基于Semi-Markov模型沥青路面性能衰变规律研究

为解决在路面使用性能预测过程中预测值与实测值间误差波动较大这一问题,采用Semi-Markov模型对山东省某国道的使用性能进行预测,同时将预测结果与实测数据进行对比。结果显示,Semi-Markov模型能够有效预测道路使用寿命,且对早期道路使用状况的预测结果精确度更高,而随着预测年限的延长,预测结果受道路养护措施的影响很大,需采取主动干预措施进行修正,Semi-Markov模型为准确预测沥青路面早期使用性能变化趋势并得到合理的养护决策提供可靠依据。

基于UGF和Semi-Markov方法的反应堆泵机组多状态可靠性分析

将通用发生函数(UGF)与半马尔可夫过程(Semi-Markov Process)相结合,对反应堆泵机组进行多状态可靠性分析。给出多状态系统可靠性分析的UGF算法模型,推导多状态设备性能状态的Semi-Markov过程概率表达式,定义设备、系统性能值的定量描述方法。以性能参数是否满足需求值做为系统成功与失效的判据,对比分析反应堆泵机组在需求性能条件下的多状态可用度与2状态可用度结果,并给出系统在任务周期内的平均性能值。结果表明,该方法能够定量分析部分失效对系统可靠性的影响,降低传统的2态可靠性分析方法产生的不必要的保守程度。

基于Semi-Markov的模块化多电平换流器的可靠性分析及其冗余配置策略

目前,对于模块化多电平换流器(MMC)的可靠性分析大多认为其子模块的寿命函数符合指数分布,但实际上其子模块的寿命函数更接近于Weibull分布。利用Semi-Markov过程建立MMC的数学模型,结合频率和持续时间法对存在不同冗余度的系统进行可靠性指标的定量分析。对MMC进行损耗分析,分析冗余度对其损耗的影响。采用分目标乘除法对MMC的冗余度进行优化,使其在具有高可靠性的同时保持损耗最小。通过实例分析可知,当换流器直流侧母线电压为±800 kV,子模块的额定电压为3 kV时,最佳冗余度为1.86%。

基于模糊概率齐次Semi-Markov过程的核动力系统可靠性分析

研究了将模糊集合理论与齐次Semi-Markov过程相结合的方法对清晰事件-模糊概率系统进行可靠性分析。给出三角形模糊数算法和将核动力系统设备可靠性数据源通用数据进行三角形模糊化处理的方法,推导系统状态概率计算的模糊概率齐次Semi-Markov过程算法模型,并给出模糊核矩阵的计算方法。实例研究表明,该方法能够基于已有的通用数据进行系统失效概率的不确定性分析,从而弥补仅采用点估计值所得分析结果的不完备性。

基于Semi-Markov链的高速车轮缺陷退化模型

为了给高速车轮的维修决策提供科学的理论支持,提出了一种基于Semi-Markov链的高速车轮退化模型并研究得到车轮4个关键部位的缺陷退化规律。首先,对超声探伤获得的缺陷数据进行统计分析,提出分部位的多状态模型,再选择合适的随机分布并估算出分布参数;然后将各部位模型合并建立一个整车轮的缺陷退化模型;最后,采用MATLAB编程计算得到整个车轮的一系列随走行里程变化的超限概率值。结果表明,当前针对动车组轮对实行的超声波探伤检测周期的设定非常合理。

RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.

Reliability Evaluation of Two-Stage Directed Semi-Markov Repairable Network Systems

A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc. The availability of the system is discussed by using Markov renewal theory, Laplace transform and probability analysis methods. A numerical example is given to illustrate the results obtained in the paper.

