Papers by Keyword: Stochastic Model

Abstract: Recently, more attention has been paid to the development of gas hydrate deposits, the use of gas-hydrated technologies, suitable for energy-efficient transportation of natural gas, the separation of gas mixtures, production and storage of cold, desalinating of seawater, etc. Hydrate formation is one of the main processes of gas-hydrate technological installations. In the article a model is proposed that describes the kinetics of the formation of hydrate in disperse systems, which are characteristic for real conditions of operation of gas-hydrate installations, on the basis of a stochastic approach using Markov chains. An example of numerical calculations is presented on the basis of the proposed model of the dynamics of the total mass of gas hydrates, and changes in the velocity of their formation and size distribution at different values of the nucleation constants and growth rate of the gas hydrates, and results of these calculations are analyzed. It is shown that the rate of formation of hydrate has a maximum value in half the time period of the whole process. The obtained results of the calculations of the dynamics the total mass of gas hydrates are in good agreement with the results of calculations by the equation of kinetics Kolmogorov-Avrami. The proposed model can be applied to the inverse problem: the determination of the nucleation constants and the rate of growth of gas hydrates by the results of the dynamics of the formation of hydrate and the changes in the fractional composition of the generated gas hydrates.

Abstract: The study is focused on the experimental verification of a proposed polynomial stochastic fatigue crack growth model. The model was assumed that the fatigue crack growth rate equals to a deterministic polynomial function multiplied by a stationary lognormal random factor. Compact-tension specimens cut from a 2024-T351 aluminum-alloy plate were used for fatigue crack growth experiments under constant-amplitude loads performed on thirty specimens. The comparison of median crack growth curves was made between analytical and experimental outcomes. For extreme case of lognormal random variable, the comparisons of the fatigue crack growth curve, percentile fatigue crack growth curve, probability of crack exceedance, and distribution function of random time between analytical and experimental results were also investigated.

Abstract: In this paper, a stochastic model with a saturation infection rate representing HIV internal virus dynamics is investigated. We prove that the model exists non-negative solutions. Then we analyse the asymptotic behavior of the model. Finally, numerical simulations are presented to illustrate our mathematical findings.

Abstract: Reprogramming in lossy wireless sensor networks is a dynamic process. Dijkstra’s shortest path algorithm is used in previous work to represent the multi-hop propagation of data packets, however, it is not accurate enough to use a static model to capture the behaviors of stochastic multi-hop propagation. In this paper, we propose a stochastic multi-hop model in the analytical approach by randomly setting weight values for links between nodes. From simulations, the results of the analytical approach match that of simulations when incorporated with the stochastic multi-hop model.

Abstract: The brake system maintenance of railway wagons consists, amongst other matters, brake shoe replacement whose wear in time exceeds the maximum allowable limit. Their absence in stock leads to the maintenance process stagnation. This causes additional costs of procurement and very high costs because of shortage. Thus, the main objective in control of the brake shoe stocks, in a company carrying out maintenance activities of railway wagons is that of determining the quantity ordered and the interval between orders. Their optimal values will be reached when storage costs, expressed by the cost function (the total mean value of the costs) are minimal, leading to a normal unfolding of the corrective maintenance activities. For the management of the spare parts stocks to be applied various methods, depending on the certainty or uncertainty knowledge of the level demand; of their delivery time and of their supply costs. For avoiding increasing penalty costs due to lack in stock the authors propose, after the estimation of the relative variability of demand for these spare parts, the stochastic modelling utilisation, the demand and delivery time being discrete random variables (depending on season, type and random rhythmicity of the falls), known being the request repartitions of the brake shoes on the basis of statistical records. The research results led to the determination of the value necessary to brake shoes stock so that, the total losses of the company in which carried out the maintenance activities to be minimised, and to establish the range of cost in which is allowed the acquisition of a such spare part when she is missing from the stock.

Abstract: The paper deals with a new approach in data analysis of a measured mechanical parameter. The classic approach is mainly based on the deterministic statistics that cant cover the whole field of a complete analysis. The stochastic approach, to be used in this paper, offers far more information about the mechanical parameter and can take into account the non-linearity of the signal, eventually, the mechanical parameter itself. Starting from the point of view that, in real life, there is no steady evolution of any parameter, we decide to take into account the importance of the non-linear components of any signal. After e thorough investigation, we hope we could make the difference between the noise, as non-linear components of the measured parameter, and the useful non-linear components (e.g. important shocks, typically met within a vehicles transmission). Using the stochastic modeling procedures, we aimed at issuing comprehensive, accurate and valuable dynamic models of the phenomenon. These models cam be used in a large variety of situations, from describing the process, to evaluating the health of a mechanical system and to controlling a real-time process based on the pre-set models (previously drawing a map of the systems normal behavior and permanently assessing the deviation from it and acting accordingly). The data were measured within the transmission system of a military vehicle. Specifically, we have gathered information about torque and angular speed of different shafts of the driveline. As everybody knows, the power flows within any vehicles transmission in transient modes mainly and it is accompanied by plenty of noise. It is rather challenging to separate (filter) the useful signal form the noise but, on the other hand, it is the only way to achieve useful data. Therefore, a spectral analysis is a must, but not the conventional one, which has its drawbacks, but a multi-spectral one, which is able to insulate the noise. Moreover, starting from the analysis developed with this method, mathematical models, both in discrete and continuos time can be achieved. It is easy to notice that the models that we have achieved are featured by a very good accuracy. We could push the data processing even further, getting generalized models that provide the needs we have mentioned before, with respect to the mapping of a normal (averaged) behavior of a system, to be used in controlling procedures.

Abstract: In industrial engineering and management, to know the demand quantities of downstream manufacturer is an important issue which can help the upstream suppliers to control and predict the level of manufacturing process. The supplier may encounter competitors who also provide the materials or product to the same downstream manufacturer. This paper proposes a stochastic model to forecast the total demand of the manufacture company with characteristic function. This model can be used to detect the quantities which are provided from other competitors to the same manufacturer.

Abstract: Based on the experimental study of response of the gravel cushion under the horizontal vibration loads, analyzed internal shear modulus changes process in the granular layer , which are the changing characteristics caused by the self-organization, particles movement and compacting degree. We simulated the response process of shear modulus in the granular layer by using the Poisson process, discussed the development of shear modulus after several vibration and established the model.

Abstract: The paper describes a summary of the complex approach to evaluation of quasi-brittle structures/structural members made of (advanced) cement based composites. It reviews chosen aspects and results of nonlinear stochastic analysis of structural members made of these composites and inserts them into the complex methodology. Application example illustrates the methodology.

Abstract: The study is focused on the formulation of a proposed polynomial stochastic fatigue crack growth model. Assuming the fatigue crack growth rate equal to a deterministic polynomial function in terms of fatigue crack size multiplied by a stationary lognormal random factor accounting for the statistical scatter of the fatigue crack growth, the analytical solutions of fatigue crack growth function and median crack growth function in term of model parameters were derived. Two extreme cases, lognormal random variable and lognormal white noise, of the proposed model were also investigated, and the analytical solutions of the distribution function of the random crack size at any service time and distribution function of random time to reach a specified crack size were obtained.