Deterministic Values Research Articles

ДИФФЕРЕНЦИАЛЬНОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССОВ РАСПРОСТРАНЕНИЯ И ЛИКВИДАЦИИ ИНФЕКЦИОННЫХ ЗАБОЛЕВАНИЙ ЛЕСНЫХ НАСАЖДЕНИЙ

The destabilization of the sustainable state of forests and the associated deterioration of the sanitary climate are mainly associated with their diseases. One of the main tasks of forest pathology monitoring is the detection of foci of disease of stands and the fight against their spread. In this paper, we propose a mathematical description of the processes of the spread and elimination of infectious diseases of forest plantations using the deterministic SIR (Susceptible, Infected, Recovered) model, the main provisions of which are basic in the interpretation of various kinds of infectious diseases, often taking the form of epidemics. Assuming the constancy of the total number of healthy infected subjects during the spread of the disease and the direct proportional dependence of the infection rate on the number of infected, the results obtained indicate that: a) if at the initial moment of time the number of infected individuals does not exceed a certain deterministic value, then plants do not become infected over time; b) in cases if this number is greater than a fixed value, then the part of individuals susceptible to the disease will become infected. It is shown that despite the abstract nature and the impossibility of probabilistic interpretation of the detection of foci of the disease, the proposed differential model can be effective in solving the problems of the spread, localization and prediction of tree diseases and is used, practically, for any closed biological and ecological system

ЗАДАЧИ ШОУОЛТЕРА–СИДОРОВА И КОШИ ДЛЯ ЛИНЕЙНОГО УРАВНЕНИЯ ДЗЕКЦЕРА С КРАЕВЫМИ УСЛОВИЯМИ ВЕНТЦЕЛЯ И РОБЕНА В ОГРАНИЧЕННОЙ ОБЛАСТИ

Deterministic and stochastic initial boundary value problems for the Dzekzer equation describing the evolution of the free surface of a filtering fluid in a bounded region with a smooth boundary are considered. Wentzell and Robin conditions are set on the boundary of the domain, and either the Showalter-Sidorov condition or the Cauchy condition is taken as the initial condition. Note that for the filtration model under study, the Wentzell condition is considered, which is not a classical condition. In recent years, the boundary condition has been considered in the mathematical literature from two points of view (classical and neoclassical). Since Cauchy and Showalter–Sidorov initial conditions have been studied earlier in various situations, in this work, in the particular case of classical Wentzell and Robin conditions, by methods of the theory of degenerate holomorphic semigroups, exact solutions have been constructed, which allow to determine quantitative predictions of changes in geochemical regime of groundwater under unpressurized filtration. Nelson–Glicklich derivative theory was used in stochastic case. In particular, the investigation of the set problems in the context of Wentzell boundary conditions allowed to determine the processes occurring at the boundary of two media (in the region and at its boundary).

Practical Approach to Digitally Simulate Nonsynoptic Wind Velocity Profiles and Its Implications on the Response of Monopole Towers

AbstractIn the numerical simulation of stochastic nonstationary wind loads, rapidly varying wind speed fluctuations about a deterministic mean value typically represent the sole source of random va...

Effects of spatial autocorrelation structure for friction angle on the runout distance in heterogeneous sand collapse

This paper proposes a stochastic method for analyzing the runout distance of sand collapse considering the spatial variability of shear strength, in which random field theory and generalized interpolation material point method are integrated into a Monte-Carlo simulation basis. The random field is generated by Cholesky matrix decomposition method and implemented into the material point level, hence heterogeneity and large deformations are simultaneously considered in the modeling process. A sand collapse case is simulated with both homogeneous and heterogeneous condition assumptions by the proposed method. The effect of five theoretical autocorrelation functions (ACFs) on the runout distance of the collapse is highlighted since the ACFs are commonly adopted to characterize the spatial variability of soil properties due to sparse site observation data. It is shown that the deterministic analysis may underestimate the runout distance, while the heterogeneous model provides realistic results. Moreover, five ACFs and different coefficients of variation of friction angle (COVφ) are compared to investigate their influences on the runout distance modeling. The results show that the uncertainty of runout distance increases with the increase in COVφ. Meanwhile, the variances of the runout distance also become larger with COVφ increasing. Based on the proportion of the runout distance which exceeds the deterministic value, the results indicate that the deterministic analysis notably underestimates the risk induced by large runout distances in real heterogeneous granular flows (e.g., landslide, debris-avalanches).

