Numerical path integration of a non-homogeneous Markov process

The numerical path integration method, based on Gauss-Legendre integration scheme, is applied to a Duffing oscillator subject to both sinusoidal and white noise excitations. The response of the system is a Markov process with one of the drift coefficients being periodic. It is a non-homogeneous Markov process that does not have a stationary probability distribution. When applying the numerical procedure, the values of transition probability density at the Gaussian-Legendre quadrature points need only be calculated for time steps of the first period of the sinusoidal excitation, and they can be saved for use in all subsequent periods. The numerical procedure is capable of capturing the evolution of the probability density from an initial distribution to one that is changing and rotating periodically in the phase space.     

Poisson limit theorem for countable Markov chains in Markovian environments

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The dividend function in the jump-diffusion dual model with barrier dividend strategy

A dual model of the perturbed classical compound Poisson risk model is considered under a constant dividend barrier. A new method is used in deriving the boundary condition of the equation for the expectation function by studying the local time of a related process. We obtain the expression for the expected discount dividend function in terms of those in the corresponding perturbed compound Poisson risk model without barriers. A special case in which the gain size is phase-type distributed is illustrated. We also consider the existence of the optimal dividend level.     

结构内力概率密度演化的向量马氏过程方法

本文提出了位移加载机制下求解无启发持性结构结点力的概率密度演化规律的方法。该方法将力与非线性构形状态演化联合起来。组成力-状态混合向量马氏过程。采用分离式分析方法进行状态转移概率速度分析。然后建立力-状态联合概率密度演化方程。求解这一方程可分别得到非线性构形状态演化和结点力随机演化的概率结构。意味深长的是，非线性构形状态的演化方程可以直接由力-状态联合演化方程推导出来。而力的概率演化方程则不能实现力与状态之间的解耦。     

Exponential stability of stochastic generalized porous media equations with jump

Stochastic generalized porous media equation with jump is considered. The aim is to show the moment exponential stability and the almost certain exponential stability of the stochastic equation.     

Stochastic Vibration Model of Gear Transmission Systems Considering Speed-Dependent Random Errors

A dynamic and stochastic simulation model is developed for analyzing the vibration of gear transmission systems with consideration of the influence of the time-variant stiffness, loads, and gear transmission errors. The gear transmission system is viewed as a non-linear, time-correlated and stationary stochastic system. The transmission errors of gears are decomposed into harmonic and random components based on the spectral analysis. To simulate the random component, a second order Markov process with time-variant parameters considering influence of rotational speed is proposed and the method to determine the model parameters based on the random error of measured gear transmission error is developed. A simulation system is developed. The input to the simulation system is a white Gaussian noise process and harmonic errors, and the output is the rotational vibration acceleration of gears. Experiments are carried out to verify the proposed model. The influences of the random error on vibration acceleration are examined using the developed simulation system.     

Markovian Diffusive Representation of Nonrational Distributed Random Processes and Application to Turbulence Simulation over Structures

Vehicles moving through the atmosphere or ocean are frequently subjectto distributed random excitations. This situation occurs for examplewhen turbulent boundary layers develop over their surfaces since thewall pressure fields are distributed random fields. It also occurs whenlarge-scale turbulent flows are encountered by the vehicles such asturbulent winds for an aircraft. These random fields may inducestructural vibrations, mechanical loads, fatigue and damage. They arefrequently described by spectral models (Corcos or Chase models forturbulent boundary layers, Dryden or Von Karman models for turbulentwinds) which involve nonrational terms.For such nonrational models, the development of a Markovian timesimulator relies on a rational approximation of the wavevector-frequencyspectrum obtained from an identification stage. This paper presents ageneral method to manage this stage, that provides us with a family ofstable rational approximations that converges towards the true model asthe dimension increases. These approximations are then used to simulatethe random field.We first give an exact but infinite dimensional state spacerepresentation of any nonrational distributed random field. It is basedon a diffusive formulation and the frequential decoupling property ofthe spatial Fourier transform. Then the discretization of this exactmodel leads to stable finite-dimensional approximations over aprescribed frequency range.The approach is applied to the simulation of a theoretical two-dimensional(2D) turbulent wind spectrum.     

随机损伤过程和依赖于时间的损伤概率分布

本文用马尔柯夫过程描述一般损伤现象,将确定性损伤发展方程随机化为随机微分方程,并得其相应的 Fokker-Planck 方程的封闭解,该解即依赖于时间的损伤概率分布,其包含了某些对可靠性工程有意义的特殊情况。     

捷联惯导角速度匹配传递对准方法研究

潜器用SINS在释放前摇摆基座上进行初始传递对准时，主惯导与子惯导之间不仅会因安装而产生常值失准角，而且会因为舰体的变形产生不确定失准角。用二阶马尔可夫对舰体变形进行了建模，并对角速度匹配传递对准方法进行了研究。计算机仿真验证了舰体变形模型的可行性，角速度匹配传递对准方案可以有效、快速地为潜器提供高精度的导航姿态基准。     

Stability analysis for milling process

In this article, the stability of a milling process is studied by using a semi-discretization method. The model of the workpiece–tool system includes loss-of-contact effects between the workpiece and the tool and time-delay effects associated with the chip-thickness variation. In addition, feed-rate effects are also considered. The governing system of equations is a non-autonomous, delay-differential system with time-periodic coefficients. Stability of periodic orbits of this system is studied to predict the onset of chatter and numerical evidence is provided for period-doubling bifurcations and secondary Hopf bifurcations. Stability charts generated using the semi-discretization method are found to compare well with the corresponding results obtained through time-domain simulations.     

