Combination of structural reliability and interval analysis

In engineering applications, probabilistic reliability theory appears to be presently the most important method, however, in many cases precise probabilistic reliability theory cannot be considered as adequate and credible model of the real state of actual affairs. In this paper, we developed a hybrid of probabilistic and non-probabilistic reliability theory, which describes the structural uncertain parameters as interval variables when statistical data are found insufficient. By using the interval analysis, a new method for calculating the interval of the structural reliability as well as the reliability index is introduced in this paper, and the traditional probabilistic theory is incorporated with the interval analysis. Moreover, the new method preserves the useful part of the traditional probabilistic reliability theory, but removes the restriction of its strict requirement on data acquisition. Example is presented to demonstrate the feasibility and validity of the proposed theory.

Interval Motion Accuracy Reliability Analysis of Manipulators Based on Chebyshev Inclusion Polynomial

Motion accuracy of space manipulators has direct effects on the ability of the systems to perform specified tasks. However, some design variables are inherently interval parameters due to uncertainties in geometric structures, material properties, and so on. This paper presents Chebyshev inclusion function(CIF) for approximating the dynamic responses function of parametrically excited systems. Motion accuracy reliability(MAR) of space manipulators was evaluated based on mechanism reliability analysis methods and interval uncertainty model. To illustrate the accuracy of the proposed method, a two-link manipulator with interval parameters was demonstrated. The results showed that the proposed method required much fewer samples to obtain more accurate reliability compared with the traditional Monte Carlo simulation(MCS). Finally, the sensitivity analysis was performed to facilitate the optimization design by using global sensitivity analysis.

Interval Estimation for the Stress-Strength Reliability with Bivariate Normal Variables

We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distributional accuracy. Simulations studies are provided to show the performance of the proposed method relative to existing ones in terms of coverage probability and average length. An empirical example is given to illustrate its usefulness in practice.

Non-probabilistic fuzzy reliability analysis of pile foundation stability by interval theory

Randomness and fuzziness are among the attributes of the influential factors for stability assessment of pile foundation. According to these two characteristics, the triangular fuzzy number analysis approach was introduced to determine the probability-distributed function of mechanical parameters. Then the functional function of reliability analysis was constructed based on the study of bearing mechanism of pile foundation, and the way to calculate interval values of the functional function was developed by using improved interval-truncation approach and operation rules of interval numbers. Afterwards, the non-probabilistic fuzzy reliability analysis method was applied to assessing the pile foundation, from which a method was presented for non- probabilistic fuzzy reliability analysis of pile foundation stability by interval theory. Finally, the probability distribution curve of non- probabilistic fuzzy reliability indexes of practical pile foundation was concluded. Its failure possibility is 0.91%, which shows that the pile foundation is stable and reliable.

Reliability Analysis of a Powerloom Plant Using Interval Valued Intuitionistic Fuzzy Sets

In this paper, we investigate the reliability analysis of a powerloom plant by using interval valued intuitionistic fuzzy sets (IVIFS). Herein, we modeled a powerloom plant as a gracefully degradable system having two units A(n) and B(m) connected in series. The reliability ofncomponents of unitAandmcomponents of unitBis assumed to be an IVIFS defined over the universe of discourse [0, 1]. Thus, the reliability of the system obtained is an IVIFS that covers the inherited uncertainty in data collection and reliability evaluation of a powerloom plant.

Structural Interval Reliability Algorithm Based on Bernstein Polynomials and Evidence Theory

Structural reliability is an important method to measure the safety performance of structures under the influence of uncertain factors.Traditional structural reliability analysis methods often convert the limit state function to the polynomial form to measure whether the structure is invalid.The uncertain parameters mainly exist in the form of intervals.This method requires a lot of calculation and is often difficult to achieve efficiently.In order to solve this problem,this paper proposes an interval variable multivariate polynomial algorithm based on Bernstein polynomials and evidence theory to solve the structural reliability problem with cognitive uncertainty.Based on the non-probabilistic reliability index method,the extreme value of the limit state function is obtained using the properties of Bernstein polynomials,thus avoiding the need for a lot of sampling to solve the reliability analysis problem.The method is applied to numerical examples and engineering applications such as experiments,and the results show that the method has higher computational efficiency and accuracy than the traditional linear approximation method,especially for some reliability problems with higher nonlinearity.Moreover,this method can effectively improve the reliability of results and reduce the cost of calculation in practical engineering problems.

