Structural Strength Degradation Model Based on Non-stationary Gamma Process

Strength degradation is a stochastic and irreversible process.Gamma process is an independent nonnegative increment process which can be used to describe the characteristics of strength degradation.It is unreasonable to choose a linear function to describe the strength degradation trend considering that the degradation rate may change over time.So,a non-linear power law is proposed to describe the strength degradation trend based on preliminary work.It is more general compared with the linear one and the inadequacy of strict linear assumption is overcome.Then,the model parameters of non-stationary Gamma process are estimated based on the maximum likelihood method.Finally,it is proved that the non-stationary Gamma process can accurately reflect the strength degradation law through comparative analysis of a real example.

Valuation of European and American Options under Variance Gamma Process

Geometric Brownian Motion (GBM) is widely used to model the asset price dynamics. Option price models such as the Black-Sholes and the binomial tree models rely on the assumption that the underlying asset price dynamics follow the GBM. Modeling the asset price dynamics by using the GBM implies that the log return of assets at particular time is normally distributed. Many studies on real data in the markets showed that the GBM fails to capture the characteristic features of asset price dynamics that exhibit heavy tails and excess kurtosis. In our study, a class of Levy process, which is called a variance gamma (VG) process, performs much better than GBM model for modeling the dynamics of those stock indices. However, valuation of financial instruments, e.g. options, under the VG process has not been well developed. Here, we propose a new approach to the valuation of European option. It is based on the conditional distribution of the VG process. We also apply the path simulation model to value American options by assuming the underlying asset log return follow the VG process. Such a model is similar with that proposed by Tiley [1]. Simulation study shows that the proposed method performs well in term of the option price.

Condition-based Maintenance Optimization for Gamma Deteriorating Systems under Performance-based Contracting

With the further development of service-oriented,performance-based contracting(PBC)has been widely adopted in industry and manufacturing.However,maintenance optimization problems under PBC have not received enough attention.To further extend the scope of PBC’s application in the field of maintenance optimization,we investigate the condition-based maintenance(CBM)optimization for gamma deteriorating systems under PBC.Considering the repairable single-component system subject to the gamma degradation process,this paper proposes a CBM optimization model to maximize the profit and improve system performance at a relatively low cost under PBC.In the proposed CBM model,the first inspection interval has been considered in order to reduce the inspection frequency and the cost rate.Then,a particle swarm algorithm(PSO)and related solution procedure are presented to solve the multiple decision variables in our proposed model.In the end,a numerical example is provided so as to demonstrate the superiority of the presented model.By comparing the proposed policy with the conventional ones,the superiority of our proposed policy is proved,which can bring more profits to providers and improve performance.Sensitivity analysis is conducted in order to research the effect of corrective maintenance cost and time required for corrective maintenance on optimization policy.A comparative study is given to illustrate the necessity of distinguishing the first inspection interval or not.

基于非齐次Gamma过程的滚动轴承磨损随机过程建模方法

针对滚动轴承的磨损这一时变随机退化过程,采用Gamma过程进行建模,开展了多组定时递进的加速寿命试验,按照标准GB T 25769—2010测量得到了对应不同试验时长轴承的游隙数据,通过极大似然法与遗传算法对该过程的尺度参数与形状参数进行了最优估计,参数估计的结果验证了Gamma过程的非齐次性质。最后,将建立的退化过程模型与原始数据进行对比,模型拟合一致性较好。

Estimating the resistance of aging service-proven bridges with a Gamma process-based deterioration model

The environmental or anthropogenic factors, to which the in-service bridges are subjected,are responsible for the reduction of bridge performance, and finally lead to great service risk for bridges and increase the probability of substantial economic losses. Probabilitybased estimate of bridge resistance is an essential indicator for the bridge condition evaluation and for optimization of bridge maintenance/repair decisions. It places an emphasis on the proper probabilistic models of structural properties and assessment methods. Making full use of historical service load information may improve the accuracy of bridge performance assessment with reduced epistemic uncertainty for existing aging bridges. In to-date analyses to update the bridge resistance with past service information,the models of resistance deterioration have been assumed as either deterministic or fully correlated, which may differ significantly from the realistic case. With this regard, this paper proposes a novel method for updating the resistance of service-proven bridges with a realistic deterioration model. The Gamma stochastic process has been suggested in the literature to describe the probabilistic behavior of structural time-dependent resistance and thus is adopted in this paper. An illustrative bridge is presented to demonstrate the applicability of the proposed method. Parametric examples are conducted to investigate the role of resistance deterioration model in the updated estimate of bridge resistance with historical service information.

