Application Of Probabilistic Methods Research Articles

Creep rupture data assessment – new uncertain challenges require new uncertain answers

ABSTRACT For the service life calculation of high-temperature components the knowledge of the creep behaviour of the materials used remain essential. Over decades, many methods have been developed for extrapolating creep rupture strengths. The challenge with these Creep Rupture Data Assessments (CRDAs), however, always remains evaluating the predictive accuracy of creep life. New computer-aided calculation methods allow the use of extensive data on the casts and other experimental data, as well as the application of probabilistic methods. Within the ECCC, software tools are being developed that both leverage the capabilities of new powerful computer-aided computational methods and allow for simultaneous assessment with post-assessment testing in accordance with ECCC recommendations. The authors would like to point out that despite all available tools and guidelines, the expertise and experience of the assessor is an indispensable guarantor for a reliable evaluation.

ОБ ОСОБЕННОСТЯХ ПРИМЕНЕНИЯ ВЕРОЯТНОСТНЫХ МЕТОДОВ В ПРОЦЕССАХ ОБРАБОТКИ ИНФОРМАЦИИ И СИСТЕМНОМ АНАЛИЗЕ

The applicability of probabilistic methods in various fields of science is due to their universality when considering any problem. First of all, using probabilistic methods in system analysis, we can abstractly evaluate various elements or groups of elements in the system, which ultimately gives us an idea of its functioning and possible deviations that arise during the interaction of many elements. Conditional «objectivity» of the final conclusions allows leading engineers, heads of departments and departments to make important and at the same time rational decisions regarding engineering structures, economic systems and other forms of complex structural systems, on the functioning of which most of human life depends at the present time.

Организационно-технологическое моделирование эксплуатации инженерных систем зданий с позиций стоимостного критерия систем обслуживания с перерывами

In recent years, there has been an increased interest in the application of probabilistic methods, in particular. the theory of queuing, to the evaluation of the effectiveness of the activities of management companies in the organization of the operation of technical systems of residential buildings.
 The article considers the M|G|1 service system with the possibility of breaks in the work of repair teams for basic requirements, when, for example, repair teams work on third-party orders. The optimization problem is solved from the point of view of the cost criterion. As controlled factors, the probability of a break α and its duration are proposed. Under fairly general assumptions about the behavior of the system at breaks, it is established that the optimal value of the probability α is either zero or one. Necessary and sufficient conditions are given under which a break should be implemented, i.e. α=1. With a constant duration of breaks, the conditions are determined under which α=1, and the duration of the break is optimal.

СТАТИСТИЧЕСКОЕ ПРОГНОЗИРОВАНИЕ НАКОПЛЕНИЯ 137Cs В ПРОДУКЦИИ РАСТЕНИЕВОДСТВА НА РАДИОАКТИВНО ЗАГРЯЗНЕННЫХ ТЕРРИТОРИЯХ

Purpose: the development of statistical models for forecasting the accumulation of 137Cs in crop production, model parameterisation and prognostic estimates for the territories of the Bryansk region contaminated with 137Cs because of the Chernobyl accident. Material and methods: The use of a probabilistic approach for correct predictive assessments of the safety of agricultural products from radioactively contaminated agricultural lands has been substantiated. Analytical models were developed in the framework of a probabilistic approach to predict the risks of radioactive contamination of crop products, to assess the permissible levels of contamination of arable lands and the time of their natural remediation. Results: Based on a statistical analysis of radioecological survey data, it was established that the 137Cs contamination density of the soil follows a lognormal distribution law with a high level of significance. For farms in the south-western districts of the Bryansk region, it was shown that, if the average values of 137Cs content in crop production corresponded to the established standard, the risks of its excess could reach 30 %. This is due to the variability of 137Cs soil contamination densities and migration parameters. The dependences of limiting soil contamination densities of 137Cs on the risk of exceeding the standards (RES) of the content of this radionuclide in products were presented. The time of natural rehabilitation of arable agricultural land with a given risk for products of 10 % can exceed 30 years. Conclusion: The application of probabilistic methods to predict the consequences of 137Cs contamination of agricultural lands makes it possible to correct practical recommendations developed on the basis of a deterministic approach. The results of prognostic calculations are the basis for planning and evaluating the possibility of returning territories contaminated by 137Cs to economic use. The developed methodology and models can be used in the development of decision support systems for the remediation of agricultural lands exposed to radioactive fallout.

