Numerical method for Weibull generalized renewal process and its applications in reliability analysis of NC machine tools

In generalized renewal process (GRP) reliability analysis for repairable systems, Monte Carlo (MC) simulation method instead of numerical method is often used to estimate model parameters because of the complexity and the difficulty of developing a mathematically tractable probabilistic model. In this paper, based on the conditional Weibull distribution for repairable systems, using negative log-likelihood as an objective function and adding inequality constraints to model parameters, a nonlinear programming approach is proposed to estimate restoration factor for the Kijima type GRP model I, as well as the model II. This method minimizes the negative log-likelihood directly, and avoids solving the complex system of equations. Three real and different types of field failure data sets with time truncation for NC machine tools are analyzed by the proposed numerical method. The sampling formulas of failure times for the GRP models I and II are derived and the effectiveness of the proposed method is validated with MC simulation method. The results show that the GRP model is superior to the ordinary renewal process (ORP) and the power law non-homogeneous Poisson process (PL-NHPP) model.     

Dirichlet Gaussian mixture model: Application to image segmentation

Gaussian mixture model based on the Dirichlet distribution (Dirichlet Gaussian mixture model) has recently received great attention for modeling and processing data. This paper studies the new Dirichlet Gaussian mixture model for image segmentation. First, we propose a new way to incorporate the local spatial information between neighboring pixels based on the Dirichlet distribution. The main advantage is its simplicity, ease of implementation and fast computational speed. Secondly, existing Dirichlet Gaussian model uses complex log-likelihood function and require many parameters that are difficult to estimate. The total parameters in the proposed model lesser and the log-likelihood function have a simpler form. Finally, to estimate the parameters of the proposed Dirichlet Gaussian mixture model, a gradient method is adopted to minimize the negative log-likelihood function. Numerical experiments are conducted using the proposed model on various synthetic, natural and color images. We demonstrate through extensive simulations that the proposed model is superior to other algorithms based on the model-based techniques for image segmentation.     

可修复系统事后维修可靠性仿真

指出了Markov方法和Monte-Carlo方法在可修复系统可靠性仿真中存在的问题,并提出了一种新的方法,称为RSS方法,从理论上系统地阐述了RSS方法的基本原理及算法过程,并在理论上验证了其正确性.利用RSS方法可以对事后维修可修复元件和系统的可靠性进行仿真.RSS方法不受系统元件寿命分布类型限制,计算量小,仿真时间短,精度高,仿真结果具有确定性,弥补了Markov方法和Monte-Carlo方法的不足,具有实际可靠性工程应用价值.给出了并联和串联可修复系统事后维修可靠性仿真实例.     

Evaluating Unavailability of a Repairable System Consisting of Components with Significantly Different Reliabilities

A new fast simulation method is proposed for evaluation of unavailability of a repairable system. Its idea is to order failure trajectories according to their ranks that promotes rational experiment organization. The estimates are unbiased and possess a bounded coefficient of variation. A numerical example is considered.     

Optimizing discrete stochastic systems using simulated annealing and simulation

The objective of this paper is to present an integrated approach of two models: simulation and optimization. This approach is used to determine the design parameters of stochastically constrained systems where the measure of performance is available only via simulation. The optimization model is solved using simulated annealing (SA) for parameter selection followed by the use of Monte Carlo simulation to evaluate the measure of performance. Based on the expected simulation output, the parameter set is either accepted or rejected. A modified rejection/acceptance criterion is presented for the proposed SA algorithm taking into consideration the stochastic system constraints. Moreover, a control variate is employed as a variance reduction technique in order to obtain an efficient estimate of performance measure. The proposed approach is tested using three real cases of the multi-echelon repairable item inventory systems (MERIIS). The results show that the proposed method is efficient in determining an optimal choice of spares and repair channels in these systems.     

