An Improved Markov Chain Model Based on Autocorrelation and Entropy Techniques and Its Application to State Prediction of Water Resources

According to the relationships among state transition probability matrixes with different step lengths, an improved Markov chain model based on autocorrelation and entropy techniques was introduced. In the improved Markov chain model, the state transition probability matrixes can be adjusted. The steps of the historical state of the event, which was significantly related to the future state of the event, were determined by the autocorrelation technique, and the impact weights of the event historical state on the event future state were determined by the entropy technique. The presented model was applied to predicting annual precipitation and annual runoff states, showing that the improved model is of higher precision than those existing Markov chain models, and the determination of the state transition probability matrixes and the weights is more reasonable. The physical concepts of the improved model are distinct, and its computation process is simple and direct, thus, the presented model is sufficiently general to be applicable to the prediction problems in hydrology and water resources.

Testing and Evaluation for Web Usability Based on Extended Markov Chain Model

As the increasing popularity and complexity of Web applications and the emergence of their new characteristics, the testing and maintenance of large, complex Web applications are becoming more complex and difficult. Web applications generally contain lots of pages and are used by enormous users. Statistical testing is an effective way of ensuring their quality. Web usage can be accurately described by Markov chain which has been proved to be an ideal model for software statistical testing. The results of unit testing can be utilized in the latter stages, which is an important strategy for bottom-to-top integration testing, and the other improvement of extended Markov chain model (EMM) is to present the error type vector which is treated as a part of page node. this paper also proposes the algorithm for generating test cases of usage paths. Finally, optional usage reliability evaluation methods and an incremental usability regression testing model for testing and evaluation are presented. Key words statistical testing - evaluation for Web usability - extended Markov chain model (EMM) - Web log mining - reliability evaluation CLC number TP311. 5 Foundation item: Supported by the National Defence Research Project (No. 41315. 9. 2) and National Science and Technology Plan (2001BA102A04-02-03)Biography: MAO Cheng-ying (1978-), male, Ph.D. candidate, research direction: software testing. Research direction: advanced database system, software testing, component technology and data mining.

A Fuzzy Probability-based Markov Chain Model for Electric Power Demand Forecasting of Beijing, China

In this study, a fuzzy probability-based Markov chain model is developed for forecasting regional long-term electric power demand. The model can deal with the uncertainties in electric power system and reflect the vague and ambiguous during the process of power load forecasting through allowing uncertainties expressed as fuzzy parameters and discrete intervals. The developed model is applied to predict the electric power demand of Beijing from 2011 to 2019. Different satisfaction degrees of fuzzy parameters are considered as different levels of detail of the statistic data. The results indicate that the model can reflect the high uncertainty of long term power demand, which could support the programming and management of power system. The fuzzy probability Markov chain model is helpful for regional electricity power system managers in not only predicting a long term power load under uncertainty but also providing a basis for making multi-scenarios power generation/development plans.

Transient particle transport prediction based on lattice Boltzmann method-based large eddy simulation and Markov chain model

Fast and accurate prediction of particle transport is essential for the determination of as-needed mitigation strategies to improve indoor air quality.Several methods have been proposed to achieve this goal.However,they mainly based on the Reynolds-averaged Navier-Stokes(RANS)approach,which may affect the accuracy of particle calculations.Considering the lattice Boltzmann method(LBM)can execute high-speed large eddy simulation(LES)while Markov chain model performs well for particle calculations.This study proposed an LBM-LES-Markov-chain framework for indoor transient particle transport simulation.The performance of the proposed framework was investigated in a two-zone ventilated chamber,and compared to the CFD-LES based models.Results show that the proposed framework is as accurate as but faster than the CFD-LES based models.The mean normalized root-mean-square deviations of the proposed model is 12%,similar to the CFD-LES-Lagrangian(15%)and CFD-LES-Eulerian(13%)models.The computing time of the proposed model is 5.66 h,shorter than the CFD-LES-Lagrangian(153 h)and CFD-LES-Eulerian(15.03 h)models.Furthermore,we further compared the framework with CFD-RNG based Markov chain model,CFD-RANS based models,and FFD-Markov-chain model and found that it is an alternative for the fast prediction of indoor particle concentration.

