阿伦尼斯模型下可靠性增长数据的统计分析

本文以阿伦尼斯（Arrhenius）模型作为环境应力模型，解决利用不同环境应力下可靠性增长试验数据，求试验结束时设备可靠度的置信下限问题。给出了模型参数的极大似然估计，进而求出可靠度的置信下限。模拟研究结果表日月，上述方法效果良好，估计的精度能满足工程要求。     

时变AR模型的一种定阶方法

自回归（AR）模型的定阶对其分析结果的准确性、效率和可靠性具有重要影响。对时变AR模型的定阶问题进行了深入研究,提出了一种基于采样频率以及分析频率之比的定阶方法。对一质量随时间变化的悬臂梁进行了有限元建模,运用计算所得到的振动响应建立了梁的时变AR模型,利用所提方法进行了该模型的定阶,采用递推最小二乘法对梁的模态频率进行了估计。对一质量时变的悬臂梁进行了试验,对采集的振动响应信号建立了时变AR模型并识别了其振动模态频率。模拟计算和试验结果都表明,提出的时变AR模型定阶方法是有效且可行的,且识别算法具有一定的抗噪性。     

Modeling of structural mechanics,moisture diffusion,and heat conduction coupled with physical aging in thin plastic plates

This paper offers an approach to model the coupled physics of structural mechanics, moisture diffusion, and heat conduction together with physical aging. The modeling is performed on a glassy polymer blend and hence incorporates the material viscoelastic behavior. Determination of the coupling coefficients, which link the governing equations of the mechanisms to each other, is particularly challenging. In this work, an estimation procedure has been used to determine the coupling coefficients, based on the experimental data reported in our recent papers. The effects of physical aging on mechanical stress–strain are also included using the shift factors, which were specified experimentally. The effect of physical aging on moisture diffusion is also modeled using a time-varying boundary condition. Experimental verification of the model shows that the developed model is capable of predicting the deflection of plastic parts subjected to hygrothermal conditions; i.e., conditions where moisture diffusion and physical aging phenomena are influential.     

前后向时间序列模型联合估计的时变结构模态参数辨识

为提高时变结构模态参数辨识精度和抗噪声能力,提出一种前后向泛函向量时变自回归滑动平均（FS-VTARMA）时间序列模型联合估计的模态参数辨识方法。首先建立前后向FS-VTARMA模型联合估计的均方误差形式的费用函数,其次引入非平稳信号中前向模型和后向模型估计系数的近似共轭关系,再利用两步最小二乘法（2SLS）得到时变模型系数,最后把时变模型特征方程转换为广义特征值问题提取出模态参数。利用时变刚度系统非平稳振动信号验证该方法,结果表明：能有效地克服前向模型估计中模态参数一步延迟以及起始时刻无法准确获得,以及后向模型估计中模态参数一步超前以及终止时刻无法准确获得的缺点,具有更高的模态参数辨识精度和更强的抗噪声能力。     

Reliability Estimation for Accelerated Life Tests Based on a Cox Proportional Hazard Model with Error Effect

In this paper, a Cox proportional hazard model with error effect applied on the study of an accelerated life test is investigated. Statistical inference under Bayesian methods by using the Markov chain Monte Carlo techniques is performed in order to estimate the parameters involved in the model and predict reliability in an accelerated life testing. The proposed model is applied to the analysis of the knock sensor failure time data in which some observations in the data are censored. The failure times at a constant stress level are assumed to be from a Weibull distribution. The analysis of the failure time data from an accelerated life test is used for the posterior estimation of parameters and prediction of the reliability function as well as the comparisons with the classical results from the maximum likelihood estimation. Copyright © 2017 John Wiley & Sons, Ltd.     

Discrimination between accelerated life models via Approximate Bayesian Computation

Accelerated life testing (ALT) is widely used in high-reliability product estimation to get relevant information about an item's performance and its failure mechanisms. To analyse the observed ALT data, reliability practitioners need to select a suitable accelerated life model based on the nature of the stress and the physics involved. A statistical model consists of (i) a lifetime distribution that represents the scatter in product life and (ii) a relationship between life and stress. In practice, several accelerated life models could be used for the same failure mode and the choice of the best model is far from trivial. For this reason, an efficient selection procedure to discriminate between a set of competing accelerated life models is of great importance for practitioners. In this paper, accelerated life model selection is approached by using the Approximate Bayesian Computation (ABC) method and a likelihood-based approach for comparison purposes. To demonstrate the efficiency of the ABC method in calibrating and selecting accelerated life model, an extensive Monte Carlo simulation study is carried out using different distances to measure the discrepancy between the empirical and simulated times of failure data. Then, the ABC algorithm is applied to real accelerated fatigue life data in order to select the most likely model among five plausible models. It has been demonstrated that the ABC method outperforms the likelihood-based approach in terms of reliability predictions mainly at lower percentiles particularly useful in reliability engineering and risk assessment applications. Moreover, it has shown that ABC could mitigate the effects of model misspecification through an appropriate choice of the distance function.     