Methodology for modelling stochastic optimization of innovative development of enterprises using probabilistic methods

The article proposes the results of a scientific study based on the construction of mathematical models of stochastic optimization using probabilistic methods aimed at the innovative development of timber industry enterprises. The construction of economic and mathematical models is a necessary direction when forecasting various processes.The construction of stochastic optimization models based on economic and mathematical modelling makes it possible to establish a number of the most significant cause-effect relationships of technological, resource and effective indicators using formalization parameters, as well as determine the nature of the likely relationship between the indicators. The most relevant from a scientific and practice-oriented point of view for modelling the dynamics of technological and innovative development of an enterprise is the application of probabilistic methods using production functions.When applying production functions, in a scientific approach, many average indicators were used, taking into account various production and technological relationships of the production process, technological solutions and innovations. Based on the methodology of stochastic optimization in the construction of production functions in the process of economic and mathematical modelling, it is possible to form an adequate production function to build the necessary mathematical model and forecast scenarios of the dynamics of innovative development of enterprises.

Анализ организации эксплуатации инженерных систем жилых зданий на основе модели массового обслуживания с перерывами и задержками

In resent years has been increasing interest for application of probabilistic methods, in particular queueing theory for estimation of activities of managing companies of residential buildings. Maintenance of residential buildings is a set of measures that ensure the highest reliability of all elements and systems of a building. The main element of the technical operation of residential buildings is a system of scheduled prophylactic inspections and repairs. However even with its rational organization, there is always a positive probability of failure of building elements, which depends not only on the aging factors of the structure. The goal of the managing company is, on the one hand, to prevent the formation of a too long queue of emergency calls, and on the other, to complete all planned prophylactic maintenance work. 
 As a mathematical model we consider a single-server queue with vacations and close-down periods. The service team can start a scheduled preventive repair only when all request for sudden mailfunctions are satisfied.
 This period we call vacation. There is a close-down period before vacation. This time period is required for preparation and organization of the prophylactic and inspection work.
 Based on the methods of the queuing theory, the system’s characteristics that determine the quality of its work, as well as the boundaries of the change of parameters at which the system copes with the work from the standpoint of a particular criterion are defined.

Application of probabilistic method in maximum tsunami height prediction considering stochastic seabed topography

Uncertainty is a significant challenge in tsunami hazard analysis. Tsunami heights are affected by complex factors and change constantly during propagation. The heights of tsunami have random characteristics. This study proposes that the water depths (related to seabed topography) are the most important factors that affect tsunami height. But across the globe, a considerable area of seabed topography has not been measured. So it is necessary to use the method of uncertainty to consider the water depth. The Wiener process is utilized to quantify the random changes of the water depth, which can better describe the situation that water depths change in a non-monotonic way. Considering the uncertainty of water depth, a Weiner process-based probabilistic model was established for predicting the maximum tsunami height, which is different from the maximum tsunami height deterministic or stochastic model previously studied with higher prediction efficiency and good prediction accuracy. The probability distribution of maximum tsunami heights was calculated using the stochastic model. The mean value of the maximum tsunami heights was very similar to the average value of 165 actual observations of maximum tsunami heights collected from 1997 to 2017.

Application of Probabilistic Method to Evaluate the Rock Mass Foundation Influence over the Probability of Failure by Sliding of Hydraulics Structures: Case Study of Baixo Iguaçu HPP Spillway

