Adaptive probability analysis using an enhanced hybrid mean value method

This paper proposes an adaptive probability analysis method that can effectively generate the probability distribution of the output performance function by identifying the propagation of input uncertainty to output uncertainty. The method is based on an enhanced hybrid mean value (HMV+) analysis in the performance measure approach (PMA) for numerical stability and efficiency in search of the most probable point (MPP). The HMV+ method improves numerical stability and efficiency especially for highly nonlinear output performance functions by providing steady convergent behavior in the MPP search. The proposed adaptive probability analysis method approximates the MPP locus, and then adaptively refines this locus using an a posteriori error estimator. Using the fact that probability levels can be easily set a priori in PMA, the MPP locus is approximated using the interpolated moving least-squares method. For refinement of the approximated MPP locus, additional probability levels are adaptively determined through an a posteriori error estimator. The adaptive probability analysis method will determine the minimum number of necessary probability levels, while ensuring accuracy of the approximated MPP locus. Several examples are used to show the effectiveness of the proposed adaptive probability analysis method using the enhanced HMV+ method.     

Approximate mean value analysis for stochastic marked graphs

An iterative technique for the computation of approximate performance indices of a class of stochastic Petri net models is presented. The proposed technique is derived from the mean value analysis algorithm for product-form solution stochastic Petri nets. In this paper, we apply the approximation technique to stochastic marked graphs. In principle, the proposed technique can be used for other stochastic Petri net subclasses. In this paper, some of these possible applications are presented. Several examples are presented in order to validate the approximate results     

用于软件可靠性分析的分解方法

随机Petri网(SPN)是一种有力的系统建模和分析工具.但SPN在应用中经常碰到状态空间爆炸问题.分解压缩技术是解决随机网状态空间指数性增长的有效方法之一.介绍了一种获得SPN可靠性模型瞬时状态的分解方法.该方法在保证评价和预测可靠性精确度的基础上,不仅能有效地降低可靠性描述与分析的复杂度,还扩大了分解压缩技术的适用范围.     

An improved high-moment method for reliability analysis

For reliability analysis, there may be several potential distributions for a random variable due to limited samples available. For the same reason, a distribution may not be available. Simply assuming a normal distribution may result in a large error for the reliability prediction. Moment-based methods use only moments of random variables for reliability analysis and can effectively address the problem of multiple distributions or lack of distributions. The existing moment-based methods, however, may produce large errors or may result in instability in the analysis process. This study extends the high-moment method for higher accuracy of the reliability prediction by including the parameters ignored by the existing high-moment method. The proposed method derives the reliability index from the first four moments of random input variables based on the statistical properties of the standard normal random variable. Compared with the existing method, the proposed method is more accurate and stable for problems for which the distributions of input random variables are unknown. Numerical examples show the improved accuracy from the proposed method.     

Sliced mean variance-covariance inverse regression

Inverse regression methods have gained popularity over the last 10 years or so. More recently these methods have been applied to the classification problem. Sliced inverse regression (SIR) is equivalent to linear discriminant analysis and as such it detects mean differences between the classes. Sliced average variance estimation (SAVE) is designed to detect differences between the means, variances and covariances of the predictors across the classes. However, in SAVE each difference in variance across the groups takes up a dimension, and hence SAVE can have difficulty detecting mean differences and covariance differences. In this paper, we propose a new data analytic method, called sliced mean variance-covariance regression (SMVCIR) which can readily detect both first and second order differences between the classes even when many variance differences exist. Further, our procedure is based on an ordering of the dimensions based on their relative importance which is quite beneficial to interpretation. In particular, we demonstrate that useful data-analytic information about mean and covariance differences can be obtained from SMVCIR when SAVE finds many dimensions due to variance differences. Finally, the advantages of SMVCIR over SIR and SAVE are exemplified using a new data set from the enology literature.     