基于小波分解的时变信道盲辨识

针对传统的信道盲辨识算法很难适应时变信道模型的问题，提出了一种基于小波多分辨率分解的时变信道盲辨识算法．该算法首先应用小波多分辨率分解原理来近似建模时变信道；然后，利用信道输出序列的二阶统计量对时变信道的小波分解模型的小波系数进行两级盲辨识；最后，应用估计的小波系数即可重构时变信道的冲激响应．仿真结果表明，该算法可很好地完成周期时变信道的盲辨识与盲均衡任务．     

Bayes approach in RDT using accelerated and long-term life data

A common problem of reliability demonstration testing (RDT) is the magnitude of total time on test required to demonstrate reliability to the consumer’s satisfaction, particularly in the case of high reliability components. One solution is the use of accelerated life testing (ALT) techniques. Another is to incorporate prior beliefs, engineering experience, or previous data into the testing framework. This may have the effect of reducing the amount of testing required in the RDT in order to reach a decision regarding conformance to the reliability specification. It is in this spirit that the use of a Bayesian approach can, in many cases, significantly reduce the amount of testing required.We demonstrate the use of this approach to estimate the acceleration factor in the Arrhenius reliability model based on long-term data given by a manufacturer of electronic components (EC). Using the Bayes approach we consider failure rate and acceleration factor to vary randomly according to some prior distributions. Bayes approach enables for a given type of technology the optimal choice of test plan for RDT under accelerated conditions when exacting reliability requirements must be met. These requirements are given by a hypothetical consumer by two different ways. The calculation of posterior consumer’s risk is demonstrated in both cases.The test plans are optimum in that they take into account Var{λ|data}, posterior risk, E{λ|data}, Median λ or other percentiles of λ at data observed at the accelerated conditions. The test setup assumes testing of units with time censoring.     

Lyapunov stability of columns, pipes and rotating shafts under time-dependent excitation

Structural or mechanical systems governed by non-autonomous partial differential equations are considered. The systems are such that they would be conservative in the absence of dissipation and time variation of the loading parameter. They possess an equilibrium state, and sufficient conditions for its stability are obtained with the use of Lyapunov's direct method. Three problems are treated: a column with a time-varying axial load, a pipe conveying fluid with time-varying velocity, and a rotating shaft with time-varying angular velocity. These excitations appear in coefficients of the equations of motion, and the stability conditions involve the excitations and their time rates of change     

Two-dimensional wavelet transform for reliability-guided phase unwrapping in optical fringe pattern analysis

This paper theoretically discusses modulus of two-dimensional (2D) wavelet transform (WT) coefficients, calculated by using two frequently used 2D daughter wavelet definitions, in an optical fringe pattern analysis. The discussion shows that neither is good enough to represent the reliability of the phase data. The differences between the two frequently used 2D daughter wavelet definitions in the performance of 2D WT also are discussed. We propose a new 2D daughter wavelet definition for reliability-guided phase unwrapping of optical fringe pattern. The modulus of the advanced 2D WT coefficients, obtained by using a daughter wavelet under this new daughter wavelet definition, includes not only modulation information but also local frequency information of the deformed fringe pattern. Therefore, it can be treated as a good parameter that represents the reliability of the retrieved phase data. Computer simulation and experimentation show the validity of the proposed method.     

Reliability analysis of exponentiated Poisson-exponential constant stress accelerated life test model

Accelerated life testing is an efficient tool frequently adopted for obtaining failure time data of test units in a lesser time period as compared to normal use conditions. We assume that the lifetime data of a product at constant level of stress follows an exponentiated Poisson-exponential distribution and the shape parameter of the model has a log-linear relationship with the stress level. Model parameters, the reliability function (RF), and the mean time to failure (MTTF) function under use conditions are estimated based on eight frequentist methods of estimation, namely, method of maximum likelihood, method of least square and weighted least square, method of maximum product of spacing, method of minimum spacing absolute-log distance, method of Cramér-von-Mises, method of Anderson–Darling, and Right-tail Anderson–Darling. The performance of the different estimation methods is evaluated in terms of their mean relative estimate and mean squared error using small and large sample sizes through a Monte Carlo simulation study. Finally, two accelerated life test data sets are considered and bootstrap confidence intervals for the unknown parameters, predicted shape parameter, predicted RF, and the MTTF at different stress levels, are obtained.     