In the last decades, accidents involving dams and other hydraulic structures have become more frequent, increasing social pressure on the existing dams safety conditions. This fact demands commitment of professionals and companies with new plant project safety approaches. The failure of a hydroelectric concrete structure can be caused by several factors, however the main causes of failure are related to exceptional floods and foundation-related problems, which are the focus of this paper. In order to understand the influence of the rock mass characteristics, especially the contact plan with the concrete structure, this work considers the variability of geotechnical parameters, drainage efficiency, specific gravities and seismic acceleration to determine the probability of failure of these structures. To achieve this objective, the work makes use of a case study, the spillway of Baixo Iguacu HPP, on Parana/Brazil during its design and construction phase, determining the probability of failure by sliding. The study reproduces the foundation condition throughout a FEM hydrogeological model and determines the acting uplift through seepage analysis. The probability of failure was determined by Monte Carlo method using the probability distribution of each variable, performing 5,000,000 evaluations for each simulation. Simulations were performed for flow range varying from the ecological flow (200 m3/s) to exceptional floods with 10,000 years of recurrence time (56,362 m3/s) and its respective water levels. The most critical condition found was the extended operation at the minimum (ecological) flow, while for a normal operation, at the flow of 2598 m3/s, the order of the probability of failure is one in a million. The paper show how using hydrogeological model can lead to more realistic values of uplift pressures than using simplified methods recommended in the international guidelines, and consequently lead to a more realistic probability of failure.

Probabilistic Assessment of Historic Reinforced Concrete Bridge

This paper is aimed at the reliability analysis of an existing reinforced concrete bridge from 1908. The load bearing capacity is assessed in accordance with valid standards using the partial factor method and probabilistic approach. Load bearing capacities obtained by these methods are critically compared. The application of probabilistic method leads to 40 % higher load bearing capacity then the partial factor method used for structural design.

Application of Probabilistic Method to Stability Analysis of Gravity Dam Foundation over Multiple Sliding Planes

The current challenge to the engineering profession is to carry out probabilistic methods in practice. The design point method in generalized random space (DPG method) associated with the method of divided difference can be utilized to deal with the complex problem of probability calculation of implicit performance function with nonnormal and correlated variables. For a practical concrete gravity dam, the suggested method is performed to calculate the instability probability of the dam foundation over multiple sliding places. The general conclusions drawn in the paper are identical to those in other research and the method is proved to be feasible, accurate, and efficient. As the same analysis principle, the method can also be used in other similar fields, such as in fields of slopes, earth-rock dams, levees, and embankments.

Application of Probabilistic Methods for the Assessment of Structural Load Bearing Capacity

The paper presents the application of methodology for the assessment of reliability and structural load bearing capacity using advanced methods of probabilistic FEM analysis in combination with mathematical modelling of degradation processes of concrete and reinforcement. The durability, serviceability and ultimate limit states are assessed. The authors deal with the validation of load bearing capacity of the bridge on the 3rd class road built in the 1st quarter of 20th century in the Czech Republic. Regarding the reliability requirements according to Standards and, considering the current state of the structure, the actual value of load bearing capacity is assessed. By reason of the time-consuming FEM analyses the stratified Latin Hypercube Sampling (LHS) method is used for generation of input random variables.

Application of probabilistic methods to characterize soil variability and their effects on bearing capacity and settlement of shallow foundations: state of the art

This paper presents the applications of probabilistic methods to analyze the load-displacement behavior of shallow foundations supported by uncertain and spatially variable soils. The paper describes the types and sources of uncertainties in soil properties that dictate the bearing capacity and settlement of shallow foundations and characterizes their probabilistic distributions. General probabilistic analysis methods that are commonly used in foundation engineering applications such as first order second moment (FOSM) method, tornado diagram method, Monte Carlo (MC) simulation method, random finite element method (RFEM), and reliability-based design (RBD) method are briefly described. A thorough summary of the applications of these methods in determining the probabilistic bearing capacity, settlement, and differential settlement of shallow foundations from the research literature is presented.

Deterministic and probabilistic assessment of the critical buckling strength of ships’ grillages (gross panels)

An analytical method for control of the strength of a grillage (gross panel) under unidirectional in-plane axial load is proposed. It allows us to solve the following tasks: (i) calculation of the critical stiffness of transverse girders, (ii) calculation of the maximum unidirectional in-plane compression load when the structure's scantlings are known (iii) and calculation of the required structure's scantlings when the unidirectional in-plane compression load is given. The proposed procedure is helpful in the application of probabilistic methods without employing specialised computer programmes, which is an advantage when fast (although approximate) evaluation is needed for the grillage critical buckling strength (e.g. ship's deck structure) before applying the finite-element method (FEM) analysis. Results of analytical approach are compared and confirmed using FEM data. A probabilistic method for control of the strength of ship's deck structure under unidirectional in-plane axial load is proposed. It allows us to assess the effect of deterioration due to corrosion on the deck's buckling strength while avoiding the use of specialised computer programmes.

