任意寿命分布单元表决系统备件需求量的解析算法

表决结构广泛存在于装备的可靠性设计中。针对表决系统备件需求计算困难、不准确的问题,提出了一种基于寿命分布等效的表决系统备件需求量计算方法。首先通过R 等效方法将系统中的非指数单元转化为指数单元;而后将多指数单元表决系统等效为伽马系统并给出等效伽马系统参数的经验计算公式;在此基础上以可用度为保障约束指标,利用伽马分布的可加性得到备件计算结果;最后在实际算例中,通过与仿真结果的比较表明,此解析算法对于指数单元具有较高精度,对于非指数单元,在可用度较高的情况下亦能满足精度要求。     

控制系统中随机信号的仿真与分析

对仿真中用到的各种随机信号的数学模型进行了讨论。定量分析了有限带宽白噪声模块BLWN，给出了设定谊模块参数的关系式．对有色噪声的仿真进行了定量的分析和验证。分析了指数相关随机过程的数学模型，指出仿真时可用均匀分布来代替泊松分布，并给出了相应的M函数文件。文中还讨论了仿真中用BLWN模块来近似给出指数相关随机过程的方法。     

非线性时变系统的部分指数稳定性分析

讨论了非线性时变系统平凡解的部分指数稳定性和全局部分指数稳定性。分别利用数量与向量Lyapunov函数并结合数量与向量比较原理,得到了保证系统平凡解部分指数稳定和全局部分指数稳定的一系列充分条件。作为特殊情形,对于一类定常拟线性系统,在一定的条件下,若其对应的线性系统的平凡解是部分渐近稳定的,利用二次型Lyapunov函数得到了保证拟线性系统的平凡解是全局部分指数稳定的一个代数判据,这些结果在实际应用中具有一定的指导意义。最后用两个数值例子对所得主要结果加以阐明。     

Delay-dependent exponential stability of impulsive stochastic systems with time-varying delay

The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay.Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors,few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems.Firstly,the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem.Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities.In particular,the estimate of the exponential convergence rate is also provided,which depends on system parameters and impulsive effects.The obtained results show that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows,and impulses may be used as controllers to stabilize the underlying stochastic system.Numerical examples are given to show the effectiveness of the results.     

Exponential Sums over Finite Fields

This is an expository paper on algebraic aspects of exponential sums over finite fields. This is a new direction. Various examples, results and open problems are presented along the way, with particular emphasis on Gauss periods, Kloosterman sums and one variable exponential sums. One main tool is the applications of various p-adic methods. For this reason, the author has also included a brief exposition of certain p-adic estimates of exponential sums. The material is based on the lectures given at the 2020 online number theory summer school held at Xiamen University. Notes were taken by Shaoshi Chen and Ruichen Xu.     

延时耦合复杂动力网络的全局混沌同步

利用Lyapunov稳定性理论,结合线性矩阵不等式方法,给出了具有耦合延时的复杂动力网络全局指数同步的时滞无关和时滞相关的若干条件.同时以Duffing混沌系统为例,应用时滞相关条件,得到了保证同步状态全局指数稳定的时滞上界,并与已有结论作比较,验证了结论的保守性有所减弱.数值仿真结果也说明理论分析的正确性.     

威布尔型多不可修部件备件需求确定方法

针对Weibull型多不可修部件的备件需求确定问题, 提出一种基于Monte-Carlo模拟的方法, 能够较为方便地得到结果, 该方法同样也适用于其它几种分布类型备件量的确定. 在此基础上, 又研究了工程应用中利用指数方法确定Weibull型备件需求量的适应性问题. 从理论上证明了利用指数方法近似计算单部件的备件量具有保守性, 并通过实例计算表明指数方法确定多部件备件量也具有保守性. 简要分析了保守的程度与保障时间、 保障度、部件数量以及Weibull形状参数的关系. 最后给出指数方法的应用时机.     

Optimization of Background Value in GM(1,1) Model

This article has proved that discrete function with homogeneous exponential law will become discrete function with non-homogeneous exponential law if the function with homogeneous exponential law accumulates, while discrete function with homogeneous exponential law is generated by inversely accumulating the discrete function with non-homogeneous exponential law. Based on the error analysis of the model GM(1,1), researchers use the discrete function with non-homogeneous exponential law to fit the accumulated sequence in order to propose a new method for optimizing background value in model GM(1,1). There are plenty of data simulations and models. And it shows that the new model broke through restrictions of using coefficient, and it still improved its matching and prediction precision.     

Exponential stability for cellular neural networks: an LMI approach

A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks （DCNNs） is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.     