Accelerated Degradation Tests: Modeling and Analysis

High reliability systems generally require individual system components having extremely high reliability over long periods of time. Short product development times require reliability tests to be conducted with severe time constraints. Frequently few or no failures occur during such tests, even with acceleration. Thus, it is difficult to assess reliability with traditional life tests that record only failure times. For some components, degradation measures can be taken over time. A relationship between component failure and amount of degradation makes it possible to use degradation models and data to make inferences and predictions about a failure-time distribution. This article describes degradation reliability models that correspond to physical-failure mechanisms. We explain the connection between degradation reliability models and failure-time reliability models. Acceleration is modeled by having an acceleration model that describes the effect that temperature (or another accelerating variable) has on the rate of a failure-causing chemical reaction. Approximate maximum likelihood estimation is used to estimate model parameters from the underlying mixed-effects nonlinear regression model. Simulation-based methods are used to compute confidence intervals for quantities of interest (e.g., failure probabilities). Finally we use a numerical example to compare the results of accelerated degradation analysis and traditional accelerated life-test failure-time analysis.     

Accelerated failure time models for reliability data analysis

Despite the popularity of the proportional hazards model (PHM) in analysing many kinds of reliability data, there are situations in which it is not appropriate. The accelerated failure time model (AFT) then provides an alternative. In this paper, a unified treatment of the accelerated failure time model is outlined for the standard reliability distributions (Weibull, log-normal, inverse Gaussian, gamma). The problem of choosing between the accelerated failure time models and proportional hazard models is discussed and effects of misspecification are reported. The techniques are illustrated in the analysis of data from a fatigue crack growth experiment.     

A Bayesian framework for accelerated reliability growth testing with multiple sources of uncertainty

Reliability growth tests are often used for achieving a target reliability for complex systems via multiple test‐fix stages with limited testing resources. Such tests can be sped up via accelerated life testing (ALT) where test units are exposed to harsher‐than‐normal conditions. In this paper, a Bayesian framework is proposed to analyze ALT data in reliability growth. In particular, a complex system with components that have multiple competing failure modes is considered, and the time to failure of each failure mode is assumed to follow a Weibull distribution. We also assume that the accelerated condition has a fixed time scaling effect on each of the failure modes. In addition, a corrective action with fixed ineffectiveness can be performed at the end of each stage to reduce the occurrence of each failure mode. Under the Bayesian framework, a general model is developed to handle uncertainty on all model parameters, and several special cases with some parameters being known are also studied. A simulation study is conducted to assess the performance of the proposed models in estimating the final reliability of the system and to study the effects of unbiased and biased prior knowledge on the system‐level reliability estimates.     

Reliability of Space-Shuttle Pressure Vessels With Random Batch Effects

In this article we revisit the problem of estimating the joint reliability against failure by stress rupture of a group of fiber-wrapped pressure vessels used on Space-Shuttle missions. The available test data were obtained from an experiment conducted at the U.S. Department of Energy Lawrence Livermore Laboratory (LLL) in which scaled-down vessels were subjected to life testing at four accelerated levels of pressure. We estimate the reliability assuming that both the Shuttle and LLL vessels were chosen at random in a two-stage process from an infinite population with spools of fiber as the primary sampling unit. Two main objectives of this work are (1) to obtain practical estimates of reliability taking into account random spool effects and (2) to obtain a realistic assessment of estimation accuracy under the random model. Here, reliability is calculated in terms of a “system” of 22 fiber-wrapped pressure vessels, taking into account typical pressures and exposure times experienced by Shuttle vessels. Comparisons are made with previous studies. The main conclusion of this study is that, although point estimates of reliability are still in the “comfort zone,” it is advisable to plan for replacement of the pressure vessels well before the expected lifetime of 100 missions per Shuttle Orbiter. Under a random-spool model, there is simply not enough information in the LLL data to provide reasonable assurance that such replacement would not be necessary.     

