Exponential stability of impulsive jump linear systems with Markov process

The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.

Exponential martingale for compound Poisson process with latent variable and its applications

In this article, we construct an exponential martingale for the compound Poisson process with latent variable. With the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic risk measure for the compound Poisson process and a deviation inequality for the ruin probability of the partly shifted risk process.

Exact Run Length Evaluation on a Two-Sided Modified ExponentiallyWeighted Moving Average Chart for Monitoring

A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for theperformance evaluation on control charts. This paper proposes the explicit formula for evaluating the average runlength on a two-sided modified exponentially weighted moving average chart under the observations of a first-orderautoregressive process, referred to as AR(1) process, with an exponential white noise. The performance comparisonof the explicit formula and the numerical integral technique is carried out using the absolute relative change forchecking the correct formula and the CPU time for testing speed of calculation. The results show that the ARL ofthe explicit formula and the numerical integral equation method are hardly different, but this explicit formula ismuch faster for calculating the ARL and offered accurate values. Furthermore, the cumulative sum, the classicalEWMA and the modified EWMA control charts are compared and the results show that the latter is better for smalland intermediate shift sizes. In addition, the explicit formula is successfully applied to real-world data in the healthfield as COVID-19 data in Thailand and Singapore.

Monoexponential Microsecond Decay of Blue Photoluminescence in Aged Porous Silicon Prepared with Ar^(+) 488nm

Blue photoluminescence is observed in aged porous silicon samples anodized under Ar^(+)488 nm laser illumination.No samples have been undergone any heating treatment process.Both nanosecond and microsecond decay of blue photoluminescence have been measured.Samples show a good monoexponential microsecond decay with lifetimes of about 5.3μs.Photoluminescence excitation spectra of blue and red Photoluminescence indicate there is a large Stokes shift(about 800-900meV)in the excitation spectra of red photoluminescence while no this marked Stokes shift in that of blue photoluminescence.The possible origin of the photoluminescence is discussed based on the experimental results.

Hyper-exponential jump-diffusion model under the barrier dividend strategy

In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via martingale stopping.

Convergence of Invariant Measures of Truncation Approximations to Markov Processes

Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.

Poisson Process and Its Application to the Storm Water Overflows

The homogenous Poisson process is often used to describe the event arrivals. Such Poisson process has been applied in various areas. This study focuses on the arrival pattern of storm water overflows. A set of overflow data was obtained from the storm water pipeline of a municipality. The aim is to verify the overflow arrival pattern and check whether the Poisson process can be applied. The adopted method is the analysis over the inter-arrival times. The exponential distribution test is conducted on the annual data set as well as the entire data set. The results show that all data sets follow the exponential distribution. With the verification of Poisson process, specific examples are also given to show how the Poisson process properties can be used in the management of storm water pipeline management. For other data that are featured with various heterogeneities, the homogenous Poisson process might not be able to be verified and used. Under such circumstances, non-homogenous survival model can be used to simulate the arrival process.

ASYMPTOTICS OF THE SOLUTIONS TO STOCHASTIC WAVE EQUATIONS DRIVEN BY A NON-GAUSSIAN LéVY PROCESS

In this article, we consider the long time behavior of the solutions to stochastic wave equations driven by a non-Gaussian Lévy process. We shall prove that under some appropriate conditions, the exponential stability of the solutions holds. Finally, we give two examples to illustrate our results.

Nonlinear Statistical Process Monitoring Based on Control Charts with Memory Effect and Kernel Independent Component Analysis

A novel nonlinear combination process monitoring method was proposed based on techniques with memo- ry effect （multivariate exponentially weighted moving average （MEWMA）） and kernel independent component analysis （KICA）. The method was developed for dealing with nonlinear issues and detecting small or moderate drifts in one or more process variables with autocorrelation. MEWMA charts use additional information from the past history of the process for keeping the memory effect of the process behavior trend. KICA is a recently devel- oped statistical technique for revealing hidden, nonlinear statistically independent factors that underlie sets of mea- surements and it is a two-phase algorithm., whitened kernel principal component analysis （KPCA） plus indepen- dent component analysis （ICA）. The application to the fluid catalytic cracking unit （FCCU） simulated process in- dicates that the proposed combined method based on MEWMA and KICA can effectively capture the nonlinear rela- tionship and detect small drifts in process variables. Its performance significantly outperforms monitoring method based on ICA, MEWMA-ICA and KICA, especially for lonu-term performance deterioration.