Affine Arithmetic-Based Reliable Estimation of Transition State Boundaries for Uncertain Markov Chains

Markov Chain-based models have been extensively used in numerous power system applications, ranging from decision support systems, to reliability and resilience analysis. The state transition probabilities, which determine the overall model dynamics, have been traditionally described by deterministic values. This common assumption might not be suitable for analyzing modern power systems, where large number of complex and correlated uncertainties could significantly affect the correct evaluation and estimation of both model parameters and model outputs. In addressing that problem, this paper advocates the role of affine arithmetic, by proposing a reliable framework for Markov Chain transient analysis in the presence of data uncertainties. The main idea is to represent the uncertainties in state transition probabilities through affine forms, which then allow to apply affine arithmetic-based operators and to identify the corresponding transient state probabilities. Two case studies are presented and discussed, in order to demonstrate the effectiveness of the proposed methodology in practical power system problems and applications.

A comparative analysis of the requirements of Russia and the United States to the fire resistance of building structures of oil refineries and petrochemical plants

Introduction. Currently, national standards and codes of practice contain deterministic values of the fire resistance of building structures of facilities of the Russian fuel and energy complex (FEC), while a probabilistic approach to determining their fire resistance is not specified in the Russian regulatory documents. The methodology of the probabilistic approach to the fire resistance of structures is detailed in API 2218 “Fireproofing Practices in Petroleum and Petrochemical Processing Plants”, developed by the American Petroleum Institute.Methods. A comparative analysis of the Russian regulatory documents on fire safety and API 2218 in terms of the established concepts of fireproofing and requirements for the fire resistance limits of building structures of oil and gas industry facilities, is carried out.Results. It was established that the Russian Federation has no regulatory documents establishing methods based on the probabilistic approach, including determination of the required fire resistance limits and points of application of fire-resistant coatings at facilities of the fuel and energy complex by analogy with international standard API 2218.Conclusion. Based on the analysis, it was concluded that approaches to the philosophy of the fire resistance of structures of buildings and structures of the fuel and energy complex in the documents under consideration are fundamentally different. In order to improve the Russian regulatory and technical framework, governing fire safety and fire resistance, it is proposed to consider the requirements of foreign documents that take into account proven international engineering and technical practices, in particular, the use of a probabilistic approach taking into account hydrocarbon fires.

Production effect evaluation of shale gas fractured horizontal well under variable production and variable pressure

Most shale gas production prediction models are established on the ideal production conditions (the constant pressure and constant production condition), deviating from the production performance characteristics of shale gas wells with variable production and pressure and leading to large error in unknown model parameter inversion of the actual shale gas wells, and obviously showing great limitations in characterizing the dynamic production performance and predicting EUR of shale gas wells for variable production-pressure. Furthermore, the material balance equation is more common in solving the variable production and pressure of shale gas wells issues, but it is only suitable for characterizing boundary flow. In this paper, a semi-analytical productivity prediction model of shale gas well for constant pressure was established and validated by the practical production data. Then the material balance pseudo time and linear superposition pseudo time were introduced respectively to modify the true pseudo time in the proposed productivity prediction model to demonstrate that the linear superposition pseudo time was proper to obtain the unknown fracture inversion parameters compared to material balance pseudo time during the variable pressure-production of actual shale gas wells. Finally, the Monte Carlo method in the IHS numerical software was adopted to analyze the impact of the fracture half-length uncertainty on the probability distribution of EUR, which showed that the P50 value is closer to the deterministic EUR value predicted by the analytical production prediction model. Research indicates that it is of certain theoretical reference to reduce the risk of production prediction during the production of shale gas wells and guide the optimization of development plans.

