两部件组成的系统的可靠度的置信下限

设系统由两令部件组成，两个部件的寿命均服从指数分布．本文利用样本空间排序法，针对各部件获得定总时有替换的寿命试验数据，给出了系统可靠度的精确置信下限及其有效的计算方法．     

独立维修两部件并联系统可靠性的进一步分析

本文考虑了具有独立维修规则的两个不同型部件并联系统的可靠性问题，在一个部件的寿命为指数分布，维修分布为Ｅｒｌａｕｇ分布，另一个部件的寿命和维修分布均为一般连续型分布的条件下，我们得到了并系统的主要可靠性指标。     

系统最佳维修策略研究

一个复杂系统通常由多个不同部件组成，考虑到这些部件有各自不同的失效率及维修时间，本提出了一种新的维修策略模型，该模型考虑了不同部件的差异性及对系统的不同重要性，在一定可用度要求下，使系统总平均费用达到最小的最佳预防维修周期，并给出了相应的仿真算法。     

修理工可多重休假的n部件串联可修系统可靠性分析

本文把修理工多重休假的概念引入ｎ部件串联可修系统。假定休假时间和每个部件的修理时间为一般连续型随机变量，每个部件的失效分布为负指数分布。利用向量Ｍａｒｋｏｖ过程方法，求出了该系统的可靠性指标。     

考虑多失效行为的平衡系统可靠性建模与计算

平衡系统的可靠性建模与相关指标计算是可靠性理论与工程领域的研究热点之一。针对由多部件构成的串联平衡系统,假设每个部件受环境冲击影响逐渐退化,呈现出多种状态;系统的性能平衡取决于部件的状态及其排列位置,即当系统中退化程度超过某一阈值的部件分布在某一特定区域时,系统失去性能平衡。考虑单部件失效导致系统失效和三类系统性能失衡导致系统失效四类失效行为,构建了考虑多失效行为的平衡系统可靠性模型。运用有限马尔可夫链嵌入法推导了部件的相关概率指标以及系统可靠度。最后以液压支架系统为例,验证了所提出模型与方法的有效性。     

一种新型的N部件串联可修系统及其可靠性分析

本文研究一种Ⅳ部件串联可修系统的一个新模型，该模型在经典。部件串联可修系统中引入了修理工可多重延误休假的概念，并且考虑了修理工使用修理设备在修理失效部件过程中可能因修理设备失效而立即更换修理设备对整个系统可靠性造成的影响,假定修理工的延误休假时间、部件的寿命和修理设备的寿命均服从指数分布，部件的修理时间、修理设备的更换时间和修理工的休假时间均服从一般连续型分布，通过使用补充变量法和广义马尔可夫过程方法得到了系统和修理设备的一些重要可靠性指标．     

非平方损失函数下Gamma部件可靠性的Bayes估计

Lwin和Singh对部件寿命x服从Г(t,λ,k)分布,当形状参数k已知,尺度参数未知时对部件可靠性进行Bayes估计。考虑到实际问题的需要,对损失函数应加上测度不变性的要求,本文取损失函数在参数λ的先验分布分别为指数Beta分布和Gamma分布的情况下,讨论了Gamma部件各项可靠性指标的Bayes估计,且把Lwin和Singh所做的结果看作本文的特例。设部件的寿命x服从其中:t>0,λ>0,k>0为已知的形状参数,尺度参数λ未知。那么部件的可靠度函数与平均寿命分别为:     

自保护相依多部件系统的预防维修建模及策略优化

自保护技术作为自愈技术的一种,能够使系统在环境或工况条件变化的干扰下以较高可靠性运行。本文构建了一个新的具有相依主要部件和辅助部件的系统可靠性模型,其中主要部件的退化速率与工作中的辅助部件的数量有关。此外,基于定期检测和预防维修策略,本文利用半再生过程技术求解了系统的长期运行平均成本,并以长期运行平均成本最小化为目标给出了系统的最优预防维修策略。最后,以镗刀系统为例,利用所提方法给出了预防更换阈值和检测周期的最优值,以期望为实际维修行为决策提供理论参考。     