Ornstein-Uhlenbeck过程刻画的股票市场下的最优超额损失再保险和投资

本文在扩散逼近风险模型下研究了保险公司的最优投资和再保险策略.假设保险公司可购买超额损失再保险,并将盈余投资于无风险资产和风险资产组成的金融市场,其中风险资产价格模型受Ornstein-Uhlenbeck过程影响.保险公司的目标是使终端财富的期望指数效用最大化.利用随机控制理论和HJB方程,推导出了最优策略和值函数的显式表达式.最后,通过数值分析讨论了模型参数对最优策略和值函数的影响.

利用SE-GPR模型对甲醇/柴油混合燃料柴油机性能的预测

为了对柴油机的经济性和排放参数进行高效、准确的预测,根据4190型船用柴油机实验数据与边界参数,建立AVL-BOOST甲醇/柴油混合燃料柴油机仿真模型;利用模型进行仿真实验,并建立甲醇掺混比、废气再循环(exhaust gas recirculation,EGR)率、喷油提前角和进气压力4个控制参数对有效油耗率和NO x排放预测数据集;利用该数据集对5种不同核函数的高斯过程回归(Gaussian process regression,GPR)模型进行训练;最后将最优的平方指数高斯过程回归(squared exponential-Gaussian process regression,SE-GPR)模型、AVL-BOOST仿真数据和柴油机实验数据进行对比。结果表明:在数据量为180组时,SE-GPR模型对有效油耗率和NO x排放均取得拟合关联度99%以上,均方根误差(root mean square error,RMSE)分别为1.859,0.3445,平均绝对误差(mean absolute error,MAE)分别为0.954,0.2489;并且,相较于AVL-BOOST仿真实验,SE-GPR模型对实验数据具有更好的拟合性。

基于AHP与TOPSIS的水电站能效管理水平评价方法研究

针对现有水电站能效管理水平评价方法的不足,将层次分析法(AHP)和优劣解距离法(TOPSIS)引入评价过程中,综合考虑经济、安全和管理3个方面的因素,构建了水电站能效管理评价指标体系;针对九分位标度法的不足,采用指数标度法确定各指标权重;分别利用TOPSIS方法和专家打分法对定量指标、定性指标进行评分,并进一步实现水电站能效管理水平的综合评价;以某实际水电站为例,分析和计算2018-2022年的水电站能效管理水平得分,结果表明该电站能效管理水平总体上呈上升趋势。

智能电网用电异常诊断和调控策略

为了针对智能电网不同异常用电的原因制定分类调整方法,提出了基于二次根式函数电价调整和计算定界的策略,该策略基于自动过程控制和模糊综合评价进行监控、诊断及分类调整。首先,通过指数加权移动平均值作为自动过程控制的控制变量并确定上下界来监控用电量,建立监控模型;其次,用模糊综合评价法诊断异常用电原因;最后,根据不同原因制定分类调整策略,建立电价需求响应调整模型。算例仿真结果表明,提出的基于二次根式函数电价调整策略在调整频次、残差标准误差、全社会福利和电力公司利润等方面均优于线性函数调整。应用模糊综合评价方法能有效分析异常用电原因,制定分类调整策略能消除异常并获得平稳波动用电量。

Exponential and Strong Ergodicity for Markov Processes with an Application to Queues

For an ergodic continuous-time Markov process with a particular state in its space,the authors provide the necessary and sufficient conditions for exponential and strong ergodicity in terms of the moments of the first hitting time on the state.An application to the queue length process of M/G/1 queue with multiple vacations is given.

