Reliability calculation of time-consuming problems using a small-sample artificial neural network-based response surface method

An important step when designing and assessing the reliability of existing structures and/or structural elements is to calculate the reliability level described by failure probability or reliability index. Since calculating the structural response of complex systems such as bridges is usually a time-consuming task, the utilization of approximation methods with a view to reducing the computational effort to an acceptable level is an appropriate solution. The paper introduces a small-sample artificial neural network-based response surface method. An artificial neural network is used as an approximation (a so-called response surface) of the original limit state function. In order to be as effective as possible with respect to computational effort, a stratified Latin hypercube sampling simulation method is utilized to properly select training set elements. Subsequently, the artificial neural network-based response surface is utilized to calculate failure probability. To increase the accuracy of the determined failure probability, the response surface can be updated close to the failure region. This is performed by finding a new anchor point, which lies close to the design point of the limit state function. The new anchor point is then used to prepare the updated training set. The efficiency of the proposed method is tested for different training set sizes using a nonlinear limit state function taken from the literature, and the reliability assessment of three concrete bridges, one with explicit and two with implicit limit state functions in the form of finite element method models.

     

An efficient method for statistical moments and reliability assessment of structures

The probability density function (PDF) of a performance function can be constructed from the perspective of first four statistical moments, and the failure probability can be evaluated accordingly. Since the shifted generalized lognormal distribution (SGLD) model will be fitted to recover the PDF based on the first four statistical moments, the evaluation of statistical moments of the performance function is of critical significance for the structural reliability analysis. This paper presents a new method for statistical moments and reliability assessment of structures with efficiency and accuracy, especially when large variabilities in the input random vector and nonlinearities are considered . First, a numerical method is established based on rotating the points in the quasi-symmetric point method (Q-SPM), which is very efficient for evaluating the statistical moments. This numerical method is called the rotational quasi-symmetric point method (RQ-SPM). The optimal angles of rotation in RQ-SPM can be determined via an optimization problem, where the objective function is adopted as minimizing the differences between the marginal moments of input random variables estimated by the points after rotation and their exact values. By doing so, the information of marginal distributions and their tail distributions could be better reproduced, which is of paramount importance to the statistical moments assessment of the performance function, especially for the high-order moments. Once the statistical moments are available, the PDF of the performance function can be recovered by the SGLD model. Finally, the failure probability can be evaluated by a simple integral over the PDF of the performance function. Several numerical examples are given to demonstrate the efficacy of the proposed method. Comparisons of the new method, the original Q-SPM, the univariate dimension reduction method (UDRM) and the bivariate dimension reduction method (BDRM) are also made on the statistical moments assessment. The results manifest the accuracy and efficiency of the proposed method for both the statistical moments and reliability assessment of structures.     

Estimating parameter distributions in structural reliability assessment using the Transferable Belief Model

This paper applies the Transferable Belief Model (TBM) interpretation of the Dempster-Shafer theory of evidence to estimate parameter distributions for probabilistic structural reliability assessment based on information from previous analyses, expert opinion, or qualitative assessments (i.e., evidence). Treating model parameters as credal variables, the suggested approach constructs a set of least-committed belief functions for each parameter defined on a continuous frame of real numbers that represent beliefs induced by the evidence in the credal state, discounts them based on the relevance and reliability of the supporting evidence, and combines them to obtain belief functions that represent the aggregate state of belief in the true value of each parameter. Within the TBM framework, beliefs held in the credal state can then be transformed to a pignistic state where they are represented by pignistic probability distributions. The value of this approach lies in its ability to leverage results from previous analyses to estimate distributions for use within a probabilistic reliability and risk assessment framework. The proposed methodology is demonstrated in an example problem that estimates the physical vulnerability of a notional office building to blast loading.     

