were well fit for normal distribution. Weibull distribution could describe the probability distribution law of compression strength, and lognormal distribution could reflect the probability distribution law of shear strength, respectively. The standard value of each mechanical strength was determined and compared in accordance with two methods. This illustrated that a significant difference between these two methods is evident in the case of modulus of elasticity (MOE), compression strength (CS), and shear strength (SS), while modulus of rupture (MOR) and tensile strength (TS) yielded similar data. The improvement in mechanical strengths was remarkably affected by the increase in density. Moreover, the microstructure of wood scrimber has a good ratio of deformation with respect to density, which can be significantly explained by compressive densification. The results suggest that the deformation ratio increased from 49.75% to 78.67%, which might reflect the variation in macroscopic mechanical strength of wood scrimber.

Numerical study of the influence of the parameters of statistical distribution of the structural elements’ ultimate strength on deformable bodies’ fracture processes

This work is dedicated to the numerical study of the influence of the parameters of statistical distribution of the structural elements’ ultimate strength on fracture processes of deformable bodies with stress concentrators. The loading diagrams, the macro level behavior and the damaging process kinetics have been studied using various probability distribution laws and their standard deviations. The main types of the damage accumulation process have been identified. The approach basing on the analysis of the solutions of the boundary value problems within the elasticity theory has been proposed in order to predict the fracture process kinetics, the corresponding parameters have been introduced. Advantages, limitations and potential practical use of the proposed methodology have been discussed. It has been concluded that the statistical distribution of the structural elements’ strength properties should be taken into account in the numerical modeling of the fracture processes to ensure the reliability and safety of critical structures.

Aircraft turnaround time dynamic prediction based on Time Transition Petri Net.

Accurate aircraft turnaround time prediction is an important way to coordinate the operation time of airport ground service and improve the efficiency of airport operation. In this paper, by analyzing the aircraft turnaround operation process, a description model based on Time Transition Petri Net is proposed. The model describes the flight turnaround operation process and the logical relationship of the operation. According to the model, a dynamic prediction method of turnaround time based on Bayesian theorem is designed. According to the actual landing time of the flight, the aircraft turnaround time is predicted. The specific method is to obtain the prior probability distribution and joint distribution law of each operation link according to the flight history data, and use Shapiro-Wilke to test the prior probability distribution of each link. Based on the analysis and comparison between the actual turnaround data of a large airport in China and the forecast data proposed in this paper, the root-mean-square error 3.75 minutes and the mean absolute error 3.40 minutes can be calculated. This paper contributes to the improvement of flight punctuality rate and airport clearance level.

A Probable Approach to Reliability Assessment of Reinforced Plates

A scheme for solving the problem of determining the probability of failure and probabilistic (statistical) characteristics of the failure loading magnitude of a composite material plate is considered. The plate structure is a flat homogeneous matrix with stochastically distributed rigid rod inclusions. The geometric parameters of inclusions are considered independent random variables with given probability distribution laws. The expressions for the failure loading distribution function, the probability of failure, the mean value, and the dispersion of the failure loading were received and presented. Their dependence on the type of stress state, the inclusion number, and matrix Poisson’s ratio were studied graphically.

Эффективность применения лесозаготовительных машин с манипулятором на лесосеке

An improvement of methods and models for preliminary estimation of the performance of harvesters in timber production intends to support better justification of the use of certain harvester types and technologies for specific natural and production conditions. It is possible to increase the accuracy of calculation models with a more complete and realistic description of the production environment and operational processes. The article presents a modelling of the harvester’s movements across cutting areas for selecting a position with the highest number of accessible trees. The investigational process involved the creation of an algorithm along with a simulation model and the statistical processing of the results. The problem-solving process required consideration of the tree’s distribution within the cutting region. The data arrays, which were necessary for efficiency evaluation in the simulation model and its software implementation, were the following: the distance between the working stands of the machine with the maximum number of available trees, the time of cyclic processing, and the number of trees in the area. The results of the statistical analysis of the data are presented with justification from the theoretical laws of probability distribution. The choice of machine working stands, which considered the arrangement of the trees, was estimated using the productivity per hour index. The index was calculated with a constant distance parameter that is equal to the difference between the maximum and the minimum manipulator’s movement, and it was also calculated for a stand with a maximum number of accessible trees. The calculation function for the index involves random variables that characterize the working conditions of the stand. The index itself is conceded as a random variable. The values for it were found by statistical data processing. A comparison of the values determined a high probability of a significant increase in the productivity of the harvester. At the stand with the maximum number of trees, it is estimated at around 8 % with a standard deviation of 0.199. For citation: Makarenko A.V. Effective Positioning in Cutting Area of a Harvester Using Computer Modelling. Lesnoy Zhurnal = Russian Forestry Journal, 2023, no. 4, pp. 120–135. (In Russ.). https://doi.org/10.37482/0536-1036-2023-4-120-135