A probabilistic strategy to evaluate scour around bridge deepwater foundations considering a reliability assessment

Currently, an increasing number of deepwater foundations have been built in marine regions, and most of them have to deal with scour problems. Recent design codes of superstructures usually adopt the probability-based method, in which loads are treated as probabilistic parameters. However, for the design of substructures, the impact of scour is generally regarded as a deterministic value represented by the estimated scour depth. This inconsistency in the design strategies brings difficulties in considering the uncertainties associated with scour effects. Fundamentally, this is due to the challenges in the scour estimation using a probabilistic method. Based on an augmented scour database analyzed using the artificial neural-network (ANN), this study quantifies the uncertainties of four types of scour predictive methods. Based on this, it proposes a probabilistic approach for scour estimation according to different cases. Six typical conditions and two practical cases were analyzed using the probabilistic approach. The overall reliability index showed that all these existing scour estimation methods have certain limitations, including inconsistent reliability and unreliable scour depth predictions. To prevent these problems, a concept based on the probability of nonexceedance of a given scour depth has been proposed, which was determined by different target reliability requirements.

Numerical calculation of wear in rolling contact based on the Archard equation: Effect of contact parameters and consideration of uncertainties

Wear in rolling contact is a complex phenomenon because it is multi-scale and multi-physical by nature and involves many strongly correlated parameters. It makes the numerical calculation of wear very challenging. In order to simulate wear, a better understanding of the influencing parameters involved in the wear calculation is of importance. This work presents a new numerical calculation of railway wheel wear based on Archard's equation combined with a spatial statistic approach called the Universal Kriging technique. The influence of factors, such as the contact mechanics model and the wear coefficient were studied through numerical experiments. The outcomes provide a new insight into the roles of the contact modelling and of the uncertainties of the wear coefficient in the numerical calculation of wear under various contact conditions. By considering the uncertainties of the wear coefficient, the approach provides a min.-max. range for wear estimation instead of a single deterministic value; furthermore, it can provide a detailed wear distribution over the contact patch for damage analysis. In combination with an accurate model of wheel-rail contact, this new wear model offers a more realistic wear prediction compared to the methods presently used for wheel wear estimation in railway vehicles.

Probabilistic Assessment and Uncertainty Analysis of CO2 Storage Capacity of the Morrow B Sandstone—Farnsworth Field Unit

This paper presents probabilistic methods to estimate the quantity of carbon dioxide (CO2) that can be stored in a mature oil reservoir and analyzes the uncertainties associated with the estimation. This work uses data from the Farnsworth Field Unit (FWU), Ochiltree County, Texas, which is currently undergoing a tertiary recovery process. The input parameters are determined from seismic, core, and fluid analyses. The results of the estimation of the CO2 storage capacity of the reservoir are presented with both expectation curve and log probability plot. The expectation curve provides a range of possible outcomes such as the P90, P50, and P10. The deterministic value is calculated as the statistical mean of the storage capacity. The coefficient of variation and the uncertainty index, P10/P90, is used to analyze the overall uncertainty of the estimations. A relative impact plot is developed to analyze the sensitivity of the input parameters towards the total uncertainty and compared with Monte Carlo. In comparison to the Monte Carlo method, the results are practically the same. The probabilistic technique presented in this paper can be applied in different geological settings as well as other engineering applications.

The conjugate gradient algorithm on a general class of spiked covariance matrices

We consider the conjugate gradient algorithm applied to a general class of spiked sample covariance matrices. The main result of the paper is that the norms of the error and residual vectors at any finite step concentrate on deterministic values determined by orthogonal polynomials with respect to a deformed Marchenko–Pastur law. The first-order limits and fluctuations are shown to be universal. Additionally, for the case where the bulk eigenvalues lie in a single interval we show a stronger universality result in that the asymptotic rate of convergence of the conjugate gradient algorithm only depends on the support of the bulk, provided the spikes are well-separated from the bulk. In particular, this shows that the classical condition number bound for the conjugate gradient algorithm is pessimistic for spiked matrices.