Probabilistic analysis of processes of accumulation of damages at the action of the static and cyclic loadings

Difficult character of cooperation of constructive elements with environment, and also among themselves, the casual nature of durability of materials and service conditions of engines demand in calculations on durability of application of probabilistic methods of the analysis and use of indicators of the theory of reliability. In-process created and grounded probabilistic approach to the durability’s reliability of elements of constructions of GTE analysis. The methods of probabilistic description of characteristics of durability of materials of details and probabilistic estimation of static and cyclic damaged of the controlled details are developed for a flight cycle. The probabilistic approachs are explored to the calculation of long-statical, high- and low-cyclic tireless damaged of details of engines and accumulated damaged on the basis of methods of the linear and nonlinear summation of damages as sums of independent and dependent casual sizes, casual sequences and casual processes. As a result, it is possible to estimate basic probabilistic characteristics of accumulated damageability and numbers of cycles for which accumulated damageability exceeds a critical level. The methodology for estimation of resource and other indicators of operability of CE AC (GTE) according to known probabilistic characteristics of accumulated damageability is developed.

Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets

When one tries to simulate quantum spin systems by the Monte Carlo method, often the 'minus-sign problem' is encountered. In such a case, an application of probabilistic methods is not possible. In this paper the method has been proposed how to avoid the minus sign problem for certain class of frustrated Heisenberg models. The systems where this method is applicable are, for instance, the pyrochlore lattice and the $J_1-J_2$ Heisenberg model. The method works in singlet sector. It relies on expression of wave functions in dimer (pseudo)basis and writing down the Hamiltonian as a sum over plaquettes. In such a formulation, matrix elements of the exponent of Hamiltonian are positive.

Some New Developments in the Theory of Path Integrals, with Applications to Quantum Theory

A survey of recent developments concerning rigorously defined infinite dimensional integrals, mainly of the type of “Feynman path integrals,” is given. Both the theory and its applications, especially in quantum theory, are presented. As for the theory, general results are discussed including the case of polynomially growing phase functions, which are handled by exploiting the connection with probabilistic functional integrals. Also applications to continuous measurement theory and the stochastic Schrodinger equation are given. Other applications of probabilistic methods in non relativistic quantum theory and in quantum field theory, and their relations with statistical mechanics, are discussed.

Probabilistic framework for the estimation of the adult and child toxicokinetic intraspecies uncertainty factors.

Human health risk assessments use point values to develop risk estimates and thus impart a deterministic character to risk, which, by definition, is a probability phenomenon. The risk estimates are calculated based on individuals and then, using uncertainty factors (UFs), are extrapolated to the population that is characterized by variability. Regulatory agencies have recommended the quantification of the impact of variability in risk assessments through the application of probabilistic methods. In the present study, a framework that deals with the quantitative analysis of uncertainty (U) and variability (V) in target tissue dose in the population was developed by applying probabilistic analysis to physiologically-based toxicokinetic models. The mechanistic parameters that determine kinetics were described with probability density functions (PDFs). Since each PDF depicts the frequency of occurrence of all expected values of each parameter in the population, the combined effects of multiple sources of U/V were accounted for in the estimated distribution of tissue dose in the population, and a unified (adult and child) intraspecies toxicokinetic uncertainty factor UFH-TK was determined. The results show that the proposed framework accounts effectively for U/V in population toxicokinetics. The ratio of the 95th percentile to the 50th percentile of the annual average concentration of the chemical at the target tissue organ (i.e., the UFH-TK) varies with age. The ratio is equivalent to a unified intraspecies toxicokinetic UF, and it is one of the UFs by which the NOAEL can be divided to obtain the RfC/RfD. The 10-fold intraspecies UF is intended to account for uncertainty and variability in toxicokinetics (3.2x) and toxicodynamics (3.2x). This article deals exclusively with toxicokinetic component of UF. The framework provides an alternative to the default methodology and is advantageous in that the evaluation of toxicokinetic variability is based on the distribution of the effective target tissue dose, rather than applied dose. It allows for the replacement of the default adult and children intraspecies UF with toxicokinetic data-derived values and provides accurate chemical-specific estimates for their magnitude. It shows that proper application of probability and toxicokinetic theories can reduce uncertainties when establishing exposure limits for specific compounds and provide better assurance that established limits are adequately protective. It contributes to the development of a probabilistic noncancer risk assessment framework and will ultimately lead to the unification of cancer and noncancer risk assessment methodologies.