An improved TRPD method for time-variant reliability analysis

In this paper, an improved time-variant reliability analysis method based on stochastic process discretization (iTRPD) is proposed. Firstly, the time-variant reliability problem is transformed into a time-invariant series system reliability problem. Then the first order reliability method (FORM) is employed to analyze the reliability of each component of the system, and a corresponding approach is given to calculate the correlation coefficient matrix of all the components’ performance functions. Finally, the target time-variant reliability can be obtained with the reliability index vector and the correlation coefficient matrix of the involved components. In this study, the iTRPD is further applied to the system reliability problems, and hence a corresponding time-variant system reliability analysis method is also developed. Four numerical examples are investigated to demonstrate the effectiveness of the proposed methods.     

Experiments with improved approximate mean value analysis algorithms

Approximate mean value analysis (MVA) is a popular technique for analyzing queueing networks because of the efficiency and accuracy that it affords. In this paper, we present a new software package, called the improved approximate mean value analysis library (IAMVAL), which can be easily integrated into existing commercial and research queueing network analysis packages. The IAMVAL packages include two new approximate MVA algorithms, the queue line (QL) algorithm and the fraction line (FL) algorithm, for analyzing multiple class separable queueing networks. The QL algorithm is always more accurate than, and yet has approximately the same computational efficiency as, the Bard–Schweitzer proportional estimation (PE) algorithm, which is currently the most widely used approximate MVA algorithm. The FL algorithm has the same computational cost and, in noncongested separable queueing networks where queue lengths are quite small, yields more accurate solutions than both the QL and PE algorithms.     

Heavy traffic analysis of polling models by mean value analysis

In this paper we present a new approach to derive heavy-traffic asymptotics for polling models. We consider the classical cyclic polling model with exhaustive or gated service at each queue, and with general service-time and switch-over time distributions, and study its behavior when the load tends to one. For this model, we explore the recently proposed mean value analysis (MVA), which takes a new view on the dynamics of the system, and use this view to provide an alternative way to derive closed-form expressions for the expected asymptotic delay; the expressions were derived earlier in [R.D. van der Mei, H. Levy, Expected delay in polling systems in heavy traffic, Adv. Appl. Probab. 30 (1998) 586–602], but in a different way. Moreover, the MVA-based approach enables us to derive closed-form expressions for the heavy-traffic limits of the covariances between the successive visit periods, which are key performance metrics in many application areas. These results, which have not been obtained before, reveal a number of insensitivity properties of the covariances with respect to the system parameters under heavy-traffic assumptions, and moreover, lead to simple approximations for the covariances between the successive visit times for stable systems. Numerical examples demonstrate that the approximations are accurate when the load is close enough to one.     

A novel evidence-based fuzzy reliability analysis method for structures

Epistemic uncertainties always exist in engineering structures due to the lack of knowledge or information, which can be mathematically described by either fuzzy-set theory or evidence theory (ET) In this work, the authors present a novel uncertainty model, namely evidence-based fuzzy model, in which the fuzzy sets and ET are combined to represent the epistemic uncertainty. A novel method for combining multiple membership functions and a corresponding reliability analysis method is also developed. In the combination method, the combined fuzzy-set representations are approximated by the enveloping lines of the multiple membership functions (smoothed by neglecting the valleys in the membership functions curves) and the Murphy’s average combination rule is applied to compute the basic probability assignment for focal elements. Then, the combined membership function is transformed to the equivalent probability density function by means of a normalizing factor. Finally, the Markov Chain Monte Carlo (MCMC) subset simulation method is used to solve reliability by introducing intermediate failure events. A numerical example and two engineering examples are provided to demonstrate the effectiveness of the proposed method.     

A method for system reliability analysis with change-over operation

Abstract

When fault tree analysis (FTA) is used in analysing the system reliability including human functions, the correspondence between an abnormal event and the human reaction against it may become ambiguous. In order to supplement this defect, a case study has been conducted in this research to develop a new technique termed ‘Corrective Operation Diagram Analysis’, and an attempt has been made to establish the correspondence between the reliability analysis of equipment/hardware using FTA and human reliability analysis.     