Rethinking the uncertainty of African swine fever virus contamination in feed ingredients and risk of introduction into the United States.

Economically relevant pathogens, such as African swine fever virus (ASFV), have been shown to survive when experimentally inoculated in some feed ingredients under the environmental conditions in transoceanic transport models. However, these models did not characterize the likelihood of virus survival under various time and temperature processes that feed ingredients undergo before they are added to swine diets. Here, we developed a quantitative risk assessment model to estimate the probability that one or more corn or soybean meal ocean vessels (25,000 tonnes) contaminated with ASFV would be imported into the United States annually. This final probability estimate was conditionally based on five likelihoods: the probability of initial ASFV contamination (p0), ASFV inactivation during processing (p1) and transport (p2), recontamination (pR), and ASFV inactivation while awaiting customs clearance at United States entry (p3). The probability of ASFV inactivation was modelled using corn and soybean (extruded or solvent extracted) processing conditions (times and temperatures), D-values (time to reduce 90% or 1-log) estimated from studies of ASFV thermal inactivation in pork serum (p1), and survival in feed ingredients during transoceanic transport (p2 and p3). 'What-if' scenarios using deterministic values for p0 and pR (1%, 10%, 25%, 50%, 75%, and 100%) were used to explore their impact on risk. The model estimated complete inactivation of ASFV after extrusion or solvent extraction processes regardless of the initial ASFV contamination probability assumed. The value of recontamination (ranging from 1% to 75%) was highly influential on the risk of one ASFV-contaminated soybean meal vessel entering the United States. Median risk estimates ranged from 0.064% [0.006%-0.60%; 95% probability interval (PI)], assuming a pR of 1.0%, up to 4.67% (0.45%-36.50% 95% PI) assuming a pR of 75.0%. This means that at least one vessel with ASFV-contaminated soybean meal would be imported once every 1563-21 years, respectively. When all raw corn was assumed to be contaminated (p0=100%), and no recontamination was assumed to occur (pR=0%), the median probability of one vessel with ASFV-contaminated corn entering the United States was 2.02% (0.28%-9.43% 95% PI) or once every 50 years. Values of recontamination between 1% and 75% did not substantially change the risk of corn. Days of transport, virus survival during transport (D-value), and number of vessels shipped were the parameters most influential for increased likelihood of a vessel with ASFV-contaminated soybean meal or corn entering the United States. The model helped to identify knowledge gaps that are most influential on output values and serves as a framework that could be updated and parameterized as new scientific information becomes available. We propose that the quantitative risk assessment model developed in this study can be used as a framework for estimating the risk of ASFV entry into the United States and other ASFV-free countries through other types of imported feed ingredients that may potentially become contaminated. Ultimately, this model can be used to develop risk mitigation strategies and critical control points for inactivating ASFV during feed ingredient processing, storage, and transport, and contribute to the design and implementation of biosecurity measures to prevent the introduction of ASFV into the United States and other ASFV-free countries.

Scenario forecasting for wind power using flow-based generative networks

Wind power prediction is an integral part of power system operations and planning. Due to rising penetrations of wind turbines, fluctuation and intermittence of wind powers seriously limit the accuracy of power forecasts. A popular way to mitigate this challenge is to provide a range of possible scenarios instead of deterministic point forecasting values, so operators can account for the uncertainties. This paper proposes a model-free scenario forecasting approach for wind powers using flow-based generative networks, which generate a set of high-quality scenarios to represent possible behaviors based on historical wind powers and deterministic point forecasting values. Firstly, an unsupervised deep learning framework is proposed to learn the latent patterns in historical wind power curves. Then, a large number of possible future scenarios are obtained by solving an optimization problem. Simulation results show that the proposed approach has better performance than popular baselines such as variational auto-encoder and generative adversarial networks.