Methods for Estimating Associated Risks of Sinkhole Occurrences: A Demonstration Using Available Data from the Ruhr Valley Region of Germany

The generation of sinkholes in the Ruhr valley region in Germany is caused by many centuries of coal mining at various depths and, at the least, by residual underground open spaces that do not stay stable with time. Due to the unknown distribution of underground spaces and their undefined, decreasing stability with time, probability calculations provide a somewhat successful approach in order to obtain information about the risks of sinkhole generation and possible relations to structural, geological, mining, and other influences. In this article, we demonstrate procedures and strategies for probabilistic calculations of sinkhole generation. In order to explain the basic steps of data organization and calculation, we provide an application of some of the quantitative methods, using an example from a local data set (sinkholes from a map of the Muddental region) combined with the corresponding structural geological map. This example illustrates the basic methods and clarifies the application of probabilistic methods. Due to the small database available, it was not possible to develop the results further, and thereby provide a final unequivocal classification of the dominant causes to understand the risks of sinkhole occurrences. Nevertheless, should further information be made accessible by the relevant authorities, one will be able to improve and statistically sharpen the arguments given here using the probabilistic methods, and so more clearly define the best possible correlations for estimation and prediction of sinkhole occurrences. The main point made, even with the limited data available to date, is that the methods provide powerful tools to help describe systematically the causes and risks of sinkhole occurrences. Current information from the Ruhr valley region would indicate that preventative methods are not being used on a routine basis; rather, postsinkhole occurrence filling with cement and renovation of badly damaged structures is the norm. It is to be hoped that the methods given in this article will soon be applied to help control the sinkhole problem and dangers.

Adapting Probabilistic Methods To Conform to Regulatory Guidelines

Summary Probabilistic methods have introduced inconsistent interpretations of how they should be applied while still complying with reserves certification guidelines. The objective of this paper is to present and discuss some pitfalls commonly encountered in the application of probabilistic methods to evaluate reserves. Several regulatory guidelines that should be followed during the generation of recoverable hydrocarbon distributions are discussed. An example also is given to understand the evolution of reserves categories as a function of probabilities. Most of the conflicting reserves interpretations can be attributed to the constraints of regulatory bodies [e.g., the U.S. Securities and Exchange Commission (SEC)] and the current SPE/World Petroleum Congresses (WPC) reserves definitions in which reserves categories are expressed in terms of the probabilities of being achieved. For example, proved reserves are defined as those hydrocarbon volumes with at least a 90% probability of being equaled or exceeded (P90). Unfortunately, these definitions alone fall short as guidance on how to derive the distributions from which these percentiles will be calculated. This may lead to distributions that do not comply with the remaining guidelines. While a P90 can be calculated from a noncomplying distribution, proved reserves may not be assigned at this percentile level.

Use of risk assessment in the nuclear industry with specific reference to the Australian situation

The use of risk assessment in the nuclear industry began in the 1970s as a complementary approach to the deterministic methods used to assess the safety of nuclear facilities. As experience with the theory and application of probabilistic methods has grown, so too has its application. In the last decade, the use of probabilistic safety assessment has become commonplace for all phases of the life of a plant, including siting, design, construction, operation and decommissioning. In the particular case of operation of plant, the use of a ‘living’ safety case or probabilistic safety assessment, building upon operational experience, is becoming more widespread, both as an operational tool and as a basis for communication with the regulator. In the case of deciding upon a site for a proposed reactor, use is also being made of probabilistic methods in defining the effect of design parameters. Going hand in hand with this increased use of risk based methods has been the development of assessment criteria against which to judge the results being obtained from the risk analyses. This paper reviews the use of risk assessment in the light of the need for acceptability criteria and shows how these tools are applied in the Australian nuclear industry, with specific reference to the probabilistic safety assessment (PSA) performed of HIFAR.