Time-varying confidence interval forecasting of travel time for urban arterials using ARIMA-GARCH model

To improve the forecasting reliability of travel time, the time-varying confidence interval of travel time on arterials is forecasted using an autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity （ARIMA-GARCH） model. In which, the ARIMA model is used as the mean equation of the GARCH model to model the travel time levels and the GARCH model is used to model the conditional variances of travel time. The proposed method is validated and evaluated using actual traffic flow data collected from the traffic monitoring system of Kunshan city. The evaluation results show that, compared with the conventional ARIMA model, the proposed model cannot significantly improve the forecasting performance of travel time levels but has advantage in travel time volatility forecasting. The proposed model can well capture the travel time heteroskedasticity and forecast the time-varying confidence intervals of travel time which can better reflect the volatility of observed travel times than the fixed confidence interval provided by the ARIMA model.

The AMSAA-BISE Model with Gap Intervals

In this paper, the AMSAA-BISE model with missing data is discussed. The ML estimates of model parameters and current MTBF are given, and the chi-squared test and a plot for cumulative number of failures versus cumulative testing time are used to test the goodness of fit for the model. This paper concludes with a numerical example to verify the model.

Improved Discrete Interval-Valued Stress-Strength Interference Model Based on Extended Universal Generating Function

In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.

MODIFIED SCHEME BASED ON SEMI-ANALYTIC APPROACH FOR COMPUTING NON-PROBABILISTIC RELIABILITY INDEX

A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures.

Reliability Analysis for Complex Systems Based on Dynamic Evidential Network Considering Epistemic Uncertainty

Fault tolerant technology has greatly improved the reliability of modern systems on one hand and makes their failure mechanisms more complex on the other.The characteristics of dynamics of failure,diversity of distribution and epistemic uncertainty always exist in these systems,which increase the challenges in the reliability assessment of these systems significantly.This paper presents a novel reliability analysis framework for complex systems within which the failure rates of components are expressed in interval numbers.Specifically,it uses a dynamic fault tree(DFT)to model the dynamic fault behaviors and copes with the epistemic uncertainty using Dempster-Shafer(D-S)theory and interval numbers.Furthermore,an approach is presented to convert a DFT into a dynamic evidential network(DEN)to calculate the reliability parameters.Additionally,a sorting method based on the possibility degree is proposed to rank the importance of components represented by interval numbers in order to obtain the most critical components,which can be used to provide the guidance for system design,maintenance planning and fault diagnosis.Finally,a numerical example is provided to illustrate the availability and efficiency of the proposed method.

DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

A preventive opportunistic maintenance method for railway traction power supply system based on equipment reliability

Conventional maintenance mode for the traction power supply system(TPSS)is to perform scheduled regular maintenance activities for power supply equipment,while such maintenance mode may result in undue maintenance tasks and low efficiency due to different degradation processes of different sorts of equipment.To address this problem,this paper introduces a preventive opportunistic maintenance(POM)method for TPSS based on equipment reliability.Firstly,a POM model is established by considering the equipment reliability degradation process based on Weibull distribution.Then,by considering the total power outage time in the planned operation cycle of TPSS as the optimization objective,the optimal maintenance scheme of TPSS is formulated by iterative method of maintenance strategies.The proposed method is verified by introducing practical maintenance strategies and fault record data of the traction transformer,circuit breaker and disconnector in an actual TPSS of a railway administration.Results show that the presented method can make full use of the existing fault data to develop a POM scheme for TPSS.It can improve maintenance efficiency and reduce power outage time,providing guidance to formulate scientific maintenance strategies for TPSS.

Structural Reliability Modeling Based on Imprecise Probability Theory under Insufficient Data

Traditional structural reliability analysis methods adopt precise probabilities to quantify uncertainties and they are suitable for systems with sufficient statistical data.However,the problem of insufficient data is often encountered in practical engineering.Thus,structural reliability analysis methods under insufficient data have caught more and more attentions in recent years and a lot of nonprobabilistic reliability analysis methods are put forward to deal with the problem of insufficient data.Non-probabilistic structural reliability analysis methods based on fuzzy set,Dempster-Shafer theory,interval analysis and other theories have got a lot of achievements both in theoretical and practical aspects and they have been successfully applied in structural reliability analysis of largescale complex systems with small samples and few statistical data.In addition to non-probabilistic structural reliability analysis methods,structural reliability analysis based on imprecise probability theory is a new method proposed in recent years.Study on structural reliability analysis using imprecise probability theory is still at the start stage,thus the generalization of imprecise structural reliability model is very important.In this paper,the imprecise probability was developed as an effective way to handle uncertainties,the detailed procedures of imprecise structural reliability analysis was introduced,and several specific imprecise structural reliability models which are most effective for engineering systems were given.At last,an engineering example of a cantilever beam was given to illustrate the effectiveness of the method emphasized here.By comparing with interval structural reliability analysis,the result obtained from imprecise structural reliability model is a little conservative than the one resulted from interval structural reliability analysis for imprecise structural reliability analysis model considers that the probability of each value is taken from an interval.