Effect of errors on the directional characteristics of a phased antenna array with an arbitrary arrangement of elements

Currently, various types of antenna arrays (AA) are widely used in radio navigation, radar and telecommunication systems. They have a number of advantages related to the possibilities of electronic control of their characteristics and adaptation to signal-interference conditions compared to single emitters. To create the required shape of the radiation pattern, as well as the orientation of its maximum in space, it is necessary to send signals of a certain amplitude and phase to the AA elements, so to form an appropriate amplitude-phase distribution (APD). The error in setting the APD, along with errors in the alignment and determination of the position of the phase centers of individual emitters, have a significant impact on the parameters and characteristics of the AA. Errors in the installation of elements on the canvas of the AA and the deviation of their power supply from the calculated APD lead to a decrease in characteristics, which can be assessed by three criteria: a decrease in directivity (antenna gain); an increase in the level of the side lobes; a change in the accuracy of the installation and the shape of the main beam. An analytical expression for calculating the error can be obtained only for cases of an ordered arrangement of AA elements. The article presents the results of the analysis of the influence of technological errors on the directional characteristics of an AA with an arbitrary arrangement of antenna elements. Statistical averaging of an ensemble of realizations obtained by performing multiple calculations with random sets of parameters is used for the analysis. The laws of probability distribution can be any. The results of calculations for uniformly distributed errors are given as an example.

Improving the energy efficiency of wind turbines for charging batteries

The article describes the method for determining the optimal angular velocity and the number of turns of the generator winding on permanent magnets powered by a wind turbine operating in specific operating conditions according to the wind speed regime. The optimization criterion is the maximum potential of energy that can be used to charge the battery. The permissible power of the generator and wind turbine, current and battery charging voltage are accepted as limiting factors. The restriction is provided by connecting a ballast resistor to the generator output. The power developed by the turbine is determined taking into account the wind energy utilization factor, which depends on the angular velocity of its shaft and wind speed. Two variants of power limitation are compared: by limiting the angular velocity by aerodynamic means and by stopping the wind turbine. The return of energy to charging in both cases is determined taking into account the distribution of wind speeds, obeying the Weibull probability distribution law. As an example, the calculation of the possible annual power generation for charging a battery with a capacity of 200 A∙h with a voltage of 24 volts from a synchron generator with a number of poles of 48 driven by a wind turbine with a radius of 2 meters, operating in an area with an average wind speed of 5 m/s. The calculation shows that for the parameters and operating conditions of the electrical installation used in the example, the maximum annual energy output (3.3 × 103 kWh) is observed at optimal 11 turns of the winding at each of the poles of the generator. The deviation of the number of turns from the optimal one in both directions by 2 times leads, with the same dimensions of the wind turbine, to a decrease in annual energy output by 3...5 times, which is a clear proof of the need to carry out such a calculation for each specific wind turbine.