基于集对分析联系数故障树的BA系统可靠性分析*

为了有效管理和监测建筑设备自动化系统（BAS）,提高系统可靠性,基于集对分析联系数和故障树理论研究了BA系统的可靠性分析方法。详细分析可能引起BA系统故障的各种因素,建立系统的故障树模型,并确定了系统故障原因的各种可能组合方式;引入中间状态概率的概念结合集对分析联系数理论建立了BA系统的可靠性评定模型;通过BA冷源系统的仿真实例验证了模型的可靠性和有效性。实验表明,该模型便于发现系统的薄弱环节,从而有效提高了系统的可靠性。     

基于T-S模糊故障树方法的惯性导航系统可靠性评估

针对传统故障树模型在复杂系统可靠性评估中的局限性,引入T-S模糊故障树建模方法对惯性导航系统进行可靠性评估分析.在建立T-S模糊故障树的基础上,以模糊门算法表征事件之间的逻辑关系,确定了基于基本事件模糊概率和故障程度的复杂系统可靠性评估方法,并对事件进行了概率重要度和关键重要度分析.案例分析表明,T-S模糊故障树分析方...     

An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals

The reliability analysis approach based on combined probability and evidence theory is studied in this paper to address the reliability analysis problem involving both aleatory uncertainties and epistemic uncertainties with flexible intervals (the interval bounds are either fixed or variable as functions of other independent variables). In the standard mathematical formulation of reliability analysis under mixed uncertainties with combined probability and evidence theory, the key is to calculate the failure probability of the upper and lower limits of the system response function as the epistemic uncertainties vary in each focal element. Based on measure theory, in this paper it is proved that the aforementioned upper and lower limits of the system response function are measurable under certain circumstances (the system response function is continuous and the flexible interval bounds satisfy certain conditions), which accordingly can be treated as random variables. Thus the reliability analysis of the system response under mixed uncertainties can be directly treated as probability calculation problems and solved by existing well-developed and efficient probabilistic methods. In this paper the popular probabilistic reliability analysis method FORM (First Order Reliability Method) is taken as an example to illustrate how to extend it to solve the reliability analysis problem in the mixed uncertainty situation. The efficacy of the proposed method is demonstrated with two numerical examples and one practical satellite conceptual design problem.     

改进的J-M模型及其在软件安全性评估中的应用

分析了软件可靠性和安全性之间的关系;针对安全软件测试剖面和操作剖面有不同的故障检测率,以及软件故障剔除时有引入新故障的可能,通过改变Jelinski-Moranda(J-M)可靠性模型相关假设及参数,提出了一个既能描述安全软件测试剖面与操作剖面不同,又能描述故障引入率的软件安全性评估模型;并给出了该安全性评估模型的性能度量.最后,对同一组铁路信号控制安全软件的失效数据进行分析,结果表明改进后的J-M评估模型比原J-M模型有着更好的拟合能力和预测能力.     

基于GO法的航空电子设备可靠性评估

针对传统电子设备在可靠性评估中存在精度和效率较低问题,提出一种基于GO法的可靠性评估方法。该方法引入状态累积概率,建立考虑共有信号处理的GO模型,给出某航空电子设备监测模块基于GO法的可靠性评估实例。与传统Monte—carlo方法进行比较,结果证明该方法更简单、直观,具有更高的计算精度、仿真效率,且更容易解决复杂多态、时序问题。     

An efficient method of solving design optimization problems with arbitrary random distributions in gradient-based design spaces

Reliability-Based Design Optimization (RBDO) algorithms, such as Reliability Index Approach (RIA) and Performance Measure Approach (PMA), have been developed to solve engineering optimization problems under design uncertainties. In some existing methods, the random design space is transformed to standard normal design space and the reliability assessment, such as reliability index from RIA or performance measure from PMA, is estimated in order to evaluate the failure probability. When the random variable is arbitrarily distributed and cannot be properly fitted to any known form of probability density function, the existing RBDO methods cannot perform reliability analysis in the original design space. This paper proposes a novel Ensemble of Gradient-based Transformed Reliability Analyses (EGTRA) to evaluate the failure probability of any arbitrarily distributed random variables in the original design space. The arbitrary distribution of the random variable is approximated by a merger of multiple Gaussian kernel functions in a single-variate coordinate that is directed toward the gradient of the constraint function. The failure probability is then estimated using the ensemble of each kernel reliability analysis. This paper further derives a linearly approximated probabilistic constraint at the design point with allowable reliability level in the original design space using the aforementioned fundamentals and techniques. Numerical examples with generated random distributions show that existing RBDO algorithms can improperly approximate the uncertainties as Gaussian distributions and provide solutions with poor assessments of reliabilities. On the other hand, the numerical results show EGTRA is capable of efficiently solving the RBDO problems with arbitrarily distributed uncertainties.     