Design of Gamma Spectrum Data Acquisition and Processing System Based on ARM / DSP

Research for detecting or obtaining radionuclide by gamma energy spectrum data acquisition and process system is one of the key issues about intelligent measurement of gamma-ray spectrum. For this reason, a software and hardware implementation schematic design based on ARM ( Advanced RISC Machines) + DSP ( Digital Signal Processor) architecture for gamma energy spectrum data acquisition and processing system is proposed. The paper discusses in detail some key technologies such as communication interface design between microcontroller ARM and digital signal processor DSP,distribution scheduling under multi-task in the ARM-Linux,DSP handling procedures for multi-channel A / D high-speed sample. At the same time,because the traditional Gaussian fitting to determine the boundary of peak is not ideal,it puts forward a weighting factor of Gaussian function least squares fitting realize boundary determined. Finally gamma-spectrum data from sodium iodide NaI( TI) scintillation detector is tested and processed in the new system. The results show that gamma energy spectrum data acquisition and process system is perfect functionality, stable and convergence in unimodal. Compared with data from conventional energy spectrometers,the system can keep better energy resolution in a wide range of pulse pass rate.

基于DL-Gamma的滚动轴承剩余寿命预测方法

针对滚动轴承特征提取困难、寿命分布难以获取的问题,将深度学习(Deep Learning)方法和伽玛过程(Gamma Process)结合提出了一种基于DL-Gamma的滚动轴承寿命预测方法。分别以振动信号典型时域频域特征和利用连续小波变换得到原始信号的时频图作为一维时间序列数据和二维图像序列数据,结合深度卷积神经网和双向长短时记忆网络构建混合输入网络,将一维时间序列数据和二维图像序列数据输入网络得到性能退化因子,利用伽玛过程对性能退化因子曲线进行建模,实现剩余寿命预测。试验结果表明,该方法可有效预测滚动轴承剩余寿命,且预测结果克服传统方法滞后性明显的缺点,有利于实际应用。

考虑个体差异的车轮二元相关退化可靠性分析

由于动车组车轮受加工装配及工况载荷等不确定因素的影响,车轮退化过程复杂,存在显著的个体差异及多个性能退化特征量,且多个退化特征量间相互耦合,仅考虑单个性能特征量难以全面反映其退化过程。因此,以轮缘和轮径作为车轮退化特征量,通过随机化尺度参数表征车轮个体差异,采用Gamma过程和Copula函数建立二元相关退化模型,并根据赤池信息准则(Akaike Information Criterion, AIC)筛选Copula函数,得到可靠度解析式。基于某型动车组车轮实测磨耗数据,对车轮进行可靠性分析,同时通过车辆动力学模型进行仿真验证。结果显示:考虑二元相关时的可靠性结果比仅考虑一元退化更贴近车辆实际运行情况;根据动力学仿真结果体现了考虑个体差异的必要性,表明所提模型能够更准确地表征车轮退化过程,可为可靠性分析以及维修决策优化提供理论支撑。

钢梁腐蚀相关性对钢-混组合梁桥体系可靠度的影响

服役环境中钢主梁的腐蚀本质上是一个随机过程,腐蚀深度随机变量既有时变性亦有空间性。现有测量方法只能获得单根钢梁腐蚀深度数据,尚不能明确结构体系腐蚀深度变量的联合分布模式,可能导致腐蚀结构体系可靠度计算模型失真。以某钢-混凝土组合梁桥为研究对象,首先建立了钢主梁腐蚀深度增长Gamma随机过程模型,并利用钢梁腐蚀深度实测数据对模型进行了验证;然后采用Kendall秩相关系数量化表征主梁腐蚀深度相关性,推导了腐蚀钢梁的时变抗力计算公式;最后基于Copula函数提出了考虑主梁腐蚀相关性的梁桥体系失效概率计算方法,对比研究了钢梁腐蚀相关性对钢-混组合简支梁桥体系可靠度的影响。研究结果表明:桥梁运营前期腐蚀相关性对梁桥受力性能影响较小,在运营中后期,中高程度的腐蚀相关性将会对梁桥体系的可靠度影响较大。研究提出了钢梁腐蚀空间相关性量化方法,获得了更精确的钢-混组合梁桥体系可靠度计算方法,可为组合梁桥体系的时变可靠度评定提供参考。

