Methods Of Stochastic Processes Research Articles

Invariable distribution of co-evolutionary complex adaptive systems with agent's behavior and local topological configuration.

In this study, we developed a dynamical Multi-Local-Worlds (MLW) complex adaptive system with co-evolution of agent's behavior and local topological configuration to predict whether agents' behavior would converge to a certain invariable distribution and derive the conditions that should be satisfied by the invariable distribution of the optimal strategies in a dynamical system structure. To this end, a Markov process controlled by agent's behavior and local graphic topology configuration was constructed to describe the dynamic case's interaction property. After analysis, the invariable distribution of the system was obtained using the stochastic process method. Then, three kinds of agent's behavior (smart, normal, and irrational) coupled with corresponding behaviors, were introduced as an example to prove that their strategies converge to a certain invariable distribution. The results showed that an agent selected his/her behavior according to the evolution of random complex networks driven by preferential attachment and a volatility mechanism with its payment, which made the complex adaptive system evolve. We conclude that the corresponding invariable distribution was determined by agent's behavior, the system's topology configuration, the agent's behavior noise, and the system population. The invariable distribution with agent's behavior noise tending to zero differed from that with the population tending to infinity. The universal conclusion, corresponding to the properties of both dynamical MLW complex adaptive system and cooperative/non-cooperative game that are much closer to the common property of actual economic and management events that have not been analyzed before, is instrumental in substantiating managers' decision-making in the development of traffic systems, urban models, industrial clusters, technology innovation centers, and other applications.

A Multi-objective integrated approach to address sustainability in a meat supply chain

Many supply chains have taken action to consider the principles of sustainability in their business over the past two decades. However, addressing sustainability is still a challenge due to imposing some restrictions. This could be more challenging in a food supply chain because of consuming a large amount of natural resources and its connection to public health. Regarding this significance, this research develops a mechanism to integrate all the primary functions of a meat supply chain given three pillars of sustainability: (i) cost, (ii) social aspect, and (iii) environmental aspect. To this end, we develop a three-objective mathematical formulation to integrate supplier selection, production planning, and product distribution in a meat supply chain. This study also identifies criteria representing suppliers’ impact on the environment and utilizes a Stochastic Analytic Hierarchy Process (SAHP) and TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) methods to gauge that impact and evaluate suppliers’ scores. Furthermore, a solution method is designed based on the Normalized Normal Constraint method to generate Pareto-optimal solutions. Lastly, we apply the developed mathematical formulation and the solution methodology using a numerical study inspired by a real case in Ontario, Canada. The results demonstrate that the developed solution methodology can generate diverse and practical Pareto-optimal solutions in which social and environmental aspects could be improved significantly by incurring a minor extra cost.

Mathematical, algorithmic and software support of synphase detection of radio signals in electronic communication networks with noises

Mathematical (radio signal model as a periodically correlated stochastic process and synphase method of its processing) and algorithmic support for synphase detection of stochastic-periodic radio signals in electronic communication networks with noise by calculating new detection indicators in the form of correlation components, which ensure effective making a decision regarding the presence or the absence of a useful radio signal in obstacles of different power. For a more detailed assessment of the calculated indicators of radio signal detection in the form of correlation components, were used averaged estimates. Software for synphase detection of radio signals in electronic communication networks with a graphical user interface is implemented in the Matlab environment. The process of synphase detection of radio signals in electronic communication networks with noise was investigated and the effectiveness of the application of new detection indicators was ascertained.

Rolling bearing fault feature extraction method based on GWO-optimized adaptive stochastic resonance signal processing