随机跳变广义双指数分布下的双重跳跃扩散模型及应用

结合非对称双指数分布与有偏双指数分布构建了广义双指数分布,该分布能充分展现金融市场的有偏、非对称与尖峰厚尾特征. 借鉴Kou提出的双指数跳跃扩散模型,构建和分析了广义双指数分布下的单层跳跃扩散模型(GDED-KDJ),考虑到金融序列的异方差性与波动跳跃性,参考Eraker提出的双重跳跃扩散模型, 进一步将GDED-KDJ模型扩展为随机跳变广义双指数分布下的双重跳跃扩散模型,分析了新模型具备的一般性、有偏性、非对称性与尖峰厚尾性,进而从理论上证明了新模型的优越性. 同时,还研究了新模型的条件似然函数及MCMC迭代求解算法.最后,利用金融危机期间我国主要三种金属期货价格的三月连 续数据进行实证,结果也进一步表明新模型的可行性、有效性与优越性.     

动态多模型指数平滑法融合的在线预测方法

针对传统预测算法实时性差、难以适应多种数据变化情况、参数无法根据数据的实时变化进行在线调整等问题,提出了一种动态多模型指数平滑法融合的在线预测算法。该算法根据历史数据的预测误差,动态调整指数平滑法的平滑系数,以及1次、2次、3次指数平滑法的融合权值,实时得到对传感器测量参数的准确预测。仿真表明,该算法在多种数据变化情况下均优于单一采用指数平滑法。     

动态多模型指数平滑法融合的在线预测方法

针对传统预测算法实时性差、难以适应多种数据变化情况、参数无法根据数据的实时变化进行在线调整等问题,提出了一种动态多模型指数平滑法融合的在线预测算法。该算法根据历史数据的预测误差,动态调整指数平滑法的平滑系数,以及1次、2次、3次指数平滑法的融合权值,实时得到对传感器测量参数的准确预测。仿真表明,该算法在多种数据变化情况下均优于单一采用指数平滑法。     

熵损失函数下广义指数分布的可靠性估计

在广义指数分布场合下, 讨论了其参数、可靠性指标的估计及性质. 基于熵损失函数, 在共轭先验分布下, 通过对分布函数进行变换, 获得了该分布参数、可靠性指标的 UMVUE、最小风险同变估计、Bayes 估计和经验 Bayes 估计, 并证明了形如 [cT(x) + d]^-1 的一类估计的容许性. 最后运用 Monte-Carlo 方法对各种估计的 MSE 进行了模拟比较. 结果表明, 经验贝叶斯估计精度较高.     

Exponential stability of linear distributed parameter switched systems with time-delay

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems (DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS’ exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities (LOIs) where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.     

某型光学经纬仪寿命分布及可靠性的研究

本文对某型光学经纬仪的寿命试验数据进行了拟合优度检验。某结果是：指数分布、双参数指数分布、Ｗｅｉｂｕｌｌ分布、极值分布都能适用。在此基础上对这些分布进行鉴别，指出指数分布是该产品较合适的寿命分布。由此也给出了产品的ＭＴＢＦ及可靠性下限。这表明该仪器的可靠性已高于外国先进标准的规定指标。     

Stabilization of Discrete-Time Dynamical Systems Under Event-Triggered Impulsive Control with and Without Time-Delays

This paper investigates the issue of stabilization for discrete-time dynamical systems (DDS) by event-triggered impulsive control (ETIC). Based on some relatively simple threshold constants, three levels of event conditions are set and thus the ETIC scheme is designed. Three cases for ETIC with and without time-delays and data dropouts are studied respectively, and the criteria on exponential stability are derived for the controlled DDS. The stabilization in the form of exponential stability is achieved for DDS under the designed ETIC with or without time-delays. And in the case of the ETIC data dropouts, the conditions of exponential stabilization are derived for DDS and the maximal allowable dropout rates for ETIC are estimated. Finally, one example with numerical simulations is worked out for illustration.     

时滞分布参数系统的指数渐近稳定性

基于Lyapunov稳定性理论,利用辅助函数方法研究由变时滞分布参数控制系统所导出的滑动模运动方程的指数渐近稳定性问题,获得了一类滑动模运动方程指数渐进稳定的充分条件,建立了滑动模运方程解的指数渐近稳定性定理。这就为研究时滞分布参数系统的变结构控制问题奠定了理论基础。     

抽象记忆时间的无记忆性及其在真随机模拟中的应用

给出抽象记忆时间的指数分布规律，通过连续随机变量的小数分布及其极限性质，利用计算机间隔时间存储的功能，给出了一种真随机模拟的计算机实现方法，并指出了它们在系统科学、人工智能以及遗传进化算法等中的应用。     

Exponential Stability of Interval Time-Varying Dynamical System with Multidelay

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关于一类线性时不变切换系统的脉冲控制

针对一类线性时不变脉冲切换系统,利用Lyapunov函数导出了一种有效的控制方法.首先,建立了这类系统在任意切换率下稳定与渐近稳定的充分条件;然后,给出了这类系统在设定的切换率下指数稳定的判别准则;最后,给出了一个数值例子及仿真来阐明结论的正确性.