基于指数扩散过程的退化模型误指定分析

退化模型是对性能退化产品进行可靠性分析的基础,鉴于误用模型直接影响可靠性评估的精度,研究将适用范围广泛的指数扩散过程模型误指定为3种常见的维纳过程模型、伽马过程模型和逆高斯过程模型,通过引入相对偏差和相对变异率两个指标,以量化模型误指定对产品平均寿命的影响程度,并采用GaAs激光器数据和蒙特卡罗方法进行实例验证。结果表明,模型误指定将对产品平均寿命估计带来较大影响,在性能退化产品的可靠性研究中应尽量选取适用范围更广的指数扩散过程模型,以提高可靠性评估的准确性。

Exponential change of measure for general piecewise deterministic Markov processes

We consider a general piecewise deterministic Markov process(PDMP) X = {X_t}_(t≥0) with a measure-valued generator A, for which the conditional distribution function of the inter-occurrence time is not necessarily absolutely continuous. A general form of the exponential martingales that are associated with X is given by■By considering this exponential martingale to be a likelihood-ratio process, we define a new probability measure and show that the process X is still a general PDMP under the new probability measure. We additionally find the new measure-valued generator and its domain. To illustrate our results, we investigate the continuous-time compound binomial model.

A Concise Proof of the Relation between Poisson Process and Exponential Distribution

Using the memoryless property of the exponential distribution, we have proved again that the relation between the Poisson process and the exponential distribution, that is, the stochastic process {N(t), t≥0} is said to be a Poisson process with arrival rate λ(】0) if and only if the sequence of interarrival times {τ n,n≥1} are independent and identically distributed according to an exponential distribution with parameter λ, where N(t) denotes the arrival number in (0,t\].. It′s noting that the proof provided in this paper is concise and intuitive.

基于刚度模型和高斯过程回归模型的重载工业机器人分步标定方法

针对串联工业机器人由于关节柔性导致的重载下绝对定位精度较低的问题,提出了一种机器人定位误差分步标定方法。采用局部指数积模型对机器人进行几何误差标定。提出了一种基于建模和机器学习的非几何误差标定方法。在该部分中,首先建立了机器人的刚度模型对非几何误差中最主要的变形误差进行标定,然后采用数据驱动的高斯过程回归(GPR)模型对残余误差进行标定。实验结果表明,该方法可以有效提高机器人带载下的绝对定位精度,并且具有位置精度不随载荷变化而产生明显波动的优点。

一类具有Ornstein-Uhlenbeck过程的随机捕食者-食饵模型的指数绝灭、平稳分布和概率密度函数

该文建立了一类具有Ornstein-Uhlenbeck过程、恐惧效应、Crowley-Martin型和修正的Leslie-Gower型功能反应函数的捕食者-食饵模型.首先通过构造合适的Lyapunov函数证明了全局解的存在唯一性,随后获得了两物种指数绝灭和平稳分布存在的充分条件.进一步通过求解相应的Fokker-Planck方程得到了概率密度函数的具体表达式.最后通过三个数值例子验证了理论结果的可行性,其研究表明随机干扰的波动强度和回复速率均会影响种群的生存.

基于新型幂次指数趋近律滑模控制算法的研究

针对传统滑模控制存在抖振与收敛速度缓慢的问题,提出一种新型幂次指数趋近律的滑模控制方法。首先上述趋近律结合了双曲正切函数与符号函数的特征进行了切换函数上的改进,滑模系数影响因子引入了系统误差与滑模状态变化量,使其能够自适应调节滑模到达过程的收敛速度并对其进行分阶段调节,还利用切换函数的特征分析了趋近滑模面双侧切换区间的范围;其次分析了自适应新型幂次指数趋近律的收敛区域和收敛时间,并证明了此趋近律的存在性、可达性与稳定性;最后将新型幂次指数趋近律和其它各种传统趋近律运用到经典二阶系统进行了对比,仿真结果表明新型幂次指数趋近律能够更好的提升收敛速率以及削弱抖振的产生。