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Real-time reliability prediction for dynamic systems with both deteriorating and unreliable components

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Science in china(Series F) 2009年第11期52卷 2234-2246页

作者： XU ZhengGuo1,2. JI YinDong2.3 & ZHOU DongHua1,2. 1 department of Automation, tsinghua University,{2., china 2.tsinghua National Laboratory for Information Science and Technology, tsinghua University,{2., china 3 Research Institute of Information Technology (RIIT), tsinghua University,{2., china department of Automation Tsinghua University Beijing 100084 China tsinghua National Laboratory for Information Science and Technology Tsinghua University Beijing 100084 China Research Institute of Information Technology (RIIT) Tsinghua University Beijing 100084 China

As an important technology for predictive maintenance, failure prognosis has attracted more and more attentions in recent years. Real-time reliability prediction is one effective solution to failure prognosis. Considering a dynamic system that is composed of normal, deteriorating and unreliable components, this paper proposes an integrated approach to perform real-time reliability prediction for such a class of systems. For a deteriorating component, the degradation is modeled by a time-varying fault process which is a linear or approximately linear function of time. The behavior of an unreliable component is described by a random variable which has two possible values corresponding to the operating and malfunction conditions of this component. The whole proposed approach contains three algorithms. A modified interacting multiple model particle filter is adopted to estimate the dynamic system＇s state variables and the unmeasurable time-varying fault. An exponential smoothing algorithm named the Holt＇s method is used to predict the fault process. In the end, the system＇s reliability is predicted in real time by use of the Monte Carlo strategy. The proposed approach can effectively predict the impending failure of a dynamic system, which is verified by computer simulations based on a three-vessel water tank system.

关键词： reliability failure prognostics dynamic systems fault prediction particle filtering interacting multiple model exponential smoothing,predictive maintenance

Dimensions of a class of high-dimensional homogeneous Moran sets and Moran classes

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Progress in Natural Science:Materials International 2002年第9期12卷 17-22页

作者： YAN Ping(department of Mathematical Sciences, tsinghua University,{2., china) Tsing Hua Univ Dept Math Sci Beijing 100084 Peoples R China

A class of high-dimensional homogeneous Moran sets and Moran classes are introduced and some dimensional properties are studied. The Hausdorff dimension, modified lower box-counting dimension, lower and upper box-counting dimension, and packing dimension of high-dimensional homogeneous and partial homogeneous Cantor sets are determined. Moreover, a kind of fractal E is obtained, which is not regular but with the property Dimw(Ed) = dDimw(E), where w denotes any of the dimensions mentioned above.

关键词： Moran set Moran class homogeneous Cantor set partial homogeneous Cantor set dimension.

Γ-CONVERGENCE OF INTEGRAL FUNCTIONALS DEPENDING ON VECTOR-VALUED FUNCTIONS OVER PARABOLIC DOMAINS

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Chinese Annals of Mathematics,Series B 2000年第2期21卷 249-258页

作者： JIAN HUAIYU(department of Mathematical Sciences, tsinghua University,{2., china.) department of Mathematical Sciences Tsinghua University Beijing 100084 China

This paper studies Γ-convergence for a sequence of parabolic functionals, where the integrand f is nonconvex, and periodic on the first variable. The author obtains the representation formula of the Γ-limit. The results in this paper support a conclusion which relates Γ-convergence of parabolic functionals to the associated gradiend flows and confirms one of De Giorgi’s conjectures partially.

关键词： Γ-convergence Parabolic-minima Nonconvex functionals Parabolic equations

Effects of Si Content and the Addition Amount of Al-3B Master Alloy on the Solidification Structures of Hypoeutectic Al-Si Alloys

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Rare Metals 2001年第3期20卷 168-173页

作者： Donghui Wang,Jianguo Li, Yankang Zheng, Bingzhe Bai department of Materials Science and engineering, {2. University, beijing 100084, china Tsing Hua Univ Dept Mat Sci & Engn Beijing 100084 Peoples R China

Effects of Si content and the addition amount of Al-3B master alloy on the solidification structures of hypoeutectic Al-Si alloys were studied. The addition amounts of the master alloy were 0.2., 0.4%, 0.7% and 1% (mass fraction, so as the follows), respectively. The Si content of Al-Si binary alloys investigated varied from 1% to 11%. The observation of macrostructures of non-refined samples showed that 3% Si constitutes a transition point at which the minimum grain size can be obtained. It was also found that Al-3B master alloy can shift the transition point towards a higher Si value when its addition amount increases, making this point appear at 4%, 5% and 6% Si as its addition amount increases up to 0.4%, 0.7% and 1%, respectively.