退化系统任务中止策略研究综述

对退化系统的任务中止策略展开研究。首先,将退化系统分为普通退化系统和随机过程退化系统,从多部件、多阶段、多状态等角度对普通退化系统提出的中止策略进行论述,从Wiener、Gamma等过程具有的不同性质对随机过程退化系统提出的中止策略进行论述;然后,通过讨论退化系统任务中止策略模型的实际应用可知,无人机(unmanned aerial vehicle,UAV)是目前被应用最多的领域;最后,采用CiteSpace软件对这一领域的研究热点、趋势、前沿进行分析,结果表明,基于随机过程建立退化模型,并在制定任务中止策略的同时考虑预防维护、最优检测、任务冗余以及完美或不完美维修的联合优化模型虽然难度很大,但却具有相当大的发展空间。

考虑抗力非平稳劣化和荷载相关性的桥梁可靠性分析

桥梁结构在服役期间受到环境侵蚀和均值增大的相关荷载作用,承载力降低,安全状况不容乐观。为了准确评估服役桥梁在剩余使用寿命内的安全性能,需要考虑结构抗力劣化的非平稳特性以及荷载的时间相关性。该文基于时变可靠度理论,采用Gamma分布描述结构抗力的非平稳劣化过程,并用二维联合分布函数表示相邻荷载的相关性,基于贝叶斯原理,提出了计算公式,并采用蒙特卡洛模拟(MCS)对计算结果进行了验证。对四川省某钢筋混凝土简支梁桥的时变可靠度分析结果表明:在单次条件概率分子的二重积分结果大于0.7时,公式计算结果与MCS结果接近,证明了其正确性;Gamma劣化过程的尺度参数越大,荷载的时间相关性越弱,结构失效概率越大;当作用于结构的车辆荷载年均增长率超过2%时,桥梁在30年内失效的概率较大,需要对结构进行定期监测、养护和维修。

基于gamma过程及贝叶斯估计的实时可靠性评估

由于试验时间和成本的限制,系统或元件的传统可靠性评估方法已很难适用;并且同类产品特定个体之间的可靠性存在着差异。为此,提出了一种基于退化数据的特定系统或元件的实时可靠性评估方法。采用平稳gamma过程描述系统或元件的退化过程并使用贝叶斯估计方法来实时更新其参数,在此基础上推导出精确检测和有误差检测下的系统或元件可靠度表达式。实验分析结果表明,提出的方法能实时地、更准确地评估出特定系统或元件的可靠度。这对航空航天设备的安全性有着重要意义。

基于随机参数Gamma过程的剩余寿命预测方法

为了提高剩余寿命预测的可信度,针对进行过加速老化试验的产品,提出利用Gamma过程参数的非共轭先验分布进行Bayesian统计推断的剩余寿命预测方法.将加速老化数据作为先验信息,利用Gamma过程进行老化建模,通过加速因子获得形状参数在工作应力下的折算值,使用Anderson-Darling统计量确定随机参数的先验分布.将产品工作中的少量实测数据作为现场信息,利用基于Gibbs抽样的Markov Chain Monte Carlo(MCMC)仿真得到参数的后验均值.以某型导弹电连接器为例说明了该方法的研究意义和工程应用价值.