VELOCITY AND WALL PRESSURE FLUCTUATIONS OF TURBULENT BOUNDARY LAYER

The results of the study of the velocity pulsation field and the near-wall pressure of the turbulent boundary layer, which is formed on a flexible elongated cylinder and a hydraulically smooth flat plate, are presented. Peculiarities of the interaction of the velocity and pressure fields in the boundary layer are shown; sound and pseudosonic sources of hydrodynamic noise are characterized. The integral, correlation and spectral characteristics of the field of velocity pulsations and wall pressure in the turbulent boundary layer are analyzed. The relationship between these statistical characteristics is shown, as well as the mechanisms and sources that influence the behavior of these characteristics. It is noted that large-scale vortex structures and small-scale vortices are formed in the turbulent boundary layer, which form the outer and inner regions of the boundary layer. It is established that large-scale vortex structures generate pressure fluctuations, whose probability density distribution law is close to Gaussian law, and small-scale vortices that generate high-frequency or low-wave fluctuations have a non-Gaussian law of probability distribution of pulsation density. The interaction of coherent vortex structures with each other and with the streamlined surface leads to changes in the integral, correlation and spectral characteristics of the velocity and pressure fields. It is noted that with increasing the distance between the pressure fluctuation sensors, the correlation of signals decreases, and the delay time of correlated signals increases. Thus, with the increasing of the distance between the measuring points, the correlated fluctuations are those generated by the large-scale vortex structures. It is determined that the highest levels of velocity and pressure fluctuations are generated by the large-scale vortex structures that have the highest coherence. The results obtained make it possible to characterize coherent vortex structures, their features of formation, places of origin, scales, directions and velocities of transfer.

Description of Fatigue Sensitivity Curves and Transition to Critical States of Polymer Composites by Cumulative Distribution Functions

In this paper, a novel model is presented to describe the composite mechanical properties degradation during cyclic loading. The model is based on cumulative distribution functions using. Weibull probability distribution law and beta distribution are considered. The dependences of the fatigue sensitivity coefficient on the preliminary cyclic exposure are derived. The damage value function derivative using is proposed to define damage accumulation stages boundaries. Model parameters are obtained using experimental data. Determination coefficients are calculated. A high descriptive capability is noted. Rationality and expediency of using cumulative distribution functions as the approximation of experimental data on mechanical characteristics reduction after preliminary cyclic exposure is concluded.

О некоторых моделях оптимизации производства растениеводческой продукции в условиях биологических рисков

The aim of the work is to build and use problems of parametric and stochastic programming to solve problems of optimizing the production of agricultural products under conditions of biological risks. To achieve the goal, two tasks were solved: determining the patterns of variability of some series characterizing possible risks in crop production, and building mathematical models to optimize crop production, taking into account the damage caused by plant pests. The paper proposes models for optimizing the production of crop products under conditions of biological risks. Some indicators of such tasks are described using probabilistic estimates. To optimize the production of agricultural products under the influence of biological risks, mathematical models with probabilistic estimates, as well as a parametric programming model, were built. Examples of approbation of models in the planning of production of crop production are given. The work used materials on the number of rodents, invasions of locust pests for the long-term period 2009-2020. according to the Irkutsk region. In addition, information on the yield of agricultural crops in the municipalities of the southern territory of the region, as well as data on the activities of CJSC Irkutsk Semen, located in the Irkutsk region, are involved. To model series on the number of rodents, areas of distribution of acridoids and the number of their larvae per unit area, methods of probability theory and mathematical statistics were used (technologies for constructing probability distribution laws, regression analysis and assessment of the quality of models). The variability of agricultural crop yields was assessed using the methods of constructing trends and factor dependencies. When optimizing the production of crop products, methods for constructing and solving extreme problems were used. Models of parametric and stochastic programming are proposed. At the same time, the experience of developing applied models for optimizing the production of agricultural products with and without taking into account risks was applied.

An uncertainty quantitative model of wellbore failure risk for underground gas storage in depleted gas reservoir during the construction process