具有P1优先使用权和P2优先修理权的一般两部件冷储备系统分析

本文研究两个不同型件和一个修理工组成的冷储备系统。在两部件的寿命和修理时间分布皆为一般连续型分布，部件１具有Ｐ１优先使用权和Ｐ２优先修理权的假定下，利用向量马氏过程理论和方法，导出了系统可靠性和可用性指标的明显表达式     

1200℃高温环境下部件受热前表面应变的光学测量

在大气层内飞行的高超声速飞行器外表面因气动加热处于极为恶劣的高温环境中.而气动热模拟试验中,飞行器部件受热前表面在高温环境下的变形测量非常重要且十分困难.通过建立水冷式高超声速飞行器部件受热前表面应变测量系统,结合数字图像相关方法,实现了有氧环境下耐高温Al_2O_3陶瓷材料受热前表面温度高至1 200℃的应变测量.为了验证试验结果的正确性,与Hillman给出的Al_2O_3材料热膨胀系数-温度关系式进行了对比,具有良好的吻合性.所建立的1 200℃高温应变测试系统及氧化环境下部件受热前表面应变测试方法,为高超声速飞行器受热部件的热强度分析及安全可靠性设计提供了非常重要的试验测试手段.     

On the Rate of Convergence of Projection-Difference Methods for Smoothly Solvable Parabolic Equations

A linear parabolic problem in a separable Hilbert space is solved approximately by the projection-difference method. The problem is discretized in space by the Galerkin method orientated towards finite-dimensional subspaces of finite-element type and in time by using the implicit Euler method and the modified Crank-Nicolson scheme. We establish uniform (with respect to the time grid) and mean-square (in space) error estimates for the approximate solutions. These estimates characterize the rate of convergence of errors to zero with respect to both the time and space variables.     

A multilevel characteristics method for periodic convection‐dominated diffusion problems

In this article we introduce a multilevel method in space and time for the approximation of a convection‐diffusion equation. The spatial discretization is of pseudo‐spectral Fourier type, while the time discretization relies on the characteristics method. The approximate solution is obtained as the sum of two components that are advanced in time using different time‐steps. In particular, this requires the introduction of two sets of discretized characteristics curves and of two interpolation operators. We investigate the stability of the scheme and derive some error estimates. They indicate that the high‐frequency term can be integrated with a larger time‐step. Numerical experiments illustrate the gain in computing time due to the multilevel strategy. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 107–132, 2000     

Convergence of a finite volume scheme for coagulation-fragmentation equations

This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation. A time explicit finite volume scheme is developed, based on a conservative formulation of the equation. It is shown to converge under a stability condition on the time step, while a first order rate of convergence is established and an explicit error estimate is given. Finally, several numerical simulations are performed to investigate the gelation phenomenon and the long time behavior of the solution.

     

Complexity of the Gravitational Method for Linear Programming

In the gravitational method for linear programming, a particle is dropped from an interior point of the polyhedron and is allowed to move under the influence of a gravitational field parallel to the objective function direction. Once the particle falls onto the boundary of the polyhedron, its subsequent motion is constrained to be on the surface of the polyhedron with the particle moving along the steepest-descent feasible direction at any instant. Since an optimal vertex minimizes the gravitational potential, computing the trajectory of the particle yields an optimal solution to the linear program.Since the particle is not constrained to move along the edges of the polyhedron, as the simplex method does, the gravitational method seemed to have the promise of being theoretically more efficient than the simplex method. In this paper, we first show that, if the particle has zero diameter, then the worst-case time complexity of the gravitational method is exponential in the size of the input linear program. As a simple corollary of the preceding result, it follows that, even when the particle has a fixed nonzero diameter, the gravitational method has exponential time complexity. The complexity of the version of the gravitational method in which the particle diameter decreases as the algorithm progresses remains an open question.     