基于马尔科夫链与鞍点逼近的模糊随机可靠性分析方法

针对同时存在随机不确定性和模糊不确定性的可靠性分析问题,提出了两种高效解决方法。一种是迭代马尔科夫链鞍点逼近法,该方法的基本思想是给定隶属水平下由迭代马尔科夫链和一次鞍点逼近法求得可靠度上下限,不同的隶属水平对应不同的可靠度上下限,遍历隶属水平的取值区间[0,1]即可求得可靠度隶属函数,与传统的两相Monte Carlo数字模拟法和迭代一次二阶矩法相比,该方法具有效率高和对非正态基本随机变量不需要进行正态转换的优点;第二种方法是迭代条件概率马尔科夫链模拟法,该方法在求解给定隶属度水平下的可靠度上下限时,由条件概率公式引入一个非线性修正因子,该因子的引入大大提高了功能函数为非线性的可靠性问题的求解精度。本文算例验证了所提方法的优越性。     

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介绍了运动机器人针对动态变化环境的运动控制与决策(如运动障碍物规避,运动 目标跟踪等)问题. 分别从速度空间控制决策的角度分析阐述了运动 决策的基本方法,以及各自的特点. 提出了关于随机运动障碍物与目标的避障问题以及解 决思路,从而建立起基于概率分析的全局优化的速度避障决策方案. 通过仿真试验说明了方 法的有效性,并与传统非概率分析的实时局部决策的方法进了比较与评价.     

一类Markov过程的最大绝对值过程概率密度求解的新方法

随机过程或随机系统响应的最大绝对值概率分布往往是科学与工程中关心的重要挑战性问题.本文从理论与数值上进行了Markov过程的时变最大绝对值过程及其概率分布研究.文中,通过引入扩展状态向量,构造了最大绝对值$\!$-$\!$-$\!$状态量联合向量过程,由此将不具有Markov性的最大值过程转化为具有Markov性的向量随机过程.在此基础上,通过最大绝对值$\!$-$\!$-$\!$状态量之间的关系,建立了联合向量过程的转移概率密度函数.进而,结合Chapman-Kolmogorov方程和路径积分方法,提出了最大绝对值概率密度函数求解的数值方法.由此,可以得到Markov过程最大绝对值过程的时变概率密度函数,可进一步用于结构动力可靠度分析等.通过数值算例,验证了本文所提方法的有效性. 该方法有望推广到更一般随机系统的极值分布估计之中.      

随机疲劳裂纹扩展新模型

疲劳裂纹扩展的随机特性是工程结构可靠性分析和制定检查、维修计划野性 须考虑的因素,提出疲劳裂纹随机扩展模型,不仅考虑了时间参数影响,而且还考虑了初始裂纹尺寸分布影响。模型适应范围广,由于采用了一次二阶矩近似方法简化随机过程计算,便于工程应用。     

噪声对三势阱系统混沌性质的影响

本文研究了在两种不同信嗓比的复合激励作用下，三讲系统的物理性质。通过概率密度函灵数及平均相轨线的分析，指出该系统在这两种情况下作所谓的混沌随机运动。     

Laboratory optimization of the soil digging process

A new idea for the optimization of digging using earth-working machinery is presented and experimentally verified. This idea is based on the conclusions derived from previous papers presented by the same authors, that the soil cutting trajectories incorporating the generated shear band as a part of them are the optimal ones. Dividing the whole excavation task into several repeatable cycles for which the soil free boundary before and after the experiment are similar the optimization of a single cycle plays a significant role in the energetic efficiency of the whole task. A single cycle of the working process is defined using several basing parameters. The influence of each parameter on the specific unit energy of the process was experimentally verified. Finally, a set of values for the discussed parameters is recommended for the particular soil and tool shape.     

Numerical investigations on dynamic process of muzzle flow

The integrative process of a quiescent projectile accelerated by high-pressure gas to shoot out at a supersonic speed and beyond the range of a precursor flow field was simulated numerically. The calculation was based on ALE equations and a second-order precision Roe method that adopted chimera grids and a dynamic mesh. From the predicted results, the coupling and interaction among the precursor flow field, propellant gas flow field and high-speed projectile were discussed in detail. The shock-vortex interaction, shockwave reflection, shock-projectile interaction with shock diffraction, and shock focus were clearly demonstrated to explain the effect on the acceleration of the projectile.     