控制系统动态马尔可夫过程可靠性分析

针对特定试验条件下小子样控制系统可靠性评定的特点,引入故障率分析,介绍了基于马尔可夫过程可维修控制系统的可靠性分析方法,推导了n个部件组成的串联可维修系统可用度的表达式,并针对具体工程用控制系统进行了可用度仿真计算。最后借助可靠性分析软件验证了该方法的合理性。两种方法结论一致,为其他结构可修系统的可靠性分析提供了重要的理论依据。     

GSA-based maximum likelihood estimation for threshold vector error correction model

The log-likelihood function of threshold vector error correction models is neither differentiable, nor smooth with respect to some parameters. Therefore, it is very difficult to implement maximum likelihood estimation (MLE) of the model. A new estimation method, which is based on a hybrid algorithm and MLE, is proposed to resolve this problem. The hybrid algorithm, referred to as genetic-simulated annealing, not only inherits aspects of genetic-algorithms (GAs), but also avoids premature convergence by incorporating elements of simulated annealing (SA). Simulation experiments demonstrate that the proposed method allows to estimate the parameters of larger cointegrating systems. Additionally, numerical results show that the hybrid algorithm does a better job than either SA or GA alone.     

考虑执行器性能退化的控制系统剩余寿命预测方法

工程控制系统在运行过程中，由于内外部应力的综合作用以及外部环境等的影响，其部件性能将逐渐退化，最终会导致控制系统失效.然而，由于控制系统中闭环反馈的作用，系统的输出残差可能仍在较小范围内变动，使得早期性能退化这种微小故障难以被检测到，呈现隐含退化的特点.现有文献中，针对此类在闭环反馈控制作用下部件存在隐含退化过程的控制系统剩余寿命（Remaining useful lifetime，RUL）预测问题，鲜有研究.为此，本文针对一类仅考虑执行器性能退化的确定闭环控制系统，提出一种基于解析模型的剩余寿命预测方法.该方法首先基于权值优选粒子滤波算法，利用系统的监测数据在线估计出执行器的隐含退化量，然后在每一个预测时刻通过蒙特卡洛（Monte Carlo，MC）仿真计算得到合理的失效阈值，建立基于该失效阈值的系统失效判断准则，最后将隐含退化量的估计值代入退化模型中外推出剩余寿命分布.惯性平台稳定回路控制系统的仿真实验结果验证了该方法的可行性、有效性.     

一类可修非周期Fork-Join排队网络分析

研究一类排队空间有限且服务台可修的非周期Fork-Join排队网络,给出求解稳态 概率的直接法和等效法,并计算一些排队指标和可修指标(如稳态队长、服务台的可用度和服 务台的失效概率),最后通过仿真验证其正确性.     

基于随机系数回归模型的退化过程及维修策略

随机系数回归模型是一种描述设备退化过程的重要模型.在基本随机回归系数模型的基础上,运用加速失效时间模型,加入协变量的影响,对设备的退化过程进行建模分析.针对退化过程设置两类更新阈值,一类是预防性维修更新阈值,一类是故障更新阈值.当设备的运行状态被监测到达到或超过预防性更新阈值时,设备将被预防性维修更新,一个预防性更新周期完成;当设备的运行状态被监测到达到故障阈值时,设备将被故障更新,一个故障更新周期完成.运用更新回报定理,对两类更新周期内的单位时间期望维修费用建立模型,对模型求解可得设备的最优监测区间和最优预防性维修阈值.为进一步对所建立的模型进行验证,设计仿真过程求解最优值,并运用数值案例对所建立的模型和仿真过程进行计算.     

A computational and experimental analysis of the buckling,postbuckling and initial failure of pultruded GRP columns

A two-dimensional finite element (FE) model was developed and nonlinear FE analyses were carried out, using the ANSYS software, to predict the buckling, postbuckling and initial failure loads of pultruded glass reinforced plastic (GRP) wide flange (WF) columns. Phenomenological failure criteria were proposed to predict failure initiation at the web-flange junctions of pultruded GRP WF columns, whereas the Tsai–Wu failure criterion was used for the web and flanges. Initial failure analysis was carried out with reasonable success as a post-processing operation on the nonlinear analysis results. The numerical predictions of the buckling, postbuckling and initial failure loads of pultruded GRP WF columns were in reasonably good agreement with the experimental results.     