The sensitivity of wellbore-wall failure risk under depleted formation-pressure coefficients and underground gas storage in depleted gas reservoirs during the construction process is quantitatively assessed, especially the failure risk of wellbore collapse and fracture in depleted reservoirs with ultralow formation-pressure coefficients, and to effectively guide safe construction. Based on the Mohr–Coulomb failure theory and multilevel confidence model, three typical in situ stress states (normal fault, slip fault, and reverse fault) are considered to establish an analytical model for wellbore-wall failure risk under different depleted reservoir pressure coefficients. Taking a depleted sandstone reservoir as the main reservoir for wellbore-wall stability analysis as an example, a wellbore-wall stability state visualization analysis model with three typical in situ stress states under arbitrary orientations and well deviation angles is obtained, and the uncertain probability distribution law of wellbore-wall collapse and fracture failure in a reservoir with an ultralow formation-pressure coefficient is constructed using a stochastic uncertainty simulation method with interval confidence. The distribution patterns of wellbore-wall stress fields and borehole safety density windows during the construction of depleted reservoirs are quantitatively analyzed. The results show that a safety density window with interval uncertainty estimates would be more intuitive for assessing the stability of the reservoir wellbore wall in a quantitative form, and it is observed that inclined well sections in depleted reservoirs typically have narrower safety density windows. In conclusion, the lower and upper limits of the safety density window in numerical examples are 1.4 to 1.6 g/cm3 (normal fault state), 1.2 to 1.5 g/cm3 (slip fault state), and 1.2 to 1.65 g/cm3 (reverse fault state), respectively. The research results can provide effective guidance for wellbore instability control, design, and construction of directional wells in depleted gas reservoirs.

Variability in the elastic and time-delayed properties of structural hemp fibre composites

Various papers in the open source literature have shown that the tensile properties of plant fibres are very scattered. To date, this difference has been viewed as an obstacle to the use of biobased composites in structural applications. However, this question of dispersion has yet not been extensively addressed at the composite scale. Therefore, this paper proposes a method to quantify the distribution of values of the monotonic and time-delayed properties of a woven hemp fabric-reinforced GreenPoxy composite. The variability in these properties is significantly lower than at the fibre scale and on the same order of magnitude as glass fibre composites. This paper also provides the suitable probability distribution laws for these properties, which are important inputs to ensure the optimized and reliable design of plant fibre composite structures.

Development of a method for checking vulnerabilities of a corporate network using Bernstein transformations

One of the leading areas of cybersecurity of communication networks is considered – the introduction of preventive mechanisms, among which the most promising are the methods of active security analysis. These methods allow, in addition to timely detection of vulnerabilities of the target system (analyzed system), to confirm the possibility of their implementation, that is, to validate vulnerabilities by simulating the real actions of a potential attacker. The urgent need to validate vulnerabilities out of the many identified is caused by the fact that some of them can only be theoretical, while others are exploited using malicious scripts (exploits). At the same time, the process of validating vulnerabilities is practically not studied. That is why the work carried out an experimental study of the functioning of modern tools for exploiting vulnerabilities. Based on the observations, general quantitative characteristics of the vulnerability validation process were identified. A mathematical model for the analysis of the above characteristics based on Bernstein polynomials has been developed. It is the polynomial representation of the procedure for confirming the possibility of implementing the identified vulnerabilities that makes it possible to describe the dynamics of this process, taking into account the complex and volatile nature of the environment. Analytical dependencies are obtained for the number of cases of successful and negative confirmation of vulnerabilities. In particular, negative validation cases include simply failed attempts to validate vulnerabilities, as well as attempts that resulted in critical errors on the target system during the rational cycle of validating the identified vulnerabilities. The proposed dependencies make it possible to construct the probability distribution laws for the above characteristics of the vulnerability testing process.

Modeling of input signals reflected from coastal zones and observed by small-sized radar systems from UAVs

When developing modern unmanned aerial vehicle-based onboard small-sized radar systems, which are used for monitoring of coastal zones for their operational and environmental purposes, adequate mathematical models are needed of reflections from the corresponding resolution elements of the underlying surfaces, located on the water–land interface. We consider the development of some mathematical models for such applications. We analyze two modern approaches used in developing mathematical models for input signals reflected both separately from the terrestrial and marine surfaces and simultaneously from two aforementioned surfaces at once. A statistical approach and two families of distributions are chosen for modeling the signals, which enable synthesis of efficient algorithms for modeling the fluxes of random variables. The input signals of sea surface reflections are approximated by the log-normal law, while the reflections from the land surface are approximated by the Weibull distribution. For edge-coastal modeling, it is proposed to use the law of distribution of the vector sum of the flux of random variables comprising the input signals reflected from elementary land and sea areas that simultaneously fall within the corresponding resolution element. A highlight of the models developed is the consideration of both the probability distribution laws of the reflected signals and their correlation-spectral characteristics between resolution elements, as well as the anisotropy of reflections when monitoring surfaces from several angles. The presented mathematical models are consistent with experimental data sets of reflections, obtained from coastal zones. The development of coastal reflection models and corresponding modeling algorithms reduces the required number of actual field tests and saves time for implementation of monitoring systems, and hence, limits the overhead of this implementation.