Non-probabilistic Hydraulic Turbine Blade Vibration Reliability Research Based on Fuzzy Failure Criterion

In hydraulic turbine engineering,turbine blade vibration reliability assessment is of great significance. Based on the interval mathematical theory, the variables existing in hydraulic turbine blade are described as interval variables. Considering the fuzzy failure criterion of turbine blade distancing from resonance and vibration fatigue stress,fuzzy possibilistic reliability is expressed and analyzed qualitatively taking normal bathtub function as the membership function of blade resonance failure and deflection major type function as the membership function of the intensity failure. As a result,hydraulic turbine blade vibration reliability is analyzed based on the fuzziness of variables and failure criterion. A safer working environment is provided under possibility context by comparing with the qualitative conclusions in the past literature.

Comparison of Structural Probabilistic and Non-Probabilistic Reliability Computational Methods under Big Data Condition

In this article,structural probabilistic and non-probabilistic reliability have been evaluated and compared under big data condition.Firstly,the big data is collected via structural monitoring and analysis.Big data is classified into different types according to the regularities of the distribution of data.The different stresses which have been subjected by the structure are used in this paper.Secondly,the structural interval reliability and probabilistic pre-diction models are established by using the stress-strength interference theory under big data of random loads after the stresses and structural strength are comprehensively considered.Structural reliability is computed by using various stress types,and the minimum reliability is determined as structural reliability.Finally,the advan-tage and disadvantage of the interval reliability method and probability reliability method are shown by using three examples.It has been shown that the proposed methods are feasible and effective.

Mathematical Modeling and Evaluation of Reliability Parameters Based on Survival Possibilities under Uncertain Environment

In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of prime concern.In view of this,the outcomes for the failure are required to evaluate with utmost care.In possibility theory,the reliability information data determined from decision-making experts are subjective.The samemethod is also related to the survival possibilities as against the survival probabilities.The other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy numbers.In this method,a decision-making expert is not sure of his/her estimates of the reliability parameters.Numerical experiments are performed to illustrate the efficiency of the suggested methods in this research.In the end,the paper is concluded with some future research directions to be explored for the proposed approach.

A Bootstrapping Approach for Software Reliability Measurement Based on a Discretized NHPP Model

Discrete software reliability measurement has a proper characteristic for describing a software reliability growth process which depends on a unit of the software fault-detection period, such as the number of test runs, the number of executed test cases. This paper discusses discrete software reliability measurement based on a discretized nonhomogeneous Poisson process (NHPP) model. Especially, we use a bootstrapping method in our discrete software reliability measurement for discussing the statistical inference on parameters and software reliability assessment measures of our model. Finally we show numerical examples of interval estimations based on our bootstrapping method for the several software reliability assessment measures by using actual data.

Bias and Mean Square Error of Reliability Estimators under the One and Two Random Effects Models: The Effect of Non-Normality

The coefficient of reliability is often estimated from a sample that includes few subjects. It is therefore expected that the precision of this estimate would be low. Measures of precision such as bias and variance depend heavily on the assumption of normality, which may not be tenable in practice. Expressions for the bias and variance of the reliability coefficient in the one and two way random effects models using the multivariate Taylor’s expansion have been obtained under the assumption of normality of the score (Atenafu et al. [1]). In the present paper we derive analytic expressions for the bias and variance, hence the mean square error when the measured responses are not normal under the one-way data layout. Similar expressions are derived in the case of the two-way data layout. We assess the effect of departure from normality on the sample size requirements and on the power of Wald’s test on specified hypotheses. We analyze two data sets, and draw comparisons with results obtained via the Bootstrap methods. It was found that the estimated bias and variance based on the bootstrap method are quite close to those obtained by the first order approximation using the Taylor’s expansion. This is an indication that for the given data sets the approximations are quite adequate.

基于遗传区间仿射响应面的结构时变稳健可靠性优化

为提升结构时变稳健可靠性能并兼顾区间变量参数描述精度,提出一种基于遗传区间仿射响应面的结构优化设计方法。首先,根据结构性能分析方法获取结构性能响应,并提取结构不确定性因素。其次,构建结构参数化分析模型并开展试验设计,将试验设计过程分别存储为设计变量及结构性能响应两种数据库,基于区间仿射理论初步构建结构区间仿射响应面,依据设计变量数据库的各变量样本边界及结构性能分析结果,利用遗传算法及误差最小化判别准则优化初始区间仿射响应面,并利用结构性能响应数据库验证优化后响应面的有效性。最后,结合结构性能退化行为及稳健可靠性优化方法,构建结构时变稳健可靠性优化模型并开展结构优化设计,通过工程算例验证了所提优化设计方法的合理性。算例分析表明,遗传区间仿射响应面能够更合理地反映出结构响应的波动区间,所提优化方法能够有效提升结构稳健可靠性水平。