Probabilistic nature of water and environmental standards

Determination of permissible concentrations of pollutants in relation to water bodies and water quality is the basis for further measures to form technological approaches to water treatment and wastewater treatment, to determine the standards of permissible exposure and technological indicators. The main standard, which is the basis for such calculations - the maximum permissible concentration (MPC) of pollutants or the approximate safe level of exposure (S), are threshold (deterministic) values. It is assumed that the establishment, for example, of the MPC for fisheries water bodies is based on the analysis of toxicological indicators. However, in fact, rationing is carried out on the basis of selective toxicological studies [1], which do not provide such determinism. The obtained data characterize only the influence of the selected levels of toxicant concentration on the studied organisms.

Probabilistic study on the bearing capacity of strip footing subjected to combined effect of inclined and eccentric loads

This paper investigates the importance of inherent variability of soil under strip footing subjected to combined effect of inclined and eccentric loads using probabilistic analysis. Plastic analysis is performed using lower bound formulation of finite element limit analysis. Soil is considered as cohesionless, and modelled as a random field. The random field is discretized using Karhunen-Loéve expansion method. Stochastic results of the collapse load for various conditions of internal friction angle, load inclination angle, eccentricity, vertical correlation distance and coefficient of variation of the tangent of internal friction angle are determined using Monte Carlo Simulation technique. Failure probability results are plotted as contour charts to show the effect of combined loading as well as the spatial variability of soil on the bearing capacity of strip footing. For all the cases of higher vertical correlation distances, the mean bearing capacity factor is found to be higher than the deterministic value. However, the probability of failure of the footing is reported to be more than 50% for the same case, addressing the need for probabilistic analysis. Failure contours are presented for some representative cases to display the behavior of footing due to different loading and spatial variability conditions.

Assessment of the probability of the fatigue fracture of structural components subjected to deterministic and stochastic loading taking into account the scatter in the initial crack size

An analytical approach which provides conservative estimates of the probability of fatigue brittle fracture of structural components of technical systems taking into account the scatter of the initial dimensions of crack-like defects described by the exponent probabilistic distribution is presented. The operational loading is considered both as deterministic (with loading cycles of constant amplitude and frequency) and random (stationary narrow-band Gaussian random loading) process. The crack growth kinetics is described by the modified Paris equation that takes into account the stress ratio effects. The parameters of the Paris law are considered deterministic values. An example of the assessment of the probability of fatigue failure of tubular structural component with an axial crack on the inner surface of a tube subjected to internal pressure is presented. A comparative analysis of the results obtained with and without taking into account the random nature of the operational loading is carried out. It is shown that neglection of the random nature of the operational loading leads to non-conservative estimates of the fatigue failure probability, which may differ by an order of magnitude compared to the calculation data obtained with allowance for the stochastic nature of the loading process. The developed method can be used in the implementation of probabilistic and risk-based approaches to ensuring strength, service life and safety of technical systems in real operation conditions and in adjusting standard operation programs in terms of choosing the frequency and scope of non-destructive testing.

Interactive Multiobjective Procedure for Mixed Problems and Its Application to Capacity Planning.

A problem that appears in many decision models is that of the simultaneous occurrence of deterministic, stochastic, and fuzzy values in the set of multidimensional evaluations. Such problems will be called mixed problems. They lead to the formulation of optimization problems in ordered structures and their scalarization. The aim of the paper is to present an interactive procedure with trade-offs for mixed problems, which helps the decision-maker to make a final decision. Its basic advantage consists of simplicity: after having obtained the solution proposed, the decision-maker should determine whether it is satisfactory and if not, how it should be improved by indicating the criteria whose values should be improved, the criteria whose values cannot be made worse, and the criteria whose values can be made worse. The procedure is applied in solving capacity planning treated as a mixed dynamic programming problem.