非线性系统响应功率谱密度的小波-Galerkin方法

发展了广义谐和小波在确定非线性系统随机动力响应中的应用。首先,利用周期广义谐和小波展开非线性动力微分方程,并考虑小波的联系系数后,可将动力微分方程转化为一组非线性代数方程。其次,利用Newton迭代法数值解答了非线性代数方程,得到了非线性动力响应的小波变换。最后,根据响应时变功率谱与各阶小波变换之间的关系,计算求得了非线性动力响应的功率谱密度。数值模拟显示了本文建议方法与Monte Carlo模拟之间的吻合程度。     

基于多峰分布的大尺度变形翼机构时变可靠性分析

针对机构可靠性的工程问题,提出了一种基于多峰分布的时变可靠性分析方法（iTRPD）,并应用于大尺度变形翼机构的可靠性分析。首先,将变形翼结构模型离散为几个瞬时功能函数,并将其转换为独立正态变量。然后,计算出不同时刻的瞬间可靠度与各向量间的自相关系数矩阵,得到对应的概率密度函数。最后,根据协方差特性与各向量间的相关性,利用1次高维高斯积分将独立标准正态空间的时变可靠度简化为大尺度变形翼机构整体的时变可靠度。结果表明：iTRPD在分析大尺度变形翼时变可靠性时,与蒙特卡洛仿真法（MCS）的相对误差仅为-2.842%,比常规方法TRPD好;对功能函数调用次数为415,远小于MCS的1×109次;对高维高斯积分的调用,常规时变可靠性方法为35次,iTRPD仅为1次。可见,iTRPD对涉及多模态分布的时变可靠性分析具有较高的计算精度和计算效率。     

Transient response of Bouc–Wen hysteretic system under random excitation via RBFNN method

Hysteresis normally exhibited by mechanical systems and materials is so prevalent that its response prediction under random excitation has been extensively investigated for decades. Nevertheless, the transient solution of the response, which is crucial for assessing the system’s reliability, is still a challenging topic that requires additional development. To this regard, this work proposes a semi-analytical method using the radial basis function neural network (RBFNN) to attain the transient probability density distribution of the randomly excited Bouc–Wen system. Specifically, the trial solution of the corresponding FPK equation is configured as the RBFNN with undetermined time-varying weight coefficients. By discretizing the time derivative with the Euler difference method, a loss function with time recurrence is derived and minimized to yield the time-varying optimal weight coefficients through the optimization method. Additionally, an optimized sampling strategy is adopted to reduce the burden of calculation. Finally, the Bouc–Wen hysteretic systems with softening and hardening nonlinearity are considered to investigate the performance of the adopted technique. The numerical results have shown that the evaluation process of the probability density functions(PDFs) can be captured well with sufficient accuracy and efficiency. The proposed efficient sampling technique can provide considerable efficiency improvement for the medium dimension system. The work of the paper will contribute to the reliability design of hysteretic structures in engineering.     

Integration method for reliability assessment with multi-source incomplete accelerated degradation testing data

ABSTRACT

During the product life cycle, the lifetime information will be collected at each stage, mainly from different tests at the R&D phase, field usage, and maintenance. To comprehensively conduct reliability assessments, it generally requires the integration of multi-source datasets, even that from similar products. In this article, we considered the scenario that products have been arranged with several accelerated degradation tests (ADT) under different types of accelerated stresses with dependency. The obtained data is called incomplete ADT dataset with incomplete stress conditions which fails the traditional integration method for reliability assessments. A novel method is proposed to accomplish this task through mutually exclusive set (MES) theory. The probability assignments for each dataset are given through the union set of several MESs. Then, the multi-source ADT datasets are integrated with the assigned weights of probabilities. Finally, a simulation study and a real application are given to illustrate the effectiveness of the proposed methodology.     

Remaining Life Prediction Based on Wiener Processes with ADT Prior Information

Precisely predicting the remaining life for an individual plays an important role in condition‐based maintenance, so Bayesian inference method, which can integrate useful data from several sources to improve the prediction accuracy, has became a research hot. Aiming at the situation that accelerated degradation tests have been widely applied to assess the reliability of products, a remaining life prediction method based on Bayesian inference by taking accelerated degradation data as prior information is proposed. A Wiener process with random drift, diffusion parameters is used to model degradation data, and conjugate prior distributions of random parameters are adopted. To solve the problem that it is hard to estimate the hyper parameters from accelerated degradation data using an Expectation Maximization algorithm, a data extrapolation method is developed. With acceleration factors, degradation data are extrapolated from accelerated stress levels to the normal use stress level. Acceleration factor constant hypothesis is used to deduce the expression of acceleration factor for a Wiener degradation model. Besides, simulation tests are designed to validate the proposed method. The method of constructing the confidence levels for the remaining life predictions is also provided. Finally, a case study is used to illustrate the application of our developed method. Copyright © 2015 John Wiley & Sons, Ltd.