Important Neutrosophic Rules for Decision-Making in the Case of Uncertain Data

An urgent need to make a rational decision has emerged in the world of rapid changes based on quantitative methods that reduce the proportion of risk, especially if the decisions are fateful and the decision issues are huge and complex, noting that the decision-making process and the selection of the optimal alternative depends on the quality of the data that describes the issue that the decision is intended to be taken. Because the theory of administrative decision-making depends on this data and on the type of this data if it is confirmed data or unconfirmed data and not specified with sufficient accuracy, or random data that is repeated according to a certain probability distribution law, after which the decision maker uses the methods used to obtain on the optimal decision. In this research we will study the theory of administrative decisions in the case of uncertain data, which is the situation that the decision maker faces, and he does not know anything certain about the state that nature (market or management --) will take, nor even about the possibilities of any of them, then it is assumed that the cases the possible ones are equal and they enter the analysis at the same opportunity and make a trade-off between the alternatives available to him in all circumstances. In the classical logic, a set of rules was used to help the decision maker to make the ideal decision, and since the ideal decision depends on specific classical values ​​that do not take into account the changes that may occur in the work environment, which is represented by high prices or unavailability of materials or others, it was necessary to search for a better method that helps us to avoid dealing with specific values ​​and gives us a margin of freedom. Therefore, in this research, we will study the theory of decision-making in the case of uncertain data using the Neutrosophic Logic, the logic that helps us to face fluctuations and changes that we may encounter during work, through uncertainty that the Neutrosophical values ​​have, which we will take in the elements of the profit (or loss) matrix and rely on them in the decision-making process, as we will take these values ​​in the form of fields representing the minimum field of profit (or loss) that we can get in the worst cases of nature, and represents the upper limit of the field of profit (or loss) that we can get in the best cases of nature, and we will show the most important rules used in the case of uncertain data with an applied example of each rule.

Mathematical Model of the Delay in Communication Networks Based on QS with a Time Lag

In the mathematical modeling of modern computer networks, telecommunication networks, traffic flows, logistics and many others, the methods of queuing theory are widely used. In turn, in studies of queuing systems (QS) G/G/1 with arbitrary distribution laws of intervals between adjacent requirements of the incoming flow and their service time, the spectral decomposition method (MSD) of solving the Lindley integral equation is often used. This method is based on the search for zeros and poles of the constructed spectral decomposition in the form of some fractional-rational function using numerical methods to determine the roots of polynomials. In this case, the coefficients of the polynomial in the numerator of the expansion are expressed through the unknown parameters of the distribution laws used to describe the QS. In the case of teletraffic research, usually these unknown parameters of the distribution laws can be determined through the numerical characteristics of the intervals between traffic packets by the method of moments. The purpose of this article is to present a fundamentally new mathematical model of a system formed by two flows with distribution laws shifted to the right. This is possible only for those probability distribution laws whose density functions are Laplace transformable. The main advantages of such systems, let us call them time lag systems, are that they provide less queue latency compared to conventional systems, and that they extend the range of traffic parameters. The article presents the results obtained on the average delay of requests in the queue for a system with exponential and hyper-Erlang distributions, an algorithm for calculating the average delay and the results of computational experiments in the Mathcad package.

