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Stochastic process-based degradation modeling and RUL prediction: from brownian motion to fractional brownian motion

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Science China(Information Sciences) 2021年第7期64卷 5-24页

作者： Hanwen ZHANG Maoyin CHEN Jun SHANG Chunjie YANG Youxian SUN School of Automation and Electrical Engineering University of Science and Technology Beijing State Key Laboratory of Industrial Control Technology College of Control Science and EngineeringZhejiang University Department of Automation Tsinghua University School of Automation and Electrical Engineering Linyi University Department of Electrical and Computer Engineering University of Alberta

brownian motion(BM) has been widely used for degradation modeling and remaining useful life(RUL) prediction, but it is essentially Markovian. This implies that the future state in a BM-based degradation process relies only on its current state, independent of the past states. However, some practical industrial devices such as Li-ion batteries, ball bearings, turbofans, and blast furnace walls show degradations with long-range dependence(LRD), where the future degradation states depend on both the current and past degradation states. This type of degradation naturally brings two interesting problems, that is, how to model the degradations and how to predict their RULs. Recently, in contrast to the work that uses only BM, fractional brownian motion(FBM) is introduced to model practical degradations. The most important feature of the FBM-based degradation models is the ability to characterize the non-Markovian degradations with LRD. Although FBM is an extension of BM, it is neither a Markovian process nor a semimartingale. Therefore, how to obtain the first passage time of an FBM-based degradation process has become a challenging task. In this paper, a review of the transition of RUL prediction from BM to FBM is provided. The peculiarities of FBM when addressing the LRD inherent in some practical degradations are discussed. We first review the BM-based degradation models of the past few decades and then give details regarding the evolution of FBM-based research. Interestingly, the existing BM-based models scarcely consider the effect of LRD on the prediction of RULs. Two practical cases illustrate that the newly developed FBMbased models are more generalized and suitable for predicting RULs than the BM-based models, especially for degradations with LRD. Along with the direction of FBM-based RUL prediction, we also introduce some important and interesting problems that require further study.

关键词： remaining useful life degradation model brownian motion fractional brownian motion long-range dependence

Coupling effect of brownian motion and laminar shear flow on colloid coagulation:a brownian dynamics simulation study

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Chinese Physics B 2012年第5期21卷 364-371页

作者：徐升华孙祉伟李旭 Jin Tong Wang Key Laboratory of Microgravity Institute of Mechanics Chinese Academy of SciencesBeijing 100190China National Microgravity Laboratory Institute of MechanicsChinese Academy of SciencesBeijing 100190China Department of Physics Southern University and A&M CollegeBaton RougeLA 70813USA

Simultaneous orthokinetic and perikinetic coagulations（SOPCs） are studied for small and large Peclet numbers（P e） using brownian dynamics *** results demonstrate that the contributions of the brownian motion and the shear flow to the overall coagulation rate are basically not *** the early stages of coagulation with small Peclet numbers,the ratio of overall coagulation rate to the rate of pure perikinetic coagulation is proportional to P 1/2 e,while with high Peclet numbers,the ratio of overall coagulation rate to the rate of pure orthokinetic coagulation is proportional to P 1/2 ***,our results show that the aggregation rate generally changes with time for the SOPC,which is different from that for pure perikinetic and pure orthokinetic *** comparing the SOPC with pure perikinetic and pure orthokinetic coagulations,we show that the redistribution of particles due to brownian motion can play a very important role in the *** addition,the effects of redistribution in the directions perpendicular and parallel to the shear flow direction are *** perspective explains the behavior of coagulation due to the joint effects of the brownian motion（perikinetic） and the fluid motion（orthokinetic）.

关键词： simultaneous orthokinetic and perikinetic coagulation brownian motion shear flow,colloidal aggregation

Solution of Smoluchowski coagulation equation for brownian motion with TEMOM

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Particuology 2022年第11期70卷 64-71页

作者： Mingliang Xie Qing He State Key Laboratory of Coal Combustion Huazhong University of Science and TechnologyWuhan 430074China Guangdong Provincial Key Laboratory of Distributed Energy Systems School of Chemical Engineering and Energy TechnologyDongguan University of TechnologyDongguan 523808China

The particle number density in the Smoluchowski coagulation equation usually cannot be solved as a whole,and it can be decomposed into the following two functions by similarity transformation:one is a function of time(the particle k-th moments),and the other is a function of dimensionless volume(self-preserving size distribution).In this paper,a simple iterative direct numerical simulation(iDNS)is proposed to obtain the similarity solution of the Smoluchowski coagulation equation for brownian motion from the asymptotic solution of the k-th order moment,which has been solved with the Taylor-series expansion method of moment(TEMOM)in our previous *** convergence and accuracy of the numerical method are first verified by comparison with previous results about brownian coagulation in the literature,and then the method is extended to the field of brownian agglomeration over the entire size *** results show that the difference between the lognormal function and the self-preserving size distribution is ***,the thermodynamic constraint of the algebraic mean volume is also *** short,the asymptotic solution of the TEMOM and the self-preserving size distribution form a one-to-one mapping relationship;thus,a complete method to solve the Smoluchowski coagulation equation asymptotically is established.