基于复杂模拟的战斗机系统失效敏感性分析

战斗机的系统试验往往成本较高，随着战斗机系统的日益复杂化，基于计算机模拟的表征系统失效信息的功能响应量计算也越来越耗时费力。针对此类基于复杂计算机模拟的敏感性分析问题，提出了一种结合Sobol方法和基于主动学习的Kriging模型的敏感性分析方法，称之为AK-S（Adaptive-Kriging-based Sobol）方法，AK-S方法通过Kriging预测来代替真实响应值计算，因而可以更加高效地计算各输入变量的敏感性指标并得到重要度排序。通过与直接蒙特卡洛法（直接法，MC）和传统Sobol法对数值算例的处理结果进行对比，AK-S方法的计算效率和精度得到了证明。最后，AK-S方法被应用于基于复杂模拟的实际工程案例的失效敏感性分析，并获得了敏感性指标。AK-S算法被证明在同等计算精度的条件下，其效率大大高于MC和传统Sobol法，能很好地解决工程中基于复杂计算机模拟下的失效敏感性分析问题。     

磨矿粒度动态过程的一种快速Monte Carlo仿真方法

磨矿是降低矿物粒度的工业过程,产品粒度是磨矿过程的关键质量指标. 由于磨矿粒度难以在线检测且磨矿生产过程具有综合复杂特性,难以采用传统控制方法实现磨矿粒度的控制. 因此,建立磨矿粒度和关键工艺参数的动态模型对于磨矿运行控制和优化具有重要意义. 采用总量平衡原理获得磨矿粒度的微分方程模型多数情况下无法获得解析解. 而基于Monte Carlo （MC）方法的磨矿粒度模型能够精确模拟磨矿粒度分布的动态变化,但是其仿真效率低难以实用. 本文针对这一问题提出一种新的MC仿真方法: 在定总量方法的基础上引入新的颗粒移除机制,在移除过程中动态地分配各个粒级颗粒数目并保持破裂前后各个粒级颗粒所占总颗粒数的百分比不变,避免颗粒移除过程中由于粒级差异导致的抽样误差,且避免MC仿真速度随着仿真推进下降的问题. 仿真实验验证表明,本方法能够在保证一定精度前提下显著提高磨矿粒度MC仿真的计算速度. 最后,通过一个实例介绍了本文仿真模型在磨矿优化控制中的应用.     

Approximating probability distribution of circuit performance function for parametric yield estimation using transferable belief model

This paper applies the transferable belief model （TBM） interpretation of the Dempster-Shafer theory of evidence to approximate distribution of circuit performance function for parametric yield estimation. Treating input parameters of performance function as credal variables defined on a continuous frame of real numbers, the suggested approach constructs a random set-type evidence for these parameters. The corresponding random set of the function output is obtained by extension principle of random set. Within the TBM framework, the random set of the function output in the credal state can be transformed to a pignistic state where it is represented by the pignistic cumulative distribution. As an approximation to the actual cumulative distribution, it can be used to estimate yield according to circuit response specifications. The advantage of the proposed method over Monte Carlo （MC） methods lies in its ability to implement just once simulation process to obtain an available approximate value of yield which has a deterministic estimation error. Given the same error, the new method needs less number of calculations than MC methods. A track circuit of high-speed railway and a numerical eight-dimensional quadratic function examples are included to demonstrate the efficiency of this technique.     

A computationally efficient technique for transient analysis of repairable Markovian systems

A technique to design efficient methods using a combination of explicit (non-stiff) and implicit (stiff) ODE methods for numerical transient analysis of repairable Markovian systems is proposed. Repairable systems give rise to stiff Markov chains due to extreme disparity between failure rates and repair rates. Our approach is based on the observation that stiff Markov chains are non-stiff for an initial phase of the solution interval. A non-stiff ODE method is used to solve the model for this phase and a stiff ODE method is used to solve the model for the rest of the duration until the end of solution interval. A formal criterion to determine the length of the non-stiff phase is described. A significant outcome of this approach is that the accuracy requirement automatically becomes a part of model stiffness. Two specific methods based on this approach have been implemented. Both the methods use the Runge-Kutta-Fehlberg method as the non-stiff method. One uses the TR-BDF2 method as the stiff method while the other uses an implicit Runge-Kutta method as the stiff method. Numerical results obtained from solving dependability models of a multiprocessor system and an interconnection network are presented. These results show that the methods obtained using this approach are much more efficient than the corresponding stiff methods which have been proposed to solve stiff Markov models.     