关键词： Al-3B master alloy hypoeutectic Al-Si alloy grain refinement

EXACT NONREFLECTING BOUNDARY CONDITIONS FOR AN ACOUSTIC PROBLEM IN THREE DIMENSIONS

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Journal of Computational Mathematics 2003年第1期21卷 15-24页

作者： Houde Han Chunxiong Zheng (department of Mathematical Sciences, tsinghua University,{2., china) department of Mathematical Sciences Tsinghua University 北京 100084

In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, three kinds of equivalent exact artificial boundary conditions are obtained on a spherical artificial boundary. A numerical test is presented to show the performance of the method.

关键词： Exterior problem Nonreflecting artificial boundary condition Acoustic equa-tion Three-dimensions.

Effect of Coarse Aggregate Size on Relationship between Stress and Crack Opening in Normal and High Strength Concretes

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Journal of Materials Science & Technology 2005年第5期21卷 85-94页

作者： Jun ZHANG Qian LIU and Lin WANGDepaxtment of Civil engineering, tsinghua University,{2., china department of Civil engineering Tsinghua University Beijing 100084 China

Fine and coarse aggregates play an important role in the fracture of concrete. However, quantitative informationavailable on the effect of the coarse aggregate size on the fracture properties of concrete is still limited. In the presentpaper, the effect of coarse aggregate size (single grade of 5~10, 10~16, 16~2. and 2.~2. mm) on stress-crackopening (σ-ω) relation in normal and high strength concretes (compressive strength of 40 and 80 MPa, respectively)was studied. The investigation was based on three-point bending tests implemented by fictitious crack analysis. Theresult shows that coarse aggregate size and cement matrix strength significantly influence the shape of σ-ω *** a given total aggregate content, in normal strength concrete, smaller size of aggregate leads to a high tensilestrength and a sharp stress drop after the peak stress. The smaller the coarse aggregate, the steeper the σ-ω *** contrast, in high strength concrete, the effect of aggregate size on σ-ω relation almost vanishes. A similar σ-ωrelation is obtained for the concrete except for the case of 2.~2. mm coarse aggregate size. The stress drop afterthe peak stress is more significant for high strength concrete than that for normal strength concrete. Meanwhile, thesmaller the coarse aggregate size, the higher the flexural strength. Fracture energy and characteristic length increasewith increasing coarse aggregate size in both normal and high strength concretes.

关键词： Aggregate size Stress-crack opening relation Fracture energy Bending test

THE GLOBAL ARTIFICIAL BOUNDARY CONDITIONS FOR NUMERICAL SIMULATIONS OF THE 3D FLOW AROUND A SUBMERGED BODY

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Journal of Computational Mathematics 2003年第4期21卷 435-450页

作者： Hou-de Han Xin Wen (department of Mathematical Sciences, tsinghua University,{2., china) department of Mathematical Sciences Tsinghua University Beijing 100084 China

We consider the numerical approximations of the three-dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface in a channel. One vertical side is introduced as the upstream artificial boundary and two vertical sides are introduced as the downstream artificial boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the original problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. After solving the variational problem by the finite element method, we obtain the numerical approximation of the original problem. The numerical examples show that the artificial boundary conditions given in this paper are very effective.

关键词： Ship wave Potential flow Global artificial boundary condition Finite element method.

Extremal eigenvalues of measure differential equations with fixed variation

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Science china Mathematics 2010年第10期53卷 2573-2588页

作者： ZHANG MeiRong 1,2.1 department of Mathematical Sciences,tsinghua University,{2. 100084,china 2.Zhou Pei-Yuan Center for Applied Mathematics,tsinghua University,{2. 100084,china 1. department of Mathematical Sciences Tsinghua University Beijing 100084 China2. Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing 100084 China

In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely *** taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth *** results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.

关键词： measure differential equation eigenvalue extremal value weak* topology Frechét derivative sub-differential

Experimental study on bed-load sediment transport under irregular wave and current combined flow

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Acta Oceanologica Sinica 2001年第2期20卷 271-280页

作者： Wu Yongsheng,Qin Chongren (1. department of Hydraulic engineering, {2. University, beijing 100084, china 2. School of Civil engineering, Tianjin University, Tianjin 300072. china) department of Hydraulic engineering Tsinghua University Beijing 100084 China

Using an irregularly oscillating tray and flume, a series of experiments are completed to evaluate bed-load sediment transport rate under irregular wave -current coexistent field. Testing conditions include three interaction angles 0', 45', 90' and two kinds of median sizes (0.38 and 1.10 mm). The results of transport rate show that the net sediment transport rate can be expressed approximately as the function of the maximum bottom shear stress of waves, mean shear stress of current and the grain size.

关键词： Irregular wave-current bed-load transport rate