Sequential Decision Strategies for Machine Interpretation of Speech

Recognition errors made by automatic speech recognition (ASR) systems may not prevent the development of useful dialogue applications if the interpretation strategy has an introspection capability for evaluating the reliability of the results. This paper proposes an interpretation strategy which is particularly effective when applications are developed with a training corpus of moderate size. From the lattice of word hypotheses generated by an ASR system, a short list of conceptual structures is obtained with a set of finite state machines (FSM). Interpretation or a rejection decision is then performed by a tree-based strategy. The nodes of the tree correspond to elaboration-decision units containing a redundant set of classifiers. A decision tree based and two large margin classifiers are trained with a development set to become interpretation knowledge sources. Discriminative training of the classifiers selects linguistic and confidence-based features for contributing to a cooperative assessment of the reliability of an interpretation. Such an assessment leads to the definition of a limited number of reliability states. The probability that a proposed interpretation is correct is provided by its reliability state and transmitted to the dialogue manager. Experimental results are presented for a telephone service application     

Stochastic software safety/reliability measurement and its application

Safety and reliability have become important software quality characteristics in the development of safety-critical software systems. However, there are so far no quantitative methods for assessing a safety-critical software system in terms of the safety/reliability characteristics. The metrics of software safety is defined as the probability that conditions that can lead to hazards do not occur. In this paper, we propose two stochastic models for software safety/reliability assessment: the data-domain dependent safety assessment model and the availability-related safety assessment model. These models focus on describing the time- or execution-dependent behavior of the software faults which can lead to unsafe states when they cause software failures. The application of one of these models to optimal software release problems is also discussed. Finally, numerical examples are illustrated for quantitative software safety assessment and optimal software release policies. This revised version was published online in June 2006 with corrections to the Cover Date.     

Quality evaluation for a coprime factor perturbed model set basedon frequency-domain data

Quality assessment is investigated under a probabilistic framework for a prescribed model set. The results on unfalsified probability estimation are extended from additive modeling errors to normalized coprime factor perturbations. An analytic formula has been derived for the sample unfalsified probability. It is shown that with increasing the data length, the sample unfalsified probability converges in probability to a number which is independent of experimental data. Numerical simulations show that the proposed sample unfalsified probability is appropriate in the evaluation of the quality of a model set     

Piecewise point classification for uncertainty propagation with nonlinear limit states

Reliability measures the probability that engineered systems successfully perform the intended functionalities under various sources of uncertainties. A piecewise point classification (PPC) method is proposed in this work for effectively propagating uncertainty with nonlinear limit states and approximating the probability of failure accurately. The idea is to efficiently identify a set of points near the critical region, and thus enable capturing the nonlinearity of limit states by constructing piecewise linear approximations. In PPC, the first-order reliability method (FORM) is initially employed to search the most probable point. To handle the nonlinearity of failure surfaces, a sampling-based limit state learning algorithm is then developed to search critical points near the failure surface. With all the points evaluated during the search process, a distance-based piecewise point classification method is developed as a classifier to predict failure events. Monte Carlo simulation (MCS) is finally utilized to propagate uncertainties and approximate the probability of failure, in which a large size of sample points is generated randomly and classified by the developed piecewise point classifier. Three case studies are used to demonstrate the efficacy of the developed approach.     