催化重整单元氢气气团爆炸超压分析

基于计算流体力学分析软件(FLACS),以催化重整反应单元为例建立事故模型,研究不同形状障碍物、泄漏位置,对不同泄漏时间和泄漏监测点的氢气爆炸超压的影响情况。通过研究,建立了与气体燃烧热与爆炸监测点距气团中心距离相关的最大爆炸超压模型。研究结果表明,在研究设计的遮挡物条件下,气体爆炸最大超压与折合距离在对数坐标系中均呈近似线性关系;对于不同的遮挡物,爆炸超压模型需进行修正;在反应器中部发生的事故场景,泄漏5min后最大爆炸超压明显增大。     

Study of the non-isothermal glass fibre drawing process

The glass fibre drawing process is simulated using a finite-element method. The two-dimensional energy and momentum equations are solved in their fully non-linear forms. These are coupled via the temperature-sensitive viscosity function. Both convective and radiative cooling mechanisms are taken into account on the filament surface. An effective emissivity of about 0.2 is found to be applicable to the drawing conditions in this paper. Even at this fairly low effective emissivity, radiation is found to be the dominant mode of cooling. The material thermal conductivity is found to have a small but definite influence on the filament profiles. Two-dimensionsl effects of the kinematic field are only significant up to a distance of about two orifice radii from the nozzle exit.The symbols in the square brackets show the dimensions of the parameters;M Mass,L Length,T Temperature,t Time. a Constant radius of a uniform cylinder [L] - A Local cross-sectional area of the filament [L ² ] - b _i Total tension applied on the filament boundary surface in thei ^th direction [ML/t ² ] - c Specific heat [L ² /t ² T] - D Local filament diameter [L] - f _i i ^th component of the body-force vector [L/t ² ] - h Surface convective heat transfer coefficient of the filament [M/t ³ T] - H Total equivalent heat transfer coefficient due to both convection and radiation [M/t ³ T] - k Thermal conductivity [ML/t ³ T] - M Mass-flow rate [M/t] - n Coordinate normal to the local filament surface [L] - Nu Local Nusselt number [–] - Average Nusselt number [–] - Q Rate of heat transfer [ML ² /t ³ ] - Volume-flow rate [ ³ /t] - r Radial coordinate [L] - R Local radius of the filament [L] - Re _x Reynolds number based on characteristic length scalex [–] - s Coordinate along the filament surface [L] - T Temperature [T] - u Radial component of the velocity [T/t] - U Free-stream velocity of a uniform flow [L/t] - v Local speed of a fluid particle defined by v = ;[L/t] - V Volume [L ³ ] - v _f Constant velocity of a filament with a uniform radius [L/t] - w Axial component of the velocity [L/t] - Average axial velocity of the fluid inside the tube [L/t] - z Axial coordinate, i.e. axial distance from the orifice exit [L] - Exponential coefficient of the viscosity function [T ^–1 ] - _ij Kronecker delta [–] - Emissivity or total hemispherical emissivity [–] - µ Viscosity [M/Lt] - µ ₀ Reference viscosity defined byµ = µ ₀ e ^–T [M/Lt] - Fluid density [M/L ³ ] - Stefan-Boltzmann constant [M/t ³ T ⁴ ] - Viscous dissipation function [M/Lt ³ ] - a Of air - a Based on the (constant) filament radius - C.L. Referred to the centre line of the filament - conv Referred to convection - D Dased on the diameter - f Referred to the filament local condition - g Referred to glass - i,j Species in multi-component systems - o Quantity evaluated at the orifice exit - R Based on the radius - rad Referred to radiation - s Evaluated at the filament surface - tot Referred to the total heat transfer from the filament surface - w Evaluated at the tube wall - Ambient condition - * Refers to non-dimensional quantities - — Indicating quantities averaged over the filament cross-section     

Controlled growth of silver nanoparticles in a hydrothermal process

A two-step synthesis was used to control the shape of silver nanoparticles prepared via reduction of Ag^＋ ions in aqueous Ag（NH3）2NO3 by poly（N-vinyl-2 First, a few spherical silver nanoparticles,-10 nm in size, were pyrrolidone） （PVP）. Then, in a subsequent hydrothermal treatment, the remaining Ag^＋ ions were reduced by PVP into polyhedral nanoparticles, or larger spherical nanoparticles formed from the small spherical seed silver nanoparticles in the first step. The morphology and size of the resultant particles depend on the hydrothermal temperature, PVP/Ag molar ratio and concentration of Ag^＋ ions. By using UV-visible spectroscopy （UV-vis）, transmission electron microscopy （TEM） and powder X-ray diffraction （XRD）, the possible growth mechanism of the silver nanoparticles was discussed. 2007 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V.