A generalized Markov chain model based on generalized interval probability

In the traditional Markov chain model (MCM), aleatory uncertainty because of inherent randomness and epistemic uncertainty due to the lack of knowledge are not differentiated. Generalized interval probability provides a concise representation for the two kinds of uncertainties simultaneously. In this paper, a generalized Markov chain model (GMCM), based on the generalized interval probability theory, is proposed to improve the reliability of prediction. In the GMCM, aleatory uncertainty is represented as probability; interval is used to capture epistemic uncertainty. A case study for predicting the average dynamic compliance in machining processes is provided to demonstrate the effectiveness of proposed GMCM. The results show that the proposed GMCM has a better prediction performance than that of MCM.

Driving-Cycle-Aware Energy Management of Hybrid Electric Vehicles Using a Three-Dimensional Markov Chain Model

This study developed a new online driving cycle prediction method for hybrid electric vehicles based on a three-dimensional stochastic Markov chain model and applied the method to a driving-cycle-aware energy management strategy.The impacts of different prediction time lengths on driving cycle generation were explored.The results indicate that the original driving cycle is compressed by 50%,which significantly reduces the computational burden while having only a slight effect on the prediction performance.The developed driving cycle prediction method was implemented in a real-time energy management algorithm with a hybrid electric vehicle powertrain model,and the model was verified by simulation using two different testing scenarios.The testing results demonstrate that the developed driving cycle prediction method is able to efficiently predict future driving tasks,and it can be successfully used for the energy management of hybrid electric vehicles.

An optimal pricing policy under a Markov chain model

This paper is about an optimal pricing control under a Markov chain model.The objective is to dynamically adjust the product price over time to maximize a discounted reward function.It is shown that the optimal control policy is of threshold type.Closed-form solutions are obtained.A numerical example is also provided to illustrate our results.

Valuation of Stock Loans Under a Markov Chain Model

In recent years the use of Markov chain models to model stock price movement has received increased attention among researchers.Markov chain models combine the discrete movements of a binomial tree model while retaining the Markovian properties of Brownian motion,thus allowing the best properties of both of these models.In this paper,the authors consider a Markov chain model in which the underlying market is solely determined by a two-state Markov chain.Such a Markov chain model is strikingly simple and yet appears capable of capturing various market movements.By proper selection of parameters,the Markov chain model can produce sample paths that are very similar to.or very distinct from a classical Brownian motion,as the authors demonstrate in this paper.This paper studies the stock loan valuation,or the value of a loan in which a risky share of stock is used as collateral,under such a model.Dynamic programming equations in terms of variational inequalities are used to capture the dynamics of the problem.These equations are solved in closed-form.Explicit optimal solutions are obtained.Numerical examples are also reported to illustrate the results.

D-S理论和Markov链组合的桥梁性能退化预测研究

为准确预测桥梁性能退化,考虑到数据随机性和微小扰动发生状态跳跃,提出了一种D-S(Dempster-Shafer)证据理论和Markov链组合的桥梁性能退化组合预测模型和性能退化率的概念.该模型基于指数平滑(exponential smoothing,ES)方法获得新的预测数据序列,并利用Markov链和D-S理论不断进行优化,从而实现桥梁性能退化的组合预测.实际工程的应用结果表明:性能退化率可以直观地表征在梁性能退化的速度.其次,该模型的平均相对误差为1.54%,较于回归、灰色和模糊加权Markov链模型,精度分别提高了1.11%,0.88%和2.8%,而后验差比值为0.242,小于0.35;模型的标准差为9.021,相比其他模型分别减小了3.978,3.405和7.500,而变异系数为0.109,均小于其他模型,验证了组合预测模型在精度和稳定性方面的优越性,可为在役桥梁结构性能退化预测与维护提供理论基础.