关键词： Population balance equation Particle size distribution Moment method Similarity solution brownian motion

HITTING TIME AND PLACE TO A SPHERE OR SPHERICAL SHELL FOR brownian motion

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Chinese Annals of Mathematics,Series B 1999年第2期20卷 205-214页

作者： YINCHUANCUN WURONG DepartmentofMathematics QufuNormalUniversityQufu273165China DepartmentofMathematics NankaiUniversityTianjln300071tChina.

In this paper, the authors compute the explicit formulas for the joint distributions of thehitting time and place for a sphere or concentric spherical shell by brownian motion, when theprocess starts either outside th... 详细信息

关键词： brownian motion Hitting time Hitting place Spherical shell Sphere

A kinematic model describing particle movement near a surface as effected by brownian motion and electrostatic and Van der Waals forces

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Science China(Technological Sciences) 2014年第11期57卷 2144-2152页

作者： MEI HeGeng ZHAO DeWen WANG TongQin CHENG Jie LU XinChun State Key Laboratory of Tribology Tsinghua University

Nanoparticle movement near a surface is greatly influenced by electrostatic and Van der Waals forces between the particle and the surface,as well as by brownian *** this paper,several precise equations are derived to describe the Van der Waals and electrostatic forces between a particle and a surface when the particle is removed from the *** include an equation for particle displacement under the electrostatic force,and a numerical calculation for particle displacement under the Van der Waals ***,a kinematic model is constructed to describe the particle distribution under the effects of the electrostatic and Van der Waals forces,as well as the particle’s brownian *** results show that increasing the multiply of the particle and surface zeta potential values and decreasing the ionic strength of the detergent can prevent a particle from redepositing onto a surface.

关键词： zeta potential kinematic model distribution brownian motion Van der Waals force electrostatic force post-CMPcleaning

Supercritical branching brownian motion with catalytic branching at the origin

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Science China Mathematics 2020年第3期63卷 595-616页

作者： Li Wang Guowei Zong School of Sciences Beijing University of Chemical TechnologyBeijing 100029China School of Public Health Tianjin Medical UniversityTianjin 300070China

We consider a catalytic branching brownian motion with general branching which takes place only when particles are at the origin at a rate β>0 on the local time scale. We first establish a spine decomposition for the case wherein the particles have a positive probability of having no children. Then using this tool, we obtain results regarding the asymptotic behavior of the number of particles above λt at time t for λ>0. Under an L log L condition, we prove a strong law of large numbers for this catalytic branching brownian motion.

关键词： catalytic branching brownian motion L log L

EXIT DISTRIBUTION LEAVING A BALL FROM THE CENTER AND brownian motion

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Chinese Annals of Mathematics,Series B 2004年第3期25卷 393-400页

作者： ZHANGHUIZENG JINMENGWEI YINGJIANGANG DepartmentofMathematics ZhejiangUniversityHangzhou310027China InstituteofMathematics FudanUniversityShanghai200433Cina

It is skowed that if the first exit distribution leaving any ball from the center is theuniform distribution on the sphere, then the Levy process is a scaled brownian motion.The paper also gives a characterization of ... 详细信息

关键词： First exit hitting distribution brownian motion Levy process

First Passage Density of brownian motion with Two-sided Piecewise Linear Boundaries

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1505-1520页

作者： Zhen YU Mao Zai TIAN Center for Applied Statistics School of StatisticsRenmin University of ChinaBeijing 100872P.R.China School of Mathematics and Data Science Changji UniversityChangji 831100P.R.China

The first passage time has many applications in fields like finance,econometrics,statistics,and ***,explicit formulas for the first passage density have only been obtained for a few *** paper derives an explicit formula for the first passage density of brownian motion with twosided piecewise continuous boundaries which may have some points of *** are used to obtain a simplified formula for estimating the first passage ***,the results are also generalized to the case of two-sided general nonlinear *** can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density.

关键词： Boundary non-crossing probability first density passage density two-sided piecewise continuous boundaries brownian motion

AN ENLARGEMENT OF FILTRATION FOR brownian motion

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Acta Mathematica Scientia 2011年第5期31卷 1671-1678页

作者：胡耀忠 Department of Mathematics Donghua University Department of Mathematics University of Kansas Lawrence Kansas 66045-2142 U.S.A.

Let Bt be an Ft brownian motion and Gt be an enlargement of filtration of Ft from some Gaussian random variables. We obtain equations for ht such that Bt ht is a Gt-brownian motion.

关键词： brownian motion enlargement of filtration information flow