Portfolio optimization of credit risky bonds: a semi-Markov process approach

This article presents a semi-Markov process based approach to optimally select a portfolio consisting of credit risky bonds.The criteria to optimize the credit portfolio is based on l_(∞)-norm risk measure and the proposed optimization model is formulated as a linear programming problem.The input parameters to the optimization model are rate of returns of bonds which are obtained using credit ratings assuming that credit ratings of bonds follow a semi-Markov process.Modeling credit ratings by semi-Markov processes has several advantages over Markov chain models,i.e.,it addresses the ageing effect present in the credit rating dynamics.The transition probability matrices generated by semi-Markov process and initial credit ratings are used to generate rate of returns of bonds.The empirical performance of the proposed model is analyzed using the real data.Further,comparison of the proposed approach with the Markov chain approach is performed by obtaining the efficient frontiers for the two models.

Semi-Markovian Model of Two-Line Queuing System with Losses

In the present paper, to build model of two-line queuing system with losses GI/G/2/0, the approach introduced by V.S. Korolyuk and A.F. Turbin, is used. It is based on application of the theory of semi-Markov processes with arbitrary phase space of states. This approach allows us to omit some restrictions. The stationary characteristics of the system have been defined, assuming that the incoming flow of requests and their service times have distributions of general form. The particular cases of the system were considered. The used approach can be useful for modeling systems of various purposes.

A Study of Aviation Weapon Equipment Maintenance Based on the Semi-Markov Model

Based on the Semi-Markov mathematical description, the multiple states of maintenance processes for aviation weapon equipment are studied. Six kinds of maintenance states are determined and the Semi-Markov model of the maintenance process is given. According to maintenance characteristic, the multiple states maintenance processes are divided into the wait, use and alternate stages. Through using the mathematical model for the different stages, the probability in different states and effective index on different stages are obtained. These results are available to the maintenance practice.

Definition of Laplace Transforms for Distribution of the First Passage of Zero Level of the Semi-Markov Random Process with Positive Tendency and Negative Jump

One of the important problems of stochastic process theory is to define the Laplace transforms for the distribution of semi-markov random processes. With this purpose, we will investigate the semimarkov random processes with positive tendency and negative jump in this article. The first passage of the zero level of the process will be included as a random variable. The Laplace transforms for the distribution of this random variable is defined. The parameters of the distribution will be calculated on the basis of the final results.

Risk Identification based on Hidden Semi-Markov Model in Smart Distribution Network

The smart distribution system is the critical part of the smart grid, which also plays an important role in the safe and reliable operation of the power grid. The self-healing function of smart distribution network will effectively improve the security, reliability and efficiency, reduce the system losses, and promote the development of sustainable energy of the power grid. The risk identification process is the most fundamental and crucial part of risk analysis in the smart distribution network. The risk control strategies will carry out on fully recognizing and understanding of the risk events and the causes. On condition that the risk incidents and their reason are identified, the corresponding qualitative / quantitative risk assessment will be performed based on the influences and ultimately to develop effective control measures. This paper presents the concept and methodology on the risk identification by means of Hidden Semi-Markov Model (HSMM) based on the research of the relationship between the operating characteristics/indexes and the risk state, which provides the theoretical and practical support for the risk assessment and risk control technology.

Multiyear Discrete Stochastic Programming with a Fuzzy Semi-Markov Process

Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.

基于Semi-Markov的配电可靠性成本估计

针对配电系统故障时间分布不确定的特点,提出了基于半马尔柯夫过程的可靠性成本评估通用方法。建立元件寿命、预防维修时间和修理时间服从任意分布的可靠性评估模型,引入用户停电损失函数研究系统在不完善预防维修情况下的停电损失;通过实例证明了该方法的正确性,显示出该方法对Homogenous Markov和Weibull Markov算法的兼容性、有效性,同时更清晰地反映了元件故障持续时间分布对系统可靠性经济指标的影响。

H_(∞)/Passive Synchronization of Semi-Markov Jump Neural Networks Subject to Hybrid Attacks via an Activation Function Division Approach

In this work,an H_(∞)/passive-based secure synchronization control problem is investigated for continuous-time semi-Markov neural networks subject to hybrid attacks,in which hybrid attacks are the combinations of denial-of-service attacks and deception attacks,and they are described by two groups of independent Bernoulli distributions.On this foundation,via the Lyapunov stability theory and linear matrix inequality technology,the H_(∞)/passive-based performance criteria for semi-Markov jump neural networks are obtained.Additionally,an activation function division approach for neural networks is adopted to further reduce the conservatism of the criteria.Finally,a simulation example is provided to verify the validity and feasibility of the proposed method.