Probabilistic Fatigue Damage Estimation for Rotorcraft Life-Limited Components

Condition-based maintenance programs for modern helicopters rely on algorithmic techniques to estimate the useful life remaining for life-limited components. Regime-recognition-based condition-based maintenance programs involve a regime recognition step and a damage estimation step in which damage is calculated based on the identified regimes. Recently, new probabilistic regime recognition algorithms have been developed that produce probability distributions over the regimes, rather than deterministic regime classifications. However, to date, there has been no method to convert regime distributions to damage estimates. This paper proposes a technique to compute a probability distribution over the fatigue damage for each life-limited component directly from the regime probability distributions. The method treats the incurred damage at a given time as a random variable and accumulates the total damage incurred as a sum of random variables. The damage distribution at each time is computed from the regime distribution and the regime damage rates. A primary advantage of the approach is that it captures uncertainty in the regime recognition process by treating damage as a random variable rather than a deterministic value. Simulation results illustrate the benefit of the probabilistic approach over a deterministic method, particularly for flights where there is significant uncertainty in the flown regimes.

Optimization of microenergy grid including adiabatic compressed air energy storage by considering uncertainty of intermittent parameters

AbstractIn recent years, zero‐carbon energy resources such as adiabatic compressed air energy storage with thermal energy storage have been interested due to growing concerns over global warming. This study proposes a microenergy grid including heat and power networks connected through adiabatic compressed air energy storage with thermal energy storage, which can be considered hybrid energy storage supplying power for both networks. The power network is supplied with the main grid and wind turbine systems, and the heat network is provided with heat pumps. The objective function minimizes power purchased from the main grid and power demand of heat pumps in the heat network. Since uncertainty plays a key role in the operation of integrated energy systems, the uncertainty of intermittent parameters such as active and reactive load and wind speed data has been considered in this study. Therefore, predicted values are used in the optimization problem instead of using deterministic values for such uncertain parameters. To do this, an efficient 2‐level corrective forecasting algorithm is proposed to have an accurate prediction for the day‐ahead operation of the microenergy grid. Different scenarios are presented to show the importance of the forecasting method and the utilization of adiabatic compressed air energy storage with thermal energy storage in the system’s structure. The results indicate that corrective actions on the predicted load and wind speed data decrease the operation cost of the microenergy grid from 57.13% to 13.21%. Also, it is found that neglecting adiabatic compressed air energy storage with thermal energy storage in the structure of the microenergy grid increases operation cost to 3423 US$. Other obtained results also indicate the importance of coutilization of compressed air energy storage with thermal energy storage and 2‐level corrective forecasting method leading to optimal operation of the microenergy grid.

Surgical Scheduling with Constrained Patient Waiting Times

We consider a surgical case scheduling problem with the objective of minimizing the expected time span of the schedule subject to a prespecified upper bound on the expected waiting time for each patient. The problem is challenging due to its combinatorial and nonlinear nature, and we focus on developing approximate methods to solve the problem. Specifically, we study two approximation methods. In the certainty equivalent method, we approximate the expected time span of the cases by assuming that the waiting time of each surgical case is a deterministic value. In the variance bounding method, we approximate the expected time span based on upper bounds on the variance of the surgical case waiting times. We show that the certainty equivalent method leads to a lower bound on the optimal expected time span, while the variance bounding method leads to an upper bound. Both methods suggest a simple sequencing rule, which is to sort the surgical cases in the ascending order of the surgical duration variability. Based on the upper and lower bounds, we derive a closed‐form, distribution‐free relative error bound for our sequencing rule, and show that it is uniformly bounded with respect to the number of cases. We also conduct a case study based on real‐life data on hernia repair procedures at the Jewish General Hospital in Montréal, to demonstrate our analytical models and their potential benefits for improving surgical scheduling. Finally, we conclude the paper by mentioning a few future research directions.