The failure of rolling bearings affects the function and precision of rotating machinery significantly, which has drawn lots of attention in this field. Dealing with the failure of rolling bearings, fault feature extraction is the first and most important problem. In this work, we convert the bearing fault signal into stochastic resonance dynamics equivalently. And, adaptive stochastic resonance is adopted to extract the fault signal feature. In addition, for industrial application of fault signal processing with large amplitude and noise intensity greater than 1, normalized scale transformation is introduced into adaptive stochastic resonance and then solved by fifth-order Runge–Kutta algorithm. Then, to further optimize the solving precision of stochastic resonance model, the scaling coefficient and step size of Runge–Kutta algorithm are chosen with the help of Grey Wolf Optimizer (GWO). Thus, we can obtain a fast convergence speed, high calculation accuracy and effective improvement of signal-to-noise ratio fault feature extraction method for rolling bearing fault signal processing. Finally, a comparation simulation was carried out to demonstrate the efficiency of the proposed method. Compared with Cuckoo Search Optimizer-based stochastic resonance signal processing method, the proposed method achieved a higher signal-to-noise ratio (SNR) to benefit the fault feature extraction. In summary, this work gives out a more practical and effective solution for rolling bearing fault feature extraction in rotating machinery fault diagnosis field.

Characterizing the γ-Ray Variability of Active Galactic Nuclei with the Stochastic Process Method

Gamma-ray astronomy in the time domain has been by now progressed further as the variabilities of active galactic nuclei (AGNs) on different timescales have been reported a lot. We study the γ-ray variabilities of 23 jetted AGNs by applying a stochastic process method to the ∼12.7 yr long-term light curve (LC) obtained by the Fermi-Large Area Telescope (Fermi-LAT). In this method, the stochastically driven damped simple harmonic oscillator (SHO) and the damped random-walk (DRW) models are used to model the long-term LCs. Our results show that the long-term variabilities of 23 AGNs can be characterized well by both SHO and DRW models. However, the SHO model is restricted in the overdamped mode, and the parameters are poorly constrained. The SHO power spectral densities (PSDs) are the same as those of the typical DRW PSD. In the plot of the rest-frame timescale that corresponds to the broken frequency in the PSD versus black hole mass, the intrinsic, characteristic γ-ray timescales of 23 AGNs occupy almost the same space with the optical variability timescales obtained from the accretion disk emission. This suggests a connection between the jet and the accretion disk. As with the optical variability of the AGN accretion disk, the γ-ray timescale is also consistent with the thermal timescale caused by the thermal instability in the standard accretion disk of AGNs.

Modeling of Corrosion Pit Growth for Buried Pipeline Considering Spatial and Temporal Variability

Corrosion of metal in soils has been intensively investigated in the past. However, a review of the published literature shows that there are challenges for researchers to accurately predict the corrosion growth of buried pipes with spatial and temporal variations. This paper intends to develop a methodology to predict the corrosion pit growth for buried pipelines by thoroughly considering the spatial and temporal variability of corrosion processes. The developed method integrates the corrosion science, conditional random field theory, stochastic process, and copula method into an interrelated simulation algorithm for generating corrosion pit growth fields. It is found in the paper that the shape parameter and rate parameter of the gamma process, as well as the correlation structure of corrosion processes, are not only time-variant but also exhibit spatial variability with time. It is also found that the developed method is much superior to other methods in terms of accuracy and effectiveness. The proposed method considers the correlation between corrosion processes in a long pipeline, which is more practical. It can be concluded that generating an accurate corrosion growth field fully requires consideration of the spatial and temporal variability of model parameters.

A New Neuron Ion Channel Model Under Time Varying Input Currents

In recent years, it has been argued and shown experimentally that ion channel noise in neurons can cause fundamental effects on the neuron’s dynamical behavior. Most profoundly, ion channel noise was seen to be able to cause spontaneous firing and stochastic resonance. However, Hodgkin-Huxley model affected when inserting some colored noise terms inside the conductance’s, where those effects captured by colored noise due to the gate multiplicity. This paper presents a new ion channel model under time varying periodic input currents. It firstly introduced the effect of without, with (colored noise), on the proposed model and the comparison of ion channel based on HH, Fox- Lu, and Linaro models. Additionally, in order to overcome the limitations of other parameter estimation methods, the proposed method fully constraints their models and obtains all models capabilities of reproducing the data. Finally, the relationship between the sequence of colored noise and the spike frequency are simulated efficiently each gate compared with microscopic simulations of the stochastic Markov process method. The simulation results revealed that above a critical value of the input frequency and also below a certain amplitude value, the colored terms play a very prominent role on the firing statistics. In addition, the spiking rate generated from the proposed model very close to microscopic simulations and doesn’t effect by the membrane size.