Dry and wet spell probability by Markov chain model-a case study of North Lakhimpur(Assam),India

For the purpose of crop planning and to carry out the agricultural practices,it is important to know the sequence of dry and wet periods.The present study was undertaken with the objectives to forecast dry and wet spell analysis using Markov chain model and also to find out the exact time of onset and termination of monsoon at study area for North Lakhimpur(Assam),India using weekly rainfall data for a period of 24 years.The results indicated that probability of occurrence of dry week is higher from week 1st to 14^(th) and also from week 41^(st) to 52^(nd).The range of probability of occurrence of dry week in these weeks varies from 41.67% to 100%.Probability of occurrence of wet week is higher from week 17^(th) to 40^(th).The range of probability of wet week in these weeks varies from 66.67% to 100%.Week 1^(st) to 4^(th) and 43^(rd) to 52^(nd) of the year remains under stress on an average,as there are 50% to 95.83% chances of occurrence of two consecutive dry weeks.The analysis showed that monsoon starts effectively from week 23^(rd)(4^(th) June to 10^(th) June)in North Lakhimpur.The week 25^(th)(18^(th) June to 24^(th) June)is ideal time for initiation of wet land preparation for growing short duration rice variety.Pre-monsoon effectively starts from week 14^(th)(2^(nd) April to 8^(th) April).On week 14^(th) sowing of summer maize(rain fed)may be done.Week 15^(th)(9^(th) April to 15^(th) April)is ideal time for initiation of wet land preparation for growing long duration rice variety.

Grey Markov chain and its application in drift prediction model of FOGs

A novel grey Markov chain predictive model is discussed to reduce drift influence on the output of fiber optical gyroscopes (FOGs) and to improve FOGs' measurement precision. The proposed method possesses advantages of grey model and Markov chain. It makes good use of dynamic modeling idea of the grey model to predict general trend of original data. Then according to the trend, states are divided so that it can overcome the disadvantage of high computational cost of state transition probability matrix in Markov chain. Moreover, the presented approach expands the applied scope of the grey model and makes it be fit for prediction of random data with bigger fluctuation. The numerical results of real drift data from a certain type FOG verify the effectiveness of the proposed grey Markov chain model powerfully. The Markov chain is also investigated to provide a comparison with the grey Markov chain model. It is shown that the hybrid grey Markov chain prediction model has higher modeling precision than Markov chain itself, which prove this proposed method is very applicable and effective.

基于改进Markov智能网联多车型混合流编队策略

为提高智能网联(connected and automated,CA)卡车、小车及人工驾驶卡车、小车的混合流道路通行能力,提出基于排强度和渗透率的CA车辆单独编队和合作编队策略.分别设计两种策略下混合流车辆跟驰模式,推导出基于改进Markov模型,涵盖CA车辆渗透率和排强度的车辆状态转移概率;分析两种策略下CA车辆队列分布,建立各策略下的混合流道路容量模型,并通过理论证明和仿真实验予以验证.结果表明,与不编队策略相比,两种策略下道路容量分别提高1.23%~49.62%和1.47%~60.34%,合作编队策略与单独编队策略相比能将道路容量再提高11%;当CA车辆渗透率大于50%和排强度大于0时,编队策略对道路容量的提升效果更显著,容量能提高13.27%~60.34%;单独编队策略下CA小车和CA卡车最大队列规模分别为8辆和6辆,合作编队下CA车辆最大队列规模为8辆.

On the Markov Chain Binomial Model

Rudolfer [1] studied properties and estimation of a state Markov chain binomial (MCB) model of extra-binomial variation. The variance expression in Lemma 4 is stated without proof but is incorrect, resulting in both Lemma 5 and Theorem 2 also being incorrect. These errors were corrected in Rudolfer [2]. In Sections 2 and 3 of this paper, a new derivation of the variance expression in a setting involving the natural parameters ?is presented and the relation of the MCB model to Edwards’ [3] probability generating function (pgf) approach is discussed. Section 4 deals with estimation of the model parameters. Estimation by the maximum likelihood method is difficult for a larger number n of Markov trials due to the complexity of the calculation of probabilities using Equation (3.2) of Rudolfer [1]. In this section, the exact maximum likelihood estimation of model parameters is obtained utilizing a sequence of Markov trials each involving n observations from a {0,1}-?state MCB model and may be used for any value of n. Two examples in Section 5 illustrate the usefulness of the MCB model. The first example gives corrected results for Skellam’s Brassica data while the second applies the “sequence approach” to data from Crouchley and Pickles [4].