新的基于加权均值模型的证据融合方法

针对D-S证据理论难以处理证据冲突的问题,提出了一种将Murphy平均融合方法和证据权方法相结合的证据融合方法.该方法将显著偏差证据的判别引入融合流程,实现对证据权重的区分量化,建立了加权的基本概率分配均值模型.仿真结果表明:该方法能有效区分证据的重要程度,提高了证据融合的准确性与收敛速度,较好地解决了冲突证据融合的问题.     

A new method for reliability analysis and reliability-based design optimization

Structural and Multidisciplinary Optimization - We present a novel method for reliability-based design optimization, which is based on the approximation of the safe region in the random space by a...     

An adaptive dimension decomposition and reselection method for reliability analysis

Recently, the research community in reliability analysis has seen a strong surge of interest in the dimension decomposition approach, which typically decomposes a multi-dimensional system response into a finite set of low-order component functions for more efficient reliability analysis. However, commonly used dimension decomposition methods suffer from two limitations. Firstly, it is often difficult or impractical to predetermine the decomposition level to achieve sufficient accuracy. Secondly, without an adaptive decomposition scheme, these methods may unnecessarily assign sample points to unimportant component functions. This paper presents an adaptive dimension decomposition and reselection (ADDR) method to resolve the difficulties of existing dimension decomposition methods for reliability analysis. The proposed method consists of three major components: (i) an adaptive dimension decomposition and reselection scheme to automatically detect the potentially important component functions and adaptively reselect the truly important ones, (ii) a test error indicator to quantify the importance of potentially important component functions for dimension reselection, and (iii) an integration of the newly developed asymmetric dimension-adaptive tensor-product (ADATP) method into the adaptive scheme to approximate the reselected component functions. The merits of the proposed method for reliability analysis are three-fold: (a) automatically detecting and adaptively representing important component functions, (b) greatly alleviating the curse of dimensionality, and (c) no need of response sensitivities. Several mathematical and engineering high-dimensional problems are used to demonstrate the effectiveness of the ADDR method.     

An importance learning method for non-probabilistic reliability analysis and optimization

With the time-consuming computations incurred by nested double-loop strategy and multiple performance functions, the enhancement of computational efficiency for the non-probabilistic reliability estimation and optimization is a challenging problem in the assessment of structural safety. In this study, a novel importance learning method (ILM) is proposed on the basis of active learning technique using Kriging metamodel, which builds the Kriging model accurately and efficiently by considering the influence of the most concerned point. To further accelerate the convergence rate of non-probabilistic reliability analysis, a new stopping criterion is constructed to ensure accuracy of the Kriging model. For solving the non-probabilistic reliability-based design optimization (NRBDO) problems with multiple non-probabilistic constraints, a new active learning function is further developed based upon the ILM for dealing with this problem efficiently. The proposed ILM is verified by two non-probabilistic reliability estimation examples and three NRBDO examples. Comparing with the existing active learning methods, the optimal results calculated by the proposed ILM show high performance in terms of efficiency and accuracy.

     

Subset simulation method including fitness-based seed selection for reliability analysis

Probability estimation of rare events is a challenging task in the reliability theory. Subset simulation (SS) is a robust simulation technique that transforms a rare event into a sequence of multiple intermediate failure events with large probabilities and efficiently approximates the mentioned probability. Proper handling of a reliability problem by this method requires employing a suitable sampling approach to transmit samples toward the failure set. Markov Chain Monte Carlo (MCMC) is a suitable sampling approach that solves the SS transition phase using the failed sample of each simulation level as the seed of next samples. This paper is aimed to study the seed selection effect on the SS accuracy through several seed selection approaches inspired by the genetic algorithm and particle filter and using the main PDF of the variables to assign a mass function probability to each subset sample in the failure domain. Roulette wheel (I, II), tournament and proportional probability techniques are then employed to choose the weighed samples as seeds to be placed in the MCMC to transmit the samples. To examine the capability of each approach, reliabilities of some engineering problems were investigated and results showed that the proposed approaches could find proper failure sets better than the original SS method, especially in problems with several failure domains.

     

New neural network-based response surface method for reliability analysis of structures

Neural Computing and Applications - In this paper, a new algorithm is introduced for reliability analysis of structures using response surface method based on a group method of data handling-type...