Non-fragile asynchronous reliable sampled-data control for uncertain fuzzy systems with Bernoulli distribution

In this study, the non-fragile asynchronous reliable sampled-data control for uncertain Takagi–Sugeno fuzzy systems with Bernoulli distribution is addressed. The system involves both the randomly occurring uncertainties of parameters in the fuzzy system model and randomly occurring gain perturbations of the controller. By introducing three stochastic variables, a new model structure satisfying Bernoulli distribution is formulated to describe the system and the controller. The main purpose of this study is to design the non-fragile asynchronous reliable sampled-data controller such that the considered system is finite-time bounded and possesses finite-time mixed H∞ and passive performance. Based on an improved Lyapunov–Krasovskii functional, newly bounding inequalities and stochastic processing method, new conditions satisfying the required result are derived for the uncertain fuzzy systems in terms of linear matrix inequalities. Moreover, a modified non-fragile asynchronous reliable sampled-data controller is designed. Finally, two numerical examples are given to demonstrate the effectiveness of the presented results.

How to Assess Power Law Behavior Using Stochastic Process Methods: A Note of Caution

Power law distributions have a certain appeal to researchers, not least because they often insinuate a general empirical law. Hence, searching for them in data generated by social and political processes has become popular. In the political science literature, however, power law behavior has rarely been assessed rigorously. Relying mainly on qualitative appraisals of log–log plots, merely a necessary, but no sufficient, condition of power law behavior is tested. This letter therefore seconds the note of caution expressed recently. Moreover, it showcases the use of a principled statistical framework to test power law behavior in a quantitative manner. Applying this method to a seminal case in political science, the results of the analysis invite an empirical as well as theoretical refinement of the claim that changes in public budgets follow a power law. In a more general sense, the letter wishes to contribute to a more thorough practice of stochastic process methods in political science.

Fleet Size and Rebalancing Analysis of Dockless Bike-Sharing Stations Based on Markov Chain

In order to improve the dynamic optimization of fleet size and standardized management of dockless bike-sharing, this paper focuses on using the Markov stochastic process and linear programming method to solve the problem of bike-sharing fleet size and rebalancing. Based on the analysis of characters of bike-sharing, which are irreducible, aperiodic and positive-recurrence, we prove that the probability limits the state (steady-state) of bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then a new “Markov chain dockless bike-sharing fleet size solution” algorithm is proposed. The process includes three parts. Firstly, the irreducibility of the bike-sharing transition probability matrix is analyzed. Secondly, the rank-one updating method is used to construct the transition probability random prime matrix. Finally, an iterative method for solving the steady-state probability vector is therefore given and the convergence speed of the method is analyzed. Furthermore, we discuss the dynamic solution of the bike-sharing steady-state fleet size according to the time period, so as improving the practicality of the algorithm. To verify the efficiency of this algorithm, we adopt the linear programming method for bicycle rebalancing analysis. Experiment results show that the algorithm could be used to solve the disordered deployment of dockless bike-sharing.

An integrated constrained fuzzy stochastic analytic hierarchy process method with application to the choice problem

The ability of the analytical hierarchy process (AHP) when applied to the choice problem in the context of group decision making under uncertainty has been often criticised. AHP is not able to fully capture the various opinions and the uncertainty associated with the lack of information. This work develops an integrated constrained fuzzy stochastic analytic hierarchy process (IC-FSAHP) method in order to deal with the aforementioned drawbacks. IC-FSAHP combines two existing fuzzy AHP (FAHP) methods and further extends its applicability by implementing stochastic simulations. A case study has been conducted in order to assess the ability of IC-FSAHP; the results showed that IC-FSAHP is able to capture the uncertainty and multiple DMs' opinions. This paper also discusses the effect that the number of DMs has in enhancing rank discrimination. Besides, the possibility of the occurrence of rank reversal because of the use of IC-FSAHP has been analysed. The results showed that the ranking of alternatives was preserved throughout the changes in the number of alternatives, however, rank reversal occurred in the case of changes in judgements scales. By comparing the U-uncertainty in fuzzy global priorities obtained using IC-FSAHP to that obtained using an existing FSAHP method, we show that our method is capable of minimising the risk of losing important knowledge during the computations. We also discuss how IC-FSAHP can decrease the uncertainty and increase the reliability of the decisions by means of robust computations.