基于互Box-Cox变换和Markov链风速云模型的发电系统充裕度评估

为准确计及风速随机性和自相关性对风电并网系统充裕度的影响,建立基于互Box-Cox变换和Markov链的风速云模型,并将该模型与时序Monte Carlo模拟法结合,提出计及风速随机性和自相关性的风电并网系统充裕度评估方法。仿真结果表明,所提模型产生的仿真风速样本与实测风速样本具备相似的概率分布特性和自相关性,所提方法可较精确地评估风电并网系统充裕度及风电容量可信度。

Identifying the dependency pattern of daily rainfall of Dhaka station in Bangladesh using Markov chain and logistic regression model

Bangladesh is a subtropical monsoon climate characterized by wide seasonal variations in rainfall, moderately warm temperatures, and high humidity. Rainfall is the main source of irrigation water everywhere in the Bangladesh where the inhabitants derive their income primarily from farming. Stochastic rainfall models were concerned with the occurrence of wet day and depth of rainfall for different regions to model the daily occurrence of rainfall and achieved satisfactory results around the world. In connection to the Markov chain of different order, logistic regression is conducted to visualize the dependence of current rainfall upon the rainfall of previous two-time period. It had been shown that wet day of the previous two time period compared to the dry day of previous two time period influences positively the wet day of current time period, that is the dependency of dry-wet spell for the occurrence of rain in the rainy season from April to September in the study area. Daily data are collected from meteorological department of about 26 years on rainfall of Dhaka station during the period January 1985-August 2011 to conduct the study. The test result shows that the occurrence of rainfall follows a second order Markov chain and logistic regression also tells that dry followed by dry and wet followed by wet is more likely for the rainfall of Dhaka station and also the model could perform adequately for many applications of rainfall data satisfactorily.

高等院校教师人才流动的Markov-chain预测模型

介绍并解析随机过程理论中的马尔科夫过程与马尔科夫链;针对高等院校教师人才流动变化过程,利用马尔科夫过程分析方法建立描述人员流动变化趋势的Markov-chain预测模型,详细阐述了模型的算法步骤.以某所高等院校教师人才流动的状态转移数据作为算例,运用新建立的预测模型,对该院校教师人才的流动趋势做出了预测分析.最后,将教师进修状态纳入分析范围,进行了教师职业生涯和职务发展趋势预测的深入分析.应用模型对实际算例的求解结果表明:Markov-chain预测模型及算法,叙述简洁、运算方便,为高等院校教师人才流动,乃至其他行业人才流动的预测提供了一种新的、有效的思路和方法.

MULTI-DIMENSIONAL MARKOV CHAIN–BASED ANALYSIS OF CONFLICT PROBABILITY FOR SPECTRUM RESOURCE SHARING

In this paper, we consider the optimal problem of channels sharing with het-erogeneous traffic （real-time service and non-real-time service） to reduce the data conflict probability of users. Moreover, a multi-dimensional Markov chain model is developed to analyze the performance of the proposed scheme. Meanwhile, performance metrics are derived. Numerical results show that the proposed scheme can effectively reduce the forced termination probability, blocking probability and spectrum utilization.

Option Pricing and Hedging under a Markov Switching Lévy Process Model

In this paper, we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging. In this model, the market interest rate, the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process. We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure. The option price using this model is obtained by the Fourier transform method. We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging.

基于相似日的Grey-Markov与BP_Adaboost的短期光伏功率预测

针对相似日对光伏功率预测精度的影响,提出基于相似日的Grey-Markov与BP_Adaboost的光伏功率预测方法。为获取不同相似日,分别以辐照度和温度为相似变量,通过二维欧氏距离选取两组相似日;基于两组相似日数据,用灰色GM(1,1)模型预测光伏功率的总体趋势,用马尔科夫链对灰色模型的预测结果进行修正,得到两组预测结果;用BP_Adaboost对两组预测结果进行集成,以获得更高的预测精度。仿真结果表明,该方法提高了结果的预测精度与鲁棒性,可为光伏电站并网提供重要参考信息。