具有失效链路的star网络可靠性分析

star互连网络作为大规模处理器系统网络模型的重要候选之一,其可靠性问题一直为人们所关注.在链路可靠概率模型的基础上,分别采用不同的分析方法对star网络的可靠性进行了分析,建立了相应的可靠性模型.这些可靠性模型指出了链路可靠性与网络可靠性之间的约束关系.模拟实验结果表明,在现有大规模集成电路技术的条件下,这些可靠性分析方法都是可行的,而且star网络的可靠性可以控制在一个理想的范围内.     

分布式系统可靠性模型

文章首先给出分布式系统的一般描述;然后采用建立在图论、概率论及布尔代数基础上的网络分析法建立了分布式系统的可靠性模型,用以综合考虑系统拓朴结构、任务集、通讯路径集和处理单元集等对系统可靠性的影响;最后,针对二维TORUS网,给出了建模实例以及模型的有关应用。     

基于自适应Kriging模型的不确定可靠性功能优化算法研究

产品研发中功能失效是一个复杂的系统性工程,失效过程包含大量不确定性因素。为此,构建了自适应Kriging的不确定可靠性功能优化算法,进行产品总体功能失效分析、认知集合可信任度、样本点的生成、自适应Kriging计算及优选功能组合,获取在指定的概率约束下的最优解。以大数定律及极限定理为基础,保证了样本点在重要区域及Kriging模型的收敛条件。以工程机械储能系统为例,说明算法的迭代性、收敛性、准确性及稳定性。结果表明,该算法能够得出准确的敏感度,节省计算时间,提高计算效率。     

On the probability of the formation of local groups in random point images

Original programming, combinatorial, and geometric schemes are presented. They have been developed and used by the authors to calculate exact analytical formulas that describe the probability of the formation of local groups of a given size in random point images. Formulas, which will be discussed below, arise in the assessment of the reliability detection of point images, when they are detected by scanning the aperture that has a limited number of thresholds. In this paper, significant attention is paid to the formulation and solution of difficult combinatorial problems that have been encountered in the course of the investigation and that are associated with new generalization of the Catalan numbers.     

Gompertz software reliability model: Estimation algorithm and empirical validation

Gompertz curve has been used to estimate the number of residual faults in testing phases of software development, especially by Japanese software development companies. Since the Gompertz curve is a deterministic function, the curve cannot be applied to estimating software reliability which is the probability that software system does not fail in a prefixed time period. In this article, we propose a stochastic model called the Gompertz software reliability model based on non-homogeneous Poisson processes. The proposed model can be derived from the statistical theory of extreme-value, and has a similar asymptotic property to the deterministic Gompertz curve. Also, we develop an EM algorithm to determine the model parameters effectively. In numerical examples with software failure data observed in real software development projects, we evaluate performance of the Gompertz software reliability model in terms of reliability assessment and failure prediction.     

基于改进粗糙集概率模型的鲁棒医学图像分割算法*

基于参数化模型的图像分割算法对复杂的医学图像分割精度较低,对此提出一种基于改进粗糙集概率模型的鲁棒医学图像分割算法。首先,将粗糙集的上下逼近与概率边界区引入最大期望算法中,表征每个类簇;然后,将图像的灰度分布建模为一个有限数量的混合粗糙集概率分布;最终,通过马尔可夫随机场引入图像的空间信息,提高图像分割算法的鲁棒性。基于合成脑部MR(核磁共振)图像库与真实脑部MR图像库的分割实验结果显示,本算法的分割精度与鲁棒性均优于其他参数化模型的分割算法及其他专门的脑部MR图像分割算法。     

航段油耗深度学习高质量区间预测算法

为提高给定置信水平下航段油耗区间预测结果的可靠性和稳定性,提出航段油耗深度学习高质量区间预测算法.通过对初级数据源进行按航段分类、无量纲化等预处理,提高预测结果的可靠性和算法的普适性;通过自适应相关参数、柔和化处理优化损失函数,进一步提高算法的可靠性、稳定性和普适性.训练得到的预测区间覆盖率在设定的置信水平周围,多次训...