STOCHASTIC PROCESSES IN PROJECT MANAGEMENT

Performance of planned activities not always leads to the achievement of planned results in innovation projects with a high degree of uncertainty. Management of such specific projects requires the usage of specific methods and processes. It is necessary to develop own stochastic process methods rather than use classical methods of deterministic management. The main peculiarity of stochastic processes of projects consists in the inability to carry out more than one experiment. Implementation of a project is a stochastic process, which is carried out only once. For the purposes of the research, stochastic project management is the process of organisation, planning and control over projects, in which the decisions and actions of managers are described by stochastic functions. If the project realisation is described by stochastic processes, the project management process is indeed described by stochastic processes. This research suggests a project management approach based on the focus on the project product and project management as stochastic processes based on stochastic functions. It is demonstrated that stochastic function values, which underlie the stochastic processes, are formed by the intellectual instruments of those involved in the project and are developed on the basis of their knowledge and skills. The latter, in turn, are the result of studying and practical work on the project. Therefore, it is difficult to predict decisions and actions of managers and contractors, even if internal and external influences on them are specified. Then, any decisions or actions of such persons with regard to the external observer are described by stochastic functions. The purpose of this study is to describe the processes of stochastic project management. The purpose of the study is the project management process. The subject of research is the methods of stochastic project management. Within the framework of the study, all groups of processes of stochastic control will be mathematically described and the conditions of their impact determined. The processes of stochastic project management are outlined and formally presented. These are the processes of project management organisation, the processes of project management support, processes of project content definition, processes of defining the resources, required for the project works, processes of project planning, processes of influence on contractors of actions (works).

Stochastic AHP and fuzzy VIKOR approach for warehouse location selection problem

PurposeThe purpose of this paper is to develop a stochastic multi-criteria decision-making approach to solute the warehouse location problem in the stochastic environment which contains uncertain condition.Design/methodology/approachIn developed approach, the weight of criteria was calculated by using the stochastic analytic hierarchy process (SAHP) method. Alternative ranking was made and evaluated by fuzzy VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje).FindingsThis study dealt with warehouse location selection problem of a supermarket that has sellers in many regions in Turkey and selected proper warehouse.Originality/valueThis study combined SAHP and fuzzy VIKOR methods as a solution approach for warehouse location selection problems.

Reliability analysis of multi-state k-out-of-n: G system with common bus performance sharing

Abstract In this paper, a multi-state k-out-of-n: G system with common bus performance sharing is proposed, in which k-out-of-n: G structure is considered, and the system state is divided into multiple levels for the first time. Such a system consists of a common bus and n multi-state units, where each unit has several performance levels to satisfy its individual random demands. If one unit has surplus performance, the performance surplus can be transmitted to other units which are experiencing performance deficiency via the common bus. The state of the system is divided into multiple levels according to the number of the units whose demands are satisfied. An algorithm based on the universal generating function (UGF) technique and the stochastic process method is proposed to evaluate the system reliability. Analytical and numerical examples are presented for demonstrating the application of the proposed method finally.

Determination of order pattern frequency analysis using the copula method

The frequency and voluminosity of orders play a crucial role in determining the operation and scheduling, as well as the bird weight to be supplied to chicken processors. Due to the variability in frequency and voluminosity of each product, part, and size, orders have stochastic characteristics in nature; hence, the proper means to investigate orders is using probability theory and the stochastic process method. In this study, copula distributions were exploited to incorporate chicken order features into frequency analysis. This approach enabled the elucidation of the complex features of order frequency and voluminosity. These probabilistic properties provide useful information for order assessments and can be used for production/chicken supply planning and further scheduling of the industry.