基于事件触发的奇异semi-Markov跳变系统的有限时间控制

为减少不必要的网络资源传输,解决实际复杂系统的有限时间问题,提出一种基于事件触发方案的奇异semi-Markov跳变系统的有限时间控制器设计方法。在事件触发方案下,用系统的时滞表示网络诱导时延,闭环系统可以建模为一个时滞系统。首先,通过构造合适的Lyapunov-Krasovskii泛函,以严格矩阵不等式的形式给出充分条件,以使事件触发方案下的闭环系统正则、无脉冲、随机有限时间有界;然后,通过求解矩阵不等式,得到状态反馈控制器的参数;最后,给出一个数值示例,通过仿真证明所提方法的有效性。

Composite Anti-Disturbance Control of Hidden Semi-Markov Jump Systems via Disturbance Observer

This paper focuses on the disturbance suppression issue of hidden semi-Markov jump systems leveraging composite control.The system consists of a semi-Markov layer and an observed mode sequence layer,and it is subject to a matched disturbance generated by an exogenous system and a mismatched disturbance that is norm bounded.The proposal is to design a composite controller based on a disturbance observer to counteract and attenuate the disturbances effectively.By constructing a special Lyapunov function comparison point,the exponential stability is analyzed with the stability criterion in the form of linear matrix inequality is established.Two simulation examples are provided to demonstrate the practical merits of the composite controller relative to the single H_(∞)control.

基于Semi-Markov模型的多态系统不完全维修决策

为提高复杂多态系统的任务完成能力,降低维修资源消耗,提出了基于Semi-Markov模型的预防性维修和修复性维修相结合的多态系统不完全维修决策方法。采用Semi-Markov模型描述部件的性能衰退过程,利用通用生成函数方法对系统的可靠性指标进行分析,在不完全维修模型基础上,从"系统级维修的角度"出发,提出了预防性维修和修复性维修相结合的不完全维修决策方法,确保系统在有限的服役期内,获得最大净效益。并以某航空发动机压气机子系统的维修决策为例进行分析,该方法可以有效的结合预防性维修和修复性维修的优势,提高了系统的任务完成能力,具有很强的通用性和工程应用价值。

THE BOREL STATE SPACE SEMI-MARKOVDECISION PROCESS WITH EXPECTED TOTAL REWARDS IN A SEMI-MARKOV ENVIRONMENT

This paper investigates the Borel state space semi-Markov decision process (SMDP) with the criterion of expected total rewards in a semi-Markov environment. It describes a system which behaves like a SMDP except that the system is influenced by its environment modeled by a semi-Markov process. We transform the SMDP in a semiMarkov environment into an equivalent discrete time Markov decision process under the condition that rewards are all positive or all negative, and obtain the optimality equation and some properties for it.

Optimal stopping time on discounted semi-Markov processes

This paper attempts to study the optimal stopping time for semi- Markov processes (SMPs) under the discount optimization criteria with unbounded cost rates. In our work, we introduce an explicit construction of the equivalent semi-Markov decision processes (SMDPs). The equivalence is embodied in the expected discounted cost functions of SMPs and SMDPs, that is, every stopping time of SMPs can induce a policy of SMDPs such that the value functions are equal, and vice versa. The existence of the optimal stopping time of SMPs is proved by this equivalence relation. Next, we give the optimality equation of the value function and develop an effective iterative algorithm for computing it. Moreover, we show that the optimal and ε-optimal stopping time can be characterized by the hitting time of the special sets. Finally, to illustrate the validity of our results, an example of a maintenance system is presented in the end.