金属化膜电容器Gamma过程性能退化建模的自助法

针对安全关键系统中长寿命高可靠性产品失效数据稀缺的问题,研究了一种部件寿命预测的自助法。首先建立了基于Gamma过程的性能退化模型。而后,考虑到各个体间的制造及运行环境等随机差异,应用自助法对个体退化数据再抽样求得了个体形状参数α和尺度参数β;在此基础上,对个体α、β再自助抽样求得总体形状参数和尺度参数;之后,运用Gamma过程寿命预测方法得到了总体任务可靠度寿命的频率分布图。最后,以金属化膜电容器为例进行了应用分析。结果表明,该方法有益于全面掌握产品的寿命特征,提高系统可靠性安全性。

基于Gamma过程的加速劣化系统模型及其最优视情维修策略

针对系统劣化速度会随役龄或维修次数的增加而逐渐加快的情况,将Gamma过程与几何过程相结合,提出一种加速劣化模型,研究了加速劣化系统的最优视情维修策略。利用更新过程理论求得系统平均费用率表达式,并给出最优检测、更换策略的数值求解算法。通过算例演示,从定量的角度分析了系统劣化速度的变化对最优检测、更换策略和系统平均费用率的影响。

基于Gamma退化过程的直升机主减速器行星架剩余寿命预测模型

鉴于Gamma过程具有平稳、独立增量等退化建模所需的属性,将其用于描述设备退化过程,并针对缺乏故障数据时难以进行剩余寿命预测的问题,利用设备运行中采集的表征其退化状态的大量间接状态参数和少量直接状态参数,建立了基于Gamma退化过程的剩余寿命预测模型;针对经验最大化算法中似然函数难以解析求解的问题,引入粒子滤波算法实现了模型参数估计;最后将模型应用于直升机主减速器行星架的剩余寿命预测,得到了不同时刻的预测结果及95%置信区间,验证了预测模型的有效性和准确性。

混凝土徐变的Gamma模型参数估计研究

针对长期荷载作用下的混凝土结构,将混凝土徐变量作为表征混凝土结构服役性能的退化指标,采用Gamma随机过程模拟混凝土徐变发展过程的不确定性。当参数c和尺度参数β为随机变量且其先验分布已知时,可利用Bayesian定理,得到c和β的后验分布和估计。作为特例,给出c为定值、β先验分布服从Gamma分布的后验分布和β后验估计值的解析表达式。最后在给定参数b和c的情况下,使用经典矩估计、极大似然估计与Bayesian估计、后验矩估计、后验极大似然估计等5种算法,融合2组混凝土徐变试验数据,对Gamma过程参数进行估计,实现混凝土徐变过程模拟,并以误差平方和最小为准则,将徐变模拟结果进行比较,结果发现Bayesian估计和后验估计法优于经典估计法,尤以Bayesian估计法为最佳。

Condition-based maintenance policy for gamma deteriorating systems

A condition-based maintenance model for gamma deteriorating system under continuous inspection is studied. This methodology uses a gamma distribution to model the material degradation, and the impact of imperfect maintenance actions on the system reliability is investigated. The state of a degrading system immediately after the imperfect maintenance action is assumed as a random variable and the maintenance time follows a geometric process. Furthermore, the explicit expressions for the long-run average cost and availability per unit time of the system are evaluated, an optimal policy （ε^＊） could be determined numeri- cally or analytically according to the optimization model. At last, a numerical example for a degrading system modeled by a gamma process is presented to demonstrate the use of this policy in practical applications.

Gamma过程退化失效可靠性分析

退化型失效产品,可通过退化失效分析对其进行可靠性统计推断。性能退化一般是一个随机过程,并且是单调变化的,为描述产品的退化,给出了一个随机Gamma过程模型,通过求解该过程的首达时分布即可获得产品的失效分布。由于解析方法求解存在很大的难度,给出了一种基于仿真的求解方法。利用所得模型对强激光装置所用的某型金属化膜脉冲电容器进行了可靠性分析,说明了模型的适用性。

加速应力下基于Gamma过程的寿命预测方法

某型导弹电连接器属于高可靠性、长寿命产品。为了根据使用环境对其准确定寿,提出了加速应力下基于Gamma过程的寿命预测方法。以电连接器的接触电阻作为性能参量,通过温度、湿度双应力加速退化试验,获取其性能退化数据。利用Gamma过程对样品退化规律进行建模,并使用广义艾林模型描述了样品退化率与温度、湿度之间的关系。在以上基础上建立寿命预测模型;并采用极大似然法估计出模型参数,成功对该型电连接器的在特定工作条件下的寿命指标做出了预测。