Stochastic analysis of uncertain thermal parameters for random thermal regime of frozen soil around a single freezing pipe

The artificial ground freezing method (AGF) is widely used in civil and mining engineering, and the thermal regime of frozen soil around the freezing pipe affects the safety of design and construction. The thermal parameters can be truly random due to heterogeneity of the soil properties, which lead to the randomness of thermal regime of frozen soil around the freezing pipe. The purpose of this paper is to study the one-dimensional (1D) random thermal regime problem on the basis of a stochastic analysis model and the Monte Carlo (MC) method. Considering the uncertain thermal parameters of frozen soil as random variables, stochastic processes and random fields, the corresponding stochastic thermal regime of frozen soil around a single freezing pipe are obtained and analyzed. Taking the variability of each stochastic parameter into account individually, the influences of each stochastic thermal parameter on stochastic thermal regime are investigated. The results show that the mean temperatures of frozen soil around the single freezing pipe with three analogy method are the same while the standard deviations are different. The distributions of standard deviation have a great difference at different radial coordinate location and the larger standard deviations are mainly at the phase change area. The computed data with random variable method and stochastic process method have a great difference from the measured data while the computed data with random field method well agree with the measured data. Each uncertain thermal parameter has a different effect on the standard deviation of frozen soil temperature around the single freezing pipe. These results can provide a theoretical basis for the design and construction of AGF.

The development of diagnostics methodological principles of the railway rolling stock on the basis of the analysis of dynamic vibration processes of the rail

The paper discusses the preconditions of the methodology development of diagnosis system for assessing dynamic impact of the rolling stock on the basis of processing and analysis of data obtained in operation on the results of measurement of parameters that characterize dynamic vibration processes of the mechanical system of “rolling stock – track”. On the basis of usage of the processing methods of time series and stochastic processes there has been established the relationship between these dynamic processes and wheel defects, and designed experimental data processing algorithms, which in the future will be an integral part of the intellectual systems of decision making when assessing the impact level of the rolling stock on the track. The article presents some results of the experimental and theoretical research of the rail accelerations data, which have been registered during passing of the train. The computational algorithm of the specialized pre-processing of the multidimensional signal recorded by this system is described. The advantage of this algorithm is that it does not require additional information about the train speed on the section equipped with the monitoring system, about the number of wheel pairs of locomotives and train cars, and about the distances between the wheel pairs. Based on the processing results of accelerations of the rails there have been set the parameters of increase in all statistical indicators with increase in the train speed. It is noted that the level of indicators for accelerations of the rails in the vertical direction is twice as high as the corresponding parameters in the horizontal direction.

Results of the experimental research of dynamic vibration processes of the rail for rolling stocks fault diagnostics

The paper discusses the preconditions of the methodology development of diagnosis system for assessing dynamic impact of the rolling stock on the basis of processing and analysis of data obtained in operation on the results of measurement of parameters that characterize dynamic vibration processes of the mechanical system of “rolling stock-track”. On the basis of usage of the processing methods of time series and stochastic processes there has been established the relationship between these dynamic processes and wheel defects, and designed experimental data processing algorithms, which in the future will be an integral part of the intellectual systems of decision making when assessing the impact level of the rolling stock on the track.

Development of Neuron Ion Channel Model using Colored Noise Terms in the Conductance

The aim of this study is the ion channel model with noise variance as approximations to the Hodgkin-Huxley model proposed, due to the Hodgkin-Huxley model affected when inserting some colored noise terms inside the conductances, where those effects captured by colored noise because of the gate multiplicity. Firstly, it introduces the comparison of ion channel based on Fox, Lu and Linaro models. Additionally, in order to overcome the limitations of other parameter estimation methods, the proposed method fully constrains their models and obtains all model's capabilities of reproducing the data. Finally, the relationship between the sequence of colored noise and the spike frequency are simulated efficiently each gate compared with microscopic simulations of the stochastic Markov process method. In simulation results, the spiking rate generated from the proposed model very close to microscopic simulations and doesn’t effect by the membrane size.

Application of Simulation Methods of Stochastic Processes to Vortex Excitation

AbstractA description of direct simulation of crosswind loads caused by critical vortex excitation and the response of the structure to these loads are presented in this paper. Tower-like structures of circular cross-sections are considered. A proposed mathematical model of vortex excitation has been numerically implemented and a selfserving computer program was created for the purpose. This software, cooperating with the FEM system, allows for a simulation of a crosswind load and lateral response in real time, meaning that at each time step of the calculations the load is generated using information regarding displacements seen beforehand. A detailed description of the mathematical model is neglected in this paper, which is focused on numerical simulations. WAWS and AR methods are used in simulations.