A bias-corrected estimator for nonlinear systems with output-error type model structures

Parametric identification of linear time-invariant (LTI) systems with output-error (OE) type of noise model structures has a well-established theoretical framework. Different algorithms, like instrumental-variables based approaches or prediction error methods (PEMs), have been proposed in the literature to compute a consistent parameter estimate for linear OE systems. Although the prediction error method provides a consistent parameter estimate also for nonlinear output-error (NOE) systems, it requires to compute the solution of a nonconvex optimization problem. Therefore, an accurate initialization of the numerical optimization algorithms is required, otherwise they may get stuck in a local minimum and, as a consequence, the computed estimate of the system might not be accurate. In this paper, we propose an approach to obtain, in a computationally efficient fashion, a consistent parameter estimate for output-error systems with polynomial nonlinearities. The performance of the method is demonstrated through a simulation example.     

Determining optimal warranty periods from the seller's perspective and optimal out-of-warranty replacement age from the buyer's perspective

This paper considers a general repairable product sold under a failure-free renewing warranty agreement. In the case of a general repair model, there can be two types of failure: Type I failure (a minor failure), which can be rectified by minimal repairs; and type II failure (a catastrophic failure), which can be rectified only by replacement. After a minimal repair, the product is operational but the failure rate of the product remains unchanged. The aim of this paper is to determine the optimal warranty period and the optimal out-of-warranty replacement age, from the perspective of the seller (manufacturer) and the buyer (consumer), respectively, while minimizing the corresponding cost functions. We prove under mild conditions, that the optimal solution of minimizing the cost function exists and is finite. Further, a concise numerical example is demonstrated, and the sensitivity analysis of some of the parameters related to costs is carried out as well. Finally, some practical aspects of renewing the warranty policy for the practitioner and reader are addressed.     

水平门限同积模型参数的拟极大似然估计

提出了用于非平稳非线性时间序列建模的水平门限同积模型,给出了模型参数的拟极大似然估计,由于对门限参数和同积向量似然函数既不可微也不光滑,不能直接运用传统的极大似然估计．因此首先利用遗传模拟退火算法估计门限参数和同积向量,然后用极大似然估计计算其余的参数,仿真结果表明,拟极大似然估计不受模型维数限制具有有效性和可行性,此外,数值计算结果的比较分析表明遗传模拟退火优于传统的遗传算法、模拟退火和随机搜索等优化算法．     

Spike-frequency adapting neural ensembles: beyond mean adaptation and renewal theories

We propose a Markov process model for spike-frequency adapting neural ensembles that synthesizes existing mean-adaptation approaches, population density methods, and inhomogeneous renewal theory, resulting in a unified and tractable framework that goes beyond renewal and mean-adaptation theories by accounting for correlations between subsequent interspike intervals. A method for efficiently generating inhomogeneous realizations of the proposed Markov process is given, numerical methods for solving the population equation are presented, and an expression for the first-order interspike interval correlation is derived. Further, we show that the full five-dimensional master equation for a conductance-based integrate-and-fire neuron with spike-frequency adaptation and a relative refractory mechanism driven by Poisson spike trains can be reduced to a two-dimensional generalization of the proposed Markov process by an adiabatic elimination of fast variables. For static and dynamic stimulation, negative serial interspike interval correlations and transient population responses, respectively, of Monte Carlo simulations of the full five-dimensional system can be accurately described by the proposed two-dimensional Markov process.     

Failure mode and effects analysis using D numbers and grey relational projection method

Failure mode and effects analysis (FMEA) is a widely used risk assessment tool for defining, identifying and eliminating potential failures or problems in products, process, designs and services. Two critical issues of FMEA are the representation and handling of various types of assessments and the determination of risk priorities of failure modes. Many different approaches have been suggested to enhance the performance of traditional FMEA; however, deficiencies exist in these approaches. In this paper, based on a more effective representation of uncertain information, called D numbers, and an improved grey relational analysis method, grey relational projection (GRP), a new risk priority model is proposed for the risk evaluation in FMEA. In the proposed model, the assessment results of risk factors given by FMEA team members are expressed and modeled by D numbers. The GRP method is used to determine the risk priority order of the failure modes that have been identified. Finally, an illustrative case is provided to demonstrate the effectiveness and practicality of the proposed model.