ВЕРОЯТНОСТНЫЙ ПОДХОД К ОПРЕДЕЛЕНИЮ ПРОИЗВОДСТВЕННЫХ ФУНКЦИЙ

The article considers a probabilistic method for determining production functions. The method consists in finding the expected value of the function that determines the economic and mathematical principle of production. It is assumed that the factors of production and/or their specific values included in this function are random variables. It is shown that depending on the principle of production such averaging gives different probabilistic classes of production functions. Functions that are elements of the same class differ from each other in the probability distribution of the relations of production factors to their specific values. Two probabilistic classes of produc-tion functions are constructed. The first class is generated by the Leontief production principle, the second – by generalization of this principle for the case of partially or completely fungible factors of production. There are established the laws of probability distribution and the conditions, under which the linear combination of the AK-model and the Cobb-Douglas production function, as well as the CES production function, are elements of the class of Leontief production functions. It is shown that the linear production function belongs to the class of generalized Leontief production functions. The probability density functions of the products number for these two classes of pro-duction functions are found.

ANÁLISIS DE FRECUENCIA DE LA PRECIPITACIÓN MENSUAL EN LA REGIÓN JUNÍN, PERÚ

This work aimed to perform the analysis of monthly precipitation frequency for the departments of Huancavelica, Junín and Pasco. The analysis of monthly precipitation frequency was carried out with rainfall information evaluated for the period from January 1965 to December 2001 of 19 stations which are distributed according to the climatic characteristics and the homogeneity of the data in the study area, which includes the departments of Huancavelica, Junín and Pasco. Among the results of the study were identified regions that represent the monthly precipitation which are based on probability distribution laws: Exponential, Generalized Pareto, Weibull, Gumbel, GEV, Normal. Log-Normal, Gamma, Pearson type III, Log Pearson and Poisson exponential. The probability distribution laws that fit the monthly precipitation in zone I are Log-Normal and Gamma and for Zone II Gamma and Log-Normal.

PROBABILISTIC APPROACH TO MEASURING PRICE RISK OF THE ENTERPRISE

Background. Every manager faces analyzing problem and forecasting indicators in the process of making management decisions that are random variables, and therefore they are associated with risk and uncertainty. Their realization is possible in the future, but today we need to understand the risk level that can be encountered in the activity process and prepare for it in advance. Analysis of recent research and publications has shown that probabilistic approach is the most commonly used tool for risk assessment and it is based on probability theory. The aim of the article is to consider the tools of the probabilistic approach to riska ssessment. According to this approach, risk assessment is carried out for products price that have a normal law distribution and for which we can use an integrated probability distri­bution function and the key indicators that underlie its structure. Materials and methods. The methodological basis of risk analysis by the probabilistic approach is the consideration of the initial data as expected values of some random variables with known laws of probability distribution. Results. The use of tools of probabilistic approach to risk assessment of product pricing is considered. It is based on the assumption that a normal probability distribution law, an integral probability distribution function, and the key indicators that underlie its construction can be used to analyze market price risk. Conclusion. Probabilistic approach allows with minimal effort to understand the probability of obtaining the desired result, which is related to the purpose of the enterprise, or which result can be obtained with the desired probability and determine their acceptability. Keywords: risk, risk analysis, risk assessment, probabilistic approach, integral pro­bability distribution function.

Mechanical properties of fiber nano-modified rubber concrete in high temperature

The purpose of this study is to explore the mechanical properties of fiber nano-modified rubber concrete in high temperature. In this study, ordinary C30 concrete was used as the test benchmark, and 10% by volume of five kinds of rubber particles were used to replace fine aggregate to prepare rubber concrete (RC). On this basis, steel fibers with a volume ratio of 0%, 0.5%, 1.0%, 1.5% and 2.0% were added to make fully mixed steel fiber rubber concrete (SFRRC), according to the completely mixed steel fiber rubber concrete (SFRRC) Compression test, split tensile test, 4-point bending test, and fatigue test of steel fiber rubber concrete (SFRRC) with three stress levels, studied the fully mixed steel fiber rubber concrete (SFRRC) machinery of various steel fiber mixed materials Properties and the effects on the fatigue life, fatigue probability distribution law and damage progression law of steel fiber rubber concrete. The test results show that the combination of steel fiber and nano-silica can increase the crack resistance of 600-degree high-temperature concrete to 57.19% and the maximum separation tensile strength to 269.09%.