A NEW INVERSION METHOD OF TIME-LAPSE SEISMIC

Time-Lapse Seismic improves oil recovery ratio by dynamic reservoir monitoring. Because of the large number of seismic explorations in the process of time-lapse seismic inversion, traditional methods need plenty of inversion calculations which cost high computational works. The method is therefore inefficient. In this paper, in order to reduce the repeating computations in traditional, a new time-lapse seismic inversion method is put forward. Firstly a homotopy-regularization method is proposed for the first time inversion. Secondly, with the first time inversion results as the initial value of following model, a model of the second time inversion is rebuilt by analyzing the characters of time-lapse seismic and localized inversion method is designed by using the model. Finally, through simulation, the comparison between traditional method and the new scheme is given. Our simulation results show that the new scheme could save the algorithm computations greatly.     

Implicit Solution of Hyperbolic Equations with Space-Time Adaptivity

Adaptivity in space and time is introduced to control the error in the numerical solution of hyperbolic partial differential equations. The equations are discretised by a finite volume method in space and an implicit linear multistep method in time. The computational grid is refined in blocks. At the boundaries of the blocks, there may be jumps in the step size. Special treatment is needed there to ensure second order accuracy and stability. The local truncation error of the discretisation is estimated and is controlled by changing the step size and the time step. The global error is obtained by integration of the error equations. In the implicit scheme, the system of linear equations at each time step is solved iteratively by the GMRES method. Numerical examples executed on a parallel computer illustrate the method.     

The method of fundamental solutions with eigenfunction expansion method for nonhomogeneous diffusion equation

In this article we describe a numerical method to solve a nonhomogeneous diffusion equation with arbitrary geometry by combining the method of fundamental solutions (MFS), the method of particular solutions (MPS), and the eigenfunction expansion method (EEM). This forms a meshless numerical scheme of the MFS‐MPS‐EEM model to solve nonhomogeneous diffusion equations with time‐independent source terms and boundary conditions for any time and any shape. Nonhomogeneous diffusion equation with complex domain can be separated into a Poisson equation and a homogeneous diffusion equation using this model. The Poisson equation is solved by the MFS‐MPS model, in which the compactly supported radial basis functions are adopted for the MPS. On the other hand, utilizing the EEM the diffusion equation is first translated to a Helmholtz equation, which is then solved by the MFS together with the technique of the singular value decomposition (SVD). Since the present meshless method does not need mesh generation, nodal connectivity, or numerical integration, the computational effort and memory storage required are minimal as compared with other numerical schemes. Test results for two 2D diffusion problems show good comparability with the analytical solutions. The proposed algorithm is then extended to solve a problem with irregular domain and the results compare very well with solutions of a finite element scheme. Therefore, the present scheme has been proved to be very promising as a meshfree numerical method to solve nonhomogeneous diffusion equations with time‐independent source terms of any time frame, and for any arbitrary geometry. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Error Estimates for Finite Element Approximations of a Viscous Wave Equation

We consider a family of fully discrete finite element schemes for solving a viscous wave equation, where the time integration is based on the Newmark method. A rigorous stability analysis based on the energy method is developed. Optimal error estimates in both time and space are obtained. For sufficiently smooth solutions, it is demonstrated that the maximal error in the L ²-norm over a finite time interval converges optimally as O(h ^p+1 + Δt ^s ), where p denotes the polynomial degree, s = 1 or 2, h the mesh size, and Δt the time step.     

Long-time Convergence of Fully Discrete Nonlinear Galerkin Method——Case of Finite-elements

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The method of approximate particular solutions to simulate an anomalous mobile-immobile transport process

In the current work, a generalized mathematical model based on the Coimbra time fractional derivative of variable order, which describes an anomalous mobile-immobile transport process in complex systems is investigated numerically. A robust numerical technique based on the meshfree strong form method combined with an efficient time-stepping scheme is performed to compute the approximate solution of the problem with high accuracy. For this purpose, firstly, an effective implicit time discretization approach is used for discretizing the variable-order time fractional problem in the time direction. Then a global meshless technique based on the method of approximate particular solutions is performed to fully discretize the model in the spatial domain. The validity and performance of the procedure to numerically simulate the proposed generalized solute transport model on regular and irregular